TECHNICAL REPORT

DRAFT

V
Notice

This document is disseminated under the sponsorship of 

the Department of Transportation in the interest of 

information exchange. The United States Government 

assumes no liability for its contents or use thereof.
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Table of Contents

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Chapter 2: An Outline of the Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.1 HERS Analytical Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-1

2.2 The HERS Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-2

2.2.1 The Improvement Selection Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-2

2.2.2 Addressing Unacceptable Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-3

2.3 The HERS Prediction and Calculation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-8

2.4 Implementation and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-8

2.5 The HERS Milieu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-9

2.5.1 HERS Time Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-9

2.5.2 Functional Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-10

2.5.3 Pavement Condition Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-11

Chapter 3: Identifying Candidate Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.1 HERS Improvement Types and Kinds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-1

3.2 Deficiency Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-2

3.3 Identifying Improvements for Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-3

3.3.1 Addressing Ordinary Deficiencies: the Second Pass . . . . . . . . . . . . . . . . . . . . . . . . . .3-4

3.3.1.1 Aggressive Improvement Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-4

3.3.1.2 Less Aggressive Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-5

3.3.2 Addressing Unacceptable Conditions: the Optional First Pass . . . . . . . . . . . . . . . . .3-8

3.4 Default Deficiency Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-8

3.5 Discussion of Criteria Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-21

3.5.1 Unacceptability Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-21

3.5.2 Deficiency Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-21

3.5.3 Serious Deficiency Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-22

Chapter 4: HERS Internal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.1 The HERS Speed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-1

4.1.1 Free-Flow Speed and the APLVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-2

4.1.1.1 Calculating the Effect of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-2

4.1.1.2 Estimating Velocity Limited by Pavement Roughness . . . . . . . . . . . . . . . . . . . . . . . .4-3

4.1.1.3 Estimating Velocity Limited by Speed Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-5

4.1.1.4 Determining Free-Flow Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-5

4.1.2 The Effects of Grades on Free-Flow Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-6

4.1.3 Delay Due to Congestion and Traffic Control Devices . . . . . . . . . . . . . . . . . . . . . . . .4-7

4.1.3.1 Sections with Stop Signs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-8

4.1.3.2 Sections with Traffic Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-9

4.1.3.3 Sections With Stop Signs and Traffic Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-9

4.1.3.4 Free-Flow Sections, One Lane per Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-10

4.1.3.5 Free-Flow Sections, Three-Lane Two-Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-10

4.1.3.6 Free-Flow Sections, Two or More Lanes per Direction . . . . . . . . . . . . . . . . . . . . . . .4-10

4.1.4 Distance Traveled Between Traffic Control Devices . . . . . . . . . . . . . . . . . . . . . . . . .4-11
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4.2 The Pavement Deterioration Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-11

4.2.1 Equivalent Single-Axle Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-11

4.2.2 Pavement Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-13

4.2.2.1 Flexible Pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-13

4.2.2.2 Rigid Pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-14

4.2.2.3 Minimum Deterioration Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-15

4.2.2.4 Maximum Deterioration Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-16

4.3 The Travel Forecast Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-16

4.3.1 Initialization: Assuming the Baseline Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-17

4.3.2 Forecasting Baseline Traffic Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-17

4.3.2.1 Option One - Concave Geometric Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-18

4.3.2.2 Option Two - Linear Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-19

4.3.2.3 Option Three - Convex Geometric Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-19

4.3.3 Applying Elasticity to Travel Volume Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-19

4.3.4 The Simultaneous Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-21

4.3.5 Computational Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-23

4.3.6 Delay Equations by Road Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-25

4.4 The Fleet Composition Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-26

4.5 The Widening Feasibility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-29

4.6 The Capacity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-32

4.6.1 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-32

4.6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effects of Capacity Improvements 4-33

4.6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Design Year Lane Requirements 4-34

Chapter 5: Cost and Benefit Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.1 User Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1

5.1.1 Travel Time Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1

5.1.1.1 Vehicle Occupants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-2

5.1.1.2 Average Vehicle Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-2

5.1.1.3 Personal-Use Percentage of VMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-3

5.1.1.4 Vehicle Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-3

5.1.1.5 Inventory Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-5

5.1.1.6 Estimating Travel Time Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-5

5.1.2 Estimating Operating Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-6

5.1.2.1 Operating Cost Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-6

5.1.2.1.1 Component Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-8

5.1.2.1.2 Adjustment Factors for Consumption Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-9

5.1.2.1.2.1 Fuel Efficiency Adjustment Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-10

5.1.2.1.2.2 Oil Consumption Adjustment Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-10

5.1.2.1.2.3 Depreciation Rate Adjustment Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-10

5.1.2.2 Constant-Speed Operating Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-11

5.1.2.3 The Effect of Speed-Change Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-12

5.1.2.4 The Effect of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-13

5.1.2.4.1 Sections With AES Below 55 M.P.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-14

5.1.2.4.2 Sections with AES Above 55 M.P.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-14

5.1.2.5 Total Operating Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-15

5.1.3 Safety Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-15

5.1.3.1 Crash Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-15

5.1.3.1.1 Rural Two-Lane Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-16
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5.1.3.1.1.1 Non-intersection Crashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-16

5.1.3.1.1.2 Intersection Crashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-18

5.1.3.1.2 Rural Multilane Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-21

5.1.3.1.3 Rural Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-23

5.1.3.1.4 Urban Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-23

5.1.3.1.5 Urban Multilane Surface Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-24

5.1.3.1.6 Urban Two-Lane Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-24

5.1.3.1.7 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-24

5.1.3.2 Fatalities and Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-26

5.1.3.3 Secular Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-27

5.1.3.4 Costs of Crashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-28

5.1.3.4.1 Unit Costs of Crashes in 1994 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-28

5.1.3.4.2 Indexing the Costs of Crashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-30

5.2 Agency Costs and Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-31

5.2.1 Maintenance Costs for Flexible Pavements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-31

5.2.2 Maintenance Costs for Rigid Pavements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-33

5.3 External Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-33

5.4 Capital Cost of Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-36

5.4.1 Pavement and Widening Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-36

5.4.2 Alignment Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-38

5.4.2.1 Modifying Section Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-39

5.4.2.2 Cost of Improving Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-40

5.4.2.2.1 Clearing and Grubbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-40

5.4.2.2.2 Earthwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-41

5.4.2.2.3 Drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-44

5.4.2.2.4 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-44

5.4.2.2.5 Pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-44

5.4.2.2.6 Right-of-Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-45

5.4.2.2.7 Miscellaneous Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-46

5.4.2.3 Total Improvement Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-47

5.4.3 Correcting Substandard Conditions on Urban Freeways . . . . . . . . . . . . . . . . . . . . .5-47

5.4.4 State Cost Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-48

Chapter 6: Effects of HERS Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

6.1 The Effects of Improvements on Pavement Thickness . . . . . . . . . . . . . . . . . . . . . . . . .6-3

6.1.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-4

6.1.2 Simple Resurfacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-5

6.1.3 Resurfacing with Widening Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-5

6.2 The Effects of Improvements on Structural Number . . . . . . . . . . . . . . . . . . . . . . . . . .6-5

6.3 The Effects of Improvements on PSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-6

6.4 The Effects of Alignment Improvements on Pavement Characteristics . . . . . . . . . .6-7

Chapter 7: Evaluating Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

7.1 The Base Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-1

7.2 Determining the Benefit-Cost Analysis Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-2

7.2.1 Traffic Volume on Section is Constant or Increasing . . . . . . . . . . . . . . . . . . . . . . . . . .7-3

7.2.2 Traffic Volume on Section is Declining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-4

7.3 Estimating Variable Costs for the Base Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-5

7.4 Determining Costs Associated with the Candidate Improvement . . . . . . . . . . . . . .7-5
iv

7.5 Determining the Capital Costs of the Improvements . . . . . . . . . . . . . . . . . . . . . . . . . .7-5

7.6 Residual Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-6

7.6.1 A Summary Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-6

7.6.2 Detailed Description of Residual Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-6

7.7 The Benefit-Cost Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-7

7.8 Does a Section Warrant Improvement? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-10

7.9 Selecting Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-11

7.10 Improvement Selection Without Mandatory Improvements . . . . . . . . . . . . . . . . . .7-12

7.10.1 Minimum BCR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-12

7.10.2 Constrained Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-15

7.11 Selecting Mandatory Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-18

7.11.1 Unacceptable Conditions and the Constrained Fund Run . . . . . . . . . . . . . . . . . . . .7-19

7.11.2 Unacceptable Conditions and the Performance Constrained Run . . . . . . . . . . . . . .7-20

7.11.3 Unacceptable Conditions and the Minimum BCR Run . . . . . . . . . . . . . . . . . . . . . . .7-21

Chapter 8: Model Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

8.1 The System Conditions Output Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8-1

8.2 The “By Improvement Type” Output Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8-3

8.3 The “By IBCR” Output Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8-4

Appendix A: Induced Traffic and Induced Demand . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

A.1 Concepts of Induced Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Exogenous Demand Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Demand Fills Capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2

Elastic Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2

A.2 Short Run versus Long Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2

Short-Run Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2

Long-Run Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3

Induced Traffic versus Induced Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3

Disaggregation of Long Run Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4

A.3 Induced Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5

Partial and General Equilibrium Demand Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . A-6

“Gross” versus “Net” Induced Traffic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-7

Schedule Delay and Peak Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-8

A.4 Induced Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-8

Baseline Demand Forecast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-9

Breaking the Forecast Into Discrete Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-9

Long Run Shifts in the Demand Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-10

Getting to the Long Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-12

Empirical Estimates of Short and Long Run Elasticities. . . . . . . . . . . . . . . . . . . . . . A-13

Interpreting Demand Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-13

A.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-14

A.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-14

Appendix B: Demand Elasticities for Highway Travel . . . . . . . . . . . . . . . . . . . . . . . . . B-1

B.1 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

The Meaning of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

Transferability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2
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Price, Output, and Market. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

Money Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

Generalized Price and Its Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-3

Price Elasticity for a Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-3

Leakage from Component to Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-3

Expansion From Component to Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-4

B.2 Empirical Estimation of Price Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-4

From Evidence to Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-4

Construction of Travel Demand Elasticities from User Cost Components . . . . . . . B-5

Accounting Framework for Price Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-7

Estimates of Component Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-7

Components Included in the “Price”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-9

Component Shares of Total User Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-10

Empirical Estimates of Own-Price Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-10

Magnitudes of the Leakages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-11

Durations of the Short-and Long-Run Adjustment Periods. . . . . . . . . . . . . . . . . . . B-11

B.3 Conversion to Total Price Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-12

Fuel Price Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-13

Ownership Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-13

Toll Elasticities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-13

Parking Price Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-14

Time Cost Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-15

B.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-16

B.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-16

Appendix C: Basic Theory of Highway Project Evaluation. . . . . . . . . . . . . . . . . . . . . C-1

The HERS Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1

C.1 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-2

Marginal Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-2

Average Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-2

Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-3

Constructing the Demand Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-4

Project Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-5

C.2 Single-Period Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-5

Short-Run Effects of Improvements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-5

Incremental Net Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-7

NOB Based on Marginal Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-7

NOB Based on AVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-7

“Old” versus “New” Trips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-7

NOB with Price Below AVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-9

C.3 Components of Net Operating Benefit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-10

Savings on Old Trips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-11

Incremental Consumer Surplus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-11

Producer Surplus on New Trips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-12

External Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-12

Externalities in Related Markets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-13

C.4 Multi-Period Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-14

Breaking the Project Life Into Discrete Demand Periods . . . . . . . . . . . . . . . . . . . . . C-14

Growth in Demand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-15
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C.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-18

C.6 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-18

C.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-21

AppendixD: Operating Cost Equations 1

D.1 Source of HERS Operating Cost Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1

D.1.1 Region of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1

D.2 Generation of New Operating Cost Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-2

D.2.1 Determining Which Equations Require Updating . . . . . . . . . . . . . . . . . . . . . . . . . . . D-2

D.2.2 Method and Tools Employed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-2

D.2.3 Notable Exception: 3-4 Axle Combination Unit Trucks . . . . . . . . . . . . . . . . . . . . . . . D-2

D.2.4 Notable Exception: 5+ Axle Combination Unit Trucks . . . . . . . . . . . . . . . . . . . . . . . D-3

D.3 Roster of Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-3

D.4 Small Automobile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-5

D.4.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-5

D.4.2 Constant-Speed Oil Consumption (CSOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-5

D.4.3 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-6

D.4.4 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-6

D.4.5 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-7

D.5 Medium/Large Automobile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-7

D.5.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-7

D.5.2 Constant-Speed Oil Consumption (CSOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-8

D.5.3 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-8

D.5.4 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9

D.5.5 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9

D.6 4-Tire Trucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-10

D.6.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-10

D.6.2 Constant-Speed Tire Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-11

D.6.3 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-12

D.6.4 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-13

D.6.5 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-13

D.7 6-Tire Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14

D.7.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14

D.7.2 Constant-Speed Oil Consumption (CSOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14

D.7.3 Constant-Speed Maintenance and Repair (CSMR) . . . . . . . . . . . . . . . . . . . . . . . . . . D-15

D.7.4 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-15

D.7.5 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-16

D.7.6 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-16

D.8 3+ Axle Single-Unit Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-18

D.8.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-18

D.8.2 Constant-Speed Maintenance and Repair (CSMR) . . . . . . . . . . . . . . . . . . . . . . . . . . D-19

D.8.3 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-19

D.8.4 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20

D.8.5 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20

D.9 3-4 Axle Combination Unit Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-21

D.9.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-21

D.9.2 Constant-Speed Tire Wear (CSTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-22

D.9.3 Constant-Speed Maintenance and Repair (CSMR) . . . . . . . . . . . . . . . . . . . . . . . . . . D-22

D.9.4 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-23
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D.9.5 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-24

D.9.6 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-25

D.10 5+ Axle Combination Unit Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-26

D.10.1 Constant-Speed Fuel Consumption (CSFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-26

D.10.2 Excess Fuel Consumption due to Curves (CFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-27

D.10.3 Excess Tire Wear Due to Curves (CTW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-28

D.10.4 Excess Maintenance and Repair Due to Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-29

AppendixE: Detailed Description of Procedures for Incorporating Air Pollution Costs 

in HERS 1

E.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-1

E.1.1 How Improvements Affect Air Pollution Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-1

E.1.2 Critical Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-3

E.2 Estimating Air Pollutant Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-3

E.2.1 Specific Pollutants Considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-3

E.2.2 Emission Rates for HERS Vehicle Classes and Section Types . . . . . . . . . . . . . . . . . E-4

E.2.3 Future Trends in Emission Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-7

E.2.4 Final Emission Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-8

E.3 Air Pollution Damage Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-9

E.3.1 Damage Costs for Individual Air Pollutants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-9

E.3.2 Adjustments to Per-Ton Damage Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-9

E.3.3 Air Pollution Costs per Vehicle-Mile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-10

E.3.4 Assessing the Effect of Proposed Improvements on Air Pollution Costs . . . . . . . E-11

E.3.5 Likely Effects of Including Air Pollution Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-11

AppendixF: Delay Estimation for Sections with Traffic Signals and for Free-Flow Sections with Two or More Lanes per Direction 1

F.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-1

F.1.1 Input Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-1

F.1.2 Intermediate and Output Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-1

F.2 Free-Flow Sections with Two or More Lanes per Direction . . . . . . . . . . . . . . . . . . . .F-2

F.2.1 Fractions of Travel for Free-Flow Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-2

F.2.2 Volume-to-Capacity Ratios for Peak Period on Free-Flow Sections. . . . . . . . . . . . . .F-3

F.2.3 Travel Rate Without Incidents for Free-Flow Sections. . . . . . . . . . . . . . . . . . . . . . . . .F-3

F.2.4 Incident Delay for Free-Flow Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-4

F.3 Signalized Arterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-5

F.3.1 Fractions of Travel for Signalized Arterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-5

F.3.2 Volume-to-Capacity Ratios for Peak Period on Signalized Arterials. . . . . . . . . . . . .F-5

F.3.3 Zero-volume Delay Due to Traffic Signals for Signalized Arterials. . . . . . . . . . . . . .F-5

F.3.4 Travel Rate Without Incidents for Signalized Arterials. . . . . . . . . . . . . . . . . . . . . . . .F-6

F.3.5 Incident Delay for Signalized Arterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F-6

AppendixG: Unique Features of HERS-ST 1

G.1 Rural Minor Collectors and Functionally Local Roads . . . . . . . . . . . . . . . . . . . . . . . G-1

G.2 Widening Feasibility Overrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-1

G.3 Initial Pavement Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-1

G.4 Section Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-1

G.5 Capital Cost of Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-7
viii

G.6 Override Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-9

G.6.1 User-Specified Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-9

G.6.2 Tabular Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-12

G.6.3 Evaluations of Individual Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-13

G.6.4 Benefits and Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-13

G.6.4.1 Improvement Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-13

G.6.4.2 User Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-15
1-1

1 Introduction

The Highway Economic Requirements System (HERS) is a computer model designed to simulate

improvement selection decisions based on the relative benefit-cost merits of alternative improvement options. HERS is intended to estimate national level investment requirements which

assume state highway improvement selection decisions that consider the relationship between

benefits accruing to highway users and agencies, and the initial improvement cost of a potential

improvement option. Output from the HERS model is used in preparation of the Department of

Transportation’s (DOT) biennial Status of the Nation’s Surface Transportation System • Condition

and Performance • Report to Congress (C&P Report).

The HERS model is the result of the efforts to examine more carefully the costs, benefits and

national economic implications associated with highway investment options. 

This Technical Report is the fourth volume of HERS documentation. It is labeled Version 3.54

(v3.54) because it corresponds to program Version 3.54 which was used to evaluate 2000 data in

preparation of the 2002 C&P Report. It consists of detailed technical discussions of the procedures, assumptions, algorithms, and inputs of the HERS model. The first three volumes are

intended to provide a non-technical introduction to a general audience interested in using and

interpreting model generated results:

• Volume I - Executive Summary

This document provides a non-technical presentation of the model.

• Volume II - System Overview 

This volume offers a procedural summary of the model’s logic structure and the analytical, economic and engineering procedures it implements.

• Volume III - User’s Guide

This volume provides “hands-on” assistance to the analyst interested in using HERS to 

evaluate alternative highway program and policy scenarios.

Each volume is updated independently of the others. This Technical Report is the first of the

four volumes to be updated to Version 3.54.

HERS is designed to estimate the benefits resulting from potential improvements, distinguishing

three types of benefits to highway users (travel time, operating costs, and safety), two types of

benefits to highway agencies (maintenance costs and the “residual value” of an improvement at

the end of the analysis period), and one “external” benefit (reduction in damage caused by vehicle emissions). The HERS model uses benefit-cost analysis to differentiate between potential

improvements when selecting improvements for implementation. HERS v3.54 further includes

the effects of “induced traffic” and “induced demand,” reflecting user response to changes in the

generalized price over the short and long term, respectively.

HERS was developed for the Federal Highway Administration (FHWA) by Jack Faucett Associates, and is maintained and operated by the Volpe National Transportation Systems Center. The

development of HERS has benefited substantially from the FHWA’s Highway Performance

Monitoring System (HPMS) database and its associated simulation, the Analytical Process (AP).
Introduction

1-2

HERS uses the description of the current state of the highway system contained in the HPMS

database as the basis of all analyses. This database contains a detailed description of a stratified

random sample of over 100,000 sections of non-local roads. The descriptions are updated annually by State highway departments in accordance with FHWA specifications set forth in the

HPMS Field Manual.

1

Each of these “sample sections” represents a relatively large number of actual highway sections.

The total mileage of these sections (but not their number) is known and can be obtained by multiplying the length of each sample section by its “expansion factor.” All HERS estimates of costs

and benefits are obtained by analyzing individual sample sections and multiplying the results by

the appropriate expansion factor.

HERS starts with the base-year description of the highway system contained in the HPMS database and forecasts changes to the system and analyzes potential improvements for each of several “funding periods.” The number and length of the funding periods can be specified by the

user, but computation-time considerations generally allow for only a small number of funding

periods. A common HERS application uses four five-year funding periods.

For each funding period, HERS forecasts the condition of each sample section and determines

which improvements should be made. HERS considers resurfacing or reconstruction, possibly

combined with alignment improvements and/or four alternative types of widening. To the

extent that funds are reserved for this purpose, appropriate improvements may be made to eliminate any “unacceptable” conditions that can be corrected. Additional improvements to correct

“deficiencies” are then selected on the basis of a benefit-cost analysis (BCA) procedure until

available funds for the period are used up or some user-specified characterization of the highway system has been achieved. If sufficient funds are not available to correct all unacceptable

conditions, the B/C procedure is used to select which of these conditions should be corrected.

The unacceptability and deficiency criteria used by HERS are user specified.

An outline of the HERS model structure is presented in Chapter 2 of this report. At a more general level, it also presents the HERS processing cycle along with its several major variants.

The next five chapters are arranged to mirror the HERS processing cycle. Chapter 3 discusses the

procedures used within the model to identify potential improvements for any given section.

Chapter 4 then describes the models HERS uses in estimating the impacts on highway facilities

and travelers of the candidate improvements. Chapter 5 covers the methods for estimating user

costs, agency costs, and improvement costs, converting quantities such as vehicle speed, pavement condition, and potential improvements into dollars for use in benefit-cost analysis. Chapter

6 explains how improvements change the characteristics of facilities that in turn affect pavement

condition, pavement life, and user costs. Finally, the results of comparing alternatives are distilled into summary measures of benefit-cost ratios for candidate improvements.

Chapter 9 provides an overview of the output from the HERS program.

This report contains seven appendices. Appendix A, ”Induced Traffic and Induced Demand,” is

a paper discussing the theoretical underpinnings of induced traffic and induced demand related

to the concept of elasticity. The derivation of the values used by HERS for short and long run

elasticity is presented in Appendix B, ”Demand Elasticities for Highway Travel.” Appendix C,

”Basic Theory of Highway Project Evaluation,” places the HERS model within a wider context. 

1. U.S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System

Field Manual, Washington, D.C., December 1993.
HERS Technical Report v3.54

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1-3

App. D contains the equations used by HERS to determine operating costs. App E presents the

derivation of the HERS emissions cost equation, constants, and factors. The constants and factors used in calculating emissions costs are presented in App F. And App G walks through the

processing of a single section during a funding period, illustrating many of the algorithms documented in the body of this Report.
Introduction

1-4
2-1

2 An Outline of the Model Structure

This section provides an overview of the structure of the HERS system; that is, the ordering of

computational events by which the model performs its analysis. The sequencing of events is

referred to as the HERS process; the program entities which perform specific modeling functions are referred to as the HERS models. Each is introduced below, with more detailed discussion in the sections which follow.

2.1 HERS Analytical Objectives

In any given run, HERS is designed to perform one of three types of analysis as specified in the

user input field “Objective.” The user-specified objective may be in any of three possible forms:

1. Maximize the net present value of all benefits of highway improvements subject to specified constraints on funds available during the period;

2. Minimize the cost of improvements necessary to achieve a specified goal for the performance of the highway system at the end of the funding period; or

3. Implement all improvements with a benefit-cost ratio (BCR) greater than some specified

threshold value.

The three forms are also referred to as Constrained Fund, Performance Constrained, and Minimum BCR, respectively.

When Objective is set to “1”, HERS will solve for highway conditions and performance when

improvements are constrained by available funds (referred to as a “constrained fund” run).

When Objective is set to “2”, HERS will solve for the funding levels required to bring the system

to a specified level of performance (referred to as a “performance constrained” run). When

Objective is set to “3”, HERS will solve for both the required funding level and the resultant performance levels when improvements are constrained to return a minimum ratio of benefits relative to their cost (a “minimum benefit-cost ratio (BCR)” run). The model recognizes two special

cases. The first is an “engineering needs” run (sometimes referred to as “full needs”), which is a

minimum BCR run with the minimum BCR set to a very low negative number so that all sections

with deficiencies are selected for improvement. The second is a “maintain current conditions”

run in which the model first determines the level of system performance at the beginning of the

run based on user-specified parameters (for example, current highway-user costs), and selects

the least costly mix of improvements to maintain that level of performance. Each of the special

cases can be selected via a dedicated input field. Finally, while a minimum BCR run where the

minimum BCR is set to 1.0 is referred to as an “economic efficiency” run, this is not a different

type of analysis, but a specific and often used Objective 3 scenario, and was used as the Maximum Economic Investment scenario in the 2002 C&P Report.

Objective 2 scenarios, such as the Maintain User Costs scenario of the 1997 C&P Report, can be

specified as a goal for a single type of highway-user cost or highway agency cost per vehicle-mile

(e.g., number of fatalities per vehicle-mile); or it can be specified as a dollar-valued composite of

all net user and agency costs estimated by HERS (travel time costs, operating costs, fatality costs,
An Outline of the Model Structure

2-2

injury costs, property damage, and maintenance costs). The dollar-valued composite can be

obtained as a simple sum of the component costs or as the sum of two or more components with

different weights. (The run specification file provides one set of weights used in balancing components of the incremental benefit-cost ratio, and another set for balancing components of the

performance goal.) In the latter event, it is recommended (but not required) that the components

of the IBCR be given weights that are consistent with the specified goal; e.g., the goal might be

that the sum of user costs plus two times agency costs should not exceed $0.50 per vehicle-mile,

in which case it is recommended that agency costs be weighted twice as heavily as user costs in

the IBCR as well.

2.2 The HERS Process

The basic process is agreeably straightforward: forecast section condition; identify deficiencies

and potential improvements; evaluate and select improvements; and implement improvements

(or, for unimproved sections, implement the unimproved condition forecast for the end of the

period). Output statistics are accumulated, and the process is repeated for each subsequent

funding period. However, the model has two features (alternative improvement selection procedures, and mandatory correction of unacceptable conditions) which complicate the structure.

Each feature offers a pair of alternatives, which, selected independently, define four distinct logical structures.

2.2.1 The Improvement Selection Procedures

The first feature is that the model supports two improvement selection procedures. Both procedures use benefit-cost analysis to choose between potential improvements, but one procedure

chooses among improvement options for a single section at a time, while the other selects from

all potential improvements to all sections in the system. 

The “minimum BCR” alternative (Objective = 3) instructs the model to implement, for each deficient section, the most ambitious improvement which meets a minimum benefit-cost ratio.

Under this option, all deficient sections with an “economically justifiable” candidate improvement are improved. An improvement is considered “economically justifiable” if its benefit-cost

ratio is greater than or equal to the user-specified minimum. (For the “Economic Efficiency” scenario, the minimum BCR is set to 1.0.) Benefit-cost analysis is used first to determine if a section

will be improved, and second to identify the most attractive of the potential improvements. (The

improvement with the greatest BCR is considered more attractive.) The model is under no budget or performance constraints, but will implement the most attractive improvement for each

qualifying section.

The “constrained” alternative (Objective = 1 or 2) effectively compels the model to rank all

potential improvements, for all sections, in order of economic desirability (that is, ranked by

BCR). The model then selects improvements in order of decreasing BCR until a specific constraint (available funds or system performance level) has been reached. While not all economically attractive improvements may be selected, those selected will all be more economically

attractive than those not selected for implementation. When the constraint is available funds, the

program selects the set of improvements which return the maximum benefit for the capital

expenditure. When the program is constrained to attain a specific level of performance for the
HERS Technical Report v3.54

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2-3

highway system, it selects the set of improvements which will achieve those goals at the lowest

cost.

Exhibit 2-1 shows flow diagrams for these two selection procedures. In the minimum BCR version, the model selects a section’s improvement immediately after evaluating the possible

improvements. In the constrained run, the model “pre-selects” a section’s most attractive

improvement and places it on a list of potential improvements. After all sections have been evaluated, the model initiates a second selection procedure which selects improvements from the

potential list (which is ordered by BCR) until the constraint, whether a budget limit or a performance goal, has been met.

The processes for identifying potential improvements are presented in 3, ”Identifying Candidate

Improvements.”

2.2.2 Addressing Unacceptable Conditions

The second feature which can complicate the HERS selection process is the provision of a

“safety-net” to force the model to improve unacceptably deficient sections without regard for the

economic desirability of the improvement. If this option is selected, HERS will make a special

pass through all sections prior to the normal evaluation to identify low-cost improvements to

correct unacceptable conditions. Improvements selected on this basis are referred to as “mandatory improvements.” For most purposes, such as preparation of data for the Conditions and Performance Report, the model is run without selecting this option, so no mandatory improvements

are implemented. 

The processing flow after the identification of mandatory improvements varies depending upon

the analytical objective. The simplest case is illustrated in Exhibit 2-2, “Minimum BCR Run with

Mandatory Improvements.” In this case, after identifying mandatory improvements for sections

with unacceptable conditions, the program re-examines each section to identify economically

attractive improvements. On a section for which a mandatory improvement has been identified,

the model will implement either the mandatory improvement or an economically attractive

improvement which also corrects all unacceptable conditions. On sections without mandatory

improvements, the economically most attractive improvements will be implemented. 

The processing flow for a performance constrained run with mandatory improvements is shown

in Exhibit 2-3. In this type of run, the program forecasts the unimproved condition of the system

at the end of the funding period, then implements improvements until the level of system performance reaches the specified goal. If implementing the mandatory improvements alone achieves

the performance goal, no additional improvements are considered during this funding period. If

the goal has yet to be achieved, the program loops through the sections again to identify economically attractive improvements, which are ordered by BCR and selected until the goal is

attained.

Exhibit 2-4 shows the processing flow for a constrained fund run with mandatory improvements. For this scenario, the analyst specifies two funding levels: the total amount of funds to be

expended per funding period, and the amount of the total funds which are to be used for more

aggressive (that is, non-mandatory) improvements. For example, the analyst might specify that

100 million dollars be allocated for the first funding period, of which 70 million dollars is

reserved for non-mandatory improvements. After identifying mandatory improvements for all
An Outline of the Model Structure

2-4

sections, the program checks whether the cost of all mandatory improvements exceeds the 30

million dollars allocated for mandatory improvements.

If the mandatory improvements cost more than the funds allocated for them, the program selects

from the mandatory improvements in order of their BCRs until it has expended all the available

funds on the economically most attractive improvements. It then checks whether additional

Exhibit 2-1. HERS Process Flow Without Mandatory Improvements

Forecast Conditions Forecast Conditions

Evaluate potential

improvements

Select most attractive

improvement

Implement selected

improvements

Implement selected

improvements

Select most attractive

improvements for

system

Pre-select most attractive improvement

Evaluate potential

improvements

For each section:

For each funding period: For each funding period:

For each section:

 Constrained Run (without Mandatory

Improvements)

Minimum BCR run (without Mandatory

Improvements)
HERS Technical Report v3.54

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2-5

funds have been reserved for more aggressive (non-mandatory) improvements. If not, it implements the selected improvements and advances to the next funding period.

However, if funds were reserved for non-mandatory improvements, or if the mandatory

improvements cost less than the funds allocated for them, the program loops through all the sections again to identify more aggressive improvements for implementation with the remaining

funds. These improvements are selected in BCR order. 

Exhibit 2-2. Minimum BCR Run with Mandatory Improvements

Forecast Conditions

Identify inexpensive

mandatory improvement

Evaluate more aggressive improvements

Select most attractive

improvement

For each section:

For each funding period:

Implement selected

improvements

For each section:
An Outline of the Model Structure

2-6

Note that in all cases, it is possible for the model to identify a mandatory improvement for a section, and subsequently replace it with an economically more attractive improvement which corrects all the unacceptable conditions which existed on the section.

The identification of potential improvements to correct sections in unacceptable condition is discussed in paragraph 3.3.2, ”Addressing Unacceptable Conditions: the Optional First Pass.” The

process of selecting mandatory improvements, or of replacing a mandatory improvement with a

Exhibit 2-3. Performance Constrained Run With Mandatory Improvements

Performance

Goal Met?

Forecast Conditions

Identify inexpensive

mandatory improvement

Evaluate more aggressive

improvements

Pre-select most attractive improvement

For each section:

Select most attractive

improvements for system

until goal met

For each section:

Implement selected

improvements

Yes No

For each funding period:
HERS Technical Report v3.54

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2-7

more aggressive improvement, is presented in paragraph 7.11, ”Selecting Mandatory Improvements.”

Exhibit 2-4. Constrained Fund Run With Mandatory Improvements

Forecast Conditions

Identify inexpensive

mandatory improvement

Evaluate more aggressive improvements

Pre-select most attractive improvement

For each section:

Select most attractive

improvements to limit of

total funds

For each section:

Implement selected

improvements

No

For each funding period:

Reached mandatory

funding constraint?

Yes

Select most attractive

improvements to limit

of reserved funds 

Yes

No

Non-mandatory

funds available?
An Outline of the Model Structure

2-8

2.3 The HERS Prediction and Calculation Models

For each funding period, for each sample section, for each of the logical sequences, the program

performs the same set of predictions:

• predicts future traffic volume

• predicts future pavement conditions

• predicts current and future speeds

• predicts section capacity after improvement.

These predicted conditions are then used to calculate costs:

• costs to users of the highway system:

+ operating costs

+ travel time costs

+ safety costs

• agency costs:

+ capital improvement costs

+ maintenance costs

• costs associated with vehicle emissions.

The information generated by the prediction and calculation models are used within the logic

structure to evaluate and select improvements. The relationships between the prediction and

calculation models are shown in Exhibit 2-5, “Prediction and Calculation Model Linkages.” The

prediction models are discussed in detail in Chapter 4, “HERS Internal Models” and the calculation models are presented in Chapter 5, “Cost and Benefit Calculations.” 

2.4 Implementation and Output

The condition of each section is maintained in a set of data items which are originally populated

from the HPMS database. While many of these items are not changed during analysis (for example, section identification and location), others (such as traffic volume and pavement condition)

can be expected to change with each passing funding period. Improvements are implemented

through changes to applicable data items (notably pavement condition and number of lanes). 

At the beginning of each funding period, the model forecasts the condition of each section at the

end of the funding period. This basic forecast consists of predicting future traffic volume, then

calculating the effect of this traffic on the pavement condition. For sections which are unimproved during the funding period, this becomes the condition of the section at the beginning of

the subsequent funding period. Because HERS treats improved sections as receiving their

improvements at the midpoint of the funding period, determining the end of period condition of

an improved section consists of upgrading the section’s condition to reflect the improvement

and then forecasting it’s condition at the end of the period.
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At this point, the program accumulates the statistics which will be used to generate the output

pages. See Chapter 8, “Model Output,” for more details.

2.5 The HERS Milieu

2.5.1 HERS Time Frames

The HERS program operates over a set of time frames known as funding periods (FPs), as shown

in Exhibit 2-6, “HERS Time Periods.” These funding periods are equal in length, and combine to

form the overall analysis (OA) period. The set of all funding periods form a sequence, with the

first one beginning at the start of the OA period, and each succeeding funding period starting at

the end of the preceding one. HERS defines additional funding periods which start after the end

of the OA period. These “post analysis period” funding periods are the same length as the funding periods within the OA period, and extend far enough beyond the end of the OA period to

permit benefit-cost (B/C) analyses to be performed on all improvements that might be impleExhibit 2-5. Prediction and Calculation Model Linkages

Travel Forecast

Capacity Calculation

Speed Prediction

Model

Predicted Pavement

Condition

Crash Rates & Costs

(User Safety Costs)

Emission Costs

User Travel Time

Costs

User Operating Costs

Maintenance Costs

Notes: The dashed line reflects the influence of user costs on travel forecasts due to demand elasticity. The Capacity Calculation is entered only

after implementing an improvement.
An Outline of the Model Structure

2-10

mented during the OA period. Exhibit 2-6 depicts an overall analysis period consisting of four

five-year funding periods.

HERS performs B/C analyses on all improvements that might be implemented during the OA

period, but not on improvements that might be implemented after the OA period. For purposes

of the B/C analyses, HERS treats all improvements as if they were implemented at the midpoint

of the funding period. Accordingly, every benefit-cost analysis period (BCAP) extends from the

midpoint of a funding period to the midpoint of a subsequent funding period (which can extend

beyond the end of the OA period). Additionally, because of the impact of an improvement upon

the price to the user of the section, the time-frame for the elasticity calculations (shown in the

exhibit as ELAS) also run from funding period midpoint to funding period midpoint. 

2.5.2 Functional Classes

The HERS program recognizes nine functional classes of highways, including all of the urban

arterial and collector classes, and all of the rural arterial and major collector classes. Rural minor

collectors and roads functionally classified as local are not recognized by HERS. 

A large number of HERS parameters can be specified by the user with different values for each

of the nine functional classes. These include:

• Deficiency Levels 

• Serious Deficiency Levels

• Unacceptability Levels

• Minimum Tolerable Conditions

• Design Standards

• Improvement Costs

• Truck Growth Factors

• Cost of Non-Fatal Injuries

• Property Damage Cost per Crash

• Funds Available for Improvements (Fund Constrained Run)

• Highway Performance Goals (Performance Constrained Run)

• Weights for Highway Performance Goals

FP One FP Two FP Three FP Four FP Five FP Six

BCAP BCAP BCAP BCAP BCAP BCAP

ELAS ELAS ELAS ELAS ELAS ELAS

Overall Analysis Period Post-Analysis Period

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30

Exhibit 2-6. HERS Time Periods
HERS Technical Report v3.54

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2-11

• Weights for Benefit-Cost Ratio Calculation.

The Fleet Composition model also relies on functional class. (See paragraph 4.4, ”The Fleet Composition Model.”)

When performing a constrained fund run or a performance constrained run, HERS allows the

user the options of setting separate budget constraints or performance goals for each functional

class, or for certain combinations of functional classes. These combinations are shown in Exhibit

2-7, “Highway Functional System Groupings.” The user can set targets for:

• 1 group (for all functional systems combined);

• 2 groups (for the urban system and for the rural system);

• 2 groups (for the principal arterials and for the minor arterials and collectors);

• 4 groups (for urban principal arterials, for rural principal arterials, for urban minor

arterials and collectors, and for rural minor arterials and collectors); or

• 9 groups (for each of the nine functional classes distinguished by HERS).

The flow charts in Exhibits 2-1 through 2-4 are based upon the standard case where the set of

sample sections is treated as a single system (one group). However, if the user elects to use multiple functional class groups in setting performance goals or budget constraints, then during initialization, HERS takes the additional step of separating the sample sections into the component

groups, and maintains a separate section file for each group. During processing, the model processes each group in turn in a loop nested between the loops for funding periods and sections.

The structure then becomes:

Loop through each funding period...

Loop through each functional class group...

Loop through all sections in the class group...

Process a section (forecast conditions, identify potential improvements, pre-select an improvement)

End loop (all sections)

Select improvements until constraint is satisfied for the class group

Implement selected improvements for the class group

End loop (functional class group)

End loop (funding period)

2.5.3 Pavement Condition Measures

HERS uses PSR to measure pavement roughness. All internal HERS calculations (speed, operating costs, pavement deterioration, and improvement identification) are based upon PSR. The

HERS PreProcessor converts IRI to PSR using the equation:

Eq. 2.1

where:

IRI = IRI value; and

PSR = 5.0 × exp( ) SURFACT IRI ×
An Outline of the Model Structure

2-12

SURFACT = conversion factor based upon surface type.

Table 2-1, “PSR to IRI Conversion Factors,” displays the possible values for SURFACT and the

corresponding surface types. 

Single System

Rural and Urban

Princ. Art. & OtherPrinc. Art. & Other 

by Rural/Urban

By Functional Class

Number Of Groups >>> 12249

Code: Description:

Rural

 01 Principal Arterial – Interstate 1 1 1 1 1

 02 Other Principal Arterial 1 1 1 1 2

 06 Minor Arterial 1 1 2 2 3

 07 Major Collector 1 1 2 2 4

Urban

 11 Principal Arterial – Interstate 1 2 1 3 5

 12 Principal Arterial – Other Freeways and Expressways 12136

 14 Other Principal Arterials 1 2 1 3 7

 16 Minor Arterial 1 2 2 4 8

 17 Collector 1 2 2 4 9

Exhibit 2-7. Highway Functional System Groupings

Table 2-1. PSR to IRI Conversion Factors

Surface Type Conversion Factor

Flexible -0.0038

Composite -0.0046

Rigid -0.0043
HERS Technical Report v3.54

September 2002

2-13

For purposes of certain output statistics, HERS converts PSR to IRI using the equation:

Eq. 2.2

again using the conversion factors in Table 2-1.

Exhibit 2-8, “Pavement Condition Ratings,” presents descriptions of pavement characteristics

corresponding to the various PSR levels. The exhibit also displays the IRI values (for rigid pavement) for the integer PSR values from one through five. The lowest value shown for PSR (0.068)

was chosen to correspond to an IRI of 999. 

PSR and

Verbal

Rating

IRI

Value

(Rigid)a

a. Rounded to whole inches per mile.

Description

5.0 0

Very Good

Only new (or nearly new) pavements are likely to be smooth enough and sufficiently free of cracks and patches to qualify for this category. All pavements constructed or resurfaced during the data year would normally be rated very good.

4.0 52 ------------------------------------------------------------------------------------------------------

Good

Pavements in this category; although not quite as smooth as those described 

above, give a first class ride and exhibit few, if any visible signs of surface deterioration. Flexible pavements may be beginning to show evidence of rutting and fine 

random cracks. Rigid pavements may be beginning to show evidence of slight 

surface deterioration, such as minor cracks and spalling.

3.0 119 ------------------------------------------------------------------------------------------------------

Fair

The riding qualities of pavements in this category are noticeably inferior to those 

of new pavements and may be barely tolerable for high speed traffic. Surface 

defects of flexible pavements may include rutting, map cracking, and extensive 

patching. Rigid pavements in this group may have a few joint failures, faulting 

and cracking, and some pumping.

2.0 213 ------------------------------------------------------------------------------------------------------

Poor

Pavements that have deteriorated to such an extent that they affect the speed of 

free-flow traffic. Flexible pavement may have large potholes and deep cracks. 

Distress includes ravelling, cracking, rutting, and occurs over 50 percent or more 

of the surface. Rigid pavement distress includes joint spalling, faulting, patching, 

cracking, scaling, and may include pumping and faulting.

1.0 374 ------------------------------------------------------------------------------------------------------

Very Poor

Pavements that are in an extremely deteriorated condition. The facility is passable 

only at reduced speeds and with considerable ride discomfort. Large potholes 

and deep cracks exist. Distress occurs over 75 percent or more of the surface.

0.068 999

Exhibit 2-8. Pavement Condition Ratingsb

b. Source: U.S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System Field Manual, Washington, D.C., December 1987, p.IV-28. The version in the April 1994 edition excludes the verbal ratings.

IRI = ln( ) 0.2 × PSR ⁄ SURFACT
An Outline of the Model Structure

2-14
3-1

3 Identifying Candidate Improvements

The highway improvements analyzed by HERS v3.54 consist of various combinations of pavement, widening and alignment improvements. The first part of this chapter presents definitions

of these improvement types. The second portion identifies the section characteristics and types

of deficiency levels that HERS utilizes in determining whether potential improvements should

be evaluated. The third part presents the procedures used for identifying these potential

improvements. The fourth portion lists the default values for the different types of deficiency

levels. The fifth part discusses the implications of using the default deficiency level settings, and

of using values that are more or less stringent.

3.1 HERS Improvement Types and Kinds

The highway improvements considered by HERS v3.54 consist of resurfacing or pavement

reconstruction, possibly combined with some type of widening and/or alignment improvement.

Schematically, these improvement types can be viewed as being obtained by selecting one

“improvement option” from each of the columns of Table 3-1, “Improvement Options.” There

are 32 possible combinations for the options in the three columns of the table, and eight possible

combinations for the options in the first two columns. However, as HERS corrects shoulder deficiencies when reconstructing pavement, it makes no distinction between pavement reconstruction with or without shoulder improvements. The result is 28 different “types” of improvement,

or, if the third column is ignored, seven different “kinds” of improvement. 

Table 3-1 shows three distinct alignment options: improve curves, improve grades, or improve

both. In HERS 3.54, if curves (respectively, grades) are in “unacceptable” condition (as defined

later in this chapter) but grades (respectively, curves) are not, then an improvement that

improves curves (respectively, grades) to the design standard but does not modify grades

(respectively, curves) may be selected. Otherwise, only alignment improvements that result in

improving both curves and grades to the design standard are considered.

Each of the seven kinds of improvement are described briefly in Exhibit 3-1, “Kinds of Improvement.” Within each group, the improvements are listed in decreasing degree of aggressiveness.

HERS uses an additional set of extra-cost options to improve substandard urban freeways to

design standards. The four options are: surface shoulders; improve access control to full;

upgrade median type to positive barrier; and widen median to design standard. The appropriTable 3-1. Improvement Options

 Pavement Widening Alignment

 0. Resurface 0. None 0. No change

 1. Reconstruct 1. Improve shoulders 1. Improve curves

2. Widen lanes 2. Improve grades

3. Add lanes 3. Improve curves and grades
Identifying Candidate Improvements

3-2

ate improvements are only implemented on substandard urban freeways undergoing pavement

reconstruction; sections being resurfaced are not upgraded in this manner.

The HERS model differentiates between lanes added at “Normal” and “High” cost. New lanes

are added at normal cost when they do not violate the state-supplied Widening Feasibility code

(WDFEAS) for the section. The user has the option of setting the Federal Override (WDFOVR)

value to add lanes beyond those permitted by the state code up to the maximum lane limit

(MAXLNS). These lanes are added at high cost. It is possible for a section to be improved by the

addition of lanes at both cost levels: HERS reports these improvements as high cost lanes in the

output statistics. 

3.2 Deficiency Criteria

HERS recognizes a section’s need for improvement by comparing its characteristics to user-specified deficiency levels. HERS distinguishes up to three degrees of deficiency that might exist for

eight characteristics of each highway section. The eight characteristics are:

A. Reconstruction

1. Reconstruction with More Lanes - Complete reconstruction with the addition of lanes to the

existing section. Lanes added in excess of the state-coded widening feasibility code are

added at high cost – otherwise, lanes are added at normal cost. Shoulder and drainage

deficiencies are corrected.

2. Reconstruction to Wider Lanes - Complete reconstruction with wider lanes than the existing section. No additional lanes are added. Shoulder and drainage deficiencies are corrected.

3. Pavement Reconstruction - Complete reconstruction without adding or widening lanes.

Shoulder width increased to design standard if feasible, and any other shoulder or drainage deficiencies are corrected.

B. Resurfacing

1. Major Widening - The addition of lanes to an existing facility. Lanes added in excess of the

state-coded widening feasibility code are added at high cost – otherwise, lanes are added at

normal cost. This improvement includes resurfacing the existing lanes and other minor

work such as shoulder and drainage work.

2. Minor Widening - This improvement is similar to major widening except that the added

width yields wider lanes or shoulders, but no additional lanes.

3. Resurfacing with Shoulder Improvements - The overlay of existing pavement plus the widening of shoulders to design standards if feasible or the complete reconstruction of shoulders to provide additional strength. A minor amount of additional right-of-way may be

acquired.

4. Resurfacing - The overlay of existing pavement including bringing the shoulders up to

grade including minor drainage work. 

Exhibit 3-1. Kinds of Improvement
HERS Technical Report v3.54

September 2002

3-3

1. Pavement condition;

2. Surface type;

3. Volume/Capacity (V/C) ratio;

4. Lane width;

5. Right shoulder width;

6. Shoulder type;

7. Horizontal alignment; and

8. Vertical alignment.

The three degrees of deficiency are identified by three user-specified levels: DL (deficiency

level); SDL (serious deficiency level); and UL (unacceptability level). The roles of these three

levels in the HERS improvement-selection procedure are:

1. If the DL for a particular characteristic of a section is violated, HERS will analyze the benefits and costs of potential improvements that would correct this condition. If the resulting benefit/cost ratio of such an improvement is high enough, it may be selected to be

implemented.

2. If the SDL for a particular characteristic of a section is violated, then only improvements

that correct this condition are evaluated by the HERS benefit-cost analysis procedure.

3. If the user has specified that improvements are mandatory if the UL for a particular characteristic is violated, then an improvement that corrects this condition is normally

selected automatically. (See paragraph 3.3.2, ”Addressing Unacceptable Conditions: the

Optional First Pass.”) The B/C ratio for the improvement is considered by HERS only if

the limiting constraint (whether funds available or system performance level) is insufficient to correct all such conditions.

The values used by HERS are contained in an external ASCII file (DLTBLS.DAT) for convenient

user access and modification.

3.3 Identifying Improvements for Analysis

During each funding period, HERS is designed to make two passes over the entire set of sample

sections to identify improvements that might warrant implementation. The first pass is optional

and is used to identify improvements to be implemented based upon engineering criteria,

regardless of their economic desirability. During the first pass, for paved sections with unacceptable present serviceability ratings for pavement condition and for unpaved sections with unacceptable surface type or lane width, HERS selects an appropriate inexpensive improvement. If

sufficient funds are available, all such improvements are implemented without any B/C analysis. Otherwise B/C analysis is used to select the improvements to be implemented. Note: this

optional first pass is not used in the analysis for the C&P Report.
Identifying Candidate Improvements

3-4

During the second pass, HERS identifies additional deficiencies as well as appropriate improvements to address these deficiencies. B/C analysis is then used to determine which of these

improvements to implement.

The procedures used to identify improvements during each of these passes are presented below.

As the procedure used during the second pass is central to the use of B/C analysis by HERS, that

procedure is described first.

3.3.1 Addressing Ordinary Deficiencies: the Second Pass

During the second pass, HERS identifies deficiencies on the basis of the user-specified DLs and

SDLs. HERS identifies an improvement type only when a pavement or capacity deficiency exists

in the current funding period. When such a deficiency exists, HERS generally will identify at

least one improvement type that will address it. (The exception to this rule is when the only deficiency is a capacity deficiency, and additional lanes are either not needed or cannot be added,

and it is not possible to widen the section to correct any substandard shoulder or lane widths.)

The procedure for identifying improvement types to address ordinary deficiencies consists of

two components:

1. Identification of one (or, in some cases, two) “aggressive improvement type(s)” that will

correct all identified deficiencies; and 

2. Identification of any less aggressive improvement types warranting B/C analysis as possible alternatives to the first, more aggressive, improvement(s). These alternatives would

address some but not all of the segment’s deficiencies.

These two components of the procedure are discussed below.

3.3.1.1 Aggressive Improvement Types

The procedures for selecting pavement, width and alignment options are presented in Exhibit 3-

2, “Identification of Aggressive Pavement Option,” Exhibit 3-3, “Identification of Aggressive

Widening Options,” and Exhibit 3-4, “Identification of Aggressive Alignment Options,” respectively. These three procedures, taken together, identify a set of options that define a maximum

of two improvement types. 

When considering pavement options, HERS decides whether resurfacing or reconstruction is

appropriate based upon PSR at the beginning of the funding period analyzed. This reconstruction level is set by the user. As shown in Exhibit 3-2, the consideration of reconstruction can also

be triggered by the inadequacy of the current surface type. 

When considering widening options, HERS may select both an “add lanes” option and, if appropriate, the “widen lanes” option as well. This is the only situation in which HERS will identify

two aggressive improvement types for further analysis. This can occur only when:

1. Additional lanes can be added;

2. More lanes are needed in the design year, but not now;

3. Widening lanes will increase capacity without correcting the design year capacity deficiency; and
HERS Technical Report v3.54

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3-5

4. Reconstruction is needed.

HERS identifies the widen lanes option whenever the PSR is deficient, widening is feasible, and

either lanes are needed but cannot be added or lane width is deficient. The HERS decision to

widen lanes does not depend upon factors such as whether reconstruction is required, rural or

urban location and whether or not the section is an urban freeway/expressway up to design

standards.

When considering alignment options, HERS considers both horizontal and vertical alignment

improvement for rural sections and horizontal alignment improvements for urban principal

arterials. This analysis is done only for segments for which complete information about curves

and/or grades by class is available. (The HPMS Field Manual requires this information for rural

principal and minor arterials and urban principal arterials.)

3.3.1.2 Less Aggressive Alternatives

After identifying one (or two) aggressive improvement types that will address all of a section’s

deficiencies, HERS then identifies less aggressive improvement alternatives, and uses benefitcost analysis to choose among the alternatives. In general, less aggressive improvements can be

derived directly from the most aggressive improvement by:

1. Replace a widening option with no widening;

2. Replace a widening option with a less aggressive widening option; or

3. Replace improved alignment with no change in alignment.

Replacement rules 1 and 3 involve replacing a particular option with the corresponding “zerolevel” option (as defined and numbered in Table 3-1, “Improvement Options”). If HERS had

selected a single aggressive improvement type including both widening and an alignment

improvement, these two replacement rules would identify up to three less aggressive alternative

improvements for analysis (zero-option for widening, zero-option for alignment, and zerooption for both). If HERS had selected two aggressive improvement types for further analysis,

I. Reconstruct if:

A. PSR at the beginning of the funding period is less than reconstruction PSR;

B. surface type is low and deficient, and a widening option is identified; or

C. surface type is unpaved and:

1. surface type is deficient; or

2. a widening option is identified.

II. Otherwise resurface if:

A. PSR at the end of the funding period is deficient; or

B. a widening option is identified.

Exhibit 3-2. Identification of Aggressive Pavement Option
Identifying Candidate Improvements

3-6

these rules would identify up to four less aggressive alternatives, so up to six alternatives might

be analyzed for some sections. 

Although an exhaustive evaluation of all such alternatives may, at times, be of interest, it is likely

that HERS users frequently will prefer that some of these evaluations be skipped in order to

shorten run times. This is accomplished using the SDLs introduced in paragraph 3.2. When the

user-specified SDL for a section characteristic is violated, any improvement option designed to

address the deficiency is treated as “required” and HERS will not analyze the zero-level alternative. If the SDL is not violated, any improvement designed to address the deficiency is treated as

“non-required” or “optional,” and the zero-level alternative to the option is analyzed. (There is

I. For unpaved sections:

A. Widen lanes if a deficiency exists in lane width or (for collectors in the lowest volume category)

in sum of lane width and shoulder width.

II. For paved sections:

A. Add lanes if lanes can be added and 

1. more lanes are neededa or

2. pavement requires reconstruction, and more lanes will be needed in the design year

B. Widen lanes if lanes can be widened and

1. more lanes are not needed, or lanes cannot be added and

a. lane width is deficient, and PSR is deficient; or

b. design hour V/C is deficient, and capacity would be increased by widening lanesb, and

lane width is less than design standard; or

2. If PSR is deficient, and design hour V/C is not deficient but will be in the design year, and

capacity would be increased by widening lanesb, and lane width is less than the design

standard, and

a. section is an urban freeway by design type; or 

b. the reconstruction option has been identified solely as a result of a pavement or surface

type deficiency.

C. Otherwise, improve shoulders if:

1. shoulder width is less than the design standard, widening is feasible, design hour V/C is

deficient, and capacity would be increased by improving shouldersb;

2. shoulder width is deficient, widening is feasible, and PSR is deficient; or

3. shoulder type is deficient and PSR is deficient.

Exhibit 3-3. Identification of Aggressive Widening Options

a. “More lanes are needed” means V/C is deficient both now and in the design year.

b. On some sections with initial capacity coded in the HPMS data base, widening lanes or shoulders may not result in any increase in capacity (because the calculated capacity after widening is no higher than the coded capacity). For such sections, the “widen lanes” and “improve shoulders” options do not produce any benefits recognized by

HERS. For such sections, these improvements are analyzed by HERS only if they address a “serious deficiency”.
HERS Technical Report v3.54

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3-7

no SDL for pavement condition, since the decision on whether to reconstruct or resurface a section is primarily based on the reconstruction level. HERS does not directly compare reconstruction alternatives with resurfacing alternatives for an individual section.) 

Replacement rule 2 is used only in the special case in which a lower-level widening option (e.g.,

improve shoulders, or widen lanes) is required (because the SDL for shoulder-width or shoulder-type is violated), but a non-required higher-level widening option (e.g., widen lanes or add

lanes) is included in the aggressive improvement identified by HERS. In this case, HERS considers the required lower-level widening option as an alternative to the aggressive improvement,

rather than evaluating the zero-level alternative.

If the user has elected to enable ULs (unacceptability levels), and if the capacity of a section is

expected to violate the user-specified UL during the expected design life for a pavement

improvement being considered, a capacity improvement option is treated as a required accompaniment to that pavement improvement, regardless of whether the capacity SDL is currently

being violated. In this case, the zero-level alternative widening option would not be evaluated.

This requirement enables HERS to avoid a situation in which capacity becomes unacceptable at a

time when resurfacing (or reconstruction) is not normally performed.

If all SDLs are set equal to the corresponding DLs, then normally only the “most aggressive”

improvements identified by the procedures of Exhibits 3-2 through 3-4 are analyzed. If the SDLs

are relaxed completely (that is, the SDL for the V/C ratio is set high and all other SDLs are set to

zero), all alternatives generated by replacement rules 1 and 3 are evaluated. The implications of

how the user chooses to set the DL, SDL, and UL levels are discussed more fully in paragraph

3.5. 

I. For rural sections:

A. Improve curves and/or grades if:

1. curves and/or grades by class are specified, 

2. any pavement or widening option is identified, and 

3. horizontal or vertical alignment is deficient.

II. For urban sections:

A. Improve curves if:

1. curves by class are specified, 

2. reconstruction is identified, and 

3. horizontal alignment is deficient.

Exhibit 3-4. Identification of Aggressive Alignment Options
Identifying Candidate Improvements

3-8

3.3.2 Addressing Unacceptable Conditions: the Optional First Pass

An option is available to enable the user to identify unacceptable conditions that receive greater

priority for correction than serious deficiencies. In most instances, the improvements selected to

correct the unacceptable conditions will be implemented without being subject to B/C analysis.

When the analysis is constrained by available funds, a portion of the available funds may be designated for the correction of unacceptable conditions. In the case of paved sections, whenever a

section is found to have an unacceptable PSR, an appropriate inexpensive improvement that

addresses all unacceptable conditions on the section is identified. In the case of unpaved sections, whenever a section is found to have unacceptable surface type or lane width, an appropriate inexpensive improvement that addresses all such conditions is identified. The procedure for

identifying options defining these improvements is presented in Exhibit 3-5, “Identification of

Improvement Options for Addressing Unacceptable Conditions.”

Paved sections with unacceptable PSR and unpaved sections with unacceptable surface type or

lane width will be referred to as sections with “triggering unacceptabilities”. The procedure presented in Exhibit 3-5 is designed to identify all such sections and, except for the case in which the

V/C ratio is unacceptable, the procedure is designed to identify the least expensive of the available HERS improvements that will correct all unacceptable conditions on such a section. In the

case of an unacceptable V/C ratio, the procedure selects the most aggressive widening option

warranted by the section's characteristics.

When a section has unacceptable pavement, the improvement identified by the procedure

shown in Exhibit 3-5 will generally be selected to improve the section.1

 However, the implementation of mandatory improvements is handled slightly differently depending on the user’s analytical objective, as discussed below. 

3.4 Default Deficiency Criteria

Suggested default values for the ULs, SDLs, and DLs for the eight section characteristics are presented in Tables 3-2 through 3-9. (These values were used in processing for the 2002 C&P

Report.) As indicated in the exhibits, for rural sections HERS allows separate values to be specified for three terrain types and eight combinations of functional system and average daily traffic

(AADT). For urban sections, HERS allows separate values for each of five functional systems. 

In the case of pavement condition (Table 3-2, “Default Pavement Condition Criteria (PSR)”),

SDLs are not shown, but a set of “reconstruction levels” (RLs) are. SDLs for pavement condition

are not needed because all improvements involve either resurfacing or reconstruction, and, in

HERS, only one of these two improvement options are considered for a section in any funding

period. The pavement option considered is resurfacing unless PSR is below the RL or certain surface-type deficiencies (specified in Exhibit 3-2) exist.2

1. It should be noted that (as currently implemented), for paved sections, only pavement-related conditions trigger the

correction of unacceptable conditions; but, when unacceptable pavement conditions are corrected, all other unacceptable conditions are corrected as well. This procedure, in conjunction with the procedure for addressing serious

deficiencies, guarantees that any non-pavement-related unacceptable conditions will be corrected whenever the

pavement of a section is improved. However, except when warranted by benefit-cost analysis, these conditions will

normally not be corrected as long as the section's pavement remains in reasonably good condition.
HERS Technical Report v3.54

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3-9

Tables 3-2 through 3-9 also show the HPMS minimum tolerable conditions3 (MTCs) and, in several of the tables, the design standards (DS) for rural sections used by HERS. The design standards used for median width and for curves and grades are shown in Table 3-10, “Default

2. For medium and high-type pavement, PSR is the sole determinant of whether a section should be reconstructed;

and for low-type pavement, it is the primary determinant. HERS is unable to take into account other influences on

the reconstruction decision (e.g., height of the pavement crown), because they are not currently described in the

HPMS database. 

I. For paved surfaces:

A. If at the end of the funding period the PSR is unacceptable:

1. Reconstruct if surface type is low and unacceptable;

2. Otherwise, reconstruct if at the beginning of the funding period the PSR is below the reconstruction PSR;

3. Otherwise, resurface.

B. If resurfacing or reconstruction has been selected, then:

1. For rural sections, improve curves and/or grades if horizontal and/or vertical alignments

are unacceptable, and curves and/or grades are specified by class;

2. For urban principal arterial, improve curves if horizontal alignment is unacceptable, and

curves are specified by class;

3. If V/C is unacceptable:

a. Add lanes if more lanes are needed and can be added;

b. Widen lanes if lanes can be widened:

i. if lane width is unacceptable; or

ii. if lane width is less than the design standard, and widening lanes will increase

capacity, and widening shoulders will not make V/C acceptable;

c. Otherwise, improve shoulders if shoulder width is less than design standard and

shoulders can be widened and widening shoulders will increase capacity.

4. Widen lanes if lane width is unacceptable and lanes can be widened;

5. Improve shoulders if shoulder width is unacceptable and widening is feasible;

6. Improve shoulders if shoulder type is unacceptable.

II. For unpaved surface types:

A. Widen lanes and reconstruct if lane width is unacceptable and lanes can be widened;

B. Reconstruct if surface type is unacceptable.

Exhibit 3-5. Identification of Improvement Options for Addressing Unacceptable 

Conditions

3. HPMS does not provide horizontal alignment MTCs for urban sections. The suggested values shown in Table 3-8,

“Default Horizontal Alignment Criteria,” are used by HERS for statistical purposes.
Identifying Candidate Improvements

3-10

Design Standards For Median Width,” and Table 3-11, “Default Design Standards For Curves

and Grades.” The design standards used for urban sections are shown in Table 3-12, “Default

Design Standards for Urban Sections.”

The MTCs are not used by HERS in selecting improvements; however the shoulder type MTCs

are used as design standards when shoulders are improved and the lane width MTCs are used to

specify the lane width following reconstruction of an unpaved section. Also, the MTCs for PSR

are used in determining the end of the useful pavement life. Finally, the MTCs are used for

developing some summary statistics. 
HERS Technical Report v3.54

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3-11

Table 3-2. Default Pavement Condition Criteria (PSR)

UL RL MTC DL

Rural:

1.8 2.0 3.0 3.2 Interstate: Flat 

1.8 2.0 3.0 3.2 Rolling

1.8 2.0 3.0 3.2 Mountainous

1.8 2.0 3.0 3.2 OPA AADT>6000: Flat

1.8 2.0 3.0 3.2 Rolling

1.8 2.0 3.0 3.2 Mountainous

1.5 2.0 2.8 3.0 OPA AADT<=6000: Flat

1.5 2.0 2.8 3.0 Rolling

1.5 2.0 2.8 3.0 Mountainous

1.2 1.5 2.4 2.6 MA AADT>2000: Flat

1.2 1.5 2.4 2.6 Rolling

1.2 1.5 2.4 2.6 Mountainous

1.2 1.5 2.4 2.6 MA AADT<=2000: Flat

1.2 1.5 2.4 2.6 Rolling

1.2 1.5 2.4 2.6 Mountainous

1.0 1.1 2.0 2.4 Coll.’s AADT>1000: Flat

1.0 1.1 2.0 2.4 Rolling

1.0 1.1 2.0 2.4 Mountainous

0.8 1.1 2.0 2.4 Coll.’s AADT=400-

1000:

Flat

0.8 1.1 2.0 2.4 Rolling

0.8 1.1 2.0 2.4 Mountainous

0.6 0.8 1.8 2.2 Coll.’s AADT<400: Flat

0.6 0.8 1.8 2.2 Rolling

0.6 0.8 1.8 2.2 Mountainous

Urban:

2.0 2.2 3.2 3.4 Interstate

1.8 2.0 3.0 3.2 Other Freeway & Expressway

1.6 1.8 2.8 3.0 Other Principal Arterial

1.0 1.1 2.4 2.6 Minor Arterial

0.8 1.0 2.0 2.4 Collector
Identifying Candidate Improvements

3-12

Table 3-3. Default Surface Type Criteria and Standardsa

UL SDL MTC DL DSb

Rural:

2 2 2 22c Interstate: Flat

22222 Rolling

22222 Mountainous

22222 OPA AADT>6000: Flat

22222 Rolling

22222 Mountainous

33222 OPA AADT<=6000: Flat

33222 Rolling

33222 Mountainous

33332 MA AADT>2000: Flat

33332 Rolling

33332 Mountainous

44333 MA AADT<=2000: Flat

44333 Rolling

44333 Mountainous

44333 Coll.’s AADT>1000: Flat

44333 Rolling

44333 Mountainous

44444 Coll.’s AADT=400-1000: Flat

44444 Rolling

44444 Mountainous

55554 Coll.’s AADT<400: Flat

55554 Rolling

55554 Mountainous

Urban:

2222 Interstate

2222 Other Freeway & Expressway

3322 Other Principal Arterial

4433 Minor Arterial

5544 Collectors

a. Surface Type Codes: 1 = High flexible; 2 = High rigid; 3 = Intermediate; 4 = Low; 5 = Unpaved.

b. HERS does not allow design standard of 5 (unpaved), substituting 4 if a standard of 5 is specified.

c. Design standard is high type. HERS actually uses flexible pavement for all resurfacing and for reconstruction of flexible pavements; rigid pavement is used for reconstruction of rigid and composite pavements
HERS Technical Report v3.54

September 2002

3-13

 

Table 3-4. Default Volume/Capacity Ratio Criteria

UL SDL MTC DL

Rural:

0.90 0.85 0.75 0.70 Interstate: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

0.90 0.85 0.75 0.70 OPA AADT>6000: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

0.90 0.85 0.75 0.70 OPA AADT<=6000: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

0.90 0.85 0.75 0.70 MA AADT>2000: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

0.90 0.85 0.75 0.70 MA AADT<=2000: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

0.90 0.85 0.75 0.70 Coll.’s AADT>1000: Flat

0.95 0.90 0.90 0.80 Rolling

0.98 0.95 0.95 0.90 Mountainous

1.00 1.00 1.00 0.95 Coll.’s AADT=400-1000: Flat

1.00 1.00 1.00 0.95 Rolling

1.00 1.00 1.00 0.95 Mountainous

1.00 1.00 1.00 1.00 Coll.’s AADT<400: Flat

1.00 1.00 1.00 1.00 Rolling

1.00 1.00 1.00 1.00 Mountainous

Urban: 

0.98 0.95 0.95 0.90 Interstate

0.98 0.95 0.95 0.90 Other Freeway

0.98 0.95 0.95 0.90 Other Principal Arterial

0.98 0.95 0.95 0.90 Minor Arterial

0.98 0.95 0.95 0.90 Collectors

 
Identifying Candidate Improvements

3-14

Table 3-5. Default Lane Width Criteria and Standards (Feet)a

UL SDL MTC DL DS

Rural:

11 11 12 12 12 Interstate: Flat

11 11 12 12 12 Rolling

11 11 12 12 12 Mountainous

10 11 11 12 12 OPA AADT>6000: Flat

10 11 11 12 12 Rolling

10 11 11 12 12 Mountainous

10 11 11 12 12 OPA AADT<=6000: Flat

10 11 11 12 12 Rolling

10 11 11 12 12 Mountainous

8 9 10 12 12 MA AADT>2000: Flat

8 9 10 12 12 Rolling

8 9 10 12 12 Mountainous

8 9 10 12 12 MA AADT<=2000: Flat

8 9 10 12 12 Rolling

8 9 10 12 12 Mountainous

8 9 10 12 12 Coll.’s AADT>1000: Flat

8 9 10 12 12 Rolling

8 9 10 12 12 Mountainous

8 8 8 11 11 Coll.’s AADT=400-1000: Flat

8 8 8 11 11 Rolling

8 8 8 11 11 Mountainous

8b 8 8 10 10 Coll.’s AADT<400: Flat

8 8 8 10 10 Rolling

8 8 8 10 10 Mountainous

Urban: 

11 11 12 12 Interstate

10 11 11 12 Other Freeway

9 10 10 12 Other Princ. Arterial

8 8 8 12 Minor Arterial

8 8 8 12 Collectors

a. For sections for which the database contains roadway width instead of lane width, HERS treats lane width as onehalf the roadway width.

b. For unpaved collectors in this volume category, these criteria are applied to the sum of lane width and shoulder

width.
HERS Technical Report v3.54

September 2002

3-15

Table 3-6. Default Right-Shoulder Width Criteria and Standards (Feet)

UL SDL MTC DL DS

Rural:

6 7 8 10 12 Interstate: Flat

6 7 8 9 10 Rolling

66678 Mountainous

6 7 8 9 10 OPA AADT>6000: Flat

6 7 8 9 10 Rolling

66678 Mountainous

6 7 8 9 10 OPA AADT<=6000: Flat

6 7 8 9 10 Rolling

66678 Mountainous

66678 MA AADT>2000: Flat

66678 Rolling

44468 Mountainous

45678 MA AADT<=2000: Flat

45678 Rolling

44466 Mountainous

23468 Coll.’s AADT>1000: Flat

23468 Rolling

23466 Mountainous

00244 Coll.’s AADT=400-

1000:

Flat

00244 Rolling

00244 Mountainous

00022 Coll.’s AADT<400: Flat

00022 Rolling

00022 Mountainous

Urban:

6789 Interstate

6789 Other Freeway

0568 Other Principal Arterial

0568 Minor Arterial

0366 Collectors
Identifying Candidate Improvements

3-16

Table 3-7. Default Shoulder Type Criteriaa

UL SDL MTC DL

Rural:

2222 Interstate: Flat

2222 Rolling

2222 Mountainous

2222 OPA AADT>6000: Flat

2222 Rolling

2222 Mountainous

3222 OPA AADT<=6000: Flat

3222 Rolling

3222 Mountainous

3222 MA AADT>2000: Flat

3222 Rolling

3222 Mountainous

3333 MA AADT<=2000: Flat

3333 Rolling

3333 Mountainous

3333 Coll.’s AADT>1000: Flat

3333 Rolling

3333 Mountainous

4333 Coll.’s AADT=400-1000: Flat

4333 Rolling

4333 Mountainous

4333 Coll.’s AADT<400: Flat

4333 Rolling

4333 Mountainous

Urban:

1111 Interstate

1111 Other Freeway

4222 Other Principal Arterial

4333 Minor Arterial

4333 Collectors

a. Shoulder Type Codes: 1 = Surfaced; 2 - Stabilized; 3 = Earth; 4 = Curbed.
HERS Technical Report v3.54

September 2002

3-17

Table 3-8. Default Horizontal Alignment Criteriaa

UL SDL MTC DL

Rural:

2221 Interstate: Flat

2221 Rolling

2221 Mountainous

2221 OPA AADT>6000: Flat

2221 Rolling

2221 Mountainous

3222 OPA AADT<=6000: Flat

3222 Rolling

3222 Mountainous

3222 MA AADT>2000: Flat

3222 Rolling

3222 Mountainous

3222 MA AADT<=2000: Flat

3222 Rolling

3222 Mountainous

3222 Coll.’s AADT>1000: Flat

3222 Rolling

3222 Mountainous

4332 Coll.’s AADT=400-

1000:

Flat

4332 Rolling

4332 Mountainous

4332 Coll.’s AADT<400: Flat

4332 Rolling

4332 Mountainous

Urban:

2221 Interstate

2221 Other Freeway

3221 Other Principal Arterial

a. Alignment Codes: 1 = All curves meet design standards; 2 = Some curves below design standards; 3 = Curves with reduced speed; 4 = Several curves unsafe.
Identifying Candidate Improvements

3-18

Table 3-9. Default Vertical Alignment Criteriaa

UL SDL MTC DL

Rural:

2221 Interstate: Flat

2221 Rolling

2221 Mountainous

2221 OPA AADT>6000: Flat

2221 Rolling

2221 Mountainous

3222 OPA AADT<=6000: Flat

3222 Rolling

3222 Mountainous

3222 MA AADT>2000: Flat

3222 Rolling

3222 Mountainous

3222 MA AADT<=2000: Flat

3222 Rolling

3222 Mountainous

3222 Coll.’s AADT>1000: Flat

3222 Rolling

3222 Mountainous

4332 Coll.’s AADT=400-1000: Flat

4332 Rolling

4332 Mountainous

4332 Coll.’s AADT<400: Flat

4332 Rolling

4332 Mountainous

a. Alignment Codes: 1 = All grades meet design standards; 2 = Some grades below design standards; 3 = Grades with reduced speed; 4 = Significant reduction of speed on grades.
HERS Technical Report v3.54

September 2002

3-19

Table 3-10. Default Design Standards For Median Width

(Feet)

 DS 

Rural:

64 Interstate: Flat

64 Rolling

16 Mountainous

40 OPA AADT>6000: Flat

40 Rolling

16 Mountainous

40 OPA AADT<=6000: Flat

40 Rolling

16 Mountainous

40 MA AADT>2000: Flat

40 Rolling

16 Mountainous

0 MA AADT<=2000: Flat

0 Rolling

0 Mountainous

0 Coll.’s AADT>1000: Flat

0 Rolling

0 Mountainous

0 Coll.’s AADT=400-1000: Flat

0 Rolling

0 Mountainous

0 Coll.’s AADT<400: Flat

0 Rolling

0 Mountainous

Urban:

20 Freeway/Expressway by design
Identifying Candidate Improvements

3-20

Table 3-11. Default Design Standards For Curves and Grades

Curve Grade

Class Class

Rural:

4 3 Interstate: Flat

4 3 Rolling

7 5 Mountainous

4 3 Other Principal Arterial: Flat

4 3 Rolling

7 5 Mountainous

4 3 Minor Arterial: Flat

6 3 Rolling

7 5 Mountainous

6 4 Major Collectors: Flat

7 5 Rolling

10 6 Mountainous

8 4 Minor Collectors: Flat

10 5 Rolling

12 6 Mountainous

Urban:

7 Interstate

7 Other Freeway

8 Other Principal Arterial

Table 3-12. Default Design Standards for Urban Sections

Surface Lane Shoulder

Typea Width Width

(Feet) (Feet)

2 12 10 Freeway by design

2 12 10 Other divided

2 12 9 Undivided arterials

3 12 8 Undivided collectors

a. Surface Type Codes: 1 = High flexible; 2 = High rigid; 3 = Intermediate; 4 = Low; 5

= Unpaved.
HERS Technical Report v3.54

September 2002

3-21

3.5 Discussion of Criteria Levels

The three paragraphs below provide some general discussion of the default values for the unacceptability levels, deficiency levels, and serious deficiency levels, respectively, and the effects of

using values that are more or less stringent. 

3.5.1 Unacceptability Levels

A review of Table 3-2, “Default Pavement Condition Criteria (PSR),” indicates that the default

UL values for pavement condition are slightly below the reconstruction level, and a review of

Tables 3-3 through 3-9 indicates that the other UL values represent conditions that are the same

as or (more frequently) somewhat worse than the MTCs. The default values thus suggest an

acceptance of conditions on some sections that are somewhat worse than the “minimum tolerable conditions.” (Note that if the user doesn’t want to require that unacceptable conditions be

addressed, this can be indicated using a switch in the run specifications, rather than by changing

all of the UL values.)

One obvious alternative to the UL values shown in the exhibits is the use of the MTC values as

the ULs. Default values that are somewhat worse than the MTCs are provided in the exhibits so

that:

• there is a high likelihood that sufficient funds will be available to correct conditions that

are truly unacceptable (under the proposed weaker standards of unacceptability); and

• there will be sufficient funds left over to select high B/C ratio improvements for more

mildly deficient sections.

A second alternative to the UL values shown is the use of UL values that can never be violated

(e.g., PSR = 0.0). When such UL values are specified, HERS will select improvements purely on

the basis of B/C ratios. Under these circumstances, conditions on sections with relatively low

traffic volumes may be allowed to deteriorate indefinitely. 

Within the range of UL values bounded by the alternatives discussed in the two preceding paragraphs lie a large number of alternatives that can reasonably be used as default values. The

defaults shown in Tables 3-2 through 3-9 merely represent one possible set of such values.

3.5.2 Deficiency Levels

The DLs are used to identify deficiencies that warrant analysis by HERS. Logically, the DLs may

be set at any value between the MTCs and the design standards. Relatively relaxed DLs (i.e.,

DLs that are close to the MTCs) will limit the number of potential improvements analyzed by

HERS and decrease computation time; while more stringent DLs will require HERS to analyze a

larger number of potential improvements and may permit HERS to find a more cost-effective set

of improvements to be implemented. HERS users should be aware that the optimal set of DLs

will actually vary with the particular objective function used (that is, the type of analysis

requested) and with the size of the highway-improvement budget. (The optimal DL settings will

get more stringent as the budget increases.) The DLs presented in Tables 3-2 through 3-9 are the

values used in the 2002 C&P Report.
Identifying Candidate Improvements

3-22

3.5.3 Serious Deficiency Levels

The SDLs are used by HERS to limit the number of alternative improvements analyzed for a

given section. Logically, the SDLs may be given values between the UL values and the DL values. If all SDLs are set equal to the corresponding DLs, no more than one improvement will be

analyzed for each section in a given funding period, and any improvement analyzed will

address all deficiencies identified for the section. If all SDLs are set equal to the corresponding

ULs, up to six different improvements may be analyzed for each section. (These consist of a

pavement option with or without the improve alignment option and with zero, one or two widening options.) The settings used for the SDLs thus will have a significant effect on the computation time required by HERS.

The SDLs have another potentially significant effect. When an SDL is violated for a particular

section for which no UL is violated, any improvement selected for the section must address the

specified serious deficiency. This restriction may decrease the attractiveness of improving the

section, but it also decreases the likelihood that the section will be improved without correcting

all serious deficiencies. (It does not guarantee that all serious deficiencies will be corrected since,

if an unacceptable condition develops, HERS is likely to correct the unacceptable condition without correcting other serious deficiencies.)

This second effect of the SDLs suggests that it may be appropriate to set all SDLs to the corresponding MTC values. Many of the suggested SDL default values presented in Tables 3-2

through 3-9 are, in fact, set to the corresponding MTC values. However, to make things interesting, less stringent values are used for some SDLs. 
4-1

4 HERS Internal Models

This section discusses the way HERS models discrete processes: speed calculation, pavement

wear, traffic forecasts, capacity calculations, and user, agency, and external costs. 

4.1 The HERS Speed Model

HERS uses computed vehicle speed for three purposes: calculation of travel time costs; calculation of external costs due to vehicular emissions; and calculation of vehicle operating costs1

.

Average effective speed (AES) across the section is used in the first two calculations above and

for most of the operating cost calculations. To calculate excess operating costs due to speed

change cycles induced by traffic signals and/or stop signs, HERS uses distance travelled

between traffic control devices and the average travel speed over the portions of the section

which contain signals and stop signs.

The HERS speed model has been changed from the method previously employed in HERS. The

earlier HERS version was based on the Texas Research and Development Foundation (TRDF)

adaptation2 of the “Aggregate Probabilistic Limiting Velocity Model” (APLVM), one of four

related procedures originally developed by the World Bank.3 HERS 3.54 uses a simplified version of the APLVM procedures to calculate “free-flow” speed (FFS). It then applies algorithms

developed by Science Applications International Corporation(SAIC) and Cambridge Systematics, Inc.4

 (CSI) for FHWA to incorporate the effects vehicle speed of grades (free-flow speed

uphill, or FFSUP), traffic-control devices, and congestion on.

For each section, HERS models speed for each of the seven vehicle types (except for autos and

pickup trucks) in each direction of travel. Overall average speed per section is aggregated from

the speeds of the individual vehicle types. HERS uses vehicle speed data in calculating operating costs and travel time costs.

1. See Exhibit 2-5, “Prediction and Calculation Model Linkages.”.

2. G.C. Elkins, et al., Estimating Vehicle Performance Measures, Texas Research and Development Foundation, prepared

for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., July 1987, pp. 128-

177.

3. Thawat Watanatada, Ashok M. Dhareshwar and Paulo Roberto S. Rezende Lima, Vehicle Speeds and Operating

Costs, The World Bank, Johns Hopkins University Press, Baltimore, 1987.

4. Cambridge Systematics, Inc., Harry Cohen, and Science Applications International Corp., Sketch Methods for Estimating Incident-Related Impacts, prepared for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., December 1998, Section 2.3.; Science Applications International Corporation and

Cambridge Systematics, Inc., Roadway Usage Patterns: Urban Case Studies, prepared for Volpe National Transportations Systems Center and the Federal Highway Administration, June 1994, Appendix A; Science Applications

International Corporation, et al., Speed Determination Models for the Highway Performance Monitoring System, prepared for the U. S. Department of Transportation, Federal Highway Administration, Washington, D.C, October 31,

1993; Cambridge Systematics, Inc., Revisions to the HERS Speed and Operating-Cost Procedures, prepared for the U. S.

Department of Transportation, Federal Highway Administration, Washington, D.C, January 25, 1996, Section 2;

Cambridge Systematics, Inc., 2000 Revisions to HERS, prepared for the U.S. Department of Transportation, Federal

Highway Administration, Washington, D.C., August 2002.
HERS Internal Models

4-2

4.1.1 Free-Flow Speed and the APLVM

The HERS version of APLVM involves a four-step procedure; the first three of which involve the

computation of three “limiting velocities.” These limiting velocities represent the approximate

speeds that would be obtained should a single factor (e.g., pavement condition) limit speed to a

value much lower than would otherwise be the case. The three limiting velocities5

 are:

VCURVE = maximum allowable speed on a curve;

VROUGH = maximum allowable ride-severity speed; and 

VSPLIM = maximum speed resulting from speed limits.

The fourth step is to combine the three limiting velocities, using the APLVM, to determine the

free-flow speed.

In APLVM, the dominant role in the determination of free-flow speed6 is played by the smallest

of the limiting velocities.7

 Each of the other limiting velocities are assumed to play some probabilistic role in influencing the speed of some drivers, but, except when they have values close to

that of the lowest velocity, their influence on average free-flow speed tends to be negligible. 

The following subsections describe the four steps of the HERS version of APLVM. 

4.1.1.1 Calculating the Effect of Curves

In the World Bank procedure, the effect on speed attributed to the presence of curves is represented by VCURVE. The World Bank estimates VCURVE, in meters per second:

 Eq. 4.1

where:

RC = radius of curvature (meters);

SP = superelevation; and

g = the force of gravity = 9.81 m/sec2

.

The remaining variable in Equation 4.1, FRATIO, known as the maximum perceived friction

ratio, is the ratio of the lateral force on a horizontal curve to the normal force. TRDF derived values for FRATIO of 0.103 for combination trucks and 0.155 for automobiles; and they suggest the

use of the 0.155 figure for single-unit trucks as well. HERS uses these values.

5. HERS 2.0 used four limiting velocities: VCURVE, VROUGH, VDRIVE, and VMISC. VDRIVE was a function of

vehicle characteristics and average grade, which are handled in HERS 3.54 through calculation of uphill free-flow

speed. The fourth limiting velocity, VMISC, was a replacement for a factor called “desired speed” (VDESIR) by the

World Bank and TRDF, and reflected the effects of speed limits, safety concerns, and congestion. In HERS 3.54,

these factors are represented by VSPLIM and the congestion delay algorithms applied to free-flow speed. 

6. The World Bank and TRDF use the term “steady-state speed,” or Vss, to refer to free-flow speed.

7. The original version of APLVM also uses a fifth limiting velocity, maximum allowable braking speed on downhill

sections (VBRAKE). This limitation affects only heavy trucks and only on long, steep downhill sections (e.g., a five

percent grade more than 10.5 miles long, or an eight percent grade more than three miles long). Since most HPMS

sections are less than five miles long, there are likely to be only a handful of sections for which one would find

braking speed to be a limiting factor (though, undoubtedly, some additional HPMS sections are part of longer

descents for which braking speed is indeed a factor). Accordingly, TRDF's recommendation to exclude VBRAKE

from the procedure has been adopted.

VCURVE FRATIO SP = ( ) + × g RC ×
HERS Technical Report v3.54

September 2002

4-3

Replacing radius of curvature in Equation 4.1 by degrees of curvature (DC) and converting the

equation to estimate VCURVE in miles per hour produces:

Eq. 4.2

For all arterial sections except urban minor arterials, a weighted average value of degrees of curvature can be obtained from detailed data on curves by class contained in the HPMS database.

For all collectors and for urban minor arterials, typical values of degrees of curvature are produced by existing HPMS software from horizontal alignment adequacy and type of terrain. (The

HPMS submittal software is used in preparation of the HPMS database prior to HERS’ processing the data.)

Although data on superelevation are not contained in the HPMS database, typical superelevation can be estimated from degrees of curvature using the equation:

Eq. 4.3

This equation was derived by regression from a table presented by Zaniewski8

, but fits so well

(R2 = 0.9999) as to suggest that it may be the equation that was used to generate the values in the

table.

4.1.1.2 Estimating Velocity Limited by Pavement Roughness

The effect of pavement roughness on speed is represented by VROUGH. HERS uses PSR to measure pavement roughness. Descriptions of pavement characteristics corresponding to the various PSRs are presented in Exhibit 2-8, “Pavement Condition Ratings.” 

A review of these descriptions indicates that pavement condition begins to become a limiting

factor on high speed roads at approximately the boundary between the Good (3.0 to 4.0) and Fair

(2.0 to 3.0) ratings, suggesting that VROUGH should play a minimal role in limiting speed when

PSR greater than or equal to 3.0. Similarly, the descriptions suggest 52.5 mph as an appropriate

value for VROUGH when PSR equals 2.0.

In order to avoid a speed of zero when PSR drops to zero (which can occur in HERS when funds

are short), and to allow additional user control over the function used for VROUGH, HERS

allows the user to specify VROUGH as a pair of line segments with different slopes meeting at a

user-specified breakpoint, PSRB. These parameters are specified in the parameter file

PARAMS.DAT.

Specifically, HERS uses the function:

8. J.P. Zaniewski, et al., Vehicle Operating Costs, Fuel Consumption, and Pavement Type and Condition Factors, Texas

Research and Development Foundation, prepared for U.S. Department of Transportation, Washington, D.C.,

March 1982, p. E-7.

VCURVE = 292.5 × ( ) FRATIO SP + ⁄ ( ) DC

SP

0.0 forDC ≤ 1

0.1 forDC ≥ 10, otherwise:

0.0318 0.0972 ln ++ + ( ) DC – 0.007 0.0317 × DC × DC × ln( ) DC 









=
HERS Internal Models

4-4

Eq. 4.4

where:

VR1 = value of VROUGH when PSR is zero;

VR2 = value of VROUGH when PSR = PSRB (the breakpoint); and 

VRSLOP = slope of the function when PSR > PSRB

The default values of the above parameters are:

PSRB = 1.0

VR1 = 5 mph

VR2 = 20 mph

VRSLOP = 32.59

For PSR below 2.5, the default values produce intentionally lower estimates of speed than either

the current AP procedure or that proposed by TRDF. For PSR = 1.5, they produce VROUGH = 36

mph, while TRDF's formula would produce values of 48 mph for automobiles and 44 mph for

large trucks,10 and the AP procedure would permit speeds of 49 mph. On the basis of the preceding discussion, 36 mph appears to be a more appropriate speed; however, users can choose

different values for the four parameters if higher values of VROUGH are desired.

For purposes of deriving VROUGH for unpaved sections, HERS treats these sections as having a

PSR of 1.0 (i.e., when VR1, VR2 and VRSLOP are set to their default values, VROUGH for

unpaved sections is 20 mph); the user may change this PSR value if desired.

For HERS, the same formula for VROUGH is used for all vehicle classes. Using Brazilian data,

the World Bank study11 obtained results that imply a very significant difference (about 30 mph)

between the effects of roughness on automobiles and on combination trucks; and TRDF has proposed formulas that produce a much more modest difference (two to four mph). However,

TRDF did not provide any recommended formulas for use with single-unit trucks. 

9. This represents a change from HERS v2, where the default value for VRSLOP was set at 20. The previous value

produced a limiting velocity of 60 mph for a pavement of PSR 3.0 -- This change produces a limiting velocity of 85

mph when PSR is 3.0.

10. The TRDF formulas are:

11. Elkins, et al., op. cit., pp. 144-149.

VROUGH

VR1 + ( ) VR2 – VR1 PSR

PSRB × --------------- if PSR PSRB ≤

VR2 + if VRSLOP PSR PSRB × ( ) – PSR PSRB > 









=

VROUGH 1

0.025 0.00275 – PSR = for automobiles --------------------------------------------------

VROUGH 0.9

0.0255 0.00333 – PSR = for large trucks -----------------------------------------------------
HERS Technical Report v3.54

September 2002

4-5

4.1.1.3 Estimating Velocity Limited by Speed Limits

HERS represents the effect of speed limits on speed with VSPLIM. VSPLIM is assumed to be 10

or 15 kilometers per hour greater than the speed limit. Fifteen kmph is used for urban freeways

by design and rural multilane roads with partial or full access control and a median which is

either a positive barrier or has a width of at least 4 feet. Ten kmph is used for all other sections.

These values correspond to 6.215 and 9.323 mph.

4.1.1.4 Determining Free-Flow Speed

The general formula for estimating free-flow speed, FFS, is:

Eq. 4.5

where and are parameters discussed below.

In the above equation, is a parameter that may vary with vehicle class and reflects the standard deviation of the sensitivity of drivers of vehicles in that class to the different conditions

reflected in the equation. For the moment, ignore the effect of (i.e., assume = 0). In this

case, when two factors produce very similar limiting velocities, the variation in sensitivities

results in some vehicles being limited more by one factor while some vehicles are limited more

by the other, with an overall average speed somewhat lower than either of the limiting velocities.

The smaller the value chosen for , the more this average speed approaches the lower of the two

limiting velocities.

The World Bank12 used Brazilian data to estimate for six vehicle classes, deriving values of

0.24 to 0.31. After comparing the effects of values of 0.01, 0.1 and 0.3 on the behavior of the FFS

equation, TRDF recommended a value of 0.1 for all vehicle classes.13

In Equation 4.5, is described by the World Bank as the variance of the logarithm of sectionspecific errors of observed speed. The World Bank's estimates14 for are between 0.007 and

0.036; and TRDF15 suggests using 0.01. The effect of these values for is a small upward

adjustment in FFS (of about 0.5 percent using = 0.01, and about 1.8 percent using = 0.036).

For simplicity, the effect of has been omitted from the HERS equation.

Setting = 0.1 and = 0, Equation 4.5 becomes: 

Eq. 4.6

where VCURVE is given by Equation 4.2, VROUGH by Equation 4.4, and VSPLIM is derived

from the section’s speed limit as described above.

12. Watanatada et al., op. cit., Table 4.3(a), p. 85.

13. Elkins, et al., op. cit., p. 156.

14. Watanatada et al., Table 4.3(c), p. 86. The reference uses to represent our .

15. Elkins, et al., op. cit., p. 156.

FFS σ

2

exp( ) ⁄ 2

( ) 1 ⁄ VCURVE

1

β

--

( ) 1 ⁄ VROUGH

1

β

--

( ) 1 ⁄ VSPLIM

1

β

--

+ +

      β = -------------------------------------------------------------------------------------------------------------------------------------

σ

2 β

β

σ

2

σ

2

β

β

σ

2

σ

2

σe

2

σ

2

σ

2

σ

2

σ

2

σ

2

β σ2

FFS ( ) 1 VCURVE ⁄ 10 ( ) 1 VROUGH ⁄ 10 ( ) 1 VSPLIM ⁄ 10 ( ) + + –0.1 =
HERS Internal Models

4-6

Equation 4.6 produces estimates of free-flow speed that are always below the lowest of the limiting velocities in the equation, but are exceedingly close to that velocity whenever that velocity is

appreciably smaller than the other limiting velocities.

4.1.2 The Effects of Grades on Free-Flow Speed

Using an SAIC algorithm16, HERS next calculates free-flow speed in the uphill direction (FFSUP)

for trucks17. (For “personal vehicles” - automobiles and pickup trucks - HERS assumes that

grades have no effect on free-flow speed.) First, crawl speed for the section is estimated as follows:

Eq. 4.7

where:

CRAWLS = Crawl speed in miles per hour;

j, k = constants which depend upon vehicle characteristics; and

GRADE = the average grade of the section (expressed as a fraction).

The values used for constants j and k are shown in Table 4-118. 

HERS then calculates the delay due to grades:

Eq. 4.8

where:

Eq. 4.9

16. Science Applications International Corporation, et al., Speed Determination Models for the Highway Performance Monitoring System, pp 78-79.

17. Since the HPMS database does not contain any information on the direction of grades, one-way facilities are

treated in the same way as two-way facilities; i.e., as if traffic may be moving either uphill or downhill.

Table 4-1. Values of Crawl Speed Constants by Truck Type

Vehicle Type j k

 6-Tire Truck 0.0090 0.0815

 3-4 Axle Truck 0.0090 0.2755

 4-Axle Combination 0.0090 0.2755

 5-Axle Combination 0.0090 0.2755

18. Science Applications International Corporation, et al., Speed Determination Models for the Highway Performance Monitoring System, Table 3-3, and Herbert Weinblatt, “The Effects of Grades on Truck Speed,” memorandum, Cambridge Systematics, Inc., Feb. 25, 1998.

CRAWLS = 1 ⁄ ( ) j k GRADE + ×

DGRADE a( ) 1 – exp( ) b a⁄ + if b CRAWLS FFS <

0 otherwise 

 =

b SLEN = ( ) 1 ⁄ CRAWLS – 1 ⁄ FFS
HERS Technical Report v3.54

September 2002

4-7

Eq. 4.10

DGRADE = delay in hours; and

SLEN = length of the section

The delay due to grades is then combined with free-flow speed to yield free-flow speed uphill,

FFSUP:

Eq. 4.11

4.1.3 Delay Due to Congestion and Traffic Control Devices

The CSI/SAIC algorithms address four types of highway conditions based upon number of

lanes and the presence of traffic control devices. HERS identifies two additional conditions,

defining a total of six highway classifications for use within the speed model. Table 4-2 lists the

salient characteristics of each of the six classifications, and indicates which of the equations are

used for each classification. Note that the number of lanes is not a factor when either signals or

stop signs are present on the section.

Each of the implemented algorithms consists of two or more equations. Selection of the appropriate equation hinges upon the ratio of the section’s Annual Average Daily Traffic (AADT) to

the section’s two-way peak hour capacity19. This AADT/Capacity ratio is referred to as the

ACR. Each of the routines below yields delay in hours per 1000 vehicle miles. HERS converts

this to average effective speed using the equation:

Table 4-2. HERS Highway Classifications and the Delay Algorithms

Total Lanes 

in Both 

Directions

Stop 

Signs

Traffic 

Signals HERS Classification Algorithms Used

N/A Yes No Sections with Stop Signs Urban Arterials with Unsignalized Intersections

N/A No Yes Sections with Traffic Signals Urban Arterials with Signalized Intersections

N/A Yes Yes Sections with Stop Signs and 

Traffic Signals

Both: Urban Arterials with 

Unsignalized Intersections and 

Urban Arterials with Signalized Intersections

2 No No Free-Flow Sections, One Lane 

per Direction Two-Lane Rural Sections

3 No No Free-Flow Sections, Three-Lane 

Two-way

Two-lane Rural Sections and 

modified Freeways and Multilane Rural Highways

4 or more No No Free-Flow Sections, Two or 

More Lanes per Direction

Freeways and Multilane Rural 

Highways

a 0.05 1( ) ⁄ CRAWLS – 1 ⁄ FFS 0.6 = –

FFSUP = 1 1 ⁄ ( ) ⁄ FFS + DGRADE SLEN ⁄ ( )
HERS Internal Models

4-8

Eq. 4.12

where:

AES = Average Effective Speed;

FFS = Free Flow Speed (or FFS Uphill), as calculated above; and

D = average delay in hours per 1000 vehicle miles, with delay due to

incidents, other congestion, and/or traffic control devices.

The procedures used for estimating delay on multi-lane free-flow sections and on sections with

traffic signals develop separate estimates of delay due to incidents, due to other congestion, and

due to traffic signals (where present). For other types of sections, the procedures used are older

and they do not estimate incident delay. For these sections, estimates of delay due to crashes are

inferred from HERS' estimates of the delay cost of crashes (see Chapter 5.1.3.4.1), and these estimates are used (without further adjustment) as estimates of delay due to incidents.

4.1.3.1 Sections with Stop Signs

For roads with stop signs, HERS selects an equation based upon both the AADT/Capacity ratio

and the number of stop signs per mile. The equations are presented in Table 4-3. 

where:

Dss = Delay due to stop signs and non-incident congestion in hours per

1000 vehicle miles;

Nsspm = Number of stop signs per mile (average);

FFS = Free flow speed (or free flow speed uphill); and

ACR = the AADT/Capacity ratio for the section.

19. Other than in the calculation of the AADT/Capacity ratio (used in the speed calculations and the elasticity calculations), capacity generally means one-way capacity (except for two-lane rural roads) as reported in the HPMS data

records.

Table 4-3. Delay Equations for Sections with Stop Signs

AADT/C 

Range

Stop 

Signs/ 

mile

<6

>6 and <15

<10

>10

>15

<10

>10

AES = 1 1 ⁄ ( ) ⁄ FFS D+ ⁄ 1000

Dss Nsspm 1.9 0.067 FFS 0.103 ACR 0.0145 ACR2 = × ( ) + × + × + ×

Dss Nsspm 3.04 0.067 FFS 0.029 ( ) ACR – 6 2 ( ) + × – ×

0.354 ( ) ACR – 6 2 + ×

= ×

Dss Nsspm × ( ) 3.04 0.067 + × FFS 0.064 ( ) ACR – 6 2 = + ×

Dss Nsspm 0.691 0.067 × FFS · × ( ) + 0.354 ( ) ACR – 6 2 = + ×

Dss Nsspm × ( ) 3.04 0.067 + × FFS 0.354 ( ) ACR – 6 2 = + × – 23.49
HERS Technical Report v3.54

September 2002

4-9

Total delay on these roads is estimated as the sum of the above delay plus delay due to crashes

(per 1,000 vehicle-miles). The latter value is generated by HERS' safety analysis (see Chapter

5.1.3.4.1).

4.1.3.2 Sections with Traffic Signals

For sections with traffic signals, HERS uses modified versions of the CSI/SAIC equations20 in a

multi-step process to estimate traffic volume and delay in the peak period (separately by direction) and in the offpeak period. The steps of this process are:

1. Divide total traffic volume into peak period volume (in the peak and counterpeak directions, 

separately) and offpeak volume.

2. Estimate the peak-hour Volume/Capacity ratios for the peak and counterpeak directions.

3. Estimate the "zero-volume delay" (relative to free-flow speed) that is due to traffic signals. 

This is the expected delay that a single vehicle would encounter if it were the only vehicle on 

the road.

4. Estimate the average "travel rate" (i.e., the inverse of speed, in hours per vehicle-mile) in the 

absence of incidents. Separate estimates are developed for the peak period (by direction) and 

for the offpeak period. These values include the effects of zero-volume delay.

5. Estimate additional delay due to incidents (per vehicle-mile) for the peak period (by direction) 

and for the offpeak period.

6. The results of Steps 4 and 5 are combined to produce estimates of average speed overall and 

separately for the peak and offpeak periods. The general formula for this step is:

Eq. 4.13

where:

AES = Average Effective Speed;

NITR = Non0Incident Travel Rate (hours per vehicle-mile); and

Dinc = Delay due to incidents (hours per vehicle-mile).

This procedure produces estimates of overall average speed, average speed in the peak and offpeak periods, and three components of delay (relative to free-flow speed): zero-volume delay,

incident delay, and other congestion delay. Complete equations for the first five steps of the

procedure are presented in Section I.3 of Appendix I.

4.1.3.3 Sections With Stop Signs and Traffic Signals.

To calculate the average effective speed for section with both types of traffic control devices,

HERS calculates two speeds over the section: one, as if all the devices were stop signs, and two,

as if all the devices were signals. HERS then averages these speeds together, weighted by the

ratio of traffic signals to stop signs. 

20. Cambridge Systematics, Inc., Harry Cohen, and Science Applications International Corp., Sketch Methods for Estimating Incident-Related Impacts, prepared for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., December 1998, Section 2.3; and Cambridge Systematics, Inc., 2000 Revisions to HERS,

prepared for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., August

2002.

AES 1 NITR Dinc = ⁄ ( ) +
HERS Internal Models

4-10

4.1.3.4 Free-Flow Sections, One Lane per Direction

The equation selection for two-lane roads depends only upon AADT/Capacity ratio. The equations are presented in Table 4-4. 

where:

Dcong1 = average delay due to non-incident congestion in hours per 1000

vehicle miles; and

ACR = the AADT/Capacity ratio for the section.

Total delay on these roads is estimated as the sum of the above delay plus delay due to crashes

(per 1,000 vehicle-miles). The latter value is generated by HERS' safety analysis (see Chapter

5.1.3.4.1).

4.1.3.5 Free-Flow Sections, Three-Lane Two-Way

For three-lane, two-way roads without traffic control devices, HERS assumes that the volume is

split evenly between the two directions, and that capacity is split 7:5 in favor of the two-lane

direction. This is implemented by multiplying the section’s AADT/Capacity ratio by 0.857 to

derive the AADT/Capacity ratio in the two-lane direction, and 1.2 to derive the AADT/Capacity

ratio in the one-lane direction. These modified AADT/Capacity ratios are then used in the

respective delay calculations. HERS calculates the delay in the single-lane direction using the

equations for two-lane rural roads, and in the two-lane direction using the multilane equations.

HERS then figures total delay as the average of the two.

4.1.3.6 Free-Flow Sections, Two or More Lanes per Direction

For sections with at least two lanes in each direction and no traffic signals or stop signs, HERS

uses modified versions of the CSI/SAIC equations21 in a multi-step process to estimate traffic

volume and delay in the peak period (separately by direction) and in the offpeak period. The

steps of this process correspond to those used for analyzing sections with traffic signals (see Section 6.1.3.2) with one exception: since there are no traffic signals on free-flow sections, there is no

zero-volume delay, and Step 3 of the earlier procedure is skipped. The procedure produces estimates of overall average speed, average speed in the peak and offpeak periods, and two compoTable 4-4. Delay Equations for 2-lane, 2-way Roads

AADT/C 

Range

< 10

> 10

21. Cambridge Systematics, Inc., Harry Cohen, and Science Applications International Corp., Sketch Methods for Estimating Incident-Related Impacts, prepared for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., December 1998, Section 2.3; and Cambridge Systematics, Inc., 2000 Revisions to HERS,

prepared for the U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., August

2002.

Dcong1 = 0.432 × ACR

Dcong1 9.953 1.66 ACR 0.109 ACR2 = – × + ×
HERS Technical Report v3.54

September 2002

4-11

nents of delay: incident delay and other congestion delay. Complete equations for the

procedure are presented in Section I.2 of Appendix I.

4.1.4 Distance Traveled Between Traffic Control Devices

HERS uses the distance travelled between stops when traversing a section as an input to the

operating cost model. HERS assumes that drivers stop at all stop signs, and at traffic signals

when they are red. For sections with stop signs, this distance is simply the length of the section

divided by the number of traffic control devices. For sections with traffic signals, HERS allows

for signals which might be green and not require a stop.

4.2 The Pavement Deterioration Model

HERS models pavement wear as a function of traffic and environment. First, HERS calculates

the effects of vehicular traffic on a section’s PSR. Then, HERS figures both a minimum and a

maximum rate of deterioration. The minimum rate is designed to reflect the effects of weather.

The maximum rate of deterioration is designed to limit deterioration on sections with low structural numbers22. HERS applies these limits to the PSR value (which reflects pavement wear due

to traffic) to arrive at a forecast pavement condition. HERS does not deteriorate unpaved sections, and roads without reported truck traffic are deteriorated at the minimum rate.

4.2.1 Equivalent Single-Axle Loads

Except for roads with relatively light traffic volumes, the rate of pavement deterioration is

dependent primarily on the number of 18,000 pound (18 kip) equivalent single-axle loads

(ESALs). For any time period, ESALs on the most heavily traveled lane of each sample section

are estimated using 

• total traffic for the time period; 

• percentages of single unit trucks and combination trucks on the sample section; 

• an 18-kip equivalent load factor; and

• a lane-load adjustment factor. 

The 18-kip equivalent load factor is a function of pavement type, functional class, and truck type;

values for this factor are given in Table 4-5, “Equivalent 18-KIP Load Applications per Truck.”

The lane load adjustment factor provides an estimate of the percentage of trucks that travel in the

lane most heavily used by trucks as a function of the number of lanes in one direction; these values follow the AASHTO Pavement Design Guide23 and are given in Table 4-6, “Lane Load Distribution Factors.”

22. Structural numbers (SN), which range from 1.0 to 6.0, indicate the strength of pavement. Sections whose SN is in

the range from 1.0 through 3.0 are considered “light”.

23. American Association of State Highway and Transportation Officials, AASHTO Guide for Design of Pavement

Structures, Washington, D.C., 1986.
HERS Internal Models

4-12

HERS estimates pavement deterioration using Percent Average Daily Single Unit Commercial

Vehicles and Percent Average Daily Combination Commercial Vehicles. HERS allows the user

to specify a set of annual growth factors to be applied to each section's percent truck values. (See

4.4, ”The Fleet Composition Model.”) 

For any time period beginning at t0 and ending at tf

, HERS first calculates the total traffic:

Eq. 4.14

where represents the length of the period in years. 

HERS then calculates ESALs for the time period:

Eq. 4.15

where:

Table 4-5. Equivalent 18-KIP Load Applications per Truck

Single Unit Trucks Combination Trucks

Flexible 

Pavement

Rigid 

Pavement

Flexible 

Pavement

Rigid 

Pavement

Rural:

 Interstate 0.2898 0.4056 1.0504 1.6278

Other Principal Arterials 0.3141 0.4230 1.1034 1.7651

Minor Arterials 0.2291 0.3139 1.0205 1.0819

Collectors 0.2535 0.3485 0.7922 1.3265

Urban:

Interstate and Other Freeways 

and Expressways 0.6047 0.8543 2.3517 3.7146

Other Principal Arterials 0.5726 0.8123 0.8584 1.3047

Minor Arterials 0.3344 0.4109 1.0433 1.5276

Collectors 0.8126 1.1595 0.6417 0.9968

Table 4-6. Lane Load Distribution Factors

Number of Lanes (One Direction) Lane Factor

1 1.0

2 0.9

3 0.7

4 or more 0.6

TOTRAF

AADTt0 AADTtf ( ) +

2 ----------------------------------------------------- × 365 tf t0 = × ( ) –

tf t0 ( ) –

ESALS TOTRAF PCAVSU ELFSU ( ) × × × LF

TOTRAF PCAVCM × ELF + ( ) × CM × LF

=
HERS Technical Report v3.54

September 2002

4-13

ESALS = ESALs accumulated during the time period;

PCAVSU = average percentage of single-unit trucks during the time period;

ELFSU = equivalent load factor for single unit trucks for this pavement type

and functional class (from Table 4-5);

PCAVCM = average percentage of combination trucks during the time period;

ELFCM = equivalent load factor for combination trucks for this pavement

type and functional class (from Table 4-5); and

LF = lane load distribution factor (from Table 4-6).

HERS uses one-half the length of a funding period as the time period for calculating total traffic

and incremental ESALs in order to capture changes in both AADT and average percentages of

trucks. Therefore, when estimating the number of ESALs which will accumulate during a funding period, it utilizes Equations 4.14 through Equations 4.14 and 4.15 twice, once for the first half

and once for the second half of the funding period.

4.2.2 Pavement Condition

HERS determines present and future pavement condition using AASHTO Road Test equations

that have been modified to accommodate PSR values from 0.1 to 5.0. The first step is to obtain

the number of ESALs that would have resulted in causing PSR to decline from 5.0 to its base-year

value. The number of ESALs applied during any subsequent period is then estimated and added

to the previous ESAL value. This result is then used to estimate PSR at the end of this period. 

For flexible pavement, the HPMS database contains either the structural number (SN) or pavement weight (light, medium or heavy); for rigid pavement it contains either thickness (D) or

pavement weight. If any of the optional information is not provided for a section, HERS uses

the default values shown in Table 4-7, “Pavement Section Default Values,” to obtain values

describing the initial pavement. When the pavement is improved, procedures described in

Chapter 6, ”Effects of HERS Improvements,” are used to obtain the thickness of the overlays or

of the new pavement and, for flexible pavements, a new value of SN.

4.2.2.1 Flexible Pavement

For flexible pavements, the number of ESALs that would cause PSR to decline from 5.0 to its

base-year value is obtained using the equation:

Eq. 4.16

where:

Table 4-7. Pavement Section Default Values

Pavement Section

Heavy Medium Light

SN (Flexible Pavement) 5.3 3.8 2.3

D (Rigid Pavement) 10.0 8.0 6.5

ESAL 10LOGELA =
HERS Internal Models

4-14

Eq. 4.17

Eq. 4.18

Eq. 4.19

Eq. 4.20

Eq. 4.21

and

PSRI = PSR at the beginning of the base year;

 and all logarithms are taken to the base ten.

The PSR at the end of any subsequent time period, PSRF, is then obtained by adding the number

of ESALs incurred during that time period to the initial value of ESALs, substituting PSRF for

PSRI in Equation 4.20, solving the above system of equations for PSRF, and performing the indicated computations. Solving Equation 4.20 for PSRF produces:

Eq. 4.22

where:

PDRAFpt = A user-specified pavement deterioration rate adjustment factor for

pavement type pt, normally set to one24;

and solving Equations 4.16 and 4.17 for XG produces:

Eq. 4.23

4.2.2.2 Rigid Pavement

The procedure for obtaining the pavement condition of rigid pavements differs from that used

for flexible pavements only in the equations used for XA and XB. For rigid pavements, these

equations are:

Eq. 4.24

Eq. 4.25

where D is pavement thickness.

24. If HERS is being used to analyze data for a single state, PDRAFpt can be used to reflect the effects of the state's

environment and materials used in that state. Separate values of PDRAFpt can be specified for flexible and rigid

pavement types.

LOGELA XA XG XB = + ⁄

XA = 9.36 × log( ) SNA – 0.2

XB 0.4 1094 SNA5.19 = + ⁄

XG = log( ) ( ) 5 – PSRI ⁄ 3.5

SNA SN = + ( ) 6 ⁄ SN

PSRF 5 3.5 PDRAFpt × 10XG = – ×

XG XB ESAL = × ( ) log( ) – XA

XA = 7.35 × log( ) D + 1 – 0.06

XB 1 16.24 106

× ⁄ ( ) D + 1

8.46 = +
HERS Technical Report v3.54

September 2002

4-15

4.2.2.3 Minimum Deterioration Rate

For both flexible and rigid pavements, minimum deterioration rates are used to reflect pavement

deterioration due to environmental conditions. HERS uses the following equation to calculate an

appropriate minimum deterioration rate:

Eq. 4.26

where:

t = any time of interest;

PSRMAXt = upper limit on the PSR of a given section at time t;

t0 = time at which the section was last improved or, if not known, six

months before the beginning of the HERS run;

ML = maximum life of the section in years.

The use of Equation 4.26 requires knowing the time that each section was last improved (t0) and

the PSR immediately after the improvement (PSRt0). For all improvements analyzed or selected

by HERS, this information is readily available. For improvements that occurred prior to the start

of a HERS run, the preprocessor uses the time of last improvement specified in the HPMS

dataset, if available, or the middle of the year preceding the start of the HERS run. In the former

case, the preprocessor assumes that the PSR immediately following the improvement (PSRt0) is

the maximum possible for the improvement. In the latter case, the PSR immediately following

the last improvement is estimated from the PSR at the start of the run and the traffic data for the

six-month period between the assumed time of the last improvement and the start of the run.

The maximum pavement life values for rigid and flexible pavements for three types of pavement

section (light, medium and heavy) are shown in Table 4-8, “Maximum Pavement Life Values

(Years).” 

The HERS model then enforces the minimum deterioration rate:

Eq. 4.27

where:

PSRMAXt = upper limit on PSR at time t from Equation 4.26;

PSRtESALS = PSR at time t as a function of ESALs (PSRF from Equation 4.22);

and

Table 4-8. Maximum Pavement Life Values (Years)

Surface Type Pavement Section

Heavy Medium Light

Flexible 25 20 15

Rigid 30 25 20

PSRMAXt PSRt0 × 0.3 t t – 0 ( ) ( ) ⁄ ML =

PSRMXt the lesser of 

PSRMAXt

PSRt  ESALS



 =
HERS Internal Models

4-16

PSRMXt = PSR at time t after enforcement of the minimum deterioration rate.

4.2.2.4 Maximum Deterioration Rate

A user-specified maximum PSR deterioration rate is used to limit pavement deterioration on sections with low values of SN. The default value for this maximum rate of deterioration is 0.3 per

year. This maximum rate is applied after the enforcement of the minimum deterioration rate:

Eq. 4.28

where:

t = any time of interest;

PSRt = PSR at the time t after enforcement of both the maximum and minimum deterioration rates;

t0 = time at which the section was last improved or, if not known, six

months before the beginning of the HERS run;

PSRMXt = PSR at time t after enforcement of the minimum deterioration rate

from Equation 4.27; and

MAXPDR = maximum PSR deterioration rate per year.

4.3 The Travel Forecast Model

HERS v3.10 introduced travel demand elasticity to the travel forecast model. See Appendix A,

”Induced Traffic and Induced Demand,” for a discussion of the concepts guiding these modifications to HERS. See Appendix B, ”Demand Elasticities for Highway Travel,” for a discussion of

appropriate elasticity values for use in HERS. Appendix C, ”Basic Theory of Highway Project

Evaluation,” presents the principles that apply generally to evaluating highway improvements.

HERS v3.54 implements a subset of these general principles.

This paragraph first addresses the tasks performed by HERS during initialization:

• estimating the baseline price;

• setting the baseline V/C; and

• determining the adjusted initial volume.

It then discusses the specific steps utilized by the model in:

• forecasting baseline travel;

• adjusting the baseline forecast for long run elasticity; and

• applying the short run elasticity to yield a traffic volume forecast.

PSRt the larger of 

PSRt0 MAXPDR t t0 – × ( ) –

PSRMXt



 =
HERS Technical Report v3.54

September 2002

4-17

4.3.1 Initialization: Assuming the Baseline Price

The section input data includes AADT for the data year and also for a future data year, typically

20 years beyond the data year. HERS generally assumes that the future volume forecast is based

upon a continuation of the initial level of service, as defined by volume-to-capacity (V/C) ratio

and PSR. The exception is congested sections, in which case HERS assumes the forecast includes

an improvement to increase capacity. HERS calculates the initial user price as the sum of the

operating, travel time, and safety costs at the beginning of the analysis period and saves the initial V/C ratio as the baseline V/C level. The baseline price is set equal to the initial price. However, if the section’s initial V/C ratio is equal to or greater than one, then HERS sets the baseline

V/C level to one, and calculates the baseline price at a volume consistent with a V/C of one and

a minimum PSR of two.

HERS next calculates an initial adjusted volume for the section at the beginning of the analysis

period. The adjusted volume is used as the “departure point” for the calculation of future baseline traffic volumes. During initialization, HERS calculates adjusted volume:

Eq. 4.29

where:

VADJ = adjusted volume at beginning of analysis period;

AADT = reported volume -- AADT at beginning of analysis period;

INPRI = initial price to user at beginning of analysis period;

BASPRI = baseline price; and

SRE = short run elasticity.

Note that, for sections with initial V/C less than one, the adjusted volume will equal the reported

volume because the initial price is equal to the baseline price. For sections with initial V/C

greater than one, the re-calculated baseline price is likely to be lower than the initial price (the

lower level of congestion should lower travel time costs). As a result, the adjusted volume

should be higher than the initial volume, and reflects backing out the effects of short run elasticity. 

4.3.2 Forecasting Baseline Traffic Volume

HERS provides the user with the flexibility to project baseline traffic using one of several

options, each reflecting different travel growth characteristics. Parameters for each option are

initialized by the PreProcessor, and are determined so that, were no elasticity applied, traffic volume on the section would reach the specified Future AADT value at the Future AADT Year.

Option One is for concave geometric growth, Option Two is for linear growth, and Option Three

provides for convex geometric growth, as shown in Exhibit 4-1. 

The example in Exhibit 4-1 is of a section with an initial AADT of 5000 in data year 1990. The

future AADT year is 2010, at which time the AADT will have grown to 10,000. The growth rate

is calculated for each section based upon the data in its HPMS record. The trend lines show baseline traffic volume without the application of demand elasticity. The linear growth method

(option Two) was used for the 1997, 1999, and 2002 editions of the C&P Report. 

VADJ AADT INPRISRE ( ) ⁄ ( ) BASPRISRE = ×
HERS Internal Models

4-18

4.3.2.1 Option One - Concave Geometric Growth

The geometric option projects baseline traffic by applying a constant rate of growth throughout

the analysis period. Because the volume of additional traffic each year is based upon the previous year’s volume, more vehicles are added each year. The PreProcessor calculates the growth

factor, AADTGR:

Eq. 4.30

where:

AADTGR = constant growth rate;

FAADT = Future AADT from HPMS section record;

AADT = current AADT from HPMS section record;

FAADTYR = year of Future AADT from HPMS section record; and

AADTYR = year of current AADT from HPMS section record.

AADT for any time t1 may be projected along a concave curve:

Eq. 4.31

where:

AADTt0 = known AADT at time t0.

Exhibit 4-1. Travel Growth Options

0

2000

4000

6000

8000

10000

12000

14000

16000

1990199219941996199820002002200420062008201020122014201620182020

Year

AADT

Option 1

Option 2

Option 3

AADTGR FAADT

AADT

---------------------     1 ⁄ ( ) FAADTYR AADTYR –

=

AADTt1 AADTt0 AADTGR t1 t – 0 ( ) = ×
HERS Technical Report v3.54

September 2002

4-19

4.3.2.2 Option Two - Linear Growth

The second option applies a linear, or constant, growth function throughout the period, so that

the same number of vehicles are added each year. The growth factor (AAGRSL) is calculated by

the PreProcessor:

Eq. 4.32

where:

AAGRSL = straight line growth rate.

Using the linear growth function, AADT is projected:

Eq. 4.33

This is the growth option used for the 1997, 1999, and 2002 versions of the C&P Report.

4.3.2.3 Option Three - Convex Geometric Growth

In the third option, the geometric and linear models are combined to project growth along a convex curve. This curve is the mirror image of the concave geometric curve relative to the linear

growth function, and provides for rapid initial growth followed by less aggressive growth.

Future AADT at time of interest t1 is calculated:

Eq. 4.34

4.3.3 Applying Elasticity to Travel Volume Forecasts

To calculate future traffic volume, HERS performs the following steps:

• project future baseline traffic volume by applying the section-specific growth factor to the

adjusted present volume;

• determine the future adjusted volume by applying long run elasticity to the baseline projection;

• apply short run elasticity to the adjusted volume to produce an initial, estimated volume;

• using the initial estimate as a departure point, perform a simultaneous solution to determine the equilibrium point between the demand and delay functions to arrive at a final

traffic volume.

The model applies elasticity separately to each funding period. When the traffic prediction

model calculates the volume after a time span of more than one funding period, it calculates the

AAGRSL FAADT AADT –

FAADTYR AADTYR – = --------------------------------------------------------------

AADTt1 AADTt0 AAGRSL t1 t0 = + × ( ) –

AADTt1 2 AADTt0 AAGRSL t1 t0 × ( ) + × ( ) –

AADTt0 AADTGR t1 t – 0 ( ) – ×

=
HERS Internal Models

4-20

volume for each funding period successively. The calculation period for volume prediction is

from the midpoint of one funding period to the midpoint of the following funding period, a

schedule which coincides with the implementation of improvements (at the middle of the funding period) and the benefit-cost analysis period.

The baseline projection begins with the adjusted volume from the “current” funding period (that

is, the last period for which volume data is known). The adjusted volume represents the volume

on the section before the application of within period short run elasticity. As shown in Equation

4.35, any of the baseline forecast options discussed in paragraph 4.3.2, ”Forecasting Baseline

Traffic Volume,” may be used in the calculation of baseline traffic volume at time t1 from previous long run adjusted volume (at time t0):

Eq. 4.35

where:

VBASEt1 = baseline traffic volume at the midpoint of funding period t1;

VADJt0 = adjusted traffic volume at the midpoint of the previous funding

period t0;

AAGRSL = linear growth rate (see paragraph 4.3.2);

AADTGR = constant growth rate (see paragraph 4.3.2); and

LFP = the length of a funding period.

HERS next applies the long run share of elasticity to get adjusted volume at time t1:

Eq. 4.36

where:

VADJt1 = the adjusted volume at time t1;

VBASEt1 = the baseline volume at time t1 (from Equation 4.35);

LRS = the long run share;

FINPRIt0 = the final user price at time t0, based upon the AADT at time t0; and

BASPRI = the baseline price.

Short run elasticity is applied to the adjusted volume to estimate an initial volume:

Eq. 4.37

where:

VINITt1 = the initial volume at time t1;

ALPHA = ; and

SRE = short run elasticity.

VBASEt1

VADJt0 + ( ) AAGRSL LFP ×

VADJt0 AADTGRLFP×

2 VADJt0 × ( ) + ( ) AAGRSL LFP × VADJt0 AADTGRLFP  – ×











=

VADJt1 VBASEt1 1 LRS FINPRIt0 = × ( ) + × ( ) – BASPRI ⁄ ( ) BASPRI

VINITt1 ALPHA FINPRIt0

SRE = ×

VADJt1 BASPRISRE ⁄
HERS Technical Report v3.54

September 2002

4-21

4.3.4 The Simultaneous Solution

To locate a point on the demand curve, knowing the price is sufficient to determine volume. If

the price were constant with respect to volume, there would be a simple functional relationship

with a single argument. However, as both demand and price vary with volume, HERS must find

a simultaneous resolution of the supply and demand functions. The equilibrium is the intersection of the supply and demand. 

For most of the components of price to the highway user, price does not vary with volume (that

is, the rate of flow). Pavement condition is related to cumulative usage (not immediate volume),

and the effects of volume-to-capacity (V/C) on accident costs is not well understood, so these are

treated as unit costs invariant with flow volume. The exception is congestion, which is clearly

related to V/C, although the relationship is not precisely known. 

Starting with a price (p0) that includes all components other than delay, and a demand curve, the

volume (v0) is determined from the price, as shown in Exhibit 4-2, “Adjustment of Calculated

Delay for Congestion Reduction.” To this price, adding the additional cost for delay, measured

off the curve marked “price of delay,” generates the upper curve “price with delay.” At the price

with delay corresponding to the initial volume, pd, demand would be reduced to some point to

the left of the vertical axis (this axis is not at zero volume); delay, however, would be largely

eliminated, so the price would no longer apply at this volume. The correct solution is the circled

point “equilibrium,” which balances the increase in price with the reduction in congestion. 

Ideally, this equilibrium point could be found by solving for the intersection of the two functions. While the demand curve is either a straight line or a constant elasticity curve, either of

which is a simple single-valued function with two parameters, the delay curve is more complex.

Exhibit 4-2. Adjustment of Calculated Delay for Congestion Reduction

equilibrium

delay

price with delay

demand

v0 ve

p0

pe

initial volume

without delay

initial

price

without

delay

pd

price of

delay

volume at

equilibrium

price at

equilibrium

price with delay
HERS Internal Models

4-22

The delay curve differs with each of the six road types, and for three of these has different equations for different volume levels. Because of the variety and complexity of these equations,

closed-form solutions to the supply-demand intersection are not feasible. Numerical solutions

could be obtained to any precision desired, but convergence under all possible conditions would

be difficult to ensure, and computational effort might be excessive. 

HERS instead uses the alternative approach of a numerical approximation, whose properties are:

1. Rapid convergence because of the smooth shapes of the demand and delay functions;

and

7. A fixed number of iterations (two) which necessarily limits computational effort.

This strategy is acceptable because a high degree of numerical precision is not required; the only

purpose is to adjust the volume of traffic to a reasonable level given congestion and other generalized price factors.

The approximation strategy uses the slopes of the two curves to estimate the intersection as the

apex of a triangle (as if the curves were straight lines), and uses the resulting volume adjustment

to re-estimate the slopes as the average of two slopes. In Exhibit 4-3, the first iteration is shown

in heavy solid lines, and the second iteration in heavy dashed lines. The first iteration uses the

tangents at the initial volume, VINIT, shown as sdlayi

 and sdemi (for delay and demand, respectively), to yield the volume RVOL and the price PriceRVOL. Averaging the demand slope at

RVOL with that for VINIT (sdemi

) gives the arc slope of the demand curve (shown as sdemr)

between those two points, which is a much closer approximation of the slope between the equilibrium and the initial volumes than is the tangent at VINIT. Doing the same for the delay funcExhibit 4-3. Details of Successive Approximation

sdlayi

sdemi

RVOL

sdlayr

sdemr

Velas

demand

delay

priceVelas

priceRVOL
HERS Technical Report v3.54

September 2002

4-23

tion gives the revised delay slope sdlayr, and applying the two revised slopes to VINIT produces

the second-iteration result of volume Velas and price PriceVelas. This is still not the true equilibrium point, but it is close enough. 

The lower the AADT/Capacity ratio, the more accurate this procedure becomes. The situation

displayed in Exhibit 4-3 is an extreme scenario, in that VINIT represents an AADT/Capacity

ratio of 19.5, which means the facility is operating at capacity for 15-19 hours per day. For

AADT/C under 12, the second iteration is almost indistinguishable from the first, and for

AADT/C under 8 the first iteration is indistinguishable from the equilibrium.

4.3.5 Computational Algorithms

HERS performs a sequence of steps preparatory to the simultaneous solution of the demand and

supply functions. HERS first calls upon the pavement model to determine the condition of the

pavement at time t1 based upon the initial volume estimate. Using this provisional PSR and the

initial volume, HERS:

• determines free flow speed and free flow speed uphill for each vehicle type;

• using the free flow speeds, determines the travel time cost without delay;

• calculates the operating costs at the baseline level of service (that is, with the volume to

the same level relative to capacity as per the baseline price);

• calculates the safety costs at the initial volume at time t1; and

• sums the travel time, operating, and safety costs to yield “price without delay” (PWOD).

HERS first calculates the slope of the initial demand curve:

Eq. 4.38

where:

SDEMi = initial slope of demand curve; and

PWOD = price without delay.

HERS then calculates an initial estimate of the amount of delay at the volume VINIT at time t1,

(EDLAYi

) and calculates the slope of the delay function (SDLAYi) at that volume. The specific

algorithms are based upon the SAIC/CS equations used in the speed model, and like them are

dependent upon the road type, the AADT/Capacity ratio, and the number of traffic signals and

stop signs per mile, if any. The equations for specific road types are in Tables 4-9 through 4-10 in

paragraph 4.3.6, ”Delay Equations by Road Type.” The examples below (in Equations 4.39 and

4.40) are for two-lane, two-way roads without traffic control devices where the AADT/Capacity

ratio (figured using the initial volume as AADT) is less than 10. The initial estimate of delay is

determined:

Eq. 4.39

SDEMi

PWOD( ) 1 – SRE

ALPHA SRE × = ---------------------------------------

EDLAYi 0.432 VINIT

Capacity = × ----------------------- × VOT ⁄ 1000
HERS Internal Models

4-24

where:

EDLAYi = estimate of delay at the initial volume;

VINIT = initial volume estimate (from Equation 4.37); and

VOT = value of an hour of travel time.

The slope of the delay equation at the initial volume is:

Eq. 4.40

where:

SDLAYi = slope of the delay curve at the initial volume.

The first approximation for a revised volume is the height of a triangle (laying on its side) whose

base is the initial estimate of delay and whose sides slope at SDEMi and SDLAYi (as shown in

Exhibit 4-3):

Eq. 4.41

where:

RVOL = revised volume estimate

EDLAYi = initial estimate of delay (from road type specific equation)

SDLAYi = initial slope of delay function (from road type specific equation)

This revised volume is then substituted for the initial volume in Equation 4.39 to yield a revised

estimate of delay (EDLAYr). (Note that the revised volume is also substituted for the initial volume in determining the AADT/Capacity ratio used to select the specific form of the equation.)

HERS next calculates the price associated with the initial volume:

Eq. 4.42

and the price associated with the revised volume:

Eq. 4.43

The next step is the calculation of revised slopes for the demand and delay functions. The

demand slope is taken as the difference between the initial and revised prices over the difference

between their associated volumes:

Eq. 4.44

where:

SDEMr = revised demand slope

SDLAYi = 0.432 × VOT ⁄ ( ) Capacity × 1000

RVOL VINIT = EDLAYi

SDEMi SDLAYi – + ------------------------------------------------

PriceVINIT ( ) VINIT ALPHA ⁄ ( ) 1 ⁄ ( ) SRE =

PriceRVOL ( ) RVOL A⁄ LPHA ( ) 1 ⁄ ( ) SRE =

SDEMr

PriceRVOL PriceVINIT ( ) –

( ) RVOL VINIT – = -----------------------------------------------------------------
HERS Technical Report v3.54

September 2002

4-25

The delay slope is taken as the difference between the revised and initial delay estimates divided

by the difference in the associated volumes:

Eq. 4.45

where:

SDLAYr = revised delay slope

HERS calculates the price of delay at the intersection of the revised slopes:

Eq. 4.46

and uses it to estimate the final, elasticized volume, Velas:

Eq. 4.47

4.3.6 Delay Equations by Road Type

These paragraphs contain the delay equations used for each of the four road types. Within each

road type, equations are selected based upon the AADT/Capacity ratio and the number of stop

signs per mile. The equations are based upon the SAIC25 and CSI26 equations implemented in

the speed model. The equations yielding EDLAY (the estimated delay) would replace Equation

4.39 in the computations detailed above. The equations yielding SDLAY (the slope of the delay

function) would replace Equation 4.40 as used above.

The “wheres” below apply to the equations in Tables 4-9 through 4-12 which contain the

demand equations for the four basic road types:

EDLAY = estimate of delay (equation substitutes for Equation 4.39)

SDLAY = delay slope (equation substitutes for Equation 4.40)

ACR = AADT/Capacity Ratio

VOT = value of an hour of travel time for the section

NSS = the average number of stop signs per mile

NTS = the average number of traffic signals per mile

FFS = free flow speed for the section

COMPF = is the computation factor 

25. Science Applications International Corporation and Cambridge Systematics, Inc., Roadway Usage Patterns: Urban

Case Studies, prepared for Volpe National Transportations Systems Center and the Federal Highway Administration, June 1994, Appendix A; Science Applications International Corporation, et al., Speed Determination Models for

the Highway Performance Monitoring System, prepared for the U. S. Department of Transportation, Federal Highway

Administration, Washington, D.C, October 31, 1993.

26. Cambridge Systematics, Inc., Revisions to the HERS Speed and Operating-Cost Procedures, prepared for the U. S.

Department of Transportation, Federal Highway Administration, Washington, D.C, January 25, 1996, Section 2.

SDLAYr

EDLAYr EDLAYi ( ) –

( ) RVOL VINIT – = --------------------------------------------------------

PriceDelay EDLAYi

SDEMr

SDEMr SDLAYr ( ) – = × -----------------------------------------------------

Velas ALPHA PWOD PriceDelay ( ) + SRE = ×

1 exp – ( ) –NTS ⁄ 24.4
HERS Internal Models

4-26

The two hybrid road types are treated in the same manner as in the speed model. On sections

with both stop signs and traffic signals, the final elasticized volume is the average of the volumes

on the two portions of the section, weighted by the relative numbers of stop signs and signals.

On three-lane sections in two directions, volume is split equally between the two directions, and

capacity is split 7:5 in favor of the two-lane direction. Elasticity is applied using the equations for

rural multilane roads (in the two-lane direction) and two-lane roads (in the one-lane direction).

The sum of the elasticized volumes is taken as the final elasticized volume for the section. 

 

4.4 The Fleet Composition Model

HERS decomposes the vehicle fleet into three vehicle categories which include a total of seven

vehicle types. This data on fleet composition is used by HERS when estimating speed, operating

costs, travel-time costs, section capacity, and pavement deterioration. The progression from the

entire fleet to the seven vehicle types is shown (proceeding from left to right) in Table 4-13, “Fleet

Composition.” 

Table 4-9. Delay Equations for Freeways and Multilane Rural Highways

AADT/C 

Range

<8

>8 and <12

>12

Table 4-10. Delay Equations for 2-lane, 2-way Roads

AADT/C 

Range

< 10

> 10

EDLAY 0.0797 ACR 0.00385 ACR2 = ( ) × + × × VOT ⁄ 1000

SDLAY = ( ) 0.0797 0.00385 2 + × × ACR × VOT Capacity ⁄ ( ) × 1000

EDLAY 12.1 2.95 ACR 0.193 ACR2 = ( ) – × + × × VOT ⁄ 1000

SDLAY = ( ) – 0.193 2 2.95 + × × ACR × VOT Capacity ⁄ ( ) × 1000

EDLAY 19.6 5.36 – ACR 0.342 ACR2 = ( ) × + × × VOT ⁄ 1000

SDLAY = ( ) – 0.342 2 5.36 + × × ACR × VOT Capacity ⁄ ( ) × 1000

EDLAY = 0.432 × ACR × VOT ⁄ 1000

SDLAY = 0.432 × VOT ⁄ 1000

EDLAY 9.953 1.66 – 0.109 × ACR ACR2 = ( ) + × × VOT ⁄ 1000

SDLAY = ( ) – 0.218 1.66 + × ACR × VOT ⁄ ( ) Capacity × 1000
HERS Technical Report v3.54

September 2002

4-27

Table 4-11. Delay Equations for Sections with Stop Signs

AADT/C 

Range

Stop 

Signs/ 

mile

<6

>6 and <15

<10

>10

>15

<10

>10

Table 4-12. Delay Equations for Sections with Traffic Signals

AADT/C 

Range

<7

>7 and 

<13.2

>13.2

EDLAY NSS (1.9 0.067 FFS 0.103 ACR

0.0145 ACR2× ) ) × VOT ⁄ 1000

= ( × + × + × +

SDLAY NSS × ( ) 0.103 0.029 + × ACR

VOT Capacity ⁄ ( ) ⁄ 1000

= ×

EDLAY NSS 3.04 0.067 FFS 0.029 ( ) ACR – 6 2 ( ) + × – ×

0.354 ( ) ACR – 6 2×

( × +

) × VOT ⁄ 1000

=

SDLAY NSS ( ) 0.348 0.058 – × ACR 0.708 ACR

4.248

( × + × –

) × VOT ⁄ ( ) Capacity × 1000

=

EDLAY NSS × ( ) 3.04 0.067 + × FFS 0.064 × ( ) ACR – 6 2 ( ) +

VOT

×

⁄ 1000

=

SDLAY = ( ) 0.128 × ACR – 0.768 × VOT Capacity ⁄ ( ) × 1000

SDLAY = ( ) 0.708 × ACR – 4.248 × VOT Capacity ⁄ ( ) × 1000

EDLAY NSS × ( ) 0.691 0.067 + × FFS 0.354 ( ) ACR – 6 2 ( ) + ×

× VOT ⁄ 1000

=

EDLAY NSS × ( ) 3.04 0.067 + × FFS 0.354 ( ) ACR – 6 2

23.49

( + × –

) × VOT ⁄ 1000

=

EDLAY COMPF = ( ) × ( ) 68.7 17.7 + × ACR × VOT ⁄ 1000

SDLAY = 17.7 × COMPF × VOT Capacity ⁄ ( ) × 1000

EDLAY COMPF 192.6 14.4 ( ) ACR – 7 1.16 ( ) ACR – 7 2 ( ) + × – ×

+ 0.16

×

( ) ACR – 7 2×

(

) × VOT ⁄ 1000

=

SDLAY COMPF ( ) × ( ) 14.4 2.32 – × ( ) ACR – 7 + 0.32 × ( ) ACR – 7

× VOT Capacity ⁄ ( ) × 1000

=

EDLAY 237.3 COMPF 0.16 ( ) ACR – 7 2 = ( ) × + × × VOT ⁄ 1000

SDLAY = 0.32 × ( ) ACR – 7 × VOT Capacity ⁄ ( ) × 1000
HERS Internal Models

4-28

The fleet is divided into vehicle categories based upon section-specific percentages of the two

truck classifications. These are reported in the HPMS input data record for each section. The

four wheel category consists of the percentage of total traffic which is not part of either truck category. For the disaggregation of vehicle categories to vehicle types, HERS uses factors derived

from the 1982 HPMS Vehicle Classification Case Study27. As shown in Table 4-14, “Fleet Disaggregation Factors,” these functional class dependent factors have been prorated to total 100 percent for each of the three categories. 

The HERS parameter file has entries for specifying the annual growth rate of the percentage of

truck traffic for each functional class. This is applied to the section-specific percentages for the

two truck categories to derive the new percentages for each category. For the 1997 Conditions

and Performance Report the truck growth factors were set to 1.0 (i.e., no growth).

As an example of the weighted summation process used by HERS, let VCATA, VCATSU, and

VCATCM designate the three vehicle categories (four-tire vehicles, single unit trucks, and combination trucks), VT1 through VT7 correspond to the seven vehicle types, and FAF1 through FAF7

to the fleet disaggregation factors for each of the respective vehicle types (as shown in Table 4-

14). After determining the quantity for each vehicle type (for example, travel time cost per 1000

vehicle miles), HERS calculates the quantity for each vehicle category weighted by vehicle type:

Eq. 4.48

Note that the fleet disaggregation factors are indexed by functional class. HERS next determines

the percentages of single unit and combination trucks at the time of interest (t, in years) by

applying the user specified truck growth factor (TRKFAC) for the section’s functional class to the

Table 4-13. Fleet Composition

Fleet Weighting Factor Vehicle 

Category Weighting Factor Vehicle Type

All Vehicles

Section data item: Percent Combination 

Trucks

Combination Trucks

Prorated from 

HPMS Vehicle 

Classification 

Study

Five or More Axle Combination 

Trucks

Three/Four Axle Combination 

Trucks

Section data item: Percent Single Unit 

Trucks

Single Unit 

Trucks

Prorated from 

HPMS Vehicle 

Classification 

Study

Three or More Axle Single Unit 

Trucks

Six-Tire Trucks

100% less percent of 

Single Unit and Combination Trucks

Four Tire 

Vehicles

Prorated from 

HPMS Vehicle 

Classification 

Study

Pickups & Vans

Medium/Large Automobiles

Small Automobiles

27. U. S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System

Analytical Process Technical Manual, Version 2.1, December 1987, Table IV-20.

VCATA VT1 FAF1fcVT2 FAF2fcVT3 FAF3fc = × + × + ×

VCATSU VT4 FAF4fc

VT5 FAF5fc = × + ×

VCATCM VT6 FAF6fcVT7 FAF7fc = × + ×
HERS Technical Report v3.54

September 2002

4-29

percentages of average single unit (PCAVSU) and combination trucks (PCAVCM) reported in the

section’s HPMS data record:

Eq. 4.49

where PCSU and PCCM are the percentages at the time of interest. Finally, HERS produces a

total weighted sum (TWS) combining the weighted values of the three vehicle categories:

Eq. 4.50

4.5 The Widening Feasibility Model

Six of the seven major HERS improvement options involve increasing the width of the roadway:

adding lanes, widening lanes, and improving shoulders28. Additionally, widening the median

and increasing access control are two upgrades which may be performed on rural sections (when

lanes are added) and substandard urban freeways (when they undergo reconstruction) and

which also increase the roadway width. “Widening feasibility” refers to the potential for

increasing the total width of a particular section. HERS tracks the feasibility of widening each

section, and updates the information whenever the section is improved. HERS uses the interacTable 4-14. Fleet Disaggregation Factors

Functional Classes

Four Tire Vehicles Single Unit 

Trucks

Combination 

Trucks

Small Autos

Med/Lg 

Autos

Pickups & 

Vans

Six-Tire 

Trucks

3+Axle 

SUTs

3-4 Axle 

Combos

5+ Axle 

Combos

Rural Interstate .2365 .5367 .2268 .7372 .2628 .1023 .8977

Rural OPA .1795 .5335 .2871 .7301 .2699 .1826 .8174

Rural Minor Arterial .2081 .4762 .3156 .6404 .3596 .1675 .8325

Rural Major Collector .1536 .4882 .3582 .6180 .3820 .2518 .7482

Urban Interstate .2521 .5583 .1896 .7000 .3000 .1253 .8747

Urban Other Fwy/Exwy .2521 .5583 .1896 .7000 .3000 .1253 .8747

Urban OPA .2081 .5875 .2045 .7490 .2510 .1964 .8036

Urban Minor Arterial .1976 .5998 .2027 .6590 .3410 .1765 .8235

Urban Collector .2057 .5551 .2392 .6955 .3045 .3396 .6604

28. Improving shoulders does not always increase width.

PCSU PCAVSU TRKFACfc

t = ×

PCCM PCAVCM TRKFACfc ×

t =

TWS VCATA = 1 × ( ) – PCSU – PCCM VCATSU PCSU

+ VCATCM × PCCM

+ ×
HERS Internal Models

4-30

tion of system and section-specific constraints to determine first, whether widening improvements can be implemented, and second, whether additional lanes will be added at “normal” or

“high” cost. (For information about improvements which widen the roadway, see Chapter 6,

and especially Table 6-1, “Effects of Improvements on Section Data Items -- All Sections.”) 

There are four factors in HERS which limit the potential width of any section. First, the user

specifies the maximum number of lanes (MAXLNS) allowed for each of the functional classes.

The number may be as large as 99. It is applied only when determining the number of lanes to be

added to a section; it is not used in determining the feasibility of widening existing lanes, widening shoulders or medians, or in improving access control. HERS does not remove lanes from

existing highways in order to meet this limit. 

Second, HERS will always build to an even number of lanes. Sections with an even number of

existing lanes will receive additional lanes in even-numbered increments. Sections with an odd

number of existing lanes will receive an odd number of lanes the first time HERS adds lanes to

the section, and an even number of lanes should more lanes be added in a subsequent funding

period. 

Third, each section in the HPMS database includes a Widening Feasibility (WDFEAS) code indicating the extent to which the existing road may be widened. This state-supplied code reflects

physical features along the section such as severe terrain, cemeteries and park land, and nonexpendable buildings (large office buildings, shopping centers, etc.). It does not reflect restrictions due to current right-of-way, State widening practices, politics, or expendable buildings

(single-family residences, barns, private garages, etc.). The widening feasibility codes are

described in Table 4-15. 

Fourth, the user specifies a system-wide Widening Feasibility Override (WDFOVR) code which

corresponds to the widening feasibility codes in Table 4-15. When the WDFOVR code is higher

than a section’s WDFEAS code, HERS may consider additional widening options which would

ordinarily be precluded by the WDFEAS value. Lanes that are added up to the level specified by

WDFEAS are treated as “normal cost” lanes. Additional lanes added based on the WDFOVR

code are treated as “high cost” lanes, and are priced separately in the improvement cost file.

High cost lanes are intended to represent extraordinary measures that could be taken to provide

additional capacity such as double-decking a freeway, or constructing a new facility on a parallel

route. Normal and high cost lanes are reported separately in HERS output.

The interplay of WDFEAS and WDFOVR is shown in Table 4-16, “The Role of WDFOVR in Widening.” Each table entry lists the widening improvements HERS will consider for a section of the

Table 4-15. Widening Feasibility Codes

Code Description

1 No widening is feasible

2 Partial lane may be added

3 One lane may be added

4 Two lanes may be added

5 Three or more lanes may be added
HERS Technical Report v3.54

September 2002

4-31

given widening feasibility code (WDFEAS, by column) for a specific value of the system variable

WDFOVR (by row). 

Setting the WDFOVR code to 1 is the equivalent of disabling the override feature, so that each

section’s WDFEAS code alone determines the widening options which HERS will consider. This

case is illustrated in the first row of Table 4-16. In this situation, if WDFEAS for a section is

coded as 1, no widening is considered, while if WDFEAS equals 2, HERS will consider widening

the shoulders and/or lanes. If WDFEAS is coded as 3, 4, or 5, HERS may also consider adding

normal cost lanes, improving access control, and widening medians. When WDFEAS is coded as

3, HERS will only consider adding a lane when the existing facility has an odd number of lanes.

When WDFEAS is coded as 4, HERS will consider adding one lane to a facility with an odd number of lanes, or adding two lanes to a facility with an even number of lanes.

Setting the WDFOVR code higher than 1 causes HERS to consider additional improvement

options, including high cost lanes in some cases. Note that the “Rur” and “Urb” values in Table

4-16 are the same in each column. This occurs because WDFOVR is not used in assessing

whether the median width and access control upgrades can be made to rural sections receiving

additional lanes and substandard urban freeways undergoing reconstruction. Note also that

HERS will not add lanes in excess of the MAXLNS value, regardless of how the WDFEAS or

WDFOVR variables are coded.

When evaluating improvements, HERS typically uses the initial WDFEAS value at the beginning

of the funding period to determine widening feasibility. However, when considering suppleTable 4-16. The Role of WDFOVR in Widening

WDFOVR

Widening Feasibility Code (WDFEAS)

12345

1 SH, WL +1 NCLa, SH, 

WL, Urb, Rur

+1 or 2 NCLsa, 

SH, WL, Urb

+ NCLs, SH, 

WL, Urb, Rur

2 SH, WL SH, WL +1 NCLa, SH, 

WL, Urb, Rur

+1 or 2 NCLsa, 

SH, WL, Urb

+ NCLs, SH, 

WL, Urb, Rur

3 +1 HCL, SH, 

WL

+1 HCL, SH, 

WL

+1 NCLa, SH, 

WL, Urb, Rur

a. When the existing facility has an odd number of lanes, add one normal cost lane.

+1 or 2 NCLsa, 

SH, WL, Urb

+ NCLs, SH, 

WL, Urb, Rur

4 +1 or 2 HCLsb, 

SH, WL

b. When the existing facility has an odd number of lanes, add one high cost lane.

+1 or 2 HCLsb, 

SH, WL

+1 NCLa or +2 

HCLs, SH, WL, 

Urb, Rur

+1 or 2 NCLsa, 

SH, WL, Urb

+ NCLs, SH, 

WL, Urb, Rur

5 + HCLs, SH, 

WL

+ HCLs, SH, 

WL

+1 NCLa and 

HCLs, SH, WL, 

Urb, Rur

+1 or 2 NCLsa

and HCLs, SH, 

WL, Urb

+ NCLs, SH, 

WL, Urb, Rur

where: SH = widen shoulders; WL = widen lanes; NCL = add normal cost lane(s); HCL = add high 

cost lane(s); Urb = on Urban freeways by design: improve access control to full and widen median to 

design standard; Rur = on Rural sections with added lanes: widen median and upgrade access control 

to partial.
HERS Internal Models

4-32

mental improvements, the WDFEAS value may first be adjusted downward. On rural sections

receiving additional lanes and substandard urban freeways being reconstructed, the main

improvement may consume all of the space available, and could preclude any additional

upgrades to medians or access control that HERS might otherwise have considered. To address

these situations, HERS evaluates supplemental upgrades based on a reduced WDFEAS value

that factors in the effect of the main improvement on the initial WDFEAS value. The WDFEAS

values shown in Table 4-16 represent the adjusted codes.

For example, a three-lane rural section with an initial WDFEAS of 3 might be resurfaced and

have one lane added. Adding a lane would result in reducing WDFEAS to 1, so supplemental

rural upgrades would not be considered. This reduction in WDFEAS values is why the “Rur”

value doesn’t appear in Table 4-16 in the column where WDFEAS equals 4. HERS only considers

median width and access control upgrades to rural sections when lanes are added. If the

WDFEAS value at the beginning of the funding period was 4, adding one or two lanes would

reduce the WDFEAS code to 3 or 1, respectively. Therefore, for any case in which HERS would

be considering median width and access control upgrades to rural sections, WDFEAS could not

equal 4. (If the initial WDFEAS value was 5, it would remain 5 after adding lanes.) 

HERS updates WDFEAS in response to improvements on the section. See Table 6-5, “Widening

Feasibility Code Adjustments,” for the effects of improvements on WDFEAS.

For the 2002 C&P Report, the maximum number of lanes was set to 99 for all functional classes.

The effect of setting MAXLNS to such a high number was to effectively eliminate it as a factor in

regulating roadway width, leaving each section’s WDFEAS value and the WDFOVR override

value to determine widening limits. WDFOVR was set to 1, which precluded HERS from adding

high cost lanes to any section.29

4.6 The Capacity Model

The HERS capacity model has two functions. The first is the calculation of section capacity; the

second is the calculation of the number of lanes needed to accommodate the projected traffic volume in the design year (that is, how many additional lanes are needed).

4.6.1 Capacity

For each section, HERS v3.54 develops separate estimates of capacity for the peak and offpeak

periods; and the peak-period estimates are developed separately for the peak direction and the

opposite, or “counterpeak,” direction. These three capacities are referred to as peak, counterpeak, and offpeak capacity. All three capacities are estimated using the HPMS procedure for

estimating capacity30 that is based on the 1994 and 1997 editions of the Highway Capacity Manual (HCM)31,32. Differences in the three capacities result primarily from differences in the number of available travel lanes.

29. This applies to the baseline run for the economic efficiency scenario and most of the over 400 runs executed for the

C&P Report. Some of the runs were executed with WDFOVR set to 5.

30. U.S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System

Field Manual, “Appendix I: Highway Capacity Submittal Software,” revised 1999.

31. Transportation Research Board, Highway Capacity Manual, Special Report 209. Third Edition. Washington, D.C.,

1994.
HERS Technical Report v3.54

September 2002

4-33

Corresponding to the three capacities, the three sets of lanes are referred to as peak, counterpeak,

and offpeak lanes. Peak and counterpeak lanes represent lanes in one direction only; while offpeak lanes represent lanes in both directions.

Offpeak capacity is estimated using the coded value of the number of through lanes in the offpeak period; and peak capacity is estimated using the coded value of peak lanes. The latter

value represents total through lanes for rural two- and three-lane roads and it represents peakdirection lanes for all other sections.

For sections with a peak-period directional factor that is less than 1.0, the number of counterpeak

lanes is obtained by subtracting the number of peak lanes from the sum of offpeak lanes and an

estimate of the number of extra travel lanes (if any) available during the peak period. For sections with surfaced shoulders, the maximum number of total peak-period lanes is assumed to

equal twice the number of peak lanes. For curbed sections, the maximum number of extra peakperiod lanes is assumed to equal the number of sides on which peak parking is not allowed. In

both cases, the number of extra peak-period lanes is reduced, if necessary, to guarantee that the

fraction of lanes in the counterpeak direction is no higher than the minimum number necessary

to keep congestion in the counterpeak direction lower than congestion in the peak direction.

Thus, the number of counterpeak lanes is never greater than the number of peak lanes, and it frequently is smaller.

For two-way sections, the three capacities also reflect three different directional factors. For peak

capacity, the coded directional factor is used. (This value represents the percentage of traffic

flowing in the peak direction during the design hour.) For counterpeak capacity, one minus this

value is used. For offpeak capacity on two-way sections, more balanced traffic flow is assumed,

and the “offpeak directional factor” is usually set to 0.5.33

HERS v3.54 allows the user to specify whether to use the estimates of peak capacity produced by

the above process or the values coded in the HPMS record. If the HPMS file has been processed

by a version of the submittal software that uses capacity procedures based on the 1994 and 1997

HCM, the two sets of estimates will be essentially the same. If asked to use peak capacities that

differ from those derived by the above procedure, then, for each section, HERS uses the ratio of

the coded peak capacity to the internally derived peak capacity as a scale factor. This factor,

referred to as the “capacity ratio,” is then used to adjust the internally derived estimates of offpeak and counterpeak capacity to produce values that are consistent with the coded value of

peak capacity. If HERS is asked to use the internally generated capacities, the capacity ratios are

set to 1.0

4.6.2 Effects of Capacity Improvements

The capacity effects of any improvement that may affect capacity are estimated by:

32. Transportation Research Board, Highway Capacity Manual, Special Report 209. Third Edition. Washington, D.C.,

1998. The edition number is unchanged, but updated chapters (Chapters 3, 9, 10, and 11 were extensively revised)

have December 1997 dates. Note that the TRB refers to this as “the 1997 update of the third edition.”

33. The exception occurs for sections with an odd number of total lanes in the offpeak period. For these sections, the

fraction of total lanes in the direction with the higher number of lanes is determined. The offpeak directional factor

is then set to the lower of this value and the peak-period directional factor.
HERS Internal Models

4-34

1. Using the capacity procedure to obtain new estimates of peak, offpeak, and counterpeak 

capacity; and

2. Multiplying these values by the capacity ratio to produce estimates that are consistent with the 

capacity values used prior to implementing the improvement.

4.6.3 Design Year Lane Requirements

When estimating the future traffic volume for the purpose of determining lane requirements,

HERS does not apply demand elasticity.34 Instead it projects the geometric rate of growth

AADTGR (see Equation 4.30) as in Equation 4.35, using the “fully elasticized” AADT at the begining of the current funding period for VADJ, and the number of years from the time of that AADT

to the “design year” as the “length of the funding period” (LFP).35 The design year is the length

of the design period (specified by the user in the parameter file; the default value is 20 years)

from the point of implementing the improvement, which is at the middle of the current funding

period.

The design number of lanes to be added normally is the minimum number necessary to achieve

a design year volume/capacity ratio that satisfies the user-specified widening standard.36 The

capacity used in this ratio is the peak capacity that would be produced by adding the specified

number of lanes. The design number of additional lanes may be reduced as a result of limitations on widening feasibility or on the maximum numbers of lanes allowed. This number is

user-specified for each functional class and is limited to 99 (the value used for the 2002

C&P Report). Also, sections with stop signs are assumed to be limited to a maximum of two

through lanes in each direction.

34. In one sense, this mimics the non-elastic calculations of highway engineers. Practically, it avoids the computationally intense attempt to solve for elasticity when the future capacity is unknown.

35. he default value for the design period is 20 years, which is presumed to begin at the time the improvement is

implemented. Thus, for the initial five-year funding period, the improvement is implemented at year 2.5, the

design year is year 22.5, and the exponent used is 22.5.

36. When addressing unacceptable conditions, the unacceptability level is used instead of the widening standard.
5-1

5 Cost and Benefit Calculations

HERS recognizes four broad classes of costs: 

• user costs, which are borne by the highway user;

• agency costs, such as maintenance, which are borne by the administrative agency responsible for the section; 

• external costs, which are borne by non-users of the highway system (society at large);

and

• capital improvement costs.

When performing benefit-cost analysis, HERS places the first three classes in the numerator, with

capital improvement costs being the denominator.

Benefits are reductions in costs as the result of an improvement, and are measured as the difference in costs between the base case and the improved case. (The base case can be either the

unimproved section or a less aggressive improvement.) Disbenefits are increases in cost as the

result of an improvement. It is possible for an improvement to produce both benefits and disbenefits, as when an improvement which increases average speed brings benefits resulting from

the reduction in travel time, and disbenefits from an increase in vehicle operating costs.

5.1 User Costs

HERS distinguishes the following components of user costs: travel time costs, vehicle operating

costs, and safety costs, which includes both property damage and personal injury. Within the

context of the demand elasticity model, these costs make up the user price. User benefits are

simply the difference in costs between two predicted future states of the section under consideration: typically, an improvement will lower user costs, producing a benefit. User costs are calculated by vehicle miles traveled; total user costs are a product of user costs per vehicle mile times

section length times AADT. 

5.1.1 Travel Time Costs

HERS v3.54 incorporates U.S. Department of Transportation values of time per person for personal travel and for business travel.1

 Table 5-1, “Value of One Hour of Travel Time (1995 Dollars),” presents a summary of the major components of the revised HERS estimates of the 1995

value of travel time, by vehicle type. The values used for each of the components are documented below. 

For the purpose of indexing the value of time from 1995 dollars to dollars of a subsequent year,

HERS allows separate indexing of the value of time per person, the vehicle cost, and inventory1. U. S. Department of Transportation, “The Value of Saving Travel Time: Departmental Guidance for Conducting

Economic Evaluations,” April 1997, Table 4.
Cost and Benefit Calculations

5-2

cost components. The indexes currently used for the three components are, respectively: The

U.S. Bureau of Labor Statistics (BLS) Employment Cost Index for total compensation of all civilian workers; U.S. Department of Commerce Bureau of Economic Analysis (BEA) data on average

expenditures per car; and the implicit gross domestic product (GDP) price deflator, also obtained

from BEA. The index values used to convert these components to 1997 dollars (for the 1999 C&P

Report) are, respectively: 1.059, 1.110, and 1.038. 

5.1.1.1 Vehicle Occupants

HERS obtains the value of time to vehicle occupants from the U.S. Department of Transportation

(USDOT) Departmental Guidance.2

 The values used are the values (in 1995 dollars) for travel

via surface modes. For on-the-clock travel for all occupants of four-tire vehicles, HERS uses the

recommended value for "business travel" ($18.80 per person-hour), while the value used for all

occupants of larger vehicles is the slightly lower recommended value for truck drivers ($16.50

per person-hour). For personal travel, HERS uses the recommended value for personal local

travel ($8.50 per person hour).3

5.1.1.2 Average Vehicle Occupancy

HERS derives values for average vehicle occupancy (AVO) of four-tire vehicles from 1995

National Personal Travel Survey (NPTS)4

 estimates of VMT and person-miles of travel by trip

Table 5-1. Value of One Hour of Travel Time (1995 Dollars)

Small 

Auto

Med. 

Auto

4-Tire 

Truck

6-Tire 

Truck

3-4 Axle 

Truck

4-Axle 

Comb.

5-Axle 

Comb.

Business Travel

Value per Person $ 18.80 $ 18.80 $ 18.80 $ 16.50 $ 16.50 $ 16.50 $ 16.50

Avg. Occupancy 1.43 1.43 1.43 1.05 1.0 1.12 1.12

Vehicle $ 1.09 $ 1.45 $ 1.90 $ 2.65 $ 7.16 $ 6.41 $ 6.16

Inventory - - - - - $ 0.60 $ 0.60

Personal Travel

Value per Person $ 8.50 $ 8.50 $ 8.50 - - - -

Avg. Occupancy 1.67 1.67 1.67 - - - -

Percent Personal 89% 89% 75% - - - -

Avg Value per Vehicle $ 15.71 $ 15.75 $ 17.84 $ 19.98 $ 23.66 $ 25.49 $ 25.24

2. Ibid.

3. The Departmental Guidance recommends using a higher value ($11.90 per person-hour) for personal intercity

travel, implying that, at least in rural areas, an average value for personal travel that is slightly higher than $8.50

might be appropriate. (HERS 3.54 does not accept separate values of personal travel time and vehicle occupancy

for business and personal travel. The input values of personal travel time and vehicle occupancy used by HERS

3.2 for four-tire vehicles are set so that, when combined with weighted averages of the average vehicle occupancy

values in Table 5-1, they will produce the overall average values of time shown at the bottom of the table.)

4. Oak Ridge National Laboratories, 1995 National Personal Travel Survey, Table NPTS-1, October 1997 (wwwcta.ornl.gov/npts/1995/doc/table1.pdf).
HERS Technical Report v3.54

September 2002

5-3

type. The NPTS data indicates that AVO for "work-related business" (exclusive of commuting) is

1.43, while AVO for all other purposes is 1.67. 

For combination trucks, AVO was set to 1.12 on the basis of Hertz’ analysis of the frequency of

the use of two-driver teams in crash-involved trucks.5

 Six-tire vehicles, which include pick-upand-delivery vehicles that sometimes carry a helper, were assumed to have an average occupancy of 1.05, while heavier single-unit trucks were assumed to have only one occupant.

5.1.1.3 Personal-Use Percentage of VMT

Approximately 4.7 percent of automobiles are estimated to be in commercial fleets of four or

more vehicles, excluding fleet vehicles that are individually leased or used for daily rental;6

 and

6.7 percent of the VMT of the remaining automobiles is for work-related business.7 These figures

indicate that just under 89 percent of automobile VMT represents personal travel (including

commuting), while the remainder represents business travel.

For four-tire trucks, the percentage of VMT that was not for personal use was 31 percent in 1992;8

however, this percentage has undoubtedly dropped in the last several years as small truck-based

vehicles have become increasingly popular as personal vehicles. Accordingly, HERS assumes

that personal use accounts for 75 percent of the VMT of four-tire trucks and business use

accounts for 25 percent of this VMT.

5.1.1.4 Vehicle Costs

Vehicles depreciate as a result of their use and as a result of aging that is independent of vehicle

use. The former type of depreciation is estimated by HERS’ vehicle operating-cost procedure,

while the latter type is a time-related cost incurred by all vehicle owners and included as a component of travel-time cost of commercial vehicle operators. For HERS 3.2, time-related depreciation was estimated by:

1. Estimating total annual depreciation by vehicle type, and converting these estimates to

costs per hour of vehicle operation;

2. Using a modified version of HERS to obtain estimates of usage-related depreciation (by

vehicle type) per vehicle-mile; and

3. Converting the latter estimates to costs per hour of vehicle operation, and subtracting

from the Step 1 results.9

The estimation process is described below.

For autos in commercial motor pools and four-tire trucks, total depreciation per hour was computed as the average vehicle cost per year (assuming a five-year life, with a 15 percent salvage

5. Robin P. Hertz, “Sleeper Berth Use as a Risk Factor for Tractor Trailer Driver Fatality,” 31st Annual Proceedings,

American Association for Automotive Medicine, September 1987, pp. 215-227.

6. American Automobile Manufacturers Association, Motor Vehicle Facts and Figures, 1995, Detroit, 1995, pp. 39 and

43.

7. Oak Ridge National Laboratories, op. cit.

8. U. S. Bureau of the Census, 1992 Truck Inventory and Use Survey, May 1995.

9. In earlier versions of HERS, Steps 2 and 3 were not performed. Thus, usage-related depreciation was included in

HERS estimates of travel-time costs as well as HERS estimates of operating costs. The new procedure is designed

to eliminate this double counting.
Cost and Benefit Calculations

5-4

value at the end, with initial cost from the American Automobile Manufacturers Association10)

divided by 2,000 hours per year of sign-out time (essentially the day shift or other shift when

maximal vehicle use occurs). For heavier trucks, total depreciation per hour was computed as

the average vehicle cost per year11 divided by the number of hours in service per year. Six-tire

trucks and four-axle combination trucks were assumed to be in service 2,000 hours per year; and

five-axle combinations were assumed to be in service 2,200 hours per year. Because three- and

four-axle single-unit trucks include many dump trucks that have down time between jobs, especially during cold periods of the winter, they were assumed to be used only 1,600 hours per year.

The resulting estimates of total depreciation per hour of operation are shown in the first column

of Table 5-2. The relatively high value shown for three- and four-axle single-unit trucks is the

result of the low number of hours per year that they are used and relatively small differences

between the initial costs of these vehicles and those of tractor-trailer combinations. 

The second column of Table 5-2 shows estimates of average annual mileage for the seven vehicle

types distinguished by HERS. Annual mileage for automobiles is from Highway Statistics;

12 and

annual mileage for the five categories of trucks is from the 1992 Truck Inventory and Use Survey.

13

The third column of Table 5-2 shows the estimates of mileage-related depreciation, in cents per

mile. The estimates of annual hours of operation presented above and those of annual miles per

year shown in the second column of the table were then used to convert the estimates of mileage10. American Automobile Manufacturers Association, Motor Vehicle Facts and Figures, 1996, Detroit, 1996, p. 60. 

11. Estimates of average vehicle cost per year are those used in the 1997 Federal Highway Cost Allocation Study (U.S.

Department of Transportation, July 1997). Sources used in developing thoses estimates were: Jack Faucett Associates, “The Effect of Size and Weight Limits on Truck Costs,” prepared for the U.S. Department of Transportation,

Federal Highway Administration, Washington, D.C., 1990; Maclean Hunter Market Reports, The Truck Blue Book,

January 1995, Chicago (sales prices for tractors and chassis); U.S. Bureau of the Census, Current Industrial Reports,

Truck Trailers, summaries for various years (price adjustments for trailers); and a survey of truck dealers (prices for

single-unit trucks).

Table 5-2. Estimation of Vehicle Costs (1995 Dollars)

Vehicle Type

Total 

Depreciation 

($/hr.)

Miles per 

Yeara

a. For automobiles, from Federal Highway Administration, Highway Statistics 1997, November 1999, Table VM-1;

for trucks, from U. S. Bureau of the Census, 1992 Truck Inventory and Use Survey, May 1995, Table 2a.

Mileage-Related 

Depreciation Time-Related 

Depreciation 

($/hr.) ($/mile) ($/hr.)

Small Autos $ 1.72 11,575 $ 0.109 $ 0.63 $ 1.09

Medium/Large Autos 2.02 11,575 0.098 0.57 1.45

Four-Tire Trucks 2.18 12,371 0.045 0.28 1.90

Six-Tire Trucks 3.08 10,952 0.079 0.43 2.65

3+ Axle Trucks 8.80 15,025 0.175 1.64 7.16

3-4 Axle Combinations 7.42 35,274 0.057 1.01 6.41

5+ Axle Combinations 7.98 66,710 0.060 1.82 6.16

12. Federal Highway Administration, Highway Statistics 1997, November 1999, Table VM-1.

13. Op. cit., Table 2a.
HERS Technical Report v3.54

September 2002

5-5

related depreciation to dollars per hour (as shown in the fourth column); and this result was subtracted from total depreciation to produce the estimates of time-related depreciation that are

shown in the last column of Table 5-2, and also in Row 3 of Table 5-1.

The estimates of time-related depreciation and mileage-related depreciation shown in the fourth

and fifth columns of Table 5-2 are internally consistent in that, for each vehicle type, the two values add up to the estimate of total depreciation (in the first column). These two sets of estimates

are thus appropriate for use by HERS (or by any similar system making joint use of both sets of

estimates). However, some of the individual values in the last three columns do raise questions.

In particular, the values for mileage-related depreciation for trucks appear to be low relative to

the corresponding values for automobiles.14 A brief investigation into the causes of this result

suggests that it probably is due to differences between the procedures used for automobiles and

those used for trucks in the original estimation of mileage-related depreciation.15

5.1.1.5 Inventory Costs

To compute the inventory costs for five-axle combination trucks, an hourly discount rate was

computed and multiplied by the value of a composite average shipment. The discount rate

selected was 9.8 percent, equal to the average prime bank lending rate in 1995 plus one percent.

Dividing this rate by the number of hours in a year produces an hourly discount rate is 0.0033

percent. The average payload of a five-axle combination is about 35,000 pounds. In 1993, the

average value of commodities shipped by truck was $1.35 per pound (on a ton-mile weighted

basis).17 Inflating to 1995 dollars using the GDP deflator and multiplying by the average payload produces an average payload value of roughly $50,000. The resulting time value of the

average payload is approximately $0.60 per hour (ignoring any costs for spoilage and depreciation over time).

Payload for four-axle combination trucks is lower than for five-axle combination trucks, but the

value of the cargo probably is higher. Consequently, the value per shipment was assumed to be

the same for both types of trucks.

5.1.1.6 Estimating Travel Time Costs

For each vehicle type, these values are used by HERS to develop estimates of travel time costs on

each section from the equation:

Eq. 5.1

where:

14. A comparison of Columns 4 and 1 indicates that mileage-related depreciation accounts for 28 percent of total

depreciation of medium/large automobiles and 37 percent of depreciation for small automobiles. The corresponding figures for the three types of single-unit trucks are only about half as large (13 to 19 percent). Even for five-axle

combinations, which have average annual mileages that are five times those of automobiles, mileage-related

depreciation represents only 23 percent of total depreciation. Observing that styling obsolescence is a significant

contributor to time-related depreciation for automobiles but not for trucks, this suggests that, for vehicles with

comparable annual mileages, mileage-related depreciation probably should be smaller for automobiles than for

trucks. 

15. J. P. Zaniewski, et. al., Vehicle Operating Costs, Fuel Consumption, and Pavement Type and Condition Factors, Texas

Research and Development Foundation, prepared for FHWA, June 1982, pp. 60-67.

TTCSTvt

1000

AESvt

--------------- TTVALvt = ×
Cost and Benefit Calculations

5-6

TTCSTvt = average travel-time cost (in 1995 dollars per thousand vehiclemiles) for vehicles of type vt;

AESvt = average effective speed of vehicles of type vt on the highway section being analyzed; and

TTVALvt = average value of time (in 1995 dollars) for occupants and cargo of

vehicles of type vt (as shown on the bottom line of Table 5-1).

For each section, the average travel-time cost (per thousand vehicle-miles) is obtained by taking

a weighted average of the corresponding costs for each vehicle type. In HERS the weights are

obtained by using section-specific HPMS data on the percentages of four-tire vehicles, singleunit trucks, and combination trucks, and then allocating these percentages to the seven vehicle

types using distributions (by functional system) obtained from the HPMS Vehicle Classification

Study.16 (See paragraph 4.4, ”The Fleet Composition Model.”)

5.1.2 Estimating Operating Costs

The cost of operating a vehicle on a given section is a function of costs for fuel, oil, tires, maintenance and repair, and mileage-related depreciation. This section discusses the method by which

HERS estimates operating costs. These estimates exclude the effect of taxes.17

HERS treats operating costs as having three sources, and derives its estimates using a three-step

procedure:

1. Constant-speed operating costs are estimated as a function of average effective speed,

average grade, and PSR;

2. Excess operating costs due to speed-change cycles are estimated; and

3. Excess operating costs due to curves are estimated.

Exhibit 5-1 provides an overview of the operating cost calculations.

The operating cost calculation process, as outlined above and detailed in the paragraphs below,

is performed for each of the seven vehicle types. For the two truck categories the process is performed once for each direction unless free-flow speed and uphill free-flow speed are the same

(see paragraph 4.1.1, “Free-Flow Speed and the APLVM”). The process is performed only once

for four-wheel vehicles, as HERS assumes that grades do not affect free-flow speed for these

vehicles. 

5.1.2.1 Operating Cost Components

HERS v3.54 recognizes five components of operating costs:

• fuel consumption

• oil consumption

16. U. S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System

Analytical Process Technical Manual, Version 2.1, December 1987, Table IV-20.

17. From the standpoint of the user, taxes are part of user costs. However, from the standpoint of the overall economy,

taxes are transfer payments that entail no resource costs.
HERS Technical Report v3.54

September 2002

5-7

• tire wear

• maintenance and repair

• depreciable value.

Exhibit 5-1. Operating Cost Calculation Flow

Constant Speed 

Consumption 

Rates

Effect of Speed 

Variability

Effect of Curves

Operating Cost 

Calculations

Average Effective Speed

1980 Consumption Rates (Zaniewski)

Adjustment Factors (1997)

Free-Flow Speed

Average Travel 

Speed

ADTBS*

Grades

Pavement

Condition

Usage Rates

• Fuel

• Oil

• Tires

• Maintenance and Repair

• Vehicle Depreciation

Curvature

Operating Cost per 

Vehicle Mile

Unit Costs (1997)

*ADTBS = Average Distance Traveled 

Between Stops
Cost and Benefit Calculations

5-8

All five components are included in the calculation of constant-speed costs and excess costs due

to speed change cycles: for excess costs due to curves, only fuel, tire wear, and maintenance and

repair are included. 

5.1.2.1.1 Component Prices 

Table 5-3 shows estimates of component prices in 1997 dollars for use in estimating operating

costs. The sources of these estimates are described below.

Fuel prices for two-axle vehicles were derived by subtracting federal and state gasoline taxes18

from the 1997 retail price of gasoline, and fuel prices for larger vehicles were derived by subtracting taxes on diesel fuel from the average 1997 retail price of highway diesel fuel.19

Values for the cost of oil and tires were obtained by applying appropriate price indexes to the

1995 estimates previously developed20 from the original Zaniewski estimates21. The price index

used for oil is the consumer price index (CPI)22 for motor oil, coolant, and fluids (SS47021). Tire

Table 5-3. Component Prices

(1997 dollars)

Vehicle Type Fuel 

($/gallon)

Oil 

($/quart)a

a. The unit cost for oil includes the labor charge for changing the oil.

Tires

 ($/tire)

Maintenance 

and Repair ($/

1,000 miles)

Depreciable 

Value 

($/vehicle)

Automobiles

 Small $0.871 $3.573 $45.2 $84.1 $18,117

 Medium/Large 0.871 3.573 71.5 102.1 21,369

Trucks

 Single Units

 4 Tires 0.871 3.573 78.8 129.8 23,028

 6 Tires 0.871 1.429 190.1 242.9 34,410

 3+ Axles 0.762 1.429 470.7 343.5 75,702

 Combination

 3-4 Axles 0.762 1.429 470.7 355.8 87,690

 5+ Axles 0.762 1.429 470.7 355.8 95,349

18. U. S. Department of Transportation, Federal HIghway Administration, Highway Statistics, 1997, Washington, D.C.,

1998, Table MF-121T.

19. U.S. Department of Energy, Energy Information Administration, “On-Highway Diesel Fuel Price Survey,” Form

EIA-888, 1995.

20. Cambridge Systematics, Inc., Revisions to HERS, prepared for the Federal Highway Administration, December

1997, Chapter 7.

21. J.P. Zaniewski, et.al., Vehicle Operating Costs, Fuel Consumption, and Pavement Type and Condition Factors, Texas

Research and Development Foundation, prepared for U.S. Department of Transportation, Federal Highway

Administration, Washington, D.C., June 1982, Table 2, p. 7.

22. U.S. Department of Labor, Bureau of Labor Statistics, Consumer Price Index Database.
HERS Technical Report v3.54

September 2002

5-9

costs were indexed using the CPI for tires (SETC01). The tire-cost index reflects the effects of

improvements in quality (as downward adjustments in the index) - improvements that generally

decrease the rate of tire wear. Maintenance and repair costs were indexed using the CPI for

motor vehicle maintenance and repair (SETD). 

For medium and heavy trucks, following Zaniewski, depreciable value was obtained by subtracting tire costs from the vehicle’s retail price and then subtracting ten percent salvage value.

For the three heaviest vehicles, the vehicle prices were those used by the recent Federal Highway

Cost Allocation Study23 (for three-axle dump trucks and for combinations with a tandem-axle

van semi-trailer). The retail price of a 1995 28,000 pound gross vehicle weight six-tire truck was

obtained from the Truck Blue Book24 and adjusted to include a van body.

For the two classes of automobiles, 1995 depreciable value was obtained by adjusting the 1993

values25 for changes in the average price paid for a new car.26 For four-tire trucks, 1995 depreciable value was obtained judgementally from the 1995 value for medium/large automobiles by

comparing the range of list prices of minivans and sport-utility vehicles to the range for medium

and large automobiles.27 For all vehicle classes, 1997 depreciable value was then obtained by

applying the change in the average price of a new car between 1995 and 1997.

5.1.2.1.2 Adjustment Factors for Consumption Rates

The parameters used by the operating cost equations have been indexed to reflect reductions in

fuel and oil consumption rates and depreciation rates that occurred between 1980 and 2000.

Increases in tire durability are reflected in the consumer and producer price indexes (which have

increased by only a few percent since 1980), so separate adjustments are not needed for changes

in the rate of tire wear. Similarly, no adjustments were made in the amount of maintenance

required; reductions in the requirements for routine maintenance are reflected in the data used

for adjusting maintenance costs per mile through 199528 (but not in the BLS data used for the

1995-2000 adjustment).

The adjustments for changes in fuel efficiency, oil consumption, and vehicle depreciation are discussed below.

23. U. S. Department of Transportation, FHWA, 1997 Federal Highway Cost Allocation Study, August 1997.

24. Maclean Hunter Market Reports, Truck Blue Book, Chicago, January 1995.

25. Cambridge Systematics, Inc., op. cit. The 1993 values were derived from the original Zaniewski values using the

same procedure.

26. U.S. Department of Commerce, Bureau of Economic Analysis, “Average Transaction Price of a New Car,” quoted

in American Automobile Manufacturers Association, Motor Vehicle Facts and Figures, 1996, Detroit, 1996, page 60.

This source provides a better indication of changes in vehicle prices than the appropriate components of the CPI

and PPI, because the latter indexes are adjusted (downward) to exclude the effect on prices of improvements in the

quality of new vehicles. On the other hand, none of the adjustments reflect the effects that some of these improvements have had on servicing requirements or depreciation rates (which, ideally, should be handled by modifying

the operating cost equations for maintenance and repair).

27. The alternative approach of adjusting the original Zaniewski values using data on changes in the price of a new car

was rejected because it does not adequately reflect the increase in the quality of appointments of four-tire trucks

that has occurred during the last several years. The rejected procedure produces a 1995 value of only $17,002

(instead of the $20,742 value actually used).

28. Runzheimer International, quoted in American Automobile Manufacturers Association, Motor Vehicle Facts and

Figures, 1996, Detroit, 1996, p. 58.
Cost and Benefit Calculations

5-10

5.1.2.1.2.1 Fuel Efficiency Adjustment Factor

The fuel efficiency adjustment factors for automobiles and four-tire trucks were obtained by

dividing on-road fuel efficiency for the 2000 fleet of automobiles and light trucks by corresponding 1980 values. The 1980 values were obtained from Energy and Environmental Analysis.29 The

2000 values were developed using the following data from the Transportation Energy Data Book

published annually by Oak Ridge National Laboratory (ORNL):30

• 1976-2000 sales of automobiles and 1970-2000 sales of light trucks

• 1976-2000 EPA fuel efficiencies by vehicle class

• estimated survival rates.

The surviving fleets of pre-1970 light trucks and pre-1976 automobiles were assumed to be three

times the number of surviving 1970 light trucks and 1976 automobiles, respectively. Fuel efficiencies of pre-1976 automobiles were estimated by extrapolation, while fuel efficiencies of pre1976 light trucks were assumed to be the same as those of 1976 light trucks (which are 11 percent

below those of 1977 light trucks). All averaging was performed using fuel consumption rates

(gallons per mile); and in-use fuel efficiency was assumed to be 15 percent below the EPA value.

A single 20-year fuel-efficiency adjustment factor for the three classes of heavy trucks was developed by obtaining the ratio of the 1997 and 1977 fuel-efficiency estimates for in use Class 8 trucks

developed by ORNL using data from the Truck Inventory and Use Survey (TIUS). The relatively

modest increase in fuel efficiency (39.6 percent over 20 years) is due, in part, to increases in vehicle weights.

The fuel efficiency adjustment factor for six-tire trucks was similarly developed from TIUS data

using a weighted average of fuel efficiency estimates for Class 6 trucks (19,500 to 26,000 pound

gross vehicle weight). Class 6 is the largest of the five truck classes (Classes 3-7) that consist primarily of six-tire trucks. Use of data for a single truck class minimizes the effect of changes in the

mix of six-tire vehicles occurring over the period.

The resulting fuel efficiency adjustment factors are shown in Table 5-4. 

5.1.2.1.2.2 Oil Consumption Adjustment Factor

The most common recommended oil-change interval for new automobiles was 7,500 miles in

both 1980 and 2000. However, for various reasons, some slight reduction in oil consumption

between these two years was likely. (These reasons include a reduction in the number of older

cars with shorter oil-change intervals and reduced burning of oil.) Accordingly, an oil-consumption reduction factor of 1.05 was assumed for all vehicle classes.

5.1.2.1.2.3 Depreciation Rate Adjustment Factor

The average age of the automobile fleet increased from 6.6 years in 1980 to 8.6 years in 1996.31

Extrapolating to 2000, we estimate average age to be 9.1 years, suggesting a 38 percent increase

29. Energy and Environmental Analysis, Inc., The Motor Fuel Consumption Model: Thirteenth Periodical Report, prepared

for the U.S. Department of Energy, Washington, D.C., January 1988, page B-1.

30. Oak Ridge National Laboratory, Transportation Energy Data Book, various editions.

31. R. L. Polk and Company, as quoted in American Automobile Manufacturers Association, Motor Vehicle Facts and

Figures, 1996, Detroit, 1996, p. 39.
HERS Technical Report v3.54

September 2002

5-11

in longevity (or a decline in the average rate of depreciation of about 28 percent). The same

increase in average longevity was assumed for trucks.

5.1.2.2 Constant-Speed Operating Costs

For each vehicle type (vt), constant-speed operating cost per thousand vehicle-miles (CSOPCST)

is estimated as the sum of five cost components representing costs for fuel, oil, tires, maintenance

and repair, and vehicle depreciation. The overall equation for combining these components is:

Eq. 5.2

where:

CSOPCSTvt = constant speed operating cost for vehicle type vt;

CSFC = constant speed fuel consumption rate (gallons/1000 miles);

CSOC = constant speed oil consumption rate (quarts/1000 miles);

CSTW = constant speed tire wear rate (% worn/1000 miles);

CSMR = constant speed maintenance and repair rate (% of average cost/

1000 miles);

CSVD = constant speed depreciation rate (% of new price/1000 miles);

PCAFFC = pavement condition adjustment factor for fuel consumption;

PCAFOC = pavement condition adjustment factor for oil consumption;

PCAFTW = pavement condition adjustment factor for tire wear;

PCAFMR = pavement condition adjustment factor for maintenance and repair;

PCAFVD = pavement condition adjustment factor for depreciation expenses;

COSTFvt = unit cost of fuel for vehicle type vt;

COSTOvt = unit cost of oil for vehicle type vt;

COSTTvt = unit cost of tires for vehicle type vt;

COSTMRvt = unit cost of maintenance and repair for vehicle type vt;

COSTVvt = depreciable value for vehicle type vt;

Table 5-4. Fuel Efficiency Adjustment Factors

(1997 Factors)

Vehicle Type Factor

Small Automobiles 1.550

Medium/Large Automobiles 1.550

4-Tire Trucks 1.666

6-Tire Trucks 1.344

3+ Axle Trucks 1.396

3-4 Axle Combinations 1.396

5+ Axle Combinations 1.396

CSOPCSTvt CSFC PCAFFC COSTFvt FEAFvt

+ CSOC

= × × ⁄

PCAFOC COSTOvt OCAFvt × × ⁄

0.01 × CSTW PCAFTW COSTTvt TWAFvt × × ⁄

0.01 × CSMR PCAFMR COSTMRvt × ×

+

+ MRAFvt ⁄

0.01 × CSVD PCAFVD COSTVvt + × × VDAFvt ⁄
Cost and Benefit Calculations

5-12

FEAFvt = fuel efficiency adjustment factor for vehicle type vt;

OCAFvt = oil consumption adjustment factor for vehicle type vt;

TWAFvt = tire wear adjustment factor for vehicle type vt;

MRAFvt = maintenance and repair adjustment factor for vehicle type vt; and

VDAFvt = depreciation adjustment factor for vehicle type vt.

Equations for estimating constant-speed consumption rates for fuel, oil, tires, maintenance and

repair, and vehicle depreciation are shown in Tables D-1 through D-7 in Appendix D, ”Operating Cost Equations.” In these equations, AES is average effective speed in miles per hour (an

output of the speed model), and GR is grade (in percent). The equations were estimated by

applying ordinary least squares regression to the consumption tables presented in Zaniewski,32

and have been modified to handle the higher speeds that HERS will encounter as a result of the

recent increase in speed limits. 

The Zaniewski tables represent estimated consumption rates for equipment in use in 1980 on

roads with PSR = 3.5. Exhibit D-8, “Medium/Large Automobile Constant-Speed Oil Consumption,” presents equations for estimating pavement-condition adjustment factors for oil consumption, tire wear, maintenance and repair, and vehicle depreciation. These equations also were

estimated by applying ordinary least squares regression to the adjustment factors presented in

Zaniewski.33 

Zaniewski does not provide pavement-condition adjustment factors for fuel consumption.

Accordingly, the corresponding adjustment factor used for HERS v3.54 is set to one. However,

the factor has been included in the code for symmetry and to allow development of such a factor

in the future.

5.1.2.3 The Effect of Speed-Change Cycles

HERS calculates excess operating costs due to speed-change cycles (or speed variability) for sections which have stop signs or traffic signals. The overall formula for calculating these costs is

similar to that for constant speed operating costs (see Equation 5.2) with two exceptions: the

consumption rates are derived from a different set of equations, and no pavement condition

adjustment factors are used. For each vehicle type (vt), excess operating costs per thousand vehicle-miles due to speed variability (VSOPCST) is estimated:

Eq. 5.3

where:

VSOPCSTvt = excess operating cost due to speed variability for vehicle type vt;

VSFC = excess fuel consumption rate due to speed variability (gallons/

1000 miles);

32. Op. cit., Appendix B.

33. Ibid., Figure 5 and Tables 12, 15, and 19.

VSOPCSTvt VSFC COSTFvt FEAFvt × ⁄

VSOC COSTOvt OCAFvt × ⁄

VSTW COSTTvt TWAFvt × ⁄

VSMR COSTMRvt MRAFvt × ⁄

VSVD COSTVvt VDAFvt × ⁄

+

+

+

+

=
HERS Technical Report v3.54

September 2002

5-13

VSOC = excess oil consumption rate due to speed variability (quarts/1000

miles);

VSTW = excess speed tire wear rate due to speed variability (% worn/1000

miles);

VSMR = excess speed maintenance and repair rate due to speed variability

(% of average cost/1000 miles);

VSVD = excess depreciation rate due to speed variability (% of new price/

1000 miles);

COSTFvt = unit cost of fuel for vehicle type vt;

COSTOvt = unit cost of oil for vehicle type vt;

COSTTvt = unit cost of tires for vehicle type vt;

COSTMRvt = unit cost of maintenance and repair for vehicle type vt;

COSTVvt = depreciable value for vehicle type vt;

FEAFvt = fuel efficiency adjustment factor for vehicle type vt;

OCAFvt = oil efficiency adjustment factor for vehicle type vt;

TWAFvt = tire wear efficiency adjustment factor for vehicle type vt;

MRAFvt = maintenance and repair efficiency adjustment factor for vehicle

type vt; and

VDAFvt = depreciation adjustment factor for vehicle type vt.

These equations were also derived from Zaniewski, and are only applied to sections with stop

signs or traffic signals. The equations are shown in Tables D-9 through D-15 in Appendix D.

Signals and stop signs (as a group) are assumed to be uniformly spaced on each section. (This

assumption is also used in the speed model.) Sections with both signals and stop signs are

treated as having all signals at one end of the section and all stop signs at the other end. The two

portions of the sections are analyzed separately, producing separate estimates of excess costs per

1000 cycles for the stop-sign and traffic signal portions of the section.

For each section, the estimates of excess costs per 1000 cycles are converted to excess costs per

1000 miles by dividing by the average distance between stops for stop signs and traffic signals.

For traffic signals, this denominator reflects an adjustment for the probability of actually being

stopped at a traffic signal. If both stop signs and traffic signals exist on the section, the sum of

the excess costs for the two parts of the section is used.

5.1.2.4 The Effect of Curves 

HERS uses the original Zaniewski tables34 and equations derived from those tables for estimating excess operating costs due to curves. Two-dimensional linear interpolation of table values is

used for sections with average effective speed below 55 m.p.h., and equations fit to the tables are

used for sections with average effective speed above 55 m.p.h. On sections with zero degrees of

curvature, excess costs are set to zero.

For medium and high speeds (generally above 40 m.p.h.), the Zaniewski values for excess costs

due to curves with one degree of curvature are higher (and sometimes substantially higher) than

those due to curves with two degrees of curvature. The values for one degree of curvature were

deemed to be excessive and were ignored in estimating the equations for average effective

speeds above 55 m.p.h. Similarly, the questionably high values for one degree of curvature were

34. Ibid., Appendix A, Tables A.73-A.80.
Cost and Benefit Calculations

5-14

modified to more reasonable values in the tables used for sections with average effective speeds

below 55 m.p.h.

5.1.2.4.1 Sections With AES Below 55 M.P.H.

HERS uses the individual Zaniewski tables for the effects of curves on fuel consumption, tire

wear, and maintenance and repair. (The effects of curves on vehicle depreciation and oil consumption were assumed to be negligible by Zaniewski.) During program initialization, the values in these tables are:

1. Multiplied by exogenously specified factors representing improvements since 1980 in

fuel consumption, tire wear, and maintenance and repair;

2. Multiplied by exogenously specified unit prices; and

3. Summed.

The result is a single table of excess costs due to curves for each vehicle type (in dollars per 1000

vehicle miles) as a function of curvature and speed (up to 55 m.p.h.). For individual sections,

excess costs due to curves for each vehicle type are estimated using average effective speed and

curvature on the sections and using two-dimensional linear interpolation between entries in the

table. 

5.1.2.4.2 Sections with AES Above 55 M.P.H.

For sections with average effective speeds equal to or greater than 55 m.p.h., HERS uses equations fit to the Zaniewski values given for speeds of 55-70 m.p.h. and two degrees of curvature or

more. Equations for use with sections having two or less degrees of curvature were devised to

match the modified table values. Similar to the overall formula for constant-speed operating

costs, HERS calculates the excess cost due to curves (COPCST) for each vehicle type on sections

with average effective speed greater than 55 m.p.h.:

Eq. 5.4

where:

COPCSTvt = excess operating cost due to curves for vehicle class vt;

CFC = excess fuel consumption rate due to curves (gallons/1000 miles);

CTW = excess tire wear rate due to curves (% worn/1000 miles);

CMR = excess maintenance and repair rate due to curves (% of average

cost/1000 miles);

COSTFvt = unit cost of fuel for vehicle type vt;

COSTTvt = unit cost of tires for vehicle type vt;

COSTMRvt = unit cost of maintenance and repair for vehicle type vt;

FEAFvt = fuel efficiency adjustment factor for vehicle type vt;

TWAFvt = tire wear adjustment factor for vehicle type vt; and

MRAFvt = maintenance and repair adjustment factor for vehicle type vt.

COPCSTvt CFC COSTFvt FEAFvt × ⁄

0.01 × CTW COSTTvt TWAFvt × ⁄

0.01 × CMR COSTMRct MRAFvt × ⁄

+

+

=
HERS Technical Report v3.54

September 2002

5-15

The equations used to produce CFC, CTW, and CMR are shown in Tables D-16 through D-22 of

Appendix D.

5.1.2.5 Total Operating Costs

The HERS operating cost process is implemented as two nested loops. The outer loop propels

the model through each vehicle type in turn. The inner loop is executed twice, once in each

direction for each vehicle type. The calculation of the three categories of operating costs is performed within this inner loop. When operating costs in both directions for all vehicle types have

been calculated, the model weights the costs using the procedures in paragraph 4.4, ”The Fleet

Composition Model,” to arrive at the total operating cost per vehicle mile over the section.

5.1.3 Safety Costs

The HERS safety analysis is a three-step procedure:

1. Estimate numbers of crashes using separate procedures for each of six facility types;

2. Apply functional-class-specific injury/crash ratios and fatality/crash ratios to estimate

numbers of injuries and fatalities; and

3. Multiply by appropriate cost parameters to produce estimates of the total cost of crashes.

The procedures for estimating the number of crashes are described and documented in the next

paragraph. The subsequent paragraph, 5.1.3.2, ”Fatalities and Injuries,” presents the injury/

crash ratios and fatality/crash ratios. Paragraph 5.1.3.3, ”Secular Trends,” develops estimates,

for use by HERS, of the extent to which recent secular declines in crash rates, fatality/crash

ratios, and injury/crash ratios are due to factors not analyzed by HERS. In paragraph 5.1.3.4,

”Costs of Crashes,” data from a recent report by the National Highway Traffic Safety Administration (NHTSA) is used to update HERS’ estimates of costs per injury and property damage

costs per crash, as well as to provide estimates of the cost of travel-time delay per crash.

5.1.3.1 Crash Rates

HERS estimates the numbers of crashes and crash rates using separate procedures for three types

of rural facility and three types of urban facility. The facility types distinguished are:

• freeways (by design);

• multi-lane roads and streets; and

• two-lane roads and streets.

The freeway procedures are used for all divided roads35 with four or more lanes and full access

control, and also for all one-way roads with two or more lanes and full access control. These pro35. For the purpose of the safety analysis, a divided road has a positive barrier median or a median width of at least

four feet. This definition is slightly narrower than the HPMS definition of a divided (FHWA, Highway Performance

Monitoring System Field Manual, Appendix I, pp. I-1 and I-8, January 1998). The HPMS definition, which is used by

the HERS capacity procedures, also classifies roads with curbed medians of any width as being divided. Because

narrow curbed medians provide relatively limited protection from median crossing, our safety procedure treats

roads with curbed medians and median widths of less than four feet as being undivided.
Cost and Benefit Calculations

5-16

cedures are used for these roads regardless of functional system. For all other facilities with four

or more lanes and all other one-way facilities with two or three lanes, the “multi-lane” procedures are used, again regardless of functional system. Finally, the “two-lane” procedures are

used for all two-way facilities with fewer than four lanes and for all one-lane facilities.

Five of the procedures are slightly modified versions of procedures recommended by Richard

Margiotta based on an extensive review of the literature.36 The sixth procedure is derived from

the results of an analysis by Vogt and Bared37 that was performed after the completion of Margiotta’s work.

All procedures were modified to produce estimates of crash rates per 100 million vehicle-miles

of travel (VMT) and calibrated to crash-rate data for 1995. The six procedures (after calibration)

are described in paragraphs 5.1.3.1.1 through 5.1.3.1.6, and the calibration is described in paragraph 5.1.3.1.7. 

5.1.3.1.1 Rural Two-Lane Roads

The procedure for estimating crashes on rural two-lane roads develops separate estimates of

crashes within 250 feet of an intersection and crashes on segments between intersections. Both

sets of estimates are developed using equations based on those developed by Vogt and Bared.38

These estimates are then combined:

Eq. 5.5

where

CRASH = total number of crashes on the section per 100 million VMT;

CNINT = non-intersection crashes per 100 million VMT;

CINT = crashes occurring within 250 feet of an intersection, per 100 million

VMT on the section;

and 1.056 is the calibration factor developed in paragraph 5.1.3.1.7, ”Calibration.” The procedures for estimating CNINT and CINT are presented below.

5.1.3.1.1.1 Non-intersection Crashes

The equation for estimating non-intersection crashes is based on an equation developed by Vogt

and Bared using Highway Safety Information System (HSIS) data for Minnesota and Washington.39 The HERS equation is:

36. Richard Margiotta, Incorporating Traffic Crash and Incident Information into the Highway Performance Monitoring System Analytical Process, prepared by COMSIS Corporation and Science Applications International Corporation for

FHWA, September 1996, Chapter 2.

37. Andrew Vogt and Joe Bared, “Accident Models for Two-Lane Rural Segments and Intersections,” presented at the

TRB Annual Meeting, January 1998.

38. Ibid.

39. Ibid., p. 6. Vogt and Bared also use the data from Minnesota and Washington separately to develop two additional

equations for non-intersection crashes (p. 5).

CRASH = 1.056 × ( ) CNINT CINT +
HERS Technical Report v3.54

September 2002

5-17

Eq. 5.6

where

SLEN = section length (in miles);

ADJSL = section length adjusted to exclude segments within 250 feet of an

intersection;

LW = lane width (in feet);

SHW = shoulder width (in feet);

RHR = roadside hazard rating (3.0);

DD = driveway density (per mile) (3.7 for rural type of development, 50

for dense development);

CURVi = average degrees of curvature in HPMS curve class i;

LCURVi = total length (in miles) of all curves in curve class i; 

GRDi = average percent grade in HPMS grade class i;

LGRDi = total length (in miles) of all grades in grade class i; and

CCGR = crest curve grade rate in percent per hundred feet (zero for flat terrain, 0.03 for hilly terrain, and for mountainous terrain).

In Equation 5.6, HERS uses the factor of 100 to convert the estimate of crashes from being

expressed per million VMT (as in Vogt and Bared) to being expressed per 100 million VMT in

HERS.

The ADJSL/SLEN factor adjusts the estimate of non-intersection crashes to reflect only travel

that occurs more than 250 feet from an intersection. (The procedure treats crashes occurring

within 250 feet of an intersection as intersection crashes.) For this purpose, ADJSL is obtained

from SLEN by subtracting 500/5,280 times the number of intersections; if the result is negative,

ADJSL is set to zero. This adjustment enables the HERS procedure to avoid producing unreasonably high estimates of total crashes for sections with moderate to high numbers of intersections

per mile.40

40. Vogt and Bared did not incorporate an ADJSL/SLEN adjustment in their analysis. The inclusion of this adjustment

in the HERS equation would, by itself, reduce HERS’ estimate of total crashes on rural two-lane roads. However,

since the HERS estimates are calibrated to 1995 data, the actual effect of the adjustment is to increase the size of the

calibration factor (1.056 in Equation 5.5), leaving the estimate of total crashes unchanged but shifting some crashes

from sections with high numbers of intersections per mile to sections with lower numbers of intersections per mile.

CNINT 100 × ADJSL SLEN ⁄

0.72 0.085 LW 0.059 SHW 0.067 RHR 0.0085 DD

+ 0.44 × CCGR

( – × – × + × + ×

)

× exp

LCURVi 0.045 CURVi × exp( ) ×

i

∑      SLEN

   

× ⁄

=
Cost and Benefit Calculations

5-18

Vogt and Bared use a dummy variable, STATE, to distinguish between Minnesota and Washington data. In Equation 5.6, STATE has been set to 0.5 (effectively weighting data from both states

equally), and the term corresponding to STATE has been combined with the constant term to

produce a modified constant term (0.72).

The value used in Equation 5.6 for the roadside hazard rating (RHR) is 3.0, which approximates

the average value for all sections used in the Vogt and Bared analysis.

The values used for driveway density (DD) are assumed to vary by type of development. For

rural development, driveway density should be somewhat below the median for rural types of

development, and for dense development it should be appreciably higher. The median values in

the data used by Vogt and Bared are 3.73 for Minnesota and 6.12 for Washington; the means are

6.58 and 10.12, respectively; and the maxima are 85.1 and 100, respectively. This data suggests

that it is appropriate to set DD to 3.7 where development is rural and to set it to 50 where development is dense. When these values are used with 1995 HPMS data, the VMT-weighted average

value of DD is 8.29, just slightly below 8.35, the unweighted average of the means for Minnesota

and Washington. (The value of 50 for dense development implies an average of 211 feet between

driveways.)

The values for crest curve grade rate (CCGR) were also based on a judgmental review of Vogt

and Bared data. In their data, the median values for this variable were 0.024 in Washington and

0.037 in Minnesota, suggesting that 0.03 is a reasonably typical value for hilly terrain. Similarly,

the maximum value was 2.0 in Washington (and 0.89 in Minnesota). Since most crests can be

assumed to have CCGR values that are appreciably below the maximum, a typical value of 0.4

was assumed for mountainous terrain. Finally, for flat terrain, CCGR values are likely to be zero

or close to zero; accordingly, a value of zero was used.

Finally, if necessary, the HPMS-coded lengths of curves (LCURVi

) are scaled so that their sum

equals the coded section length (SLEN); and, if necessary, a corresponding adjustment is made to

the lengths of the grades (LGRDi

).41

5.1.3.1.1.2 Intersection Crashes

Vogt and Bared used HSIS data for Minnesota to develop separate equations for estimating

crashes at three-legged intersections and crashes at four-legged intersections. The HPMS database does not distinguish between three and four-legged intersections, but it does distinguish

between:

1. Intersections with traffic signals; 

2. Intersections with stop signs on the sample section; and

3. All other intersections.

To avoid double-counting, HERS assigns all crashes at the second type of intersection to the

intersecting road and all crashes at the third type to the sample section. A portion of crashes at

intersections with traffic signals are assigned to the sample section using assumptions presented

subsequently.

41. The adjustments are made in the HERS preprocessor and are applied to all sections for which curves or grades are

coded. (Previously, adjustments were made when the total length of curves (or grades) exceeded coded section

length but not when they were less than coded section length.)
HERS Technical Report v3.54

September 2002

5-19

HERS treats all signalized intersections as four-legged intersections. “Other” intersections (i.e.,

Type 3 intersections) are treated as a mix of three- and four-legged intersections by using a

weighted average of the two Vogt and Bared equations. The weights used are 0.55 for threelegged intersections and 0.45 for four-legged intersections.42 Since all crashes at intersections

with stop signs are assigned to the intersecting road, crashes at these intersections are not estimated.

With the above assumptions, estimates of the number of crashes at intersections are obtained

from the following equations:

Eq. 5.7

Eq. 5.8

Eq. 5.9

Eq. 5.10

 where CINT and CCGR43 have been defined above and the other variables are:

VMT = vehicle miles traveled on the section in one year;

CSINT = annual crashes at signalized intersections;

COINT4 = annual crashes at “other” four-legged intersections (i.e., intersections with neither signals nor stop signs on the sample section);

COINT3 = annual crashes at “other” three-legged intersections;

NSIG = number of signalized intersections;

FSICAS = AADT/(ADT1+ADT2) = fraction of total AADT on the inventoried

section;

ADT1 = at signalized intersections, AADT on the road with the higher traffic volume;

ADT2 = at any intersection, AADT on the road with the lower traffic volume;

ADJIA = “adjusted intersection angle” (2.0);

42. The database used by Vogt and Bared contained data for 389 three-legged intersections and 327 four-legged intersections. The weights used were obtained by reducing the latter figure by an estimate of the number of signalized

intersections (based on 1995 HPMS data), all of which are treated as four-legged intersections by the HERS procedure.

43. We considered the possibility that crest curve grade rate and average curvature would have lower values in the

vicinity of an intersection than they would have for the section as a whole. However, this hypothesis was not supported by the data in Vogt and Bared.

CINT 108

VMT = ------------- × ( ) CSINT COINT + + 4 COINT3

CSINT 0.2 × NSIG FSICAS ×

7.74 0.64 ln 0.58 ( ) ADT1 × ln( ) ADT2

0.33 × CCGR – 0.053 × ADJIA + 0.11 × ND

+

+

(– + ×

)

× exp

=

COINT4 0.2 0.45 NOINT

7.74 0.64 ln 0.58 ( ) AADT × ln( ) ADT2

0.33 × CCGR – 0.053 × ADJIA + 0.11 × ND

+

+

(– + ×

)

× exp

= × ×

COINT3 0.2 0.55 NOINT

11.48 0.82 ln 0.51 ( ) AADT × ln( ) ADT2

0.26 CCGR 0.036 DC 0.027 SPDLIM

+ 0.18 × RHR3LI + 0.24 × PRTL

× + × + ×

+

+

(– + ×

)

× exp

= × ×
Cost and Benefit Calculations

5-20

NOINT = number of “other” intersections;

AADT = Annual Average Daily Traffic;

ND = number of driveways within 250 feet of a given intersection =

(500/5,280) x DD;

DC = average degrees of curvature on the section;44

SPDLIM = speed limit (mph);

RHR3LI = roadside hazard rating for three-legged intersections (2.1); and

PRTL = probability that a three-legged intersection has a right-turn lane

(0.42).

In the case of signalized intersections, AADT on intersecting roads is assumed to vary with the

functional class of the road section being analyzed. In the case of principal arterials, the intersecting road is assumed to carry less traffic than the section in question, so ADT1 is set to AADT

and ADT2 is assumed equal to one-half AADT. In the case of major collectors, the reverse is

assumed, so ADT2 is set to AADT and ADT1 is assumed equal to twice AADT. For minor arterials, traffic volumes on both roads are assumed (on average) to be equal, so ADT1 and ADT2 are

both set to AADT.

Crashes at signalized intersections are allocated to the inventoried section and to the intersecting

roads in proportion to their relative traffic volumes. Thus, FSICAS (fraction of signalized-intersection crashes attributed to the inventoried section) is two-thirds for principal arterials, one-half

for minor arterials, and one-third for major collectors.

“Other” intersections are unsignalized intersections which do not have stop signs on the inventoried section. These sections are assumed to have stop signs on the intersecting roads and relatively low volumes on these roads. For these intersections ADT2 is assumed to be the lesser of

500 and one-half AADT. All crashes at these intersections are allocated to the inventoried section

(and all crashes at intersections with stop signs on the inventoried section are allocated to the

intersecting roads).

If the total number of intersections (signalized, stop sign, and “other”) exceeds 20 per mile, the

number of each type of intersection is scaled so that the total is reduced to 20 per mile and the

scaled-down numbers are used for NSIG and NOINT in the above equations (and also for deriving ADJSL for use in Equation 5.6).

Vogt and Bared define “adjusted intersection angle” (ADJIA) to be ( - 15)2/100, where is the

departure of the intersection angle from 90°, measured in degrees. This variable equals 2.25

when = 0° or 30°, equals zero when = 15°, is below 2.0 when is between 1° and 29°, and

exceeds 2.25 when > 30°. The Vogt and Bared data for suggests that 2.0 is a reasonable

average value for ADJIA. 

Vogt and Bared assigned roadside hazard ratings of one to seven for conditions on the main road

within 250 feet of an intersection. The average value of these ratings for three-legged intersections, 2.1, has been adopted as the default value for the corresponding variable (RHR3LI) in

Equation 5.10. Similarly, the default value of 0.42 assumed for the probability that a three-legged

intersection has a right-turn lane (PRTL) represents the fraction of such intersections with rightturn lanes in the data used by Vogt and Bared.

44. See preceding footnote.

α α

α αα

α α
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The factor 0.2 in Equations 5.8 through 5.10 is used to transform the corresponding Vogt and

Bared equations, which estimate intersection crashes over a five-year period, into equations that

produce estimates of the expected numbers of annual crashes.

5.1.3.1.2 Rural Multilane Roads

The equation for estimating the number of crashes per 100 million vehicle-miles on rural multilane roads is:

Eq. 5.11

where:

RHRRML = roadside hazard rating for rural multilane roads (2.45);

AC = 1 for sections with (full or partial) access control,

= 0 for other sections;

DDRML = driveway density (per mile) for rural multilane roads (0.41 for

rural type of development, 5.6 for dense development);

INTSPM = intersections per mile (maximum =10);

RPA = 1 for rural principal arterials and rural Interstate,

= 0 for lower functional systems;

LW = lane width, in feet (between 8 and 13 feet);

SHLDW = right shoulder width, in feet (maximum = 12 feet);

MEDW = 50 if positive barrier median,

= median width, in feet, otherwise (maximum = 50); and 

DEVEL = type of development (1 for rural, 2 for dense).

Equation 5.11 is a modified version of an equation for estimating crashes on rural highways that

was fit to Minnesota HSIS data for rural four-lane roads by Wang, Hughes and Stewart.45 The

following modifications were made to the estimated equation:

• The equation has been divided by 365 times daily VMT and multiplied by 100 million in

order to produce estimates of crashes per 100 million vehicle-miles instead of annual

crashes.

• The coefficient (132.2) is the product of the coefficient from the original equation (0.0002),

the above adjustment factor (273,973), and a calibration coefficient (2.4123, see paragraph

5.1.3.1.7, “Calibration”).

• A factor, (section length)0.073, has been dropped from the equation since there does not

appear to be any reason for crash rates to vary with section length.

• Signalized intersections (which were excluded from the original analysis) have been

assumed to have the same influence on crash rates as unsignalized intersections (though

45. Jun Wang, Warren Hughes and Richard Stewart, Safety Effects of Cross-Section Design of Rural Four-Lane Highways,

FHWA Report FHWA-RD-98-071, May 1998, Equation 6.

CRASH 132.2 AADT0.073

0.131 RHRRML 0.151 AC 0.034 DDRML

0.078 INTSPM 0.572 RPA 0.0082 12 ( ) – LW

– 0.094 × SHLDW – 0.003 × MEDW + 0.429 × ( ) DEVEL – 1

+ × – × + ×

( × – × + ×

)

× exp

= ×
Cost and Benefit Calculations

5-22

this assumption may actually underestimate their influence).

• For want of HPMS data on turn lanes for rural sections, the original equation’s distinction

between intersections with turn lanes and those without turn lanes has been dropped

and the two terms combined.46

• The value, 2.45, used for roadside hazard rating (RHRRML) approximates the average

value of the ratings used by Wang, Hughes and Stewart.

• Values used for driveway density were obtained by multiplying the corresponding values used for rural two-lane roads by 0.112 (0.112 is the approximate ratio of driveway

density on two-lane rural roads in Minnesota used by Bared and Vogt to the driveway

density on four-lane roads in Minnesota used by Wang, Hughes and Stewart).

• Lane width (which was found not to be a significant variable in the original analysis47)

has been assumed to have one-tenth as much influence as it has for rural two-lane roads

(cf. Equation 5.6); this assumption appears to be more realistic than assuming that crash

rates are totally unaffected by lane width.

• Maximum values of 12 feet for right shoulder width and 50 feet for median width have

been assumed, as recommended by Margiotta;48 increases in shoulder and median

widths beyond these values are likely to have appreciably smaller effects on crash rates

than would be indicated by the exponential form of Equation 5.11.

• A maximum value of ten has been assumed for INTSPM (intersections per mile). A summary of data used in the original analysis indicates it is unlikely that any of the sections

analyzed in deriving Equation 5.11 had more than ten intersections per mile.49 The equation is relatively sensitive to INTSPM: a value of ten multiplies the result by 2.2; a value

of 20 would multiply the result by 4.8.50

• A barrier median is assumed to have the same effect on crash rates as a 50-foot median.

(Only one of the sections originally studied had a barrier median, so this effect could not

be analyzed.)

• The HPMS and HERS variable “type of development” (rural dense or rural rural) is

assumed to be a reasonable proxy for the “area location type” variable (rural municipal

or rural non-municipal) used in the original analysis, though the match may be imperfect. (“Rural municipal” may include some small urban places that would be coded as

“urban” by HPMS and HERS, and it may exclude some small rural developments that

would be coded as “rural dense” by HPMS and HERS.)

46. The coefficient (0.078) of the combined term was obtained as a weighted average of the original coefficients, using

data from Wang, Hughes and Stewart to obtain weights representing the approximate number of intersections

with turn lanes per mile (0.22) and the approximate number of intersections without turn lanes per mile (0.74).

47. The variable actually used by Wang, Hughes and Stewart was width of road surface.

48. Op. cit., Figure 2.9.

49. Wang, Hughes and Stewart, op. cit., Table 2.

50. The current HPMS database has a moderate number of sections with 20 or more intersections per mile.
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5.1.3.1.3 Rural Freeways

The equation for estimating the number of crashes per 100 million vehicle-miles on rural freeways is:

Eq. 5.12

This equation incorporates a lane-width factor into an equation originally developed by Persaud51 for four-lane freeways and calibrated to HPMS data for all rural freeways. The effect of

lane width (LW) is assumed to be the same as that assumed for other rural multilane roads. The

variables used by this equation have been defined previously.

Persaud’s equation actually estimates crashes per mile per year. Equation 5.12 was derived from

Persaud’s equation by multiplying by section length, dividing by annual VMT (equal to

365×AADT×section length), multiplying by 108, and multiplying by the estimated calibration

factor (0.8442).

Persaud also derived a separate equation for rural freeways with more than four lanes. However, for any value of AADT, the equation for freeways with more than four lanes produces

appreciably higher crash rates than the equation for freeways with four lanes, implying that

crash rates vary inversely with congestion. This result is inconsistent with those of most other

analyses.52, 53

5.1.3.1.4 Urban Freeways

The equation for estimating the number of crashes per 100 million vehicle-miles on urban freeways is:

Eq. 5.13

where ACR = AADT divided by two-way hourly capacity and the other variables have been

defined previously. This equation incorporates a lane-width factor into an equation developed

by Margiotta54 using results from Tedesco, et. al.,

55 and Margiotta and Cohen.56 The effect of

lane width is assumed to be the same as that assumed for rural multilane roads.

51. B. N. Persaud, Roadway Safety: A Review of the Ontario Experience and of Relevant Work Elsewhere, prepared for the

Ministry of Transportation, Ontario, 1992.

52. See B. Persaud and L. Dzbik, “Accident Prediction Models for Freeways,” Transportation Research Record 1401, 1993.

53. For low values of AADT (less than 24,000), crash rates were also found to be higher on freeways with more than

four lanes in FHWA’s Highway User Investment Study (as reported in HPMS Analytical Process, Volume II, Technical

Manual, 1987, page IV-41 and Appendix J). However, this result is of little significance since very few freeways

with such low values of AADT have more than four lanes. To enable HERS and the AP to avoid assuming that

adding lanes to four-lane freeways will increase crashes, Margiotta recommended that only Persaud’s equation for

four-lane freeways be used.

54. Richard Margiotta, op. cit., pp.15-19, 25 and 28.

55. Shelby A. Tedesco, et. al., “Development of a Safety Model to Assess the Impact of Implementing IVHS User Services,” Proceedings of the IVHS America 1994 Annual Meeting, April 1994.

56. Richard Margiotta and Harry Cohen, Roadway Usage Patterns: Urban Case Studies, prepared by Science Applications International Corporation and Cambridge Systematics for Volpe National Transportation Systems Center,

June 1994.

CRASH 17.64 AADT0.155 = × × exp( ) 0.0082 12 × ( ) – LW

CRASH 154.0 1.203 ACR 0.258 ACR2 0.00000524 ACR5 ( ) – × + × – ×

× exp( ) 0.0082 12 × ( ) – LW

=
Cost and Benefit Calculations

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5.1.3.1.5 Urban Multilane Surface Streets

The equation for estimating the number of crashes on urban multilane surface streets and on

urban expressways lacking full access control is:

Eq. 5.14

where:

A, B, and C = values from Table 5-5; and

NSIGPM = number of signals per mile.

The value of NSIGPM, the number of signals per mile, has a minimum value of 0.1 and a maximum value of eight. This equation was derived from an equation for estimating annual crashes

per mile that was estimated by Margiotta57 using data from Bowman and Vecellio.58 The derivation involved multiplying Margiotta’s equations by section length, dividing by annual VMT,

multiplying by 108, and incorporating calibration factors. The upper and lower limits on the

number of signals per mile were recommended by Margiotta.

5.1.3.1.6 Urban Two-Lane Streets

For two- and three-lane urban streets, crashes are estimated using the equation:

Eq. 5.15

This equation was developed by using ordinary least squares regression to fit a function of this

form to the data shown in Table 5-6 and multiplying by the calibration factor in Table 5-7. The r2

for this regression is 0.99. 

5.1.3.1.7 Calibration

The crash-rate equations were calibrated in two steps.

57. Op. cit., pp. 19-22, 25 and 29.

58. Brian L. Bowman and Robert L. Vecellio, “Effect of Urban and Suburban Median Types on Both Vehicular and

Pedestrian Safety,” Transportation Research Record 1445, 1994, pp. 169-179. This source actually provided data

only for roads with raised medians, roads with two-way left-turn lanes, and other undivided roads. (Roads with

two-way left-turn lanes are considered to be divided roads in the safety literature and are treated as such in this

report; however, they are classified as undivided in the HERS and HPMS capacity analyses.)

Table 5-5. Parameters for Crash-Rate Equation for Urban Multilane Surface Streets

Type of Section A B C

Two-Way with Left-Turn Lane 95.1 0.1498 0.4011

One-Way, or Two-Way with a median:

 1) wider than 4 feet, or

 2) curbed, or

 3) a “positive barrier”

82.6 0.1749 0.2515

Otherwise 115.8 0.1749 0.2515

CRASH A AADTB NSIGPMC = × ×

CRASH –19.6 ln 7.93 ( ) AADT ( ) ln( ) AADT 2 = × + ×
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In the first step, the equations used by the six procedures presented above were calibrated separately to crash rates for the corresponding highway types. These rates were obtained by Margiotta59 as a VMT-weighted average of rates developed by Zegeer and Williams60 using data for

four states from the HSIS. The rates used are shown in the first column of Table 5-7, “Crash

Rates Used for Calibration.” 

Table 5-6. Data Used for Estimating Crash Rates for Urban Two-Lane Streets

AADT Range Mean Value of AADT 

Within Rangea Crashes per 100 

Million VMTb

< 4,000 1,978 345

4,000 - 7,999 5,739 490

8,000 - 15,999 11,101 590

> 15,999 20,417 660

a. Weighted average mean value obtained from the 1995 HPMS database for streets to

which the “two-lane urban streets” procedure is applied (i.e., all one-lane urban streets and two-way urban streets with two or three lanes).

b. Crash rates used in original HERS safety procedure.

59. Margiotta, op. cit., pp. 7-8.

60. C.V. Zegeer and C. Williams, Calculation of Accident Rates by Roadway Class for HSIS States, University of North

Carolina Highway Research Center, June 1994. The four states used were Illinois, Maine, Minnesota and Utah.

This source contains crash rates for five states. However, rates for the fifth state, Michigan, are appreciably higher

than those for the other four states (for rural areas, they are, on average, twice as high). Accordingly, Michigan

data were excluded from our calibration.

Table 5-7. Crash Rates Used for Calibrationa

Facility Crashes per 100 

million VMT

Calibration 

Factor

Rural

 Freeway 68.0 0.8842

 Multilane 146.6 2.4123

 Two Lane 163.8 1.0557

Urban

 Freeway 131.0 1.1453

 Multilane

 Divided 439.1

 Median 0.9367

 Two-Way Left-Turn Lane 0.7494

 Undivided 554.8 1.3131

 Two-Lane 378.7 0.8743
Cost and Benefit Calculations

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In the second step, the six calibration factors were scaled uniformly to produce an overall rate of

309.7 crashes per 100 million VMT. This rate was obtained by multiplying an estimate of total

crashes in 1995 from the National Highway Traffic Safety Administration’s General Estimates

System (GES)61 by an undercapture correction factor of 1.1262 and dividing by national VMT in

that year.63 64 The calibration factors produced by this two-step procedure are shown in the

right column of Table 5-7, “Crash Rates Used for Calibration.” These factors are included in

Equations 5.5 through 5.15 as presented in paragraphs 5.1.3.1.1 through 5.1.3.1.6.

The calibration factor for urban two-lane streets results from the replacement of the step function

previously used by a continuous function and from a decline in crash rates between 1988 and

1995. (The step function was last calibrated using 1988 data.) The calibration factors for urban

multilane streets incorporate separate calibration factors developed by Margiotta65 for the three

types of multilane streets distinguished.

The other calibration factors generally represent differences, that are not explained by any of the

independent variables, between the crash rates observed in the data used in developing the original equations and the HSIS and national crash rates used in the calibration process. The high

calibration factor for rural multilane roads is due to very low average crash rates in the HSIS data

used by Wang, Hughes and Stewart in their analysis of crash rates on rural multilane roads. The

factor for rural two-lane roads incorporates an upward adjustment to counter the effect of the

ADJSL/SLEN factor that we added to Equation 5.6 (see 5.1.3.1.1.1, ”Non-intersection Crashes”).

5.1.3.2 Fatalities and Injuries

The HERS safety procedure estimates fatalities and nonfatal injuries as being directly proportional to the number of crashes, with separate ratios used for each functional system. The ratios

were obtained by: 

• taking estimates of fatality and crash rates per 100 million vehicle-miles by functional

system for 1995;66 and

a. Derived from rates developed using Highway Safety Information System data for Illi- nois, Maine, Minnesota and Utah. Separate rates were developed for each state by

C.V. Zegeer and C. Williams (Calculation of Accident Rates by Roadway Class for HSIS Status, University of North Carolina Highway Research Center, June 1994). The above rates are VMT-weighted averages of these rates developed (using 1994 HPMS data) by Richard Margiotta (Incorporating Traffic Crash and Incident Information into the Highway Performance Monitoring System Analytical Process, prepared by COMSIS Cor- poration and Science Applications International Corporation for FHWA, September 1996, Table 2.3).

61. National Highway Traffic Safety Administration, Traffic Safety Facts - 1996, Table 1.

62. Lawrence J. Blincoe and Barbara M. Faigin, The Economic Cost of Motor Vehicle Crashes, 1990, NHTSA, Report DOT

HS 807 876, 1992, as quoted in Ted R. Miller, Diane C. Lestina and Rebecca S. Spicer, “Highway Crash Costs in the

United States by Driver, Age, Blood Alcohol Level, Victim Age, and Restraint Use,” Accident Analysis and Prevention, Vol. 30, No. 2, 1998.

63. FHWA, Highway Statistics - 1995, Table VM-1.

64. No adjustment was made for differences in overall crash rates between the nine functional systems covered by

HPMS sample-section data and the three systems (rural minor arterials and the two local systems) that are not covered. To the extent that crash rates on the latter systems may be lower than average, our calibration procedure

may result in a slight upward bias in the HERS estimates of crashes on the nine systems covered by HERS. Since

the other three systems account for only 15 percent of national VMT, the effect of this bias should be fairly small.

65. Op. cit., pp. 25 and 29.

66. FHWA, Highway Statistics, 1995, Table FI-1.
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• dividing by corresponding estimates of the number of crashes per 100 million vehiclemiles by functional system produced by the new HERS procedure for estimating numbers of crashes described in the preceding chapter.67 

The resulting ratios are shown in Table 5-8, “Fatality and Injury Rates.” 

5.1.3.3 Secular Trends

Over time, the rates of injuries and fatalities in highway crashes have shown steady declines. In

the past twenty years, fatalities per 100 million vehicle-miles have declined at an average annual

rate of about four percent, and nonfatal injuries have declined at an average rate of about 2.25

percent.68 Although highway improvements have contributed to this decline, several other factors have been major contributors. These include improvements in: vehicle designs; emergency

medical care; and driver behavior (including reductions in drunk driving).

In order to allow HERS to incorporate the effects of these secular trends into its forecasts of

crashes and crash costs, the safety model allows the user to specify annual percentage declines

in:

• the rate of crashes per 100 million vehicle-miles;

• the ratio of injuries to crashes; and

67. An alternate approach for obtaining ratios by highway type (instead of by functional system) was also investigated. This approach used a calibration process that was more complicated than the one finally adopted, along

with HSIS data on numbers of crashes, fatalities and injuries by highway type in six states, and corresponding estimates of 1995 VMT obtained from HPMS sample-section data. However, the HSIS estimates of the numbers of

crashes on rural multilane roads (and, in particular, undivided rural multilane roads) in these states were found to

be inconsistent with the corresponding HPMS estimates of VMT in these states, making it impractical to calibrate

the equations appropriately.

Table 5-8. Fatality and Injury Rates

Functional System Fatalities per 

Crash

Injuries per 

Crash

Rural

 Interstate 0.01408 0.4546

 Other Principal Arterial 0.01685 0.6317

 Minor Arterial 0.01362 0.5610

 Major Collector 0.01370 0.6261

Urban

 Interstate 0.00382 0.4908

 Other Freeway or Expressway 0.00396 0.3640

 Other Principal Arterial 0.00273 0.4113

 Minor Arterial 0.00237 0.3401

 Collector 0.00257 0.3496

68. Derived from FHWA, Highway Statistics Summary to 1995, July 1997, Tables FI-210 and FI-220.
Cost and Benefit Calculations

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• the ratio of fatalities to crashes.

Estimates of annual crashes for 1988 and subsequent years are available from NHTSA’s General

Estimates System (GES).69 These values, when combined with FHWA’s estimates of annual

fatalities and nonfatal injuries,70 indicate that, over the 1988-1995 period, the average annual

rates of decline have been 1.0 percent for the ratio of (nonfatal) injuries to crashes and 1.3 percent

for the ratio of fatalities to crashes, and the rates of decline since 1990 have been appreciably

higher. Since the ratios developed in paragraph 5.1.3.2 are for 1995, the decline in these ratios is

assumed to begin in 1996. The year of the data used for calibrating the fatality and injury ratios

(currently 1995) is provided to HERS as a parameter and should be changed by the user whenever these ratios are changed.

Obtaining a forecast rate of decline to be applied to crash rates presents a somewhat greater

problem. Combining the GES estimates of annual crashes since 1988 with FHWA estimates of

annual VMT71 produces estimates of crashes per 100 million vehicle-miles that drop from 340 in

1988 to 266 in 1993, rise more slowly to 277 in 1995, and decline very slightly to 276 in 1996. The

average annual rate of decline between 1988 and 1995 (the time period used for estimating the

decline rates for the fatality and injury ratios) is 2.6 percent, but a focus on more recent data

would produce an appreciably lower annual rate of decline (and an increase if only data since

1993 is used72).

As the above discussion implies, data for the last few years suggests that there may be some

weakening in the long-term trends toward reductions in crash, fatality and injury rates. It is not

yet clear whether this weakening represents a temporary or permanent change in the secular

rates of decline in the crash, fatality and injury rates. In preparing data for the 1999 Conditions

and Performance Report, the rate of decline was set to zero (no decline).

5.1.3.4 Costs of Crashes

The HERS safety model estimates crash costs as the sum of the value of lives lost and the costs of

injuries, property damage, and delay to other highway users. The value of lives lost is estimated

by multiplying fatalities by the U.S. Department of Transportation’s estimate of the value of life

(currently $2.7 million). Unit costs for estimating the three other components of crash costs have

been derived in large part from information contained in a recent National Highway Traffic

Safety Administration (NHTSA) study of crash costs in 1994.73

5.1.3.4.1 Unit Costs of Crashes in 1994

HERS’ estimates of injury costs are derived from estimates of comprehensive costs per injury

developed by Ted Miller in 199174 and updated to 1994 dollars by NHTSA.75 These estimates,

69. National Highway Traffic Safety Administration, Traffic Safety Facts – 1996, Table 1.

70. FHWA, op. cit. Estimates of 1996 fatalities and injuries (from Highway Statistics, Table FI-1) were excluded from

this analysis because of inconsistencies between the FI-1 data and the FI-210 and FI-220 data. The latter data is currently being revised.

71. Ibid., Table FI-200; and FHWA, Highway Statistics, 1996, Table VM-1.

72. In another test, the new HERS crash-estimation procedures were applied without a temporal adjustment to 1993

and 1996 HPMS data for 42 states. The procedures indicate a 0.6 percent increase in crash rates over this three-year

period, apparently because of increased congestion. (All six procedures produce estimated crash rates that vary

with AADT or AADT per lane.) However, the increase produced by the HERS procedures is appreciably lower

than the 3.7 percent increase indicated for this three-year period by the GES and FHWA data.

73. Lawrence J. Blincoe, The Economic Cost of Motor Vehicle Crashes, 1994, NHTSA, 1996.
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which are based on the willingness-to-pay concept used by HERS, are provided by the Maximum Abbreviated Injury Scale (MAIS).76 They range from $10,840 for MAIS Level 1 to

$2,509,310 for MAIS Level 5 (and $2,854,500 for fatal injuries). Weighting the estimates for nonfatal injuries by the relative frequency of injuries of each severity77 produces an overall estimate

of $47,657 per police-reported injury.

Corresponding estimates of property-damage costs per crash and travel-delay costs per crash

were obtained by dividing the NHTSA estimates of total 1994 costs of these two types78 by an

estimate of crashes in 1994 that is consistent with the 1995 estimate used to calibrate the HERS

crash-estimation procedures.79 This step produced overall costs-per-crash estimates of $7,164

for property damage and $605 for travel delay.

The next series of steps in the development of unit cost factors for use by the HERS safety model

involved using the above overall estimates of unit costs for injuries and property damage to

develop estimates by functional system. This was accomplished by:

1. Using the new HERS procedures and 1994 HPMS data to estimate crashes, injuries and

fatalities by functional system in 1994;

2. Using unindexed values of HERS’ original 1988 estimates of unit costs of injuries and

property damage by functional system to obtain national estimates of unit costs implied

by the original unit costs; and 

3. Dividing the new estimates (in 1994 dollars) by those produced using 1988 unit costs.

This last step produced scale factors of 3.1062 for injury costs and 1.2532 for property damage

costs. These scale factors were then applied to the 1988 HERS estimates of unit costs by functional system to produce a revised set of unit costs for injuries and property damage. The

revised unit costs are shown in Table 5-9. 

Delay costs vary with AADT per lane. HERS uses the equation:

Eq. 5.16

where

DELCC = cost of delay due to crashes (per 100 million VMT);

CRASH = crash rate on the section (per 100 million VMT); and

74. Ted R. Miller, et. al., The Costs of Highway Crashes, The Urban Institute, 1991.

75. Blincoe, op. cit., Table A-1. These estimates of comprehensive costs, based on willingness to pay, are, on average,

roughly three times the NHTSA estimates of economic or “human capital” costs summarized in Table 1 of the Blincoe report.

76. An alternative to using costs by MAIS is the use of costs by police-reported “KABCO” code (killed; A, B or C

injury; property damage only). Estimates of comprehensive costs by KABCO code are available in Ted R. Miller,

Diane C. Lestia, and Rebecca S. Spicer, “Highway Crash Costs in the United States by Driver Age, Blood Alcohol

Level, Victim Age, and Restraint Use,” Accident Analysis and Prevention, Vol. 30, No. 2, 1998. However, these estimates probably should not be used with crash data from small numbers of states, since the source observes that

KABCO coding varies appreciably across states.

77. Blincoe, op. cit., Table 3.

78. Ibid., Table 1.

79. The resulting estimate of 1994 crashes, 7.28 million, was obtained by applying an undercapture correction factor of

1.12 (see paragraph 5.1.3.1.7) to the NHTSA GES estimate of crashes in 1994.

DELCC 0.0886 × AADT

LANES = ---------------------------------------- × CRASH
Cost and Benefit Calculations

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LANES = number of lanes.

The coefficient (0.0886) was set so that, when applied to 1994 data, HERS would produce an

overall average cost of delay that matches the above estimate of $605 per crash.

The assumption that the delay cost of crashes is linear with a simple measure of traffic volume

(AADT per lane) undoubtedly understates the complexity of this relationship. Hence, this simple procedure is likely to underestimate the delay cost of crashes on congested roads and to overestimate this cost on uncongested roads. 

For sections with stop signs and for free-flow sections with only one lane in one or both directions, the delay cost of crashes is multiplied by the average value of an hour of travel time to estimate hours of delay due to crashes. For these sections, this value is used as an estimate of

incident delay. For other sections, DELCC is no longer used by HERS.

5.1.3.4.2 Indexing the Costs of Crashes

HERS allows the costs of property damage, delay and injuries to be indexed from 1994 dollars to

dollars of a subsequent year using separate, user-supplied index values. For property-damage

costs, an appropriate index to use is the Consumer Price Index (CPI) component for automobile

body work.80 Using 1994 as a base year, the 1997 value of this index is 1.126, so property-damage costs per crash in 1997 are estimated as being 12.6 percent higher than in 1994.

For travel delay, the index used should be the same one as is used for the value of time, but the

base year for the travel delay index would be 1994 (instead of 1995, the year currently used for

value of time). The index currently being used for this purpose is the U.S. Bureau of Labor StatisTable 5-9. Injury and Property-Damage Costs

Functional System

Injury Cost per 

Injury

(1994 dollars)

Property-Damage 

Costs per Crash 

(1994 dollars)

Rural

 Interstate $ 52,800 $ 5,000

 Other Principal Arterial 68,300 6,300

 Minor Arterial 55,900 6,300

 Major Collector 77,650 6,300

Urban

 Interstate 55,900 6,300

 Other Freeway or Expressway 46,600 7,500

 Other Principal Arterial 49,700 7,500

 Minor Arterial 40,400 7,500

 Collector 31,100 6,300

80. U.S. Bureau of Labor Statistics, Consumer Price Index – All Urban Consumers, Series ID CUUR0000SETD01,

Motor Vehicle Body Work, http://stats.bls.gov/sahome.html (U.S. city average, not seasonally adjusted).
HERS Technical Report v3.54

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5-31

tics (BLS) Employment Cost Index (which reflects total compensation of all civilian workers).81

Using 1994 as a base year, the 1997 value of this index is 1.089.

Injury costs have previously been indexed by HERS using the CPI component for medical care.

However, since the HERS estimates of the comprehensive costs of injuries are based on willingness to pay, rather than on economic costs (which include medical costs), the cost of medical care

may not be the most appropriate basis for indexing injury costs. A measure of perceived wealth

or earnings ability is probably a better indicator of changes in willingness to pay. For simplicity,

HERS uses the BLS Employment Cost Index for this purpose (as well as for indexing the cost of

delay); therefore the 1997 value of this index is also 1.089.

5.2 Agency Costs and Benefits

For agencies in charge of building and maintaining highways, HERS recognizes two potentially

accruing benefits resulting from improving a highway section: 

• a reduction in the cost of routine maintenance resulting from resurfacing or reconstruction of pavement; and

• a reduction in the cost of the next improvement resulting from the improved condition of

the section when that improvement is implemented.

The second type of benefit is referred to as the “residual value” of the improvement. The estimation of residual value is discussed at some length in conjunction with the presentation of the

HERS benefit-cost analysis procedure under paragraph 7.6, ”Residual Value.” The HERS procedure for estimating the other type of agency benefit, reductions in maintenance costs, is presented below. These benefits take their place in the numerator of the benefit-cost equation.

In HERS, all improvements are analyzed over a benefit-cost analysis (BCA) period that begins at

the midpoint of one funding period and ends at the midpoint of some subsequent funding

period. To simplify the analysis of maintenance expenditures, a “maintenance cost (MC) period”

is defined as a period beginning at the midpoint of a funding period and ending at the midpoint

of the next funding period. Estimates of pavement maintenance expenditures over each MC

period are then derived from PSR estimates for the beginning and end of each period.

5.2.1 Maintenance Costs for Flexible Pavements

Estimates of maintenance costs per lane-mile for flexible pavements have been developed by

Witczak and Rada82 as a function of PSR and structural number (SN). Their results are presented in Table 5-10, “Maintenance Costs for Flexible Pavements.” The middle column of this

table presents estimates of maintenance costs (in 1984 dollars) incurred per lane-mile during

periods when PSR (PSI in the exhibit) drops from 4.5 to 4.0, from 4.0 to 3.5, etc. The last column

shows estimates of cumulative maintenance costs per lane-mile for a section that starts with a

81. U.S. Bureau of Labor Statistics, Employment Cost Index, Series ID: ECS10001I, Total Compensation of All Civilian

Workers, http://stats.bls.gov/sahome.html (seasonally adjusted).

82. Matthew W. Witczak and Gonzalo R. Rada, Microcomputer Solution of the Project Level PMS Life Cycle Cost Model,

University of Maryland, Department of Civil Engineering, prepared for Maryland Department of Transportation,

State Highway Administration, Baltimore, Md., December 1984, Chapter 4.
Cost and Benefit Calculations

5-32

PSR of 4.5 and has various indicated terminal PSRs ranging from 4.0 to 1.5. These estimates are

independent of the time required for the deterioration to occur. 

Regressing the values for cumulative maintenance costs shown in Table 5-10 against the values

for PSR (or PSI) and SN yields the following equation:

Eq. 5.17

where:

Table 5-10. Maintenance Costs for Flexible Pavementsa

(1984 Dollars)

a. Source: Matthew W. Witczak and Gonzalo R. Rada, Microcomputer Solution of the Project Level PMS Life Cycle Cost Model, University of Maryland, Department of Civil Engineering, prepared for Maryland Department of Transportation, State Highway Administration,

Baltimore, MD., December 1984, p. 132

Final PSI

Maintenance Cost 

Between PSI Levels

($/lane mile)

Cumulative Cost 

($/lane mile)

Low SN/traffic: (SN = 2.16)

4.0 221.57 221.57

3.5 767.03 988.60

3.0 1314.95 2302.55

2.5 1859.47 4163.02

2.0 2413.74 6576.76

1.5 2957.34 9534.10

Medium SN/traffic: (SN = 3.60)

4.0 339.10 339.10

3.5 1174.05 1513.15

3.0 2012.72 3525.87

2.5 2845.76 6371.63

2.0 3604.98 10066.61

1.5 4526.45 14593.06

High SN/traffic: (SN = 5.04)

4.0 456.63 456.63

3.5 1581.05 2037.38

3.0 2710.50 4748.18

2.5 3832.04 8580.22

2.0 4976.21 13556.43

1.5 6095.55 19651.98

COST 4427.24 1989.7 × PSR + 223.57 PSR2 7996.11 SN

– 3594.56 × SN

× + ×

PSR 403.99 SN PSR2× + × ×

= –
HERS Technical Report v3.54

September 2002

5-33

PSR = terminal PSR;

SN = structural number; and

COST = where cost is cumulative maintenance cost per lane-mile, in 1984

dollars, for the time over which the pavement is deteriorating from

an initial PSR of 4.5 to the terminal PSR.

The R2 for the above equation exceeds 0.9999.

Equation 5.17 can be modified to produce cost estimates in 1988 dollars by multiplying all coefficients by 1.2118, the ratio of the 1988 and 1984 values of FHWA's Cost Index for Highway Maintenance and Operation.83

To estimate maintenance costs per lane-mile on any section during a period beginning at time i

and ending at time f, Equation 5.17 is evaluated using the section's PSR at times i and f, and the

difference between the two results is obtained. The general form of the HERS equation to provide this result, MCOST, in 1988 dollars, is:

Eq. 5.18

This equation (Equation 5.18) would produce negative values of MCOST whenever

. To avoid this undesirable effect, 4.5 is substituted for any PSR values above

4.5. The resulting costs can be adjusted to dollars of another year. To index the 1988 dollars to

1997 dollars for use in the 1999 Conditions and Performance Report, a factor of 1.231 was used for

rural sections and 1.242 for urban sections.

5.2.2 Maintenance Costs for Rigid Pavements

In the absence of readily available information about maintenance costs for rigid pavements,

HERS assumes these costs are identical to those for flexible pavements with a structural number

(SN) of 5.625. This is the SN of flexible pavements with a thickness of 5.5 inches, the thickest flexible pavement considered by HERS.

5.3 External Costs

The HERS model includes estimates of the costs of damages from vehicular emissions of air pollutants in its calculation of benefits and disbenefits resulting from the implementation of an

improvement. HERS employs a set of tables that specify the average cost of air pollutant emissions generated per vehicle-mile by the three different HERS vehicle classes operating at various

speeds on each of the nine HERS roadway functional classes. HERS uses the projected mix of

vehicle classes and the average speed of travel on each sample section to determine the average

cost of emissions per vehicle-mile, and multiplies this value by its forecast of total vehicle-miles

to calculate the total cost of air pollutant emissions generated by travel on the section. 

83. U.S. Department of Transportation, Federal Highway Administration, Highway Statistics: 1988, U.S. Government

Printing Office, Washington, D.C., 1989, Table PT-5.

MCOST ( ) 2411 4355 + × SN PSRf PSRi – × ( ) –

( ) 270.9 489.6 + × SN PSRf

2 PSRi2 + × ( ) –

=

PSRi PSRf > ≥ 4.5
Cost and Benefit Calculations

5-34

The effect of a proposed improvement to a sample section on air pollution costs is measured by

the difference between total pollution costs generated by the forecast volumes of travel on the

section under baseline and improved conditions. Because the cost of air pollutant emissions per

vehicle-mile varies both by travel speed and among vehicle classes, this effect can be negative (a

benefit) or positive (a disbenefit) depending on how a proposed improvement affects forecast

travel volumes, the mix of vehicle types, and travel speeds on a sample section. 

HERS' estimates of the average cost of air pollutant emissions per vehicle-mile for each of its

three vehicle classes differ among the nine HERS roadway functional classes for several reasons:

• each of HERS' three vehicle classes includes several specific types of vehicles, which have 

different emission rates per vehicle-mile, and the exact mix of these individual vehicle types 

making up each vehicle class differs slightly among HERS' nine roadway functional classes;

• emission rates per vehicle-mile for the same type of vehicle traveling at the same average 

speed differ among collector, arterial, and freeway sections because the specific patterns of 

driving that produce a given average speed tend to differ among these roadway types;

• the density of development typically found along roadway sections located in urban areas is 

much higher than for rural functional classes, resulting in increased population exposure to air 

pollutant emissions and higher costs per mile of travel by all classes of vehicles on urban sections.

The average cost of air pollutant emissions per vehicle-mile for each HERS vehicle class and

roadway functional class also declines gradually over future years. The decline in air pollution

costs reflects projected reductions in the rates at which all types of vehicles emit various air pollutants, as well as projected changes in the composition of the U.S. vehicle fleet and the resulting

mix of vehicle classes operating on each roadway functional class. 

Air pollution costs during future years for each HERS vehicle class and roadway functional class

are estimated by applying an annual rate of decline to the appropriate values for the year 2000.

The average annual rate of decline in air pollution costs for each vehicle and roadway functional

class was calculated by fitting an exponential function (which represents a constant annual percentage rate of decline) using detailed estimates of air pollution costs prepared for the years 2000

and 2020. 

Table 5-11 below provides an example of HERS' estimates of air pollution damage costs. It shows

average air pollution costs per vehicle-mile of travel at selected speeds, for each of HERS' three

vehicle classes operating on Urban Arterial sections during the year 2000. Table 5-11 reveals the

typical patterns of variation in air pollution costs: at each speed, costs are higher for single-unit

trucks than for four-tire vehicles (automobiles and light-duty trucks), and highest for combination trucks, while costs for each vehicle class decline significantly from very low speeds through

moderate speeds (30-40 mph), after which they increase gradually. Appendix G of this report

includes similar tables for each of the nine roadway functional classes employed by HERS, while

Appendix F presents a complete discussion of the derivation of these costs. 
HERS Technical Report v3.54

September 2002

5-35

Table 5-11. Air Pollution Costs by Vehicle Class and Average Travel Speed:

Urban Arterial Sections

5 $0.0358419 $0.0560533 $0.1275028

6 $0.0316863 $0.0514504 $0.1211734

7 $0.0287181 $0.0481626 $0.1166524

8 $0.0264919 $0.0456968 $0.1132616

9 $0.0247604 $0.0437789 $0.1106243

10 $0.0233752 $0.0422446 $0.1085145

...

30 $0.0153292 $0.0296437 $0.0786490

31 $0.0152326 $0.0295601 $0.0784381

32 $0.0151421 $0.0294816 $0.0782404

33 $0.0150570 $0.0294080 $0.0780546

34 $0.0149769 $0.0293386 $0.0778798

35 $0.0149014 $0.0292732 $0.0777150

36 $0.0148982 $0.0292916 $0.0786260

37 $0.0148952 $0.0293089 $0.0794878

38 $0.0148923 $0.0293254 $0.0803043

39 $0.0148896 $0.0293410 $0.0810789

40 $0.0148870 $0.0293558 $0.0818147

41 $0.0148946 $0.0294674 $0.0818474

42 $0.0149019 $0.0295736 $0.0818786

43 $0.0149088 $0.0296749 $0.0819083

44 $0.0149155 $0.0297716 $0.0819367

45 $0.0149218 $0.0298640 $0.0819638

46 $0.0149325 $0.0300613 $0.0831937

47 $0.0149427 $0.0302503 $0.0843713

48 $0.0149524 $0.0304313 $0.0854998

49 $0.0149618 $0.0306050 $0.0865823

50 $0.0149708 $0.0307717 $0.0876214

...

60 $0.0151521 $0.0341296 $0.1095182

61 $0.0151613 $0.0347254 $0.1136012

62 $0.0151702 $0.0353021 $0.1175524

63 $0.0151789 $0.0358604 $0.1213782

64 $0.0151872 $0.0364013 $0.1250845

65 $0.0151953 $0.0369255 $0.1286767

66 $0.0152034 $0.0374580 $0.1323721

67 $0.0152116 $0.0379988 $0.1361736

68 $0.0152198 $0.0385481 $0.1400843

69 $0.0152280 $0.0391061 $0.1441073

70 $0.0152362 $0.0396728 $0.1482459

r 0.060576652 0.077915261 0.112967756

Combination 

Trucks

Average 

Speed 

(mph) Four-Tire 

Vehicles

Single-Unit 

Trucks

Emission Damage Cost per Vehicle-Mile of Travel by: 

(2000 $)
Cost and Benefit Calculations

5-36

5.4 Capital Cost of Improvements

HERS requires estimates of highway improvement costs to be included in the analysis of investment options. In the case of the pavement, widening and alignment improvements currently

considered by HERS, these costs are all initial costs; i.e., they are incurred at the time the

improvement is implemented. When analyzing the economic attractiveness of a potential

improvement, the improvement cost is used as the denominator in the benefit-cost equation.

This paragraph contains three parts. The first presents the initial costs of pavement and widening improvements used by HERS.

The second part presents the HERS procedure for estimating the initial cost of alignment

improvements. This cost is estimated for those portions of a section that must be reconstructed

on a modified alignment in order to bring the section's alignment up to design standards. The

cost is sensitive to the extensiveness of the required alignment improvement as well as to the

physical characteristics of the section. This cost is added to the cost of pavement and widening

improvements to obtain the full initial cost of any improvement that includes alignment

improvements.

The final part of this paragraph presents the procedure used to estimate the improvement costs

of correcting substandard conditions on urban freeways.

All figures for improvement costs presented in this chapter are expressed in 1997 dollars.84 Users

wishing output expressed in another year dollars can adjust these costs individually or all costs

can be adjusted uniformly using a cost index. FHWA's Composite Bid Price Index for FederalAid Highway Construction85 may be used as the basis for adjusting improvement costs to dollars of another year. 

5.4.1 Pavement and Widening Improvements

HERS distinguishes seven kinds of pavement and widening improvements (described in Exhibit

3-1, “Kinds of Improvement”). In HERS, the costs of pavement and widening improvements are

derived from the costs computed for the HPMS Analytical Process. The HERS costs include both

improvement and right-of-way (ROW) costs, but do not include costs such as unusual cut and

fill operations, excessive number of structures, or non-construction costs.

The scaled estimates of cost per lane-mile (for construction and ROW, combined) used by HERS

are shown in Table 5-12, “Capital Improvement Costs.” These costs are expressed in 1997 dollars

but can be scaled to any other-year dollars by the user.86

84. For the 1999 C&P Report, costs for improvements on existing alignments were entered in 1995 dollars and indexed

to 1997 dollars using factors of 1.09 (rural) and 1.068 (urban). Alignment-related costs and the costs of upgrading

substandard urban freeways were entered in 1988 dollars and converted to 1997 dollars using factors of 1.231

(rural alignment), 1.496 (urban alignment), and 1.242 (substandard freeways). 

85. Office of Infrastructure, Office of Program Administration, Price Trends for Federal-Aid Highway Construction, U.S.

Department of Transportation, Federal Highway Administration, Washington, D.C., quarterly.

86. Costs shown are derived from the improvement cost file (IMPRCOST.DAT) used in preparation of the 1999 Conditions and Performance Report (which reports on the 1997 highway system). In this file, these improvement costs are

entered in 1995 dollars: here, they have been indexed to 1997 dollars.
HERS Technical Report v3.54

September 2002

5-37

HERS also distinguishes between the costs associated with adding lanes when conventional widening is feasible (normal cost lanes), and when more expensive methods will be required (high

cost lanes). The 1997 costs used in HERS to develop the 1999 C&P Report only distinguished

between normal cost lanes and high cost lanes on urban sections. (The output statistics report

rural high cost lanes, but they are priced at the same rate as normal cost lanes.) It should be noted

that HERS uses a single estimate of improvement costs per lane-mile, rather than separate estimates for construction and ROW costs. 

Table 5-12. Capital Improvement Costs

(Thousands of 1997 Dollars per Lane-Mile) Reconstruct & Add High Cost Lanes Reconstruct & Add Normal Cost Lanes Reconstruct & Widen Lanes Reconstruct Major Widening at High Cost Major Widening at Normal Cost

Minor Widening

Resurface &

Improve Shoulders

Resurface

Rural Interstate

Flat terrain 558 558 629 524 351 351 284 195 110

Rolling terrain 653 653 694 540 374 374 305 206 106

Mountainous terrain 752 752 920 766 493 493 419 252 136

Rural Other Principal Arterial

Flat terrain 704 704 536 458 360 360 278 135 69

Rolling terrain 728 728 603 518 402 402 306 147 69

Mountainous terrain 1036 1036 790 647 750 750 436 201 101

Rural Minor Arterial

Flat terrain 611 611 413 326 355 355 231 136 58

Rolling terrain 665 665 520 444 491 491 242 138 62

Mountainous terrain 899 899 811 582 623 623 320 172 97

Rural Major Collector

Flat terrain 538 538 471 334 338 338 186 95 33

Rolling terrain 590 590 571 413 336 336 196 104 38

Mountainous terrain 789 789 730 569 574 574 261 133 48

Urban Sections

Freeways/Expressways 8256 3550 2604 1595 8380 3674 1546 462 215

Other Divided 4910 1961 1603 909 5250 2302 852 316 144

Other Undivided 3468 1268 1394 831 3917 1717 902 276 163
Cost and Benefit Calculations

5-38

HERS uses five methods to compute the cost of pavement and widening improvements. The

method used depends upon the type of improvement being implemented. The calculations are

presented in Table 5-13. 

Note that for some sections, the initial widening feasibility code allows adding lanes at both high

and normal cost at the same time. The normal cost used is the one which would be used if no

high cost lanes were included in the improvement. 

The length of the improvement is included in the equations shown in Table 5-13 rather than the

length of the section, since when a portion of a section receives an alignment improvement, those

costs are calculated separately and added to the costs for the portion of the section improved on

the existing alignment.

5.4.2 Alignment Improvements

In HERS, any of the pavement and widening improvements listed in Table 5-12 can be combined

with alignment improvements. The initial cost of any such improvement is obtained by developing separate cost estimates for the portion of the section that would be reconstructed on a modified alignment and the portion (if any) that would continue to follow the existing alignment.

Total improvement costs for the section are obtained as the sum of the two separate cost estimates.

Table 5-13. Improvement Cost Calculations

Improvement Type Cost Calculation

Reconstruct & Add High Cost Lanes 

and

Major Widening at High Cost on 

rural sections

Major Widening at High Cost on 

urban sections

Major Widening at Normal Cost on 

urban sections

Reconstruct & Add Normal Cost 

Lanes

All Other Improvement Types

where: LANESexist = the number of lanes before improvement; LANESnorm = the number of 

lanes being added at normal cost; LANEShigh = the number of lanes being added at high cost; 

COSThigh = the cost of adding a lane at high cost; COSTnorm = the cost of the improvement when 

no high cost lanes are being added; COSTtot = the total cost of the improvement; IMPLEN = the 

length of the improvement.

COST LANESexist LANESnorm ( ) +

COSTnorm LANEShigh

COSThigh ×

× +

(

)

=

× IMPLEN

COSTtot LANESnorm COSTnorm ×

LANEShigh COSThigh + ×

(

)

× IMPLEN

=

COSTtot = LANESnorm COSTnorm ×

× IMPLEN

COST LANESexist LANESnorm ( ) +

COSTnorm ×

=

× IMPLEN

COSTtot = LANESexist COSTnorm ×

× IMPLEN
HERS Technical Report v3.54

September 2002

5-39

The procedures for determining the alignment modifications to be made, estimating the cost of

these modifications, and combining this cost with the improvement cost for the remainder of the

section are presented below. The development of these procedures is presented in a separate

report prepared by Cambridge Systematics87.

5.4.2.1 Modifying Section Alignment

In HERS, an alignment improvement generally results in improving all of a section's substandard curves and grades to the design standard (as specified in Table 3-11, “Default Design Standards For Curves and Grades”). The exception to this statement occurs during the first loop of a

funding period when HERS considers only the least expensive improvement necessary to correct

any unacceptable conditions. During this loop, if curves or grades are unacceptable, but not

both, HERS selects an improvement that improves only curves or only grades to the design standard (and, if sufficient funds are available, a more aggressive improvement that improves both

curves and grades to design standards is considered during the second loop).

For any section, improvement of substandard grades is presumed to result in replacing all segments whose grade is substandard by segments with grades that just meet the design standard

for the section. The total length of these segments before improvement is denoted LVERT, and

the corresponding length after improvement is denoted LAFTV. In HERS, LAFTV is taken to be

equal to LVERT.

Similarly, for any section, improvement of substandard horizontal curves is presumed to result

in replacing all segments whose curvature is substandard by segments whose curvature just

meets the design standard. The total length of these segments before improvement is denoted

LHORIZ, and the corresponding length after improvement is denoted LAFTH. Straightening of

horizontal curves generally results in a slight reduction in overall roadway length but an appreciable increase in the length of the somewhat straightened curves. In HERS, the former effect is

ignored, while the latter effect is estimated by calculating LAFTH:

Eq. 5.19

where

SLEN = original length of the section (miles);

Li = total length of curves in class i;

Ci = average curvature of curves in class i; 

Cds = average curvature of curves in class that just meets the design standard;

and the sum is taken over all substandard classes of curves. In order to maintain the total length

of the section, the lengths of all curves that were not originally substandard are scaled downward (with no change in their curvature).

The total length of the segments with modified alignment, LNEW, is taken to be the sum of

LAFTV and LAFTH, or, if this sum is greater than the entire length of the section, LNEW is set to

87. Cambridge Systematics, Inc., FHWA Highway Economic Requirements System: Alignment Improvement Costs, prepared for Jack Faucett Associates and the Federal Highway Administration, Washington, D.C., April 1991.

LAFTH MIN SLEN

Ci

Cds

--------Li

I

, ∑       =
Cost and Benefit Calculations

5-40

the original length of the section. In the latter event, there must be some portion of the section

that must be reconstructed both to eliminate substandard grades and to eliminate substandard

curves. This portion is designated LBOTH and is equal to LAFTV + LAFTH - LNEW.88

For sections that have both substandard grades and substandard curves, the HPMS data base

provides no information about the extent of any overlap. The above definition of LBOTH

reflects the assumption that there is normally no overlap, and that, when an overlap exists, it is

as small as possible. This assumption is considered to be reasonable (because of the safety problems that would result from sharp curves located on steep grades). However, to the extent that

this assumption does not hold, it increases the length of road to be reconstructed on a modified

alignment and thus tends to increase the estimated cost of the alignment improvement.

5.4.2.2 Cost of Improving Alignment

Improvement costs for segments with modified alignment are obtained by estimating costs for

clearing and grubbing, earthwork, drainage, structures, pavement, right-of-way, guard rails and

curbs, fencing, painting, and lighting. The procedures used for estimating each of these cost

components were developed by Cambridge Systematics (op. cit.) and are summarized below.

Unit costs, in 1997 dollars, used by these procedures are shown in Table 5-14, “Unit Costs Used

for Rural Alignment Cost Computation,” and Table 5-15, “Unit Costs Used for Urban Alignment

Cost Computation.” Parameter values used in Equations 5.20 through 5.24 are shown in Table 5-

16, “Parameter Values for Alignment Cost Computation.” The unit costs may be converted as a

group to dollars of any other year using FHWA's Composite Bid Price Index for highway construction, or converted individually using the component indexes for excavation, structures, surfacing with Portland cement concrete, and resurfacing with bituminous concrete.89 

5.4.2.2.1 Clearing and Grubbing

Site preparation consists of clearing and grubbing. The total cost of clearing and grubbing,

TCCG, is estimated:

Eq. 5.20

where:

RW = roadway width after improvement (feet) (equals the number of

lanes times the lane width, plus twice the right-shoulder width,

plus the median width);

LNEW = total length of the realigned segments (miles);

UCCG = unit cost of clearing and grubbing (dollars per square yard);

terrn = terrain type; and

PCG(j,terrn) = estimated parameters that vary with terrain type (see Table 5-16).

88. The HERS variables LBOTH, LAFTV and LAFTH correspond to the quantities Lboth, (Lafter(v) -Lboth), and

(Lafter(h) - Lboth), respectively, in the Cambridge Systematics report (op. cit., pp. 4-2 through 4-4). 

89. Office of Infrastructure, op. cit. 

TCCG PCG = ( ) 1, terrn RWPCG( ) 2, terrn× × UCCG LNEW ×
HERS Technical Report v3.54

September 2002

5-41

5.4.2.2.2 Earthwork

For flat terrain (terrn = 1), total earthwork costs, TCEW, are estimated:

Table 5-14. Unit Costs Used for Rural Alignment Cost Computationa

(1997 Dollars)

Clearing and Grubbing $ 1.77 per square yard

Earthwork:

 Flat terrain

 Rolling terrain

 Mountainous terrain

$ 5.66 per cubic yard

 5.66

 6.65 

Drainage:

 Narrow pipe culverts

 Wide pipe culverts

 Small box culverts

 Wide box culverts

$ 67.48 per foot

 135.32

 612.64

 1440.75

Structures $ 903,122 each

Guard rails and curbs:

 Curbed median or shoulder

 Guard rail or concrete median

 Guard rail at shoulder

$ 152,518 per mile

 188,933

 184,401

Fencing $ 97,005 per mile 

Lighting $ 674,578 per mile

Painting of Traffic Lanes (per mile)

Number of Lanes

2468

$17,835 $29,577 $38,269 $43,218

Pavement Costs (per square yard)

Layer Thickness (inches) Aggregates Asphaltic Concrete Portland Cement

Concrete

2

3

4

6

7

8

9

10

12

13

15

 $3.99

 5.77

 7.66

 11.49

 13.76

 $5.99

 6.99

 9.53

 14.01

 19.67

$18.080

 20.91

 22.75

 24.82

 28.36

 33.09

 40.18

Surface treatment (for light pavement sections): $ 2.09

a. Source: Cambridge Systematics, Inc. FHWA Highway Economic Requirements System; Alignment Improve- ment Costs, prepared for Jack Faucett Associates and the Federal Highway Administration, Washington, D.C., April 1991, Appendix D. Adjusted to 1988 dollars by applying a factor of 0.96; 1988 dollars adjusted to 1997 dollars by applying a factor of 1.231.
Cost and Benefit Calculations

5-42

Eq. 5.21

Table 5-15. Unit Costs Used for Urban Alignment Cost Computationa

(1997 Dollars)

Clearing and Grubbing $ 2.15 per sq. yard

Earthwork:

 Flat terrain

 Rolling terrain

 Mountainous terrain

$ 6.88 per cubic yard

 6.88

 8.08

Drainage:

 Narrow pipe culverts

 Wide pipe culverts

 Small box culverts

 Wide box culverts

$ 82.01 per foot

 164.46

 744.53

 1750.90

Structures $ 1,097,539 each

Guard rails and curbs:

 Curbed median or shoulder

 Guard rail or concrete median

 Guard rail at shoulder

$ 185,351 per mile

 229,606

 224,098

Fencing $ 117,888 per mile 

Lighting $ 819,796 per mile

Painting of Traffic Lanes (per mile)

Number of Lanes

2468

$ 21,674 $ 35,944 $ 46,508 $ 52,522

Pavement Costs (per square yard)

Layer Thickness (inches) Aggregates Asphaltic Concrete Portland Cement

Concrete

2

3

4

6

7

8

9

10

12

13

15

 $4.85

 7.02

 9.31

 13.96

 16.73

 $7.29

 8.50

 11.58

 17.02

 23.91

$21.98

 25.42

 27.65

 30.16

 34.47

 40.21

 48.83

Surface treatment (for light pavement sections): $ 2.54

a. Source: Cambridge Systematics, Inc. FHWA Highway Economic Requirements System; Alignment Improve- ment Costs, prepared for Jack Faucett Associates and the Federal Highway Administration, Washington, D.C., April 1991, Appendix D. Adjusted to 1988 dollars by applying a factor of 0.96; 1988 dollars adjusted to 1997 dollars by applying a factor of 1.496.

TCEW PEW( ) 1 1, RWPEW( ) 2 1, × × [ ] PEW( ) 3 1, + WET PEW × ( ) 4 1,

× UCEW( ) 1 × LNEW

=
HERS Technical Report v3.54

September 2002

5-43

and total earthwork costs for rolling or mountainous terrain are estimated:

Eq. 5.22

where:

RW = roadway width after improvement (feet);

LNEW = total length of the realigned segments (miles);

WET = 1 in wet climate zones, 0 in other climate zones;

UCEW(terrn) = unit cost of earthworks (dollars per mile);

ARGV = average road gradient after improvement of segments whose

alignment is being modified to eliminate substandard grades; this

will be the average gradient of grade class that just meets the

design standard;

ARGH = average road gradient after improvement of segments whose

alignment is being modified to eliminate substandard curves; this

will be the average road gradient of all segments that currently

meet the design standard; and

PEW(j,terrn) = estimated parameters that vary with terrain type (see Table 5-16).

Table 5-16. Parameter Values for Alignment Cost Computationa

 j Flat Rolling Mountainous

PCG 1

2

685.00

1.07

685.00

1.07

636.00

1.14

PEW 1

2

3

4

5

439.00

1.0

1.0

2.22

---

399.00

1.10

1.00

-0.49

 0.50

853.00

1.30

1.00

-0.25

 1.50

ANBC 0.40 0.55 1.53

ANPC 1.93 2.90 3.35

PDR 1

2

1.25

1.10

 3.92

 0.84

2.22

0.90

a. Source: Cambridge Systematics, Inc. FHWA Highway Economic Requirements System:

Alignment Improvement Costs, prepared for Jack Faucett Associates and the Federal Highway Administration, Washington, D.C., April 1991, Chapter 3, Equations 3.1- 3.8.

TCEW UCEW terrn ( ) PEW( ) 1, terrn RWPEW( ) 2, terrn× ×

PEW( ) 3, terrn e

PEW( ) 4, terrn × [ ] ARGV PEW – ( ) 5, terrn [ ] +

PEW( ) 3, terrn e

PEW( ) 4, terrn × [ ] ARGH PEW – ( ) 5, terrn + [ ] +

  × ( ) LAFTH LBOTH –        

×

=
Cost and Benefit Calculations

5-44

5.4.2.2.3 Drainage

Total cost of drainage culverts, TCDR, is estimated:

Eq. 5.23

where:

ANBC(terrn) = average number of box culverts per mile, by terrain type;

ANPC(terrn) = average number of pipe culverts per mile, by terrain type;

UCBC(s) = unit cost of box culverts (dollars per mile) by size s (small or large);

UCPC(s) = unit cost of pipe culverts (dollars per mile) by size s (narrow or

wide); and

PDR(j,terrn) = estimated parameters that vary with terrain type (see Table 5-16).

Large box culverts and wide pipe culverts are used in wet climate zones; small box culverts and

narrow pipe culverts are used in other climate zones.

5.4.2.2.4 Structures

The total cost of new structures, TCSTR, is estimated by obtaining the number of structures per

mile on the original section and multiplying by the length of the segments with modified alignment and by the average cost of a new bridge:

Eq. 5.24

where:

LNEW = total length of the realigned segments (miles);

SLEN = original length of the section (miles);

NSTR = number of structures on the original section; and

ACSTR = average cost of a new bridge (dollars).

5.4.2.2.5 Pavement

The cost of pavement depends upon pavement type, the number of pavement layers, and their

thickness.

The pavement type used for the portion of a section being reconstructed on a modified alignment is determined by the type of pavement the section had before being improved. Rigid pavement is used for alignment improvements to sections with rigid or composite (flexible over rigid)

pavement, and flexible pavement is used otherwise.

For low-type flexible pavement (used for rural collectors that carry no more than 1000 vehicles

per day90), a surface treatment on a four-inch aggregate base and a four-inch aggregate sub-base

is assumed.

90. See Table 3-3, “Default Surface Type Criteria and Standards.”

TCDR ANBC terrn [ ] ( ) × UCBC s( ) + ANPC terrn ( ) × UCPC s( )

PDR( ) 1, terrn RWPDR( ) 2, terrn× × × LNEW

=

TCSTR NSTR

SLEN = ---------------- × LNEW ACSTR ×
HERS Technical Report v3.54

September 2002

5-45

For other flexible pavements, a wider range of options exists. For these pavements, the thickness

of the asphaltic concrete surface layer is obtained from Table 6-6, “Pavement Thickness After

Improvement,” and the structural number (SN) is obtained from Equation 6.1 (or set to the original value of SN for the section, if that value is higher). SN is then used to classify the pavement

section type as being light (SN ≤ 3.0), medium (3.0 < SN ≤ 4.5), or heavy (SN > 4.5). An asphaltic

concrete base is assumed for sections with an existing asphalt base, and an aggregate base is

assumed otherwise. An aggregate sub-base is assumed whenever an aggregate base is used or

when the pavement section type is classified as heavy; otherwise, it is assumed that there is no

sub-base. Finally, the thickness of the base and sub-base (if it exists) is obtained from Table 5-17. 

The total cost of pavement, TCP, for the portion of the section being reconstructed is then estimated:

Eq. 5.25

where: 

PW = pavement width, in yards;

UCPL(i,t) = unit cost for pavement layer i of thickness t (dollars per square

yard);

and the factor of 1760 is used to convert LNEW from miles to yards. Flexible pavements may

have from 1 to 3 layers (as described above); rigid pavements have only the surface layer.

The costs per square yard of aggregate, asphaltic concrete, and Portland cement concrete layers

are shown in Tables 5-14 through 5-15 for selected thicknesses. For thicknesses not shown, the

cost per square yard is obtained by linear interpolation. The exhibit also shows the cost per

square yard for surface treatment for light pavement sections.

5.4.2.2.6 Right-of-Way

Total right-of-way costs, TCROW, are estimated:

Table 5-17. Thickness of Base and Sub-base of Reconstructed Sectionsa

a. Source: U.S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring

System Field Manual, Washington, D.C., Table IV-3, August 30, 1993.

Type of Base

Type of Pavement

 Section Asphaltic Concrete Aggregate

⇓ Base Sub-base

(Aggregate)

Base Sub-base

(Aggregate)

 Light 6" none 4" 4"

 Medium 6" none 8" 8"

 Heavy 8" 8" 12" 13"

TCP 1760 PW UCPL i t ( ) ,

i = 1

I

= × × ∑ × LNEW
Cost and Benefit Calculations

5-46

Eq. 5.26

where:

UCROW = unit costs for right-of-way (in dollars per lane-mile)

indx = index to UCROW; For rural areas, specified by functional system

and terrain type; for urban areas, by facility type.

The unit costs for right-of-way, in 1997 dollars, are shown in Table 5-18, “Right-of-Way Costs for

Alignment Improvements.”91 They may be converted to dollars of another year using the appropriate FHWA price trends.92

5.4.2.2.7 Miscellaneous Costs

Miscellaneous costs estimated by HERS consist of the costs of guard rails and curbs, fencing,

lighting, and the painting of traffic lines93. Total miscellaneous costs, TMC, are estimated:

91. The costs shown in Table 5-18, “Right-of-Way Costs for Alignment Improvements,” are expressed in 1997 dollars.

In the improvement cost file, they are entered in 1988 dollars, and are converted to 1995 dollars by applying factors

of 1.231 (rural) and 1.496 (urban).

Table 5-18. Right-of-Way Costs for Alignment Improvementsa

(1997 Dollars per Lane Mile)

a. Source: Cambridge Systematics, Inc., FHWA Highway Economic Requirements System: Alignment Improvement

Costs, prepared for Jack Faucett Associates and the Federal Highway Administration, Washington, D.C., April

1991, p. D-9. Costs are shown in 1997 dollars per lane mile. Values in original table were adjusted to 1988 dollars by applying a factor of 0.96; 1988 dollars adjusted to 1997 dollars by applying factors of 1.231 (rural) and

1.496 (urban).

Rural Sections

Terrain

Flat Rolling Mountainous

Interstates $ 89,863 $ 80,015 $ 71,398

Other Principal Arterials 80,015 71,398 64,012

Minor Arterials 73,860 64,012 55,395

Major Collectors 71,398 61,550 55,395

Urban Sections

Freeways and Expressways $ 330,616

Other Divided Roads 332,112

Other Undivided Roads 263,296

92. Office of Infrastructure, op. cit..

93. See Table 5-14, “Unit Costs Used for Rural Alignment Cost Computation,” and Table 5-15, “Unit Costs Used for

Urban Alignment Cost Computation,” for the relevant unit costs.

TCROW NL UCROW i j k = × ( ) , , × LNEW
HERS Technical Report v3.54

September 2002

5-47

Eq. 5.27

where UMC(i,j) represent unit miscellaneous costs of type i and j (in dollars per mile). The

parameter i represents the type of cost:

i = 1 Curbs (j=1) or positive barrier (j=2) at median. These costs are assessed

when the original section has curbs or a positive barrier at the median.

i = 2 Curbs (j=1) or guard rails (j=2) at right shoulder. On roads with shoulders: guard rails are assumed to be used over the entire segment in rural

mountainous terrain, and over half the segment in rural rolling terrain and

on urban freeways. On other roads, guard rails are assumed not to be

used.

i = 3 Fencing is assessed for urban freeways only.

i = 4 Painting of traffic lines (j = Number of Lanes/2).

i = 5 Lighting is assessed for urban sections only.

5.4.2.3 Total Improvement Cost

For any section, the total initial improvement cost for combining pavement and widening

improvements with alignment improvements is obtained by combining the cost of reconstructing part of the section on a modified alignment with the cost of the pavement and widening

improvements made to the remainder of the section. The former cost is obtained by combining

clearing and grubbing, earthwork, drainage, structures, pavement, right-of-way, and miscellaneous costs (from Equations 5.20 through 5.27). The latter cost is obtained by multiplying the

cost per lane-mile for the pavement and widening improvements (Table 5-12, “Capital Improvement Costs”) by the length of the portion of the section (if any) that would continue to follow the

existing alignment (the unaligned portion being equal to SLEN - LNEW).

5.4.3 Correcting Substandard Conditions on Urban Freeways

HERS considers an urban freeway substandard if (a) it is an Interstate or Other Freeways and

Expressways (that is, functional class is 11 or 12), and (b) any one of the four deficiencies listed

below applies:

• the shoulders are unsurfaced;

• access control is not full

• the median type is not positive barrier; or

• the median width is less than the design standard for urban freeways and expressways

by design.

For the 1999 C&P Report, the default value for the urban median width design standard was set

to 20 feet.

TMC LNEW UMC i j ( ) ,

i = 1

5

= × ∑
Cost and Benefit Calculations

5-48

HERS will correct these deficiencies only on urban freeways which are being reconstructed.

Improving access control to full and improving the median width to the design standard each

require a lane of right-of-way as coded in the section’s widening feasibility (WDFEAS) data item.

(This data item is part of the section’s HPMS input record.) If the availability of right-of-way is

limited, precedence is given first to adding lanes, then to improving access control, and last to

improving median width. Improvement costs for each upgrade are estimated using the cost data

in Table 5-19, “Improvement Costs - Substandard Urban Freeways.”94 

The costs in Table 5-19 were derived using the following assumptions:

• The cost for improving shoulder type to surfaced is taken as the difference between costs

of resurfacing with shoulder improvement and simple resurfacing for urban freeways

(Table 5-12, “Capital Improvement Costs”);

• Improving access control to full assumes cost of one additional lane right-of-way (Table

5-18, “Right-of-Way Costs for Alignment Improvements”);

• Median barrier costs were derived from recent work95 and adjusted to 1997 dollars;

• The cost of improving the median width to design standard is taken as the combination

of one additional lane of right-of-way (Table 5-18) and the cost for resurfacing (Table 5-

12).

5.4.4 State Cost Factors

Improvement costs are further indexed by state. The cost factors are derived from Price Trends96

as a three-year rolling average, and are applied to all capital costs associated with the improvement. The index values used for the 1999 C&P Report are presented in Table 5-20, “1997 State

Cost Factors.” 

Table 5-19. Improvement Costs - Substandard Urban Freeways

(1997 Dollars)

Improvement Type Cost per Lane-Mile 

1. Shoulder Type to “Surfaced” $192,510

2. Access Control to “Full” 284,418

3. Median Type to “Positive Barrier” 150,282

4. Median Width to Design Standard 458,298

94. The costs shown in Table 5-19 are expressed in 1997 dollars. In the improvement cost file, they are entered in 1988

dollars, and are converted to 1997 dollars by applying a factor of 1.242.

95. M. G. McNally and O. Merheb, “Impacts of Jersey Median Barriers on the Frequency and Severity of Freeways

Accidents”, AAA Foundation for Traffic Safety, Washington, D.C., 1991.

96. Office of Infrastructure, op. cit.

.
HERS Technical Report v3.54

September 2002

5-49

Table 5-20. 1997 State Cost Factors

State Factor State Factor State Factor

AL 0.912 LA 1.056 OH 1.067

AK 1.725 ME 1.215 OK 1.023

AZ 0.863 MD 1.131 OR 0.977

AR 0.827 MA 1.301 PA 1.257

CA 1.096 MI 1.141 RI 0.775

CO 0.897 MN 0.904 SC 1.115

CT 0.896 MS 1.150 SD 0.713

DE 0.887 MO 0.791 TN 0.896

DC 0.923 MT 0.932 TX 0.725

FL 0.922 NE 0.981 UT 0.912

GA 1.058 NV 1.017 VT 1.287

HA 1.360 NH 0.635 VA 1.161

ID 0.567 NJ 0.808 WA 1.557

IL 1.076 NM 0.930 WV 1.165

IN 0.738 NY 1.349 WI 0.832

IA 0.707 NC 0.962 WY 0.784

KS 0.783 ND 0.862 PR 0.535

KY 1.603
Cost and Benefit Calculations

5-50
6-1

6 Effects of HERS Improvements

The effects of each HERS improvement are simulated by changing the description of the characteristics of the sample section. When evaluating potential improvements, HERS builds a temporary description of the section for each of the candidate improvements. (When analysis extends

for more than a single funding period, HERS builds a series of descriptions extending to the end

of the benefit-cost analysis period.) If HERS implements an improvement at the end of processing for a funding period, the altered description is saved for use in the following funding period. 

HERS analyzes the effects of all improvements as if they are implemented instantaneously at the

middle of a funding period instead of being spread throughout the funding period. Accordingly, by the end of a funding period, the PSR of a reconstructed section shows the effect of onehalf period of pavement deterioration. The disruptive effects of improvements are not analyzed.

Sections which do not undergo improvement during a funding period also have their section

descriptions updated to reflect forecast changes in PSR and traffic volume. This “unimproved

condition” is used as a base case in benefit-cost analysis.

Most of the effects of improvements on the “section data items” that form this description are

shown in Table 6-1, “Effects of Improvements on Section Data Items -- All Sections.” The widening options in this exhibit are assumed to be accomplished without any change in rush-hour

parking rules. Effects that occur only when lanes are added to rural sections are shown separately in Table 6-2, “Additional Effects of Adding Lanes on Data Items for Rural Sections.” The

effects of alignment improvements on alignment-related data items (curves and grades, passing

sight distance, and weighted design speed) and on pavement condition are presented in Table 6-

3, “Effects on Section Data Items of Alignment Improvements.” 

The additional effects of improving substandard conditions on urban freeways are presented in

Table 6-4, “Effects of Addressing Substandard Conditions on Urban Freeways.” In HERS, the

changes shown in Table 6-4 are implemented, if feasible, whenever a substandard urban freeway

undergoes pavement reconstruction. 

The effects of improvements on widening feasibility are presented in Table 6-5, “Widening Feasibility Code Adjustments.” Generally, when widening improvements are made, widening feasibility for future improvements is reduced. The exception is sections coded as having unlimited

widening feasibility, for which widening feasibility is never reduced. The values shown assume

that the override factor WDFOVR is set to 5, thus allowing widening in excess of the limits indicated by WDFEAS. However, the urban freeway upgrade and rural section upgrades are not

affected by WDFOVR, and WDFEAS must have a value of at least 3 for an upgrade to be implemented. For these two upgrades, note that WDFEAS is checked after it has already been

adjusted for the “main” improvement. (See paragraph 4.5, ”The Widening Feasibility Model,”

for additional discussion.) 
Effects of HERS Improvements

6-2

Table 6-1. Effects of Improvements on Section Data Items -- All Sectionsa

Section 

Attributes

Improvement Type

Reconstruct 

With More 

Lanes (High 

or Normal 

Cost)

Reconstruct 

With Wider 

Lanes

Reconstruct 

Pavement

Major Widening (High 

or Normal 

Cost)

Minor Widening

Resurface 

W/Shoulder 

Improvement

Resurface 

Pavement

Number of 

Lanesb

Design Number NC NC Design 

Number NC NC NC

Lane Width DS DS NCc DS DS NC NC

Shoulder Typed Existing or 

MTC

Existing or 

MTC

Existing or 

MTC

Existing or 

MTC

Existing or 

MTC

Existing or 

MTC NC

Right Shoulder 

Widthd DS DS DSe DS DS DSe NC

Pavement 

Condition (PSR 

Value)f

Recalculate Recalculate Recalculate Recalculate Recalculate Recalculate Recalculate

Pavement 

Thickness Recalculate Recalculate Recalculate Recalculate Recalculate Recalculate Recalculate

SN or D NC or 

Increase

NC or 

Increase

NC or 

Increase

NC or 

Increase

NC or 

Increase

NC or 

Increase

NC or 

Increase

Surface Typeg DS DS DS DS DS DS DS

Drainage

Adequacy Good Good Good Good Good Good Improve by 1 

Code Value

Peak Capacity Recalculateh Recalculateh NCi Recalculateh Recalculateh NCi NC

a. NC = No Change, MTC = set to Minimum Tolerable Conditions, and DS = set to Design Standard.

b. The design number of lanes is the number of lanes needed to accommodate projected traffic in the design year, and which would be added if widening were not constrained. The two constraints are widening feasibility and the maximum number of lanes allowed. This last number is user specified and can vary with functional class. For the 1999 C&P Report, the maximum number of lanes for all functional classes was 99.

c. For an unpaved section the improvement reconstruct pavement results in paved lane widths equal to the MTC.

d. Curbed sections remain curbed (with zero shoulder width) after improvements.

e. Shoulder only widened if feasible.

f. Changes in PSR specified in Table II-14 of HPMS/AP Technical Manual.

g. If low type pavement exists, resurfacing does not change the pavement type.

h. No change if recalculated capacity is lower than original capacity.

i. If the shoulders are widened, the value is recalculated.

Table 6-2. Additional Effects of Adding Lanes on Data Items for Rural Sections

Data Item Effect

Median Width Widen to design standard or to the extent feasible.

Median Type Set to unprotected if median width is widened and median 

type is currently “none.”

Access Control If median is added and access control is not full, set to partial.
HERS Technical Report v3.54

September 2002

6-3

6.1 The Effects of Improvements on Pavement Thickness

This section discusses the HERS procedure for estimating pavement thickness resulting from

resurfacing and reconstruction and for obtaining the corresponding structural number (SN) for

flexible pavement. As discussed in paragraph 4.2, ”The Pavement Deterioration Model,” SN is

one of the influences on the deterioration rate of flexible pavement, and the deterioration rate of

rigid pavement depends directly on pavement thickness. Additionally, the cost of alignment

improvements is affected by pavement thickness.

In HERS, the design life of a pavement normally is taken to be twenty years. This value can be

modified by the user; however, as pavement thickness is a function of the number of ESALS forecast during the design period, modifying this variable will affect pavement thickness (and hence

pavement durability). Resurfacing or reconstruction cost will be affected only to the extent that

some portion of the section has its alignment improved.

Table 6-3. Effects on Section Data Items of Alignment Improvements

Data Item Effect

Grades Substandard grades are improved to design standard.

Curves Substandard curves are lengthened and improved to design 

standard.a

Passing Sight Distance (For rural two-lane highways only) improve to typical passing 

sight distance (from 1978 data).

Weighted Design Speed Recalculate. If no data on curves by class, increase by 5 m.p.h.b

Pavement Condition 

Obtain as a weighted average of the PSR on the portion of the 

section with modified alignmentc and the PSR indicated in 

Exhibit 3.3 for the remainder of the section.

a. The procedure used for determining the extent to which curves are lengthened is presented in Chapter 5.

b. HERS contains code for adjusting weighted design speed when there is no data on curves by class, but HERS does not consider horizontal alignment improvements when these data are not available.

c. The portion of the section with modified alignment equals the sum of the portions with substandard grades or curves (after lengthening) but is no greater than the length of the section.

Table 6-4. Effects of Addressing Substandard Conditions on Urban Freeways

Data Item Effect

Shoulder Type Improve to surfaced.

Access Control Improve to full control if feasible.a

Median Type Improve to positive barrier.

 Median Width Improve to design standard if feasible.b

a. Improvement to full control is assumed to require one lane of right-of-way.

b. Improvement of median width to design standard is assumed to require one lane of right-of-way.
Effects of HERS Improvements

6-4

The following subsections present the values of pavement thickness for reconstruction, simple

resurfacing, and resurfacing and widening; and a final subsection presents the structural numbers used by HERS for reconstructed and resurfaced flexible pavements.

6.1.1 Reconstruction

Assuming that the reconstructed pavement is designed and constructed as a new pavement

structure, pavement thickness is a function of pavement material and traffic load. HERS

assumes that reconstruction of either rigid or composite (flexible over rigid) pavement is performed with rigid pavement, and that reconstruction of flexible pavement uses flexible pavement. Thicknesses used by HERS for reconstruction of flexible (asphaltic concrete) pavements to

a medium or high-type design standard are shown in Table 6-6, “Pavement Thickness After

Table 6-5. Widening Feasibility Code Adjustments

Original 

WDFEAS 

Code

WDFEAS Code After Improvement

Resurface

Resurface 

with 

Improved 

Shoulders

Reconstruct Widen 

Lanesa

Add 

Lanesb

Urban 

Freeway 

Upgradec

Rural 

Section 

Upgraded

1 (no 

widening) 1 1 1 1 1 NF NF

2 (partial 

lane) 2 2 or 1e 2 or 1e 1 1 NF NF

3 (one lane) 3 3 or 2e 3 or 2e 2 1 1f 1

4 (two lanes) 4 4 43 3 or 1g 4, 3, or 1h NAi

5 (three or 

more lanes) 5 5 555 5 5

where: NF = Not Feasible (the improvement is not made, and WDFEAS is not adjusted); NA = Not 

Applicable.

a. The adjustment is the same whether the section is resurfaced or reconstructed.

b. The adjustment is the same whether the section is resurfaced or reconstructed, and without regard for whether the lanes are added at normal or high cost.

c. Applies when correcting substandard conditions on urban freeways undergoing reconstruction. The model first

tries to improve access control, and then to widen the median to the design standard. Neither improvement is im- plemented (and WDFEAS is not adjusted) if the condition is not substandard.

d. For rural sections when lanes are added, the model will widen the median and improve access control to “partial” if feasible. Unlike the urban upgrade, a single feasibility test (and adjustment) is made for both improvements.

e. If the shoulder is not curbed and is below the design standard, it is widened to and WDFEAS reduced.

f. Only one improvement is implemented. Access control is preferred -- the median will only be widened if access control is already full.

g. If two lanes are added, the WDFEAS code is adjusted to 1 (no widening feasible). If one lane is added, the WDFEAS

code is adjusted to 3 (one lane may be added).

h. Either, neither, or both of the two improvements may be needed or implemented.

i. This value will never be tested for the rural upgrade, as a WDFEAS of 4 would have been reduced as a result of the

added lane(s).
HERS Technical Report v3.54

September 2002

6-5

Improvement,” as are thicknesses for reconstruction of rigid (Portland cement concrete) pavements. For low-type flexible pavement, only a surface treatment is used. 

6.1.2 Simple Resurfacing

HERS assumes that resurfacing is always performed using a flexible overlay. For flexible overlays over flexible, composite, or rigid pavement, the overlay thickness used by HERS varies with

traffic load in the same way as for reconstruction with flexible pavement. These thicknesses are

shown in Table 6-6.

6.1.3 Resurfacing with Widening Improvements

When resurfacing is combined with widening improvements, some part of the improved roadway will be built on land that is not already paved. In general, the newly paved area will be

structurally compatible with the resurfaced roadway. HERS treats resurfacing with widening

improvements as producing a single roadway whose characteristics are those of the original

roadway after resurfacing.

6.2 The Effects of Improvements on Structural Number

HERS assumes that resurfacing or reconstruction never reduces the structural number (SN) of

flexible pavement but may increase its value. To do this, a value of SN is obtained using an

equation that approximates the relationship between SN and pavement thickness presented in

Table IV-3 of the HPMS Field Manual1

. This equation is:

Table 6-6. Pavement Thickness After Improvement

(Inches)

 Forecast ESALs over Design Life Pavement Type 

Flexiblea b c

a. American Association of State Highway and Transportation Officials, AASHTO

Guide for Design of Pavement Structures, Washington, D.C., 1986.

b. Thickness shown for flexible pavements are also used for resurfacing flexible pave- ments with a flexible overlay.

c. For low-type pavement, assume a surface treatment only.

Rigidd

d. E.J. Yoder and M.W. Witczak, Principles of Pavement Design, John Wiley, New York City, 1975.

 ≤ 50,000 1.5 6.5

 50,001 - 150,000 2.5 6.5

 150,001 - 500,000 3.0 6.5

 500,001 - 2,000,000 4.0 8.0

 2,000,001 - 7,000,000 5.0 9.5

> 7,000,000 5.5 10.5
Effects of HERS Improvements

6-6

Eq. 6.1

where Df is pavement thickness, in inches. If the resulting value is less than the original value of

SN coded for the section, SN is set to that value. 

6.3 The Effects of Improvements on PSR

When pavement undergoes reconstruction, HERS sets its PSR to a level determined by the section’s location and surface type. These values may be set by the user. Table 6-7 lists the default

values. 

For sections being resurfaced, HERS adds an increment to the PSR at the time of the improvement. This augmented PSR value is limited to maximum PSR values. These values may be

adjusted by the user. The default values for incrementing PSR are shown in Table 6-8, “Increase

in PSR After Resurfacing,” and the default maximum PSR limits are shown in Table 6-9, “Maximum PSR After Resurfacing.” 

1. U.S. Department of Transportation, Federal Highway Administration, Highway Performance Monitoring System

Field Manual, Washington, D.C., Table IV-2, December 1, 1987.

Table 6-7. PSR Values After Reconstruction

Surface Type Rural Urban

High Flexible 4.6 4.6

High Rigid 4.6 4.6

Intermediate 4.4 4.4

Low 4.2 4.2

Table 6-8. Increase in PSR After Resurfacing

Surface Type Rural Urban

High Flexible 1.8 1.8

High Rigid 1.8 1.8

Intermediate 1.8 1.8

Low 1.8 1.8

SN 1.5 0.75 Df = + ×
HERS Technical Report v3.54

September 2002

6-7

6.4 The Effects of Alignment Improvements on Pavement Characteristics

For any section, an improvement that combines pavement reconstruction with alignment

improvements results in producing newly reconstructed pavement on the entire section. Such

improvements produce a single type of pavement and a single PSR for the entire section.

On the other hand, improvements that combine resurfacing with alignment improvements produce a single PSR only in the (relatively rare) case in which the alignment of the entire section is

improved. More commonly, such improvements produce one PSR for the portion of the section

on which alignment does not change and a higher PSR on the portion that is reconstructed on a

modified alignment. Furthermore, resurfacing of rigid or composite pavement is presumed to

be performed with a flexible overlay (producing composite pavement), while the adjoining

reconstructed pavement is presumed to be rigid. For both cases, HERS obtains a single combined PSR for the section by taking a weighted average of the PSRs on the two portions of the

section, using the lengths of these portions of the section as weights. For the case in which part

of the section receives a flexible overlay on composite or rigid pavement and part is reconstructed with rigid pavement, HERS uses the relative length of the two portions of the section to

determine whether to treat the section as having rigid or composite pavement.

Table 6-9. Maximum PSR After Resurfacing

Surface Type Rural Urban

High Flexible 4.3 4.3

High Rigid 4.3 4.3

Intermediate 4.2 4.2

Low 4.0 4.0
Effects of HERS Improvements

6-8
7-1

7 Evaluating Improvements 

After potential improvements have been identified, HERS evaluates them to gauge their economic attractiveness. HERS makes decisions about improvements on the basis of the ratio of the

net present value of each improvement's incremental benefits to the present value of the incremental costs. This ratio is referred to as the incremental benefit-cost ratio, or IBCR. The decisions HERS makes based upon IBCR are:

• Does the section warrant improvement during this funding period?

• If so, which is the economically most attractive improvement for this section?

In a constrained scenario, HERS also asks:

• Among the potential improvements to all sections in the highway system under analysis,

which are the economically most attractive?

This chapter first presents the steps HERS uses in determining the benefit-cost ratio (BCR, used

interchangeably with IBCR). It then examines how HERS uses the BCR to answer the three questions.

The evaluation process consists of determining the benefit-cost ratio of each candidate improvement. This is accomplished in several steps:identifying the base case;

1. identifying the base case;

2. determining the length of the analysis period;

3. determining the user, agency, and external costs associated with the base case;

4. determining the user, agency, and external costs associated with the candidate improvement;

5. determining the capital cost of the improvement;

6. determining the residual value of the improvement; and

7. calculating the benefit-cost ratio.

This chapter addresses the process of determining the BCR for candidate improvements. The

detailed discussions of the calculations involved are discussed in Chapter 4, ”HERS Internal

Models” (the forecast of traffic volume and pavement condition) and Chapter 5, ”Cost and Benefit Calculations” (the calculation of user, agency, external, and capital costs).

7.1 The Base Case

In a typical HERS run, when the option to force the model to address unacceptable conditions

has not been selected, the initial base case is the unimproved section. That is, the potential benefits of candidate improvements will be compared against the case in which no improvement is

made to the section. HERS uses this base case when determining whether a section warrants
Evaluating Improvements

7-2

improvement during the current funding period (see paragraph 7.8, ”Does a Section Warrant

Improvement?”). However, if the option to force the model to make mandatory improvements

to address unacceptable conditions has been selected, HERS uses the mandatory improvement

as the base case.

HERS also uses a previously selected improvement as the base case when considering more

aggressive improvements. This situation commonly arises in the selection process for constrained runs, and is also used to discover the economically most attractive improvement for a

section during a minimum BCR run. Since the differences between the costs and benefits of the

two improvements are used in calculating the benefit-cost ratio, the term ‘incremental benefitcost ratio’, or IBCR, is often used interchangeably with the term ‘benefit-cost ratio’.

7.2 Determining the Benefit-Cost Analysis Period

HERS evaluates the benefits and costs of potential improvements for different lengths of time in

order to accommodate section-specific situations and in response to two different questions

HERS evaluates: “Should the section be improved now? And if so, what is the best improvement

to make?” The benefit-cost analysis period (BCA period) can be a single funding period, or multiple funding periods in length. Analysis over a multi-period time-frame is more complex and

requires more computation than analysis over a single period.

Generally, when evaluating whether to improve the section during the current funding period,

HERS uses a benefit-cost analysis period equal in length to one funding period. This BCA period

would start at the midpoint of the current funding period, and extend to the midpoint of the next

funding period (see Exhibit 2-6, “HERS Time Periods”). When determining which of several

candidate improvements would be the best improvement for the section, a longer BCA period is

used, beginning at the midpoint of the current funding period and extending to the midpoint of

some subsequent funding period. It should be noted that when there is more than one candidate

improvement, the same BCA period is used for all of the improvements under consideration. 

Table 7-1, “Length of BCA Period,” provides a brief summary of how the last funding period of a

BCA period is determined. Benefit-cost analysis periods consist of an integral number of funding periods, and extend from the mid-point of the funding period in which the improvement is

implemented to the midpoint of some subsequent funding period. 

The opening paragraph of this chapter framed the first question asked by HERS:

• Does the section warrant improvement during this funding period?

The phrasing of this question is significant. In highway management, the issue is not whether a

section should be improved, but when? In many cases warranting careful analysis, the two most

serious alternatives are “improve during the current funding period” and “improve during the

next funding period.” For such cases, the HERS procedure usually evaluates improvements that

might be implemented during the current funding period by comparing them to a “base case” in

which the same improvement is implemented during the next funding period (and no improvement is implemented during the current funding period). Use of such a base case, in conjunction

with a procedure for estimating the residual value (see paragraph 7.6 below) of an improvement,

permits frequent use of analysis periods that are only one funding period long. 
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Consider a section for which no improvement has yet been selected during the current funding

period. The analysis of potential improvements to such a section addresses the question as to

whether any of the improvements should be implemented during the current funding period. If

the section does not have any unacceptable conditions, this analysis depends upon whether or

not traffic volume on the section is increasing. These two alternatives are discussed below; the

special case of a section with unacceptable conditions is discussed in paragraph 7.11, ”Selecting

Mandatory Improvements.”

7.2.1 Traffic Volume on Section is Constant or Increasing

Consider a section in which traffic volume is constant or increasing, and consider a potential

improvement that is likely to either warrant funding during this period or at least to come close.

If traffic is relatively constant, the annual benefits of such an improvement will also be relatively

constant over the life of the improvement; if traffic is increasing, the annual benefits will grow

over time. If the improvement is implemented in the next funding period, it will generate at

least as many benefits over its life as it would if it were implemented in the current period.

Therefore, if it is practical to implement the same improvement in the next funding period and if

it fails to be selected during the current period, it will almost certainly be selected for implementation during the following period. Accordingly, the issue is: should the improvement be implemented in this period or in the next one? Therefore, in most instances, HERS analyzes any

potential improvement to such a section by estimating the benefits and costs of implementing it

in this period relative to a base case in which it is implemented in the next period. With an

appropriate definition of the residual value of the improvement (see paragraph 7.6, “Residual

Value”) at the end of the BCA period, the BCA period can be limited to a single funding period.

Table 7-1. Length of BCA Period

Situation Being Analyzed Funding Period in Which BCA Period Ends

Section for which no improvement has yet been 

selected during the current funding period:

If section is in unacceptable condition or 

unpaved; Next funding period

Otherwise, if current funding period is the last 

one in which resurfacing is practical;

Period in which condition first becomes unacceptablea

Otherwise, if traffic volume is declining and 

improvement involves reconstruction;

Period in which condition first becomes unacceptablea

Otherwise, if traffic volume is declining; Last period in which resurfacing is practical

Otherwise. Next funding period

Section for which an improvement has already been 

selected during the current funding period.

Next period in which pavement would “normally” be improved or period in which condition becomes unacceptablea, whichever occurs 

first.

a. Unacceptable conditions that cannot be corrected (e.g., those that require more widening than is feasible) are excluded from consideration in this test.
Evaluating Improvements

7-4

The one exception to the above procedure occurs in the case of improvements that cannot be

implemented in the next funding period. Because of the mechanistic way in which HERS handles the resurfacing/reconstruction decision, this situation arises whenever the PSR of a section

drops below the “reconstruction level” during the current funding period. In this situation, a relatively inexpensive improvement (involving resurfacing) can be made during the current funding period1, but only a much more expensive improvement (involving reconstruction) can be

made in the next period. If the section is not improved in the current funding period, it is

unlikely to warrant a more expensive improvement in the next period. Accordingly, potential

improvements to such a section should be analyzed relative to a base case in which no improvement is made for a more extended time period. In HERS, any potential improvement to such a

section is analyzed by estimating the benefits and costs of implementing it in this period relative

to a base case in which improvement of the section is postponed until the PSR becomes unacceptable.

7.2.2 Traffic Volume on Section is Declining

For a section with declining traffic volume, the annual benefits tend to decline over time. An

improvement implemented during the current funding period will generate more benefits over

its life than one implemented during the next period. Accordingly, if the benefit-cost analysis

procedure indicates that the section does not warrant improvement in the current funding

period, then, unless conditions change, the procedure is unlikely to indicate that improvement is

warranted in subsequent funding periods on the basis of a benefit-cost ratio.

In this situation, if the section is paved, and the PSR is not already unacceptable, an appropriate

base case frequently consists of not improving the section until its PSR becomes unacceptable

and improving the section becomes mandatory. However, there are two cases in which a shorter

timeframe is used. One case occurs when the section is already in unacceptable condition; in this

case, a single-period BCA period is used.

The other case occurs when it is still possible to resurface the section during the next funding

period. Because reconstruction is much more expensive than resurfacing, it may not be desirable

to postpone improving the section until reconstruction is required. Accordingly, for this situation, potential improvements are analyzed relative to a base case in which no improvement is

implemented until the last funding period in which resurfacing is still practical (according to the

reconstruction-level criteria).

In the case of unpaved sections with declining traffic volume, if an improvement is not implemented in the current funding period, it may well never be implemented.2

 For such sections, a

very long (or even infinite) BCA period is appropriate. However, the benefits of improvements

to such sections will usually be low, and such improvements are likely to have relatively unat1. Although all improvements are analyzed as if they are implemented in the middle of a funding period, it is recognized that actual implementation of several improvements will be spread over an entire funding period. Accordingly, it is reasonable to presume that sections for which resurfacing is feasible at the beginning of the funding

period but not at the end can be resurfaced while resurfacing is still considered to be feasible (according to the artificial resurfacing/reconstruction decision criterion).

2. The only situation in which the improvement is implemented in a subsequent funding period occurs when its B/C

ratio is greater than one, but there are insufficient funds to implement it in the current funding period. If the userspecified assumptions allow funding of improvements with lower B/C ratios in subsequent periods than in the current period, the improvement may warrant implementation in such a subsequent period.
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tractive B/C ratios. For computational efficiency and simplicity, HERS evaluates such improvements relative to a base case in which the improvement is deferred for one funding period

resulting in some overestimation of improvement benefits. (The degree of overestimation varies

with the extent to which traffic is declining.) It is believed that this computational simplification

has no material effect on the selection of improvements for such sections; however, this assertion

has not been tested. 

7.3 Estimating Variable Costs for the Base Case

After determining the length of the BCA period, HERS calculates the costs associated with the

base case for each of the funding periods involved. First (if it has not already been calculated

while identifying candidate improvements), HERS predicts the traffic volume (see paragraph

4.3, ”The Travel Forecast Model”) and pavement condition (see paragraph 4.2, ”The Pavement

Deterioration Model”) at the end of the funding period. It then calls upon the routines which calculate the operating costs, travel time costs, safety costs, maintenance costs, and emissions costs

(see Chapter 5, ”Cost and Benefit Calculations”). The costs are calculated for the end of the funding period. This process of prediction and cost calculation is repeated for each funding period in

the BCA period.

7.4 Determining Costs Associated with the Candidate 

Improvement

The process of calculating the costs associated with the potential improvement is similar to that

for the base case. The model first simulates the effect of the improvement on the section (see

Chapter 6, ”Effects of HERS Improvements”). This establishes the pavement condition at the

time of the improvement, and HERS applies short-run elasticity to determine the new traffic volume (see paragraph 4.3.4, ”The Simultaneous Solution”). Traffic volume and pavement condition are then forecast for the end of the funding period, and the cost calculation routines are

called upon to determine the user, agency, and external costs associated with the improved section at that time. The model then repeats the prediction and cost calculation for each funding

period in the BCA period.

7.5 Determining the Capital Costs of the Improvements

For most sections being improved, HERS calculates the capital cost by multiplying the cost per

lane mile by the number of lanes and by the length of the section. The cost per lane mile depends

upon the particular improvement, the section’s functional class, and, for rural sections only, the

prevailing terrain (flat, rolling, or mountainous). For sections receiving alignment improvements, HERS employs a more complex approach (including the cost of earthwork, clearing and

grubbing, pavement, etc.) to determine the cost over the portion of the section being re-aligned.

Portions of the section not being re-aligned are costed in the same manner as sections receiving

no alignment improvements.

See paragraph 5.4, ”Capital Cost of Improvements,” for the detailed presentation of how HERS

calculates improvement costs.
Evaluating Improvements

7-6

7.6 Residual Value

This section is divided into two parts. The first part consists of a summary or overview definition of the “residual value” of an improvement. The second part provides a much more detailed

description of this value.

7.6.1 A Summary Definition

For purposes of benefit-cost analysis, HERS regards the residual value of a highway improvement as analogous to the “salvage value” of a piece of equipment. At the end of the period being

analyzed (the normal life-cycle of a piece of equipment), the equipment has some salvage value

that can be recovered by the entity that originally invested in the equipment and can be applied

toward the purchase of a replacement. Similarly, in the case of a highway improvement, at the

end of the benefit-cost analysis (BCA) period, the improvement has some residual value that

reduces the cost of the next improvement.

Residual value differs from salvage value in that, for some improvements, the residual value can

be quite high. Consider, for example, an improvement consisting of reconstruction and

improved alignment. The new pavement has a finite life, say 15 years, but the improved alignment has an effectively infinite life. Another improvement (e.g., resurfacing) will be required at

the end of 15 years, but benefits of the new alignment will continue beyond then. If the benefits

and costs of this improvement are analyzed over 15 years (i.e., until the next improvement is

required), the benefits of the improved alignment that will accrue beyond the end of this 15-year

period must be taken into consideration. To avoid the need to estimate these benefits for many

periods into the future, it is assumed that, if alignment were not improved now, it would be

improved at the end of the 15-year BCA period. The residual value of the improvement then

represents avoided costs of not improving the alignment in 15 years.

In the above example, the residual value is not limited to that of the alignment improvement.

Pavement reconstruction itself results in substantial improvement in the roadbed that significantly reduces the cost of the pavement improvements that would be required in 15 years.

7.6.2 Detailed Description of Residual Value

This section presents a formal definition of the residual value of an improvement, I1, at the end

of the benefit-cost analysis (BCA) period over which it is analyzed.

Assume that the BCA period starts at time T1 and ends at time T2.

First consider the case in which no improvements are likely between T1 and T2 regardless of

whether I1 is implemented. Then, let I3 be the most likely improvement (if any) to be made at T2

if I1 is implemented at T1. Next consider the case in which I1 is not implemented and let I2 be

the more extensive improvement required at T2 in order to produce the same conditions that

would exist if I1 were implemented at T1 and I3 were implemented at T2. Then the residual

value of I1 at time T2 is the cost of I2 minus the cost of I3. Although one would expect the residual value of an improvement to be smaller than its initial cost, this is not always the case. In particular, if I2 involves reconstruction while I1 and I3 do not, the residual value of I1 at time T2 can

be appreciably greater than the initial cost of I1.
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The present value of the residual value is then obtained by discounting the residual value back to

the beginning of the BCA period; i.e., by dividing by (1+r)n, where r is the (user-specified) discount rate and n is the length of the BCA period in years (that is, n=T2-T1). If, for example, a

value of seven percent1

 is used for the discount rate, the residual value of an improvement at the

end of twenty years is divided by 3.869 (which is equal to 1.0720) to obtain its present value.

A common special case of the above definition occurs when no improvement would normally be

made at time T2 if I1 is implemented at time T1. In this case, I2 is the improvement implemented

at time T2 to produce the same conditions at T2 that would exist if I1 were implemented at T1. 

If one or more improvements are likely between T1 and T2, the definition of the discounted

value of residual value becomes more complex. To develop a more general definition, let A1 be

the set of improvements, if any, to be made during or at the end of the BCA period if I1 is implemented at T1; and let S2 represent the resulting condition at T2. Let A0 be the set of improvements, if any, that would be made during the BCA period if I1 is not implemented at T1; and let

S3 be the resulting condition at T2. Let I2 be the improvement that would bring the section from

condition S3 to condition S2. Finally, discount the costs of I2 and of all improvements in A0 and

A1 back to time T1 by dividing the cost of each improvement by (1+r)n, where n = Ti - T1, and Ti

is the year in which the improvement is implemented. Then the (net) present value of the residual value of I1 is obtained by subtracting the discounted cost of any improvements in A1 from

the sum of the discounted cost of I1 and the discounted cost of any improvements in A0. Provided no confusion results, we may, for brevity, refer to the “present value of the residual value”

simply as the “residual value.”

The present value of the residual value is treated as an agency benefit and incorporated into the

numerator of the benefit-cost ratio. This procedure seeks to optimize the benefits obtained from

funds available during a single funding period.

7.7 The Benefit-Cost Ratio

The formal HERS benefit-cost ratio, as shown in Equation 7.1 below, compares a base case to a

potential improvement. The base case may be the unimproved section or a previously identified

improvement, in which case all potential improvements will be more aggressive than the base

case improvement. The HERS procedure includes estimation of the incremental costs and benefits of each potential improvement for each period of the benefit-cost analysis period, as well as

estimation of the improvement’s residual value at the end of the analysis period. The residual

value of the improvement is discounted back to the initial year of the analysis period and treated

as a benefit of the improvement.

Eq. 7.1

where:

IBCR = incremental benefit-cost ratio;

1. As recommended by the Office of Management and Budget, a discount rate of seven percent was used in runs supporting the 2002 Conditions and Performance Report.

IBCR

UCostB ACostB ECostB ( ) + + UCostI ACostI ECostI – ( ) + + + RV

ImpCostI ImpCostB – = -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Evaluating Improvements

7-8

UCost = user costs (travel time costs, operating costs, and safety costs) for

either the base case B or the improved case I;

ACost = agency costs (maintenance costs) for either the base case B or the

improved case I;

ECost = external costs (emissions costs) for either the base case B or the

improved case I;

RV = residual value of the improvement relative to the base case; and

ImpCost = the capital cost of either the base case B or the improved case I, or

zero when the base case is unimproved.

The actual process is slightly more complex. When the benefit-cost analysis period is longer than

one funding period in length, benefits must be calculated and accrued for each period. These

accruing benefits are then discounted back to the time of implementation. The introduction of

demand elasticity results in different traffic volumes for the base and improved case in each subsequent period. This yields a consumer surplus which must be included in the IBCR calculations

for benefit components which are dependent upon VMT. (HERS calculates consumer surplus

for operating cost benefits, safety benefits, and travel time benefits.) 

In Exhibit 7-1, “User Benefits and Consumer Surplus,” the base case is represented by the price

p0 and the volume q0, which intersect on the demand curve. The price to the user after improvement is represented by p1, and results in movement along the demand curve to yield the

increased volume q1. The rectangle labeled “user benefits” represents lower user costs on trips

which would have been made had the improvement not changed the price to the user. The triangle labeled “consumer surplus” represents benefits from the additional trips that resulted from

the lower price. 

Exhibit 7-1. User Benefits and Consumer Surplus

Demand

q 0 q1

p0

p1

incremental

consumer surplus

"old trips" "new trips"

user cost savings

vehicle volume

user

costs
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7-9

For each funding period, HERS first determines the gross benefit for each of the benefit components: travel time benefits, safety benefits, and operating cost benefits (grouped as user benefits);

maintenance cost benefits (agency benefits); and emission cost benefits (external benefits).

Maintenance costs are calculated per lane mile; all other components are per vehicle mile traveled. For each of the components, the benefit is:

Eq. 7.2

where:

BEN = the benefit for a specific cost component;

COSTB = the base case cost for a specific cost component; and

COSTI = the improvement case cost for a specific cost component.

HERS also computes a discount factor based upon the user-specified discount rate:

Eq. 7.3

where:

DFACTR = discount factor;

DRATE = 1 + the user-specified discount rate divided by 100;

LFP = length of a funding period in years; and

FPC = funding period counter pointing to funding period under analysis.

The discount factor is calculated separately for each funding period in the analysis period. HERS

next calculates the “per-vehicle” benefit for user and external benefits:

Eq. 7.4

where:

BENPV = discounted benefit per vehicle trip;

SLEN = the section length in miles;

OPBEN = operating cost benefits per VMT;

SAFBEN = safety benefits per VMT;

TTBEN = travel time benefit per VMT; and

EMBEN = emission cost benefit per VMT.

The interim total in Equation 7.4 includes the discounted benefits for each mile traveled over the

section for each day of the funding period for the benefit components expressed by VMT. However, it does not include traffic volume, neither the “old trips”, or the “new trips” which result

from the change in user price. HERS calculates the total benefit to include the benefits from “old

trips”, the consumer surplus, and the discounted maintenance cost savings:

Eq. 7.5

BEN COSTB COSTI = –

DFACTR DRATE( ) LFP FPC × ( ) – 0.5 =

BENPV LFP 365 × SLEN OPBEN SAFBEN TTBEN

EMBEN

( + ++

)

= × ×

⁄ DFACTR

TOTBEN BENPV AADTB × BENPV

AADTI AADTB –

2 ----------------------------------------------

MNCBEN DFACTR ⁄

= + × +
Evaluating Improvements

7-10

where:

TOTBEN = discounted total benefits for the funding period;

AADTB = AADT for the base case B;

AADTI = AADT for the improved case I; and

MNCBEN = maintenance cost benefit for the period.

This total, TOTBEN, is calculated for each funding period of the benefit-cost analysis period.

When benefits have been calculated for all periods of the benefit-cost analysis period, HERS calculates the IBCR for the improvement:

Eq. 7.6

where:

IBCR = the incremental benefit-cost ratio for the improvement;

TOTBENSUM = the sum of the discounted total benefits for all funding periods in

the benefit cost analysis period;

RV = the discounted residual value of the improvement;

IMPCOSTI = the capital cost of the improvement being analyzed; and

IMPCOSTB = the capital cost of the base case improvement (zero when the base

case is “no improvement.”)

7.8 Does a Section Warrant Improvement?

When considering one or more candidate improvements for a section, HERS calculates the BCR

for each of them relative to the same base case and for the same evaluation period. When the

user has not requested mandatory improvements HERS will decide whether or not the section

warrants improvement based upon the highest BCR relative to the unimproved base case.

Except for the cases discussed in paragraph 7.2 (declining traffic or the current period is the last

one in which resurfacing is practical), the benefit-cost analysis period will be one funding period

in length. HERS will not improve the section if the highest BCR is less than the qualifying

threshold. For constrained runs, the threshold is set at 1.0. For minimum BCR runs, the user

specifies the minimum BCR in the specification file. (The term “economic efficiency run” is used

for a minimum BCR run with a minimum BCR of 1.0.)

The case of a section where improvement is not warranted by benefit-cost analysis is shown in

Exhibit 7-2. Three potential improvements have been identified for the section, numbered 10, 20,

and 30. The cost of each improvement is shown on the x-axis (shown as c10, c20, and c30), and

the benefits of each improvement during the benefit-cost analysis period are plotted on the yaxis (b10, b20, and b30). For each improvement, a dotted line is drawn from the origin through

the intersection of its costs and benefits depicting the improvement’s benefit-cost ratio. These

are labeled r10, r20, and r30 (the “r” is for ratio). The dashed line drawn at 45° represents a benefit-cost ratio of 1.0. Potential improvement 10 has the highest benefit-cost ratio, as it is closest to

45°; however, as in the other two cases, the potential benefits are less than the capital costs, and

the section will not be improved. 

IBCR

TOTBENSUM + RV

IMPCOSTI IMPCOSTB ( ) – = -------------------------------------------------------------------------
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7-11

Exhibit 7-3, “Section Warranting Improvement,” illustrates the case of a section where two of the

potential improvements have initial benefit-cost ratios greater than 1.0. (These initial BCRs are

calculated over a single funding period.) In this case, potential improvement 10 has the highest

benefit-cost ratio. In a minimum BCR run, either improvement 10 or 20 will be implemented; in

a constrained run, improvements 10 and 20 will be eligible for implementation. 

When the user has specified mandatory improvements, all sections for which mandatory

improvements have been identified are deemed to justify improvement and, unless the funding

limits are reached in a constrained fund run, will be improved. Thus, if improvement 10 in

Exhibit 7-2 were a mandatory improvement, it would be implemented even though its benefitcost ratio is less than 1.0. A discussion of the selection of more aggressive improvements, including the replacement of mandatory improvements, is contained in the next section.

7.9 Selecting Improvements

As first presented in Chapter 2, ”An Outline of the Model Structure,” the HERS process has several variants depending upon the analytical objective and whether the user has stipulated that

mandatory improvements must be made to correct unacceptable conditions. Previous section in

this Chapter presented the steps HERS uses to calculate an improvement’s BCR and to determine

whether a section warranted improvement during the current funding period. This Section

examines the HERS methods for deciding which improvement to implement on sections warranting improvement and, during a constrained run, which of the sections warranting improvement will be improved and which will not be improved. The first part of this Section examines

the process when no mandatory improvements have been specified by the user, first for minimum BCR runs, followed by the process for constrained runs. The second portion of this Section

Exhibit 7-2. Improvement Not Warranted

Benefits

Costs

Benefits = Costs

(BCR = 1.0)

Imp 10

Imp 20

Imp 30

b10

b20

b30

c10 c20 c30

r10

r30

r20
Evaluating Improvements

7-12

contains a discussion of how mandatory improvements are involved in the selection process for

each of the three analytical objectives.

7.10 Improvement Selection Without Mandatory 

Improvements

In most cases, the HERS model is run without the specification of mandatory improvements.

(This includes runs used in preparation of the 1995, 1997, 1999 and 2002 C&P Reports.) As shown

in Exhibit 2-1, “HERS Process Flow Without Mandatory Improvements,” HERS uses either of

two logic flows when selecting improvements without mandatory improvements. When conducting a minimum BCR analysis, HERS is able to select an improvement for each section immediately after evaluating its potential improvements and determining that it warrants

improvement during the current funding period. During a constrained run, HERS “pre-selects”

a list of improvements for those sections warranting improvement, and, after processing all sections, selects from that list until the specified constraint has been satisfied. These two processes

are presented below in more detail.

7.10.1 Minimum BCR Analysis

When the analytic objective stipulates a minimum BCR run, every section which warrants

improvement will be improved. For these sections, then, the question HERS asks is:

• What is the economically most attractive improvement for this section?

Exhibit 7-3. Section Warranting Improvement

Benefits

Costs

Imp 10

Imp 20

Imp 30

c10 c20 c30

b10

b20

b30

r10

r20

r30

1.0
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7-13

When determining that a section warrants improvement during the current funding period,

HERS calculates BCRs for all the potential improvements and identifies the improvement with

the highest initial BCR. This improvement is designated the base case improvement. This base

case improvement might not be the most desirable improvement to implement during this

period. It may be that an improvement that costs more and generates more benefits is more

desirable. 

In Exhibit 7-4, “Initial Improvement for Minimum BCR Run,” improvement 10 has the highest

initial benefit-cost ratio relative to the unimproved base case: it’s benefit-cost line (labeled “r10”)

lies above those for improvements 20 and 30. Improvement 10 has qualified the section for

improvement, as its BCR is greater than the minimum threshold of 1.0. Improvements 20 and 30

would also have justified improvement in this funding period. Because no improvement had yet

been selected for the section, and no special conditions prevailed, the length of the benefit-cost

analysis period was set to a single funding period. (See paragraph 7.2, ”Determining the BenefitCost Analysis Period,” for details.) Improvement 10 thus becomes the new base case improvement against which the BCRs of more aggressive improvements will be calculated. 

To determine whether a more desirable improvement exists, HERS next identifies all more

aggressive improvements worth analyzing. HERS then estimates the incremental benefits and

costs of implementing each more aggressive improvement relative to the new base case improvement. 

In general, the more aggressive improvement will incorporate some widening and/or alignment

option not included in the base case improvement. If this option is not implemented in the current funding period, normally, it is not likely to be implemented until the section is next resurfaced. Accordingly, the incremental benefits and costs of immediately implementing the more

Exhibit 7-4. Initial Improvement for Minimum BCR Run

Benefits

Costs

Imp 10

Imp 20

Imp 30

r10

c10 c20 c30

b10

b20

b30

r30 1.0

r20
Evaluating Improvements

7-14

aggressive improvement are analyzed over a time frame that ends when the section would normally next be resurfaced. In HERS, the length of this time frame is limited to sixty years when

the funding period length is two years or longer and to forty years, when one-year funding periods are used.1

The example continues in Exhibit 7-5, “Selecting a More Aggressive Improvement.” Here, incremental benefit-cost ratios have been calculated for improvements 20 and 30 relative to improvement 10. The length of the benefit-cost analysis period has been determined by the “normal life”

of improvement 10, which extends for several funding periods. For the more aggressive

improvements, the longer benefit-cost analysis period allows for accrual of more total benefits at

the same level of initial capital investment. In the exhibit, the increased benefit levels (subscripted “nl” for “normal life”) are shown by the dotted lines which extend the figures for

improvements 20 and 30 along the benefits axis. Note that the BCR for the base case improvement (improvement 10 in the example) is not re-calculated over the normal life. 

Improvement 10’s initial benefit-cost ratio is still more attractive than the “normal life” BCRs of

the other two potential improvements. This is shown in Exhibit 7-5, as the two new BCRs (subscripted “nl”) lie to the right of improvement 10’s BCR. Note that the two new BCRs are drawn

as originating from the intersection of improvement 10’s costs and benefits. This is because the

normal life BCRs are calculated relative to the “base case” of improvement 10. The line representing the minimum BCR threshold of 1.0 also originates from this point. The normal life ratios

for improvements 20 and 30 lie above (to the left of) this threshold line. 

1. A review of improvements analyzed by HERS indicates that resurfacing is usually expected to occur in less than 40

years after a section is improved, sometimes in 40 years to 55 years, and never in more than 55 years.

Exhibit 7-5. Selecting a More Aggressive Improvement

Benefits

Costs

Imp 10

Imp 20

Imp 30

BCR = 1.0 relative 

to Imp 10

r10

b20nl

b30nl

r20nl r30nl
HERS Technical Report v3.54

September 2002

7-15

The algorithm examines the candidate improvements in order. Finding that improvement 20’s

BCR is greater than that of improvement 30 (both relative to improvement 10), it designates

improvement 20 as the new base case and re-calculates improvement 30’s BCR relative to

improvement 20. Once again, the length of the benefit-cost analysis period is determined by the

normal life of the base case, which in this iteration is improvement 20. In our example, improvements 10 and 20 share the same life span, although this may not always be the case. As shown in

Exhibit 7-6, improvement 30’s BCR relative to improvement 20 (labeled r30nl and originating

from the intersection of improvement 20’s costs and benefits) lies below the 1.0 threshold, therefore it is not selected to replace improvement 20 and will not be implemented. Improvement 20

is therefore selected for implementation. 

7.10.2 Constrained Analysis

In a constrained run, whether the constraint is a performance goal or a funding limit, it is possible that not all sections warranting improvement will actually be improved. HERS uses benefitcost analysis to identify the most attractive set of improvements to meet the analytical objective.

If the constraint is a funding limit, the model chooses the set of improvements which will return

the greatest net benefit for the capital investment. When the constraint is the attainment of a

specified level of highway system performance, the model chooses the set of improvements

which will meet the goal with the least expenditure of capital. 

Conceptually, the method is easily visualized: calculate BCRs for all possible improvements for

all sections, order them by BCR, and select them for implementation in order of economic attractiveness until the constraint/goal is reached. The process is the same for the two types of constraints: the difference is in determining that the constraint has been reached, either (a) all the

Exhibit 7-6. Rejecting a More Aggressive Improvement

Benefits

Costs

BCR = 1.0 relative

to Imp 20

Imp 10

Imp 20

Imp 30

b20nl

b30nl

r30nl
Evaluating Improvements

7-16

funds have been expended, or (b) enough improvements have been implemented to satisfy the

performance goal. 

In practice, HERS uses a ‘two-listed’ approach which avoids calculating incremental BCRs for

more aggressive improvements until they are actually candidates for selection. As with the minimum BCR option, HERS calculates BCRs for all candidate improvements to determine whether

the section warrants improvement during the current funding period. Typically, these are calculated over a benefit-cost analysis period extending for a single funding period. Having identified the candidate improvement with the highest initial BCR, that improvement is placed on a

list of improvements for potential selection. 

After HERS has processed all the sections in the highway system, it has a list of potential

improvements. Each list entry consists of:

• a section number, 

• an improvement number, 

• and the improvement’s BCR. 

Only sections which warrant improvement during the current funding period are placed on the

list. The improvement specified for a section is the one with the highest BCR relative to the

unimproved base case. 

The list of selected improvements is ordered by section number and contains the number of the

improvement selected for implementation on the section. If no improvement has been selected,

zero is used as the improvement number. Initially, all list entries are set to zero.

HERS begins by sorting the potential improvement list by BCR. The list is processed in order of

descending BCR. The number of the improvement from the potential list is placed on the list of

selected improvements. The model checks whether implementing this improvement violates the

funding constraint or satisfies the performance goal. If not, it examines any more aggressive

improvements which may have been identified for the section.

A more aggressive improvement might be the better choice for implementation in the current

funding period if the original selection of the less aggressive improvement was due to a bias

toward low-cost improvements resulting from restricting the original analysis to a single time

period. (This shorter analysis period is employed in order to determine whether improving the

section during this funding period is economically justified.) If this is the case, the incremental

BCR obtained for the more aggressive improvement (relative to the less aggressive improvement) will be higher than the BCR obtained for the original improvement, and an immediate

decision will be made to select the more aggressive improvement.1

 Accordingly, HERS calculates incremental BCRs for all more aggressive improvements using a benefit-cost analysis

period which corresponds to the normal life of the base case improvement. The “most recently

selected” improvement is used as the base case. If there are even more aggressive improvements,

1. The decision as to whether or not to postpone the improvement for one period is based on the BCR of the original

improvement, which is calculated over a single period. The IBCR of the more aggressive improvement is calculated

over a longer time period. In this case, if any improvement is to be implemented, it is the one with the higher IBCR

-- i.e., the more aggressive one. In order to guarantee this result, some special code is required when full implementation of either improvement results in exceeding a funding constraint or a benefits goal. In this situation, the more

aggressive improvement is implemented on some of the mileage represented by the sample section, and no

improvement is implemented on the remaining mileage; the number of miles to be improved is determined so that

the specified objective is just reached.
HERS Technical Report v3.54

September 2002

7-17

the model repeats the process using the newly selected improvement as the base case, and its

‘normal’ life as the length of the benefit-cost analysis period. 

This is illustrated in Exhibit 7-7, “Selecting Improvements in a Constrained Run.” Improvement

10 was placed on the potential improvement list for the section during the initial evaluation procedure. The selection procedure uses improvement 10 as the base case when calculating incremental BCRs for the more aggressive improvements 20 and 30, and uses the normal life of

improvement 10 as the length of the benefit-cost analysis period. The increases in benefits due to

the longer analysis period are labeled b20nl and b30nl for improvements 20 and 30, respectively. 

The incremental BCRs for improvements 20 and 30 are greater than the BCR for improvement 10.

Of the two, improvement 20 is the most attractive: its BCR, r20nl, lies above improvement 30’s

r30nl. HERS removes improvement 10 from the list of selected improvements and replaces it

with improvement 20. 

HERS then repeats the process, calculating the BCR of improvement 30 relative to improvement

20, and using the normal life of improvement 20 for the length of the analysis period. As shown

in Exhibit 7-8, “Detecting Potential Improvements in a Constrained Run,” the BCR of improvement 30 is less attractive than the BCR of improvement 20, as r30nl lies to the right of r20nl. However, improvement 30 is still attractive, as its incremental BCR is greater than 1.0 relative to

improvement 20.1 It is possible that other potential improvements for other sections will be

more attractive than improvement 30, so improvement 30 is placed on the list of potential

improvements. The potential list is then re-ordered. Improvement 30 may yet be selected for

implementation when all more attractive alternatives on other sections have been selected. 

Exhibit 7-7. Selecting Improvements in a Constrained Run

1. Had this been a minimum BCR run, improvement 30 would be selected for implementation at this point.

Benefits

Costs

Imp 10

Imp 20

Imp 30

b10

b20

b30

b20nl

b30nl

c10 c20 c30

r20nl r30nl r10
Evaluating Improvements

7-18

7.11 Selecting Mandatory Improvements

The HERS process for identifying mandatory improvements is presented in paragraph 3.3.2,

”Addressing Unacceptable Conditions: the Optional First Pass.” Normally, all mandatory

improvements will be selected for implementation. The two exceptions are when there are insufficient funds to implement all mandatory improvements (this applies to fund-constrained runs

only), and when a selected mandatory improvement is replaced by a more aggressive improvement. 

When a mandatory improvement has been identified for a section during the first processing

pass, it is subsequently identified as the base case improvement during analysis of more aggressive improvements. (When mandatory improvements are not being considered, the unimproved case is used as the base case.) This may result in the implementation of an improvement

with a BCR below the usual threshold of 1.0. While this may seem anomalous in an economic

model, the mandatory improvement feature is provided to allow the user to ensure that highways in unacceptably poor condition are improved regardless of whether the improvements can

be justified economically.

Exhibit 7-9, “Replacement of a Mandatory Improvement,” presents an example. During the initial pass, improvement 10 was selected as a mandatory improvement for the section. As a mandatory improvement, its BCR (designated r10) does not have to meet a minimum threshold.

Improvement 20 was identified during the second pass, and its incremental BCR (shown as

r20nl) was calculated using improvement 10 as the base case with the length of the analysis

period set to the normal life of improvement 10. 

Exhibit 7-8. Detecting Potential Improvements in a Constrained Run

Benefits

Costs

Imp 10

Imp 20

Imp 30

b10

b20

b30

b20nl

b30nl

c10 c20 c30

r20nl r30nl

BCR = 1.0 relative 

to Imp 20
HERS Technical Report v3.54

September 2002

7-19

While improvement 20 is certainly more attractive than the mandatory improvement 10 (r20nl

lies above r10), neither would have been selected had the user not specified the correction of

unacceptable conditions, as both of their BCRs are less than 1.0 relative to an unimproved base

case. (Both r10 and r20nl lie below the threshold designated 1.0.) However, as the mandatory

improvement 10 was used as the base case, the model calculates improvement 20’s BCR relative

to improvement 10, shown in Exhibit 7-9 as r20nl10. (The designation indicates that the BCR is

computed over the natural life of the base case improvement, and that it is relative to improvement 10.) This BCR lies above the threshold 1.010, which is relative to improvement 10. The

model therefore replaces improvement 10 with improvement 20.

The case illustrated represents a possibility which can occur in both constrained and minimum

BCR runs when mandatory improvements are specified, and results from the use of the mandatory improvement as the base case. Note that the objective of the mandatory improvement of

unacceptable conditions is still achieved: unacceptable conditions are corrected. And while the

replacement improvement (improvement 20 in the example) is not in itself attractive, it is an economically more attractive improvement than the one it replaces. 

7.11.1 Unacceptable Conditions and the Constrained Fund Run

During a constrained fund run, HERS uses benefit-cost analysis to select among potential

improvements until the available funds are expended. The user electing to have unacceptable

conditions identified and corrected during a constrained fund run will designate a portion of the

total funds for this purpose. If the designated funds are sufficient to implement all mandatory

improvements identified in the first pass, the remaining funds are available for the correction of

other deficiencies during the second pass. 

Exhibit 7-9. Replacement of a Mandatory Improvement

Benefits

Costs

Imp 10

Imp 20

b10

b20nl

1.0 1.010 r20nl10 r20nl

r10

c10 c20
Evaluating Improvements

7-20

If the designated funds are insufficient, then benefit-cost analysis is used to select the most economically attractive of the mandatory improvements for implementation. The procedure used is

the same as presented above for constrained runs (see paragraph 7.10.2), except that the universe

of potential improvements consists only of the mandatory improvements identified during the

first pass through the sections. Those mandatory improvements not selected at this point are

placed on the list of potential improvements and will be evaluated for implementation during

the second pass, competing (on the basis of their relative BCR values) with non-mandatory

improvements for the non-reserved funds. 

During the second pass, improvements selected as mandatory may be replaced by a more

aggressive improvement on that section if it presents a more economically attractive alternative. 

It is important to consider carefully the designation of funds for the correction of unacceptable

conditions. Consider the case where, during the initial funding period of a run, a large number

of unacceptable conditions may be identified, and funds remaining for use during the second

pass may be very limited. In the case of a section with two deficiencies, including one that is

unacceptable, only the unacceptable deficiency would be corrected during the initial funding

period. The other deficiency would frequently be corrected with a separate improvement

selected during a subsequent funding period - an inefficient means of correcting the two deficiencies. For this reason, when the option of correcting unacceptable conditions is exercised, it is

desirable that at least some funds be reserved in each period for implementing more aggressive

improvements. HERS allows the user to specify either (a) specific funding levels for the correction of unacceptable conditions, or (b) a maximum percentage of available funds that can be allocated for mandatory improvements for each combination of functional classes during any

funding period. (See paragraph 2.5.2 for the combinations of functional classes recognized by

HERS.)

7.11.2 Unacceptable Conditions and the Performance Constrained Run

During a performance constrained run, HERS uses benefit-cost analysis to select among potential improvements until designated system performance levels are met. The user may either

specify explicit levels of performance or require that the program maintain the current level of

system performance. If the user selects to have unacceptable conditions identified and corrected

during such a run, the program executes the first loop to identify sections with unacceptable conditions and improvements for their correction. If implementing all such improvements would

improve the system beyond the specified level, all the mandatory improvements are implemented, and no more aggressive improvements are identified. In this case, unlike the constrained fund run, HERS does not use benefit-cost analysis to select the smallest (and most

economically attractive) set of mandatory improvements which meet the specified goal.

Should the implementation of all identified improvements not bring the system performance

level to the desired goal, the second pass procedures are exercised to identify deficiencies and

improvements. As in the case of the Constrained Fund run, a more aggressive improvement

may be selected to replace an improvement originally selected to correct an unacceptable condition.
HERS Technical Report v3.54

September 2002

7-21

7.11.3 Unacceptable Conditions and the Minimum BCR Run

During a minimum BCR run, HERS evaluates potential improvements for all deficient sections

and selects the most aggressive improvement with an incremental BCR above the user specified

minimum. If the user opts to have unacceptable conditions identified and corrected during such

a run, the program executes the first loop to identify sections with unacceptable conditions and

improvements for their correction. The model then executes the second loop to identify

improvements to correct “normal” deficiencies and to identify more aggressive improvements.

Each section found to be in unacceptable condition by the first processing loop will be improved,

either with the improvement which corrects the unacceptable condition or by a more aggressive

improvement. In this case, as with constrained runs, improvements originally selected to correct

unacceptable conditions are implemented regardless of their BCR unless superseded by a more

aggressive improvement. As depicted in Exhibit 7-9, the more aggressive improvement which

replaces a mandatory improvement may not in itself have qualified for implementation had its

incremental BCR not been calculated against the mandatory improvement. 

As in a minimum BCR run in which the option to correct unacceptable conditions was not exercised, economically attractive improvements from the second processing loop will be implemented if their incremental BCRs are above the specified threshold.
Evaluating Improvements

7-22
8-1

8 Model Output

HERS is capable of producing, at the user's option, an extensive variety of statistics, describing

both the forecast state of the highway system and the costs and benefits of the improvements

selected. This chapter describes the output produced by HERS v3.54. HERS outputs a text file

suitable for printing, and separate comma-delimited text files suitable for use in spreadsheets

and databases. The printable output consists of the following:

1. One page of output summarizing the state of the system at the start of the run;

2. For each funding period, one page of output summarizing the state of the system at the

end of the funding period;

3. For each funding period and for the overall analysis period, one page of output summarizing how the system is forecast to change between the beginning and the end of the

period; and

4. For each funding period and for the overall analysis period, up to twenty-five pages of

additional output providing information on the costs and benefits associated with the

selected improvements.

The output pages are presented in three layout formats, as discussed below. The first two of

these formats are also available in comma-delimited layout. HERS places the printable output in

a single text file named by the user in the specification file (RUNSPEC.DAT). 

8.1 The System Conditions Output Format

HERS uses this format for items one through three in the above list of output pages. In addition

to the run number and run description information from the RUNSPEC file, this page contains

the following information for each of the nine functional systems in the HERS database, with

individually produced summary forecasts for the rural system, the urban system, and for the

complete system:

1. Average PSR;

2. Average IRI (inches per mile);

3. Average speed;

4. Congestion Delay (hours per 1000 vehicle-miles);

5. Total Delay (hours per 1000 vehicle-miles);

6. Total VMT;

7. Travel-time costs (dollars per thousand vehicle-miles);

8. Operating costs, listed for all vehicles combined and separately for four-tire vehicles and

for trucks (dollars per thousand vehicle-miles);
Model Output

8-2

9. Crash costs (dollars per thousand vehicle-miles);

10. Total user costs, which is a summation of travel-time costs, operating costs for all vehicles, and crash costs (dollars per thousand vehicle-miles);

11. Number of crashes (per 100 million vehicle miles);

12. Number of injuries (per 100 million vehicle miles);

13. Number of fatalities (per 100 million vehicle miles);

14. Annual maintenance costs (dollars per mile);

15. Average cost of pollution damage (dollars per 1000 vehicle-miles); and

16. Percent of total VMT on roads not meeting minimum tolerable conditions for:

• pavement condition (PSR);

• peak-hour volume/capacity ratio;

• lane width;

• right-shoulder width;

• shoulder type;

• surface type;

• horizontal alignment;

• vertical alignment.

The initial page of output in this format presents the conditions at the beginning of the analysis

period. It also includes the number of center-line miles and the number of sections in the sample.

For each funding period, HERS produces a page of output summarizing conditions at the end of

the period. This is followed by a page summarizing the changes in conditions which occurred

during the funding period. This second page of output also shows the (incremental) benefit-cost

ratio of the last improvement selected. If a constraint was placed on available funds, this page

also displays the amount of funds spent; while, if a performance goal was specified, it compares

the performance level achieved with the specified goal.

HERS produces a similar summary of the change in conditions during the overall analysis

period. 

HERS creates an output file named [run number].SS1 (where the file name is the same as the run

number entry in the RUNSPEC file) which contains the comma-delimited version of this format.

HERS generates a “page” for the initial system conditions and the conditions at the end of each

funding period. Each page contains only the sixteen data items listed above (i.e., not the number

of center-line miles, sections in the sample, etc.).
HERS Technical Report v3.54

September 2002

8-3

8.2 The “By Improvement Type” Output Format

HERS produces up to twenty-one pages of printable output in this format. This format is organized by functional class versus improvement type. The improvement type categories are duplicated: one set covers all improvements by improvement type, and the other only those

improvements which include improved alignment. The user selects which pages are to be

included in the printable output via switches in the RUNSPEC file. The twenty-one output

pages are:

1. The total initial cost of selected improvements; 

2. Lane-Miles improved; 

3. Lane-Miles of mandatory improvements selected on a priority basis to address unacceptable conditions1

;

4. Lane-Miles of non-mandatory improvements not selected on a priority basis;

5. The net present value of the residual value of all improvements; 

6. The average benefit-cost ratio of selected improvements;

7. Total benefits in the last year of the period; 

8. Maintenance costs savings in the last year of the period; 

9. User benefits in the last year of the period; 

10. Travel time savings in the last year of the period; 

11. Operating cost savings in the last year of the period; 

12. Safety benefits in the last year of the period; 

13. Crashes avoided in the last year of the period; 

14. Injuries avoided in the last year of the period;

15. Lives saved in the last year of the period;

16. VMT for improved sections in the last year of the period;

17. Miles improved;

18. Miles of mandatory improvements selected on a priority basis to address unacceptable

conditions;

19. Miles of non-mandatory improvements not selected on a priority basis.

20. Lane-Miles added to the system through widening improvements; 

1. In HERS, statistics pertaining to mandatory improvements selected to address unacceptable conditions are collected only for improvements that are not replaced by a more aggressive non-mandatory improvement selected on

the basis of its benefit-cost ratio.
Model Output

8-4

21. Emissions costs savings in the last year of the period;

Also, the first six and the last two of these optional output pages can be requested for the overall

analysis period.2 

Each page of optional output provides values for one of the above measures by improvement

type and functional system. HERS also produces summary values for all the improvement types

combined, as well as for the entire rural highway system, the entire urban highway system, and

the complete highway system. The first of the above optional pages also provides separate summaries of initial costs by functional system for mandatory improvements selected to address

unacceptable conditions and for non-mandatory improvements.3

 

HERS creates the file [run number].SS2 to hold the comma-delimited output for this format. The

comma-delimited format includes only the “all improvements” set of statistics: it does not

include the data for improvements with improved alignment. The comma-delimited output set

contains per funding period and overall analysis period statistics for initial cost of selected

improvements and the average benefit-cost ratios of selected improvements.

8.3 The “By IBCR” Output Format

HERS produces up to four printable summary sets in this format.4 The data is organized by

functional class versus improvement type, and, within each improvement type, by incremental

BCR range. Therefore, where the “by improvement type” format might show that HERS identified 4.542 billion dollars of resurfacing improvements for rural major arterials, the “by IBCR”

format could show that 1.261 billion dollars were invested in improvements with BCRs greater

than or equal to 6.0. HERS uses the following BCR ranges:

• 1.0-1.2;

• 1.2 - 2.0;

• 2.0 - 3.0;

• 3.0 - 4.0;

• 4.0 - 5.0;

• 5.0 - 6.0; and

• >= 6.0

The four summary sets are:

1. Capital requirements (initial cost);

2. Number of sample sections improved (including duplicates);

3. Miles improved; and

2. For “last year of the period” statistics (items 7 through 16), the data for the last funding period would be identical

to that for the overall analysis period.

3. See preceding footnote.

4. For this format, to refer to “pages” would be somewhat misleading, as each summary set requires more than two

physical pages to print.
HERS Technical Report v3.54

September 2002

8-5

4. Travel time benefits expressed as a percentage of total user benefits.

There is no comma-delimited output in this format.
Model Output

8-6
Concepts of Induced Demand APPENDIX A

Induced Traffic and Induced Demand A-1

APPENDIX A

Induced Traffic and Induced Demand

Douglass B. Lee, Jr., Lisa A. Klein, and Gregorio Camus

“Induced” is a term implying that a particular condition is indirectly caused by another

condition. In the case of traffic volumes, the term arose from the phenomenon that

improvements to a highway—especially capacity improvements—seemed to result in

more traffic choosing to use the road than would be the case if the highway were not

improved. To an economist, this is an example of demand elasticity. Simply recognizing

that travel demand is elastic, however, is not sufficient to reconcile the conflicting views

of engineers, planners, and environmentalists. On one side are those who argue that

transportation facilities are provided to serve land uses and support economic activity;

on the other are those who claim that whatever capacity is provided soon fills up to the

same level of congestion, gaining nothing. The truth can be better understood by defining induced demand in a way that uses the concept of elasticity.

This appendix describes the concepts guiding several modifications that were made to

the HERS model for the 1997 Conditions and Performance report to Congress. With

minor exceptions noted below, the model implements the concepts as they are described

here.

A.1 Concepts of Induced Demand

Frequent references are made in transportation planning to the concept of induced

demand, but the term remains ambiguous. The intent here is to define the relevant concepts, and show how they can represent demand for purposes of benefit-cost evaluation

of capital improvement projects.

Exogenous Demand 

Factors

Historically, demand forecasts in urban transportation planning have been based on

exogenous variables such as land use, population, employment, and income. Once these

Acknowledgments: The authors thank E. Ross Crichton, William Goldsmith, and Anthony Rufolo for valuable comments and suggestions. This appendix is published in the Transportation Research Record No.

1659 (1999).
APPENDIX A Short Run versus Long Run

A-2 Induced Traffic and Induced Demand

variables are measured or estimated, the result is a “point” estimate for traffic volume at

a future date. Demand, in this sense, is influenced by neither transportation infrastructure nor money price, but is determined entirely by exogenous factors.

Demand Fills Capacity A contrasting concept has emerged, claiming that additional capacity stimulates corresponding increases in demand. This concept embodies the “build it and they will come”

idea—or a belief in the existence of “latent demand,” which suggests that there are willing buyers who will express their demand for travel once the service is offered.1

 In

growing urban areas, the evidence from recent decades seemed to support this interpretation.

Although the idea has not been implemented as a formal forecasting method, the implication is that demand is entirely endogenous. If true, the policy choice is whether to permit travel to grow or to suppress it.

Elastic Demand Perhaps the first recognition that demand responded to endogenous factors was the

assertion that congestion is self-regulating, implying an automatic balancing of supply

and demand. More recently, the economist’s concept of demand being a relationship

between price and quantity demanded has become accepted, if not necessarily applied in

practice. From this perspective, all endogenous changes in volume are movements

along the demand curve, whether they are called latent, induced, or something else. If

“price” is generalized to include travel time, operating costs, and accidents, then

changes in capacity and alignment alter the “price” and thereby cause movements along

the demand curve.

Overall, then, travel demand is the result of a combination of both exogenous factors

that determine the location of the demand curve, and endogenous factors that determine

the price-volume point along the demand curve.

A.2 Short Run versus Long Run

The short run can be any period of time over which something remains fixed. What is

fixed might be the capacity of a highway, fuel efficiency of the vehicle fleet, locations of

employment, or anything else that changes slowly. The long run is enough time for

these characteristics to change. In transportation planning, the short run typically is

assumed to be about 1 year, but the dividing line depends upon the practical context.

Short-Run Elasticity Demand elasticity is the responsiveness of quantity demanded to changes in price. Price

is generalized for travel demand to include travel time, operating costs, and accidents, as

1 For an interpretation of latent demand, see Small (1992), pp. 112-116, or Small, Winston, and Evans (1989)
Short Run versus Long Run APPENDIX A

Induced Traffic and Induced Demand A-3

well as user charges.2 Everything included in this generalized price is an endogenous

factor with respect to induced traffic. An increase in capacity that lowers travel time, for

example, results in additional travel if the elasticity is not zero.

Short-run demand elasticity tends to be lower (i.e., less elastic) than long-run elasticity,

because more opportunities to increase or reduce consumption can be developed over

the long run than in the short run, while short-run options do not diminish in the long

run. If the price of fuel goes up, for example, highway travelers can reduce fuel consumption by taking fewer trips and chaining trips together, by carpooling to share

expenses, by driving in ways that achieve better mileage, and by taking a larger share of

trips on transit. In the long run they also can switch to more fuel-efficient vehicles, and

change their workplace and residence locations. If the price stays high, vehicle manufacturers will develop and produce more fuel-efficient vehicles, and better transit service may be offered.

Though the distinction between short-run and long-run demand is really a continuum Long-Run Elasticity

rather than two discrete states, the separation is useful both conceptually and for modeling purposes. In Figure A-1, two short run demand curves are shown in relation to their

common long run demand curve (the latter indicated by a dashed line). Demand could

be for a facility, a corridor, or even travel in a region. At a “long run” price of p1 the volume is v1 and the short run demand curve D1 applies, such that changes in the price

cause changes in volume along this demand curve in the short run. If the price drops to

p2, for example, then volume will increase to a flow of v1,s. If the price stays at that level

for the long run, then the short run demand curve will shift outward to D2, resulting in

the volume v2 at that price. If the price were then to go back up to p1, volume would

only drop to v2,s in the short run, but eventually back to v1 in the long run.

For example, secular declines in real fuel prices have led to increases in the size and

weight of vehicles and concomitant declines in their fuel economy; if the price of fuel

were to increase, gasoline consumption would drop but the vehicle fleet would take time

to evolve to a more fuel-efficient average. Changes are not necessarily completely

reversible—knowledge gained from research leading to advances in technology in, for

example, fuel efficiency, is not lost when the need is lessened, but its application tends

to diminish.

Induced Traffic versus 

Induced Demand

A similar distinction can be made between induced traffic (or induced travel) and

induced demand, by applying the short-run and long-run concepts. It is assumed that

demand is fixed in the short run, so changes in volumes are the result of movements

along the demand curve; but in the long run, the short-run demand curve can shift. In

this way, these terms are defined so that induced traffic is a movement along the shortrun demand curve, while induced demand is a movement along the long-run demand

curve, or an endogenous shift in the short-run demand curve.

2 The generalized price embodied in HERS includes time, operating costs, and accidents, but no user charges

per se. The implications of this omission are discussed in greater depth in Appendix D.
APPENDIX A Short Run versus Long Run

A-4 Induced Traffic and Induced Demand

In Figure A-1, no time direction is implied on the horizontal dimension; the shape of the

long-run demand curve does not mean that price declines over time. Nor are the shortrun demand curves necessarily ordered from one to two; demand could start at D2 and

then shift to D1. The diagram shows only the relationship between price and volume

under short-run and long-run conditions.

Disaggregation of Long 

Run Elasticity

Long-run elasticity—as with any other demand elasticity—is a ratio of the percentage

of change in quantity demanded to the percentage of change in the price of the good.

Referring to Figure A-1, the first circled point at (p1,v1) is taken to represent a point on

both the short-run and long-run demand curves. The second circled point at (p2,v2) represents the long-run result of a price change, which lies on the previous long-run

demand curve but also on a new short-run curve. The arc elasticity between the two

points is

[1]

where eLR is the long run elasticity of demand. If the following simplifications are made

for ease of presentation,

Figure A-1. Long Run Demand With Short Run Demand Curves.

b c

a

price

volume (ADT)

DLR

D2

D1

v v v v 1 1,s 2,s 2

1

2

p

p

eLR

%∆v

%∆p ----------- ∆v∆p ------ p1

v1

× ----- v2 v1 –

p2 p1 – ----------------       p1

v1

= = = × -----
Induced Traffic APPENDIX A

Induced Traffic and Induced Demand A-5

[2]

as shown in Figure A-1, then the long run elasticity can be represented as

[3]

where the first term in parentheses is the short run elasticity (eSR) and the second term is

the shift in the demand curve over the long run, represented as an elasticity. Thus the

long run elasticity is the sum of the eSR and a purely long run component which will be

called the long run share, eLRS, defined as

[4]

so

[5]

The eLRS component can be interpreted in the same way as a normal elasticity, and can

be empirically measured as the difference between the short run elasticity and the long

run elasticity estimated for the appropriate time period.3

A.3 Induced Traffic

As defined above, induced traffic is a movement along the short-run demand curve.

Common usage of the term “induced” suggests additional traffic—that is, an increase in

volume. Decreases might be called disinduced, deterred, or discouraged traffic. For

present purposes, the term refers to any endogenous change, whether positive or negative. Increased congestion or higher tolls, other things being equal, will cause a reduction in volumes. If this occurs in the short run, this is negative induced traffic.

Some of the possible sources of induced traffic include the following:

• Diverted traffic that changes its route to the improved facility;

3 See Taplin (1982) for theory.

a p2 p1 = –

b v1, s v1 = –

c v2 v1, s = –

eLR

b c +

a

----------- p1

v1

× ----- b

a

-- p1

v1

× -----       c

a

-- p1

v1

× -----       = = +

eLRS

c

a

-- p1

v1

× -----

      v2 v1, s –

p2 p1 – --------------------       p1

v1

= = × -----

eLR eSR eLRS = +
APPENDIX A Induced Traffic

A-6 Induced Traffic and Induced Demand

• Rescheduled traffic that previously used the facility at a different time, spreading or 

contracting the peak;

• Shifts from other modes, which might or might not have used the facility before, and 

which include changes in occupancy;

• Destination shifts, resulting from facility improvement; and

• Additional travel by persons already using, or in the market for, the facility.

Demand forecasts for a new or improved facility always include at least some of these

sources, although such estimates seldom explicitly recognize a generalized price as the

explanatory variable and do not produce a schedule of price-volume combinations.

Partial and General 

Equilibrium Demand 

Curves

All demand curves portrayed in this analysis are assumed to be general equilibrium

demand curves, even those for the short run. They include traffic shifted to or from

other modes or from alternative facilities. A partial equilibrium demand curve, as represented in Figure A-2, includes only the travel for those already in the market, whether

they are currently taking trips or not (e.g., a person who did not travel at all in this corridor but who chose to do so after the price was reduced, and not by shifting a trip from

another time or place). If the demand curve includes diverted travelers (from other

Figure A-2. Partial and General Equilibrium Demand Curves.

general equilibrium demand curve

partial equilibrium demand curve

incremental

consumer

surplus

trip volume

induced trips

q 1 2 q q 0

within-market

new trips

diverted

trips

old

trips

Dgeneral Dpartial

p1

p2

generalized

price
Induced Traffic APPENDIX A

Induced Traffic and Induced Demand A-7

modes, routes, times, or destinations), then it will be more elastic than the corresponding partial demand curve because more options are offered. Thus some of the (short run)

induced travel comes from new trips by persons already in the market, and some comes

from trips diverted from other markets.

For every point on the general equilibrium demand curve there is a corresponding partial demand curve, representing the hypothetical demand that would occur if there were

no substitution between markets. If the price were raised, for example, from a point on

the general equilibrium demand curve, a movement up the partial demand curve would

imply that the travelers could not divert to another time or facility. Not surprisingly,

such a demand curve cannot be observed in practice. 

Because demand forecasts usually include diverted trips, practical demand forecasts are

aimed implicitly at constructing (or locating points on) a general equilibrium demand

curve. If the demand is for a single facility, then induced traffic will appear large relative

to previous volumes, because most of the change in trips will be from diverted trips. At

the regional level, induced traffic—if it were actually estimated—would be a smaller

share of total traffic growth, because only trips diverted from other regions, plus substitutions between transportation and other goods, make up the induced share. For project

evaluation, diverted travel and other components of induced demand, as measured in

consumer surplus, represent the net valuation of systemwide impacts.4

“Gross” versus “Net” 

Induced Traffic

In Figure A-2, all of the movement along the general equilibrium demand curve stimulated by the reduction in price from p0 to p1 is labeled “induced trips.” A portion of this

induced traffic is labeled “diverted trips.” If the diverted trips are removed from the total

“gross” induced traffic, the residual might be called “net” induced traffic. Some analysts

prefer that the term induced be restricted to mean net induced trips, and the others be

left as diverted trips.5

For some purposes, this usage has an appeal, but the distinction is a difficult one to

make. A trip between the same origin and destination but using a different route is

clearly a diverted trip, but trips at other times, or to other destinations are less obvious.

If the improved facility prompts a person to go to a movie instead of renting a video,

and the video store is much closer, is this induced or diverted? Suppose the person

would have walked to the video store. Or suppose the person would have had the video

delivered, and the van would have used the same facility before it was improved. What

can be observed directly is that more vehicles use the facility after it is improved, and

that trips in the region do not go up by as large an amount as the volume on the

improved facility. Labeling which particular travel is “new” and which is “diverted,”

however, is difficult and probably not necessary.

4 See Dargay and Goodwin (1995), Mackie (1996), and Williams and Yamashita (1992).

5 Examples include Dowling (1994), Heanue (1997). Holder and Stover (1972) and SACTRA (1994).
APPENDIX A Induced Demand

A-8 Induced Traffic and Induced Demand

Schedule Delay and Peak 

Shifting

As noted earlier, changes in the generalized price may lead to changes in schedule. Peak

congestion can be at least partially avoided by leaving earlier or later than preferred. A

reduction in peak travel time will cause some travelers to join the peak because the cost

to them of schedule delay (departing at a different time than preferred) is less then the

new peak delay.6 Induced traffic, therefore, can be diverted from other times as well as

other routes.

If the demand curve represents both peak and off-peak, then the elasticity will be lower

than if peak is separated from off-peak. Because the two periods are so closely interrelated (off-peak demand depends upon peak price, and vice versa), separating them for

benefit-cost purposes can be tricky, but this is one way to include benefits from reducing

schedule delay.

A.4 Induced Demand

For purposes of evaluating costs and benefits, the overall analysis period for a project

(generally the project lifetime, e.g., twenty years) is broken into a series of discrete time

6 See Small (1992).

Figure A-3. Alternative Long Run Travel Forecasts

Historical Data

Trend Linear

Forecasts

Geometric

Logistic

Low Geometric

1,000

1,500

2,000

2,500

3,000

3,500

4,000

1980 1985 1990 1995 2000 2005 2010 2015

Annual VMT (millions)
Induced Demand APPENDIX A

Induced Traffic and Induced Demand A-9

periods, during each of which the demand curve is assumed to be fixed. A baseline long

range forecast is used to establish the short run demand curve for each period.

Baseline Demand 

Forecast

A demand forecast is a functional relationship between time and traffic volume, assuming a set of conditions. Exogenous conditions include population growth, economic

growth, land use patterns, and available substitute transportation alternatives. Endogenous conditions include capacity, level of service (LOS), and user fees. For the present

analysis, all endogenous factors are represented in the generalized price. Both capacity

and LOS, for example, would both be subsumed under travel time cost and included in

the generalized price.

The baseline long-run demand forecast assumes a generalized price, as well as whatever

exogenous factors are thought to be relevant by the forecaster. Alternative forecasts

might be constructed under different assumptions, as shown in Figure A-3. One such

forecast is selected for constructing the short run demand curves.

Breaking the Forecast 

Into Discrete Periods

The distinction between long-run induced demand and short-run induced travel is

implemented by constructing a short-run demand curve for each of the shorter demand

periods (e.g. 1-5 years), and allowing the initial curve to shift, depending upon previous

improvements. The forecast becomes a series of discrete points—shown circled in Figure A-4—that provide the calibration points for the associated short-run demand curves.

The short-run demand curve can be a straight line calibrated with an elasticity, a constant elasticity demand curve, or some other functional form that can be fitted to a single

price-quantity combination. The elasticity chosen should be appropriate to the length of

the demand period.7

Figure A-4. Baseline demand forecast for several periods

D1 D2 D3

vehicle volume

generalized

price

pbaseline

qforecast,1 qforecast,2 qforecast,3
APPENDIX A Induced Demand

A-10 Induced Traffic and Induced Demand

A single, fitted short-run demand curve is shown in Figure A-5, along with other relevant prices and volumes. The price from the previous period pfinal, t-1 is adjusted to

account for traffic growth, pavement wear, accident rates, and user fee changes that

have occurred since the previous period. The result is pno improvement. Alternative

improvements for the current period are evaluated, and, if any are feasible, the best is

implemented. This leads to the pimproved price, which becomes the initial price for the

next demand period. If no improvement is selected, the unimproved price carries into

the next period.

Long Run Shifts in the 

Demand Curve

Evolution of demand in the long run is built upon what takes place in the short run.

Operationally, induced demand is defined to be the shift in the short run demand curve

caused by the price in the previous period. If the price in all previous periods is the same

as the baseline price, then the demand curve is fitted to the baseline forecast for that

period. If an improvement is made in one period that reduces the price below the baseline price, this leads to a shifting of the demand curve outward, according to the percent

by which the price in the previous period is below the baseline price. If no improvement

is made, the price increases relative to the baseline forecast price, and the demand curve

shifts inward in the next period. These two possibilities are shown in Figure A-6. For

example, a price of pno improvement will shift the subsequent demand curve inward from

qforecast by a percentage equal to .

7 Currently, the demand period or “funding period” in HERS is five years, so the short run elasticity should be

selected to allow for adjustments that can be expected to take place within that span of time.

Figure A-5. Short Run Demand Showing Prices With and Without Improvements.

pno improvement

pimproved

pbaseline

qinitial,t

pfinal,t-1

qimproved,t qno improvement,t

generalized

price

traffic volume

qforecast,t

pbaseline pno improvement ( ) – eLRS ×
Induced Demand APPENDIX A

Induced Traffic and Induced Demand A-11

The relationship between the difference in price of the final, improved—or not

improved—price and the baseline price, for one period, and the horizontal shift in the

demand curve in the next period, is governed by the long-run share eLRS, as described

above.8 There is no long run demand curve as such, but the shift attributed to induced

demand is a displacement of the short run demand calibration point along the baseline

price line.

Incorporating induced demand, then, allows each period's demand curve to be a function of the previous period's investment, since it affects price to the user. Investment that

keeps the price in each period below the baseline price for the baseline forecast produces demand curves that shift farther and farther outward, compared with the baseline

forecast. Similarly, if improvements are not made and price is allowed to rise in each

period (e.g., due to congestion, pavement roughness, and accidents), the demand curve

will be shifted continually inward relative to the baseline.

The magnitude of this shift—the sensitivity of long-run demand to investment and pricing—is determined by the eLRS parameter. The shorter the time period for the short run,

the lower should be the long-run elasticity shift from period to period. If the long-run

induced demand parameter is zero, the location of each short-run demand curve would

be determined by the baseline forecast, without regard for which—if any—improvements were made in any demand period. Short-run movements along the demand curve

still could occur, depending on the short-run price elasticity, but there would be no

cumulative endogenous effects from one period to the next. Alternatively, with a high

8 See “Disaggregation of Long Run Elasticity” on page B-4.

Figure A-6. Long Run Induced Demand Shift From One Period to the Next.

vehicle volume

price,

cost

D1 D2

a D2b

induced demand

initial

volume

baseline

price

baseline forecast

pno improvement

pimproved

qimproved,t qno improvement,t qforecast
APPENDIX A Induced Demand

A-12 Induced Traffic and Induced Demand

eLRS, induced demand could alter the baseline forecast, even to the point of potentially

offsetting the trend of the initial forecast, such leading to growth in demand (from keeping the price low) despite a declining forecast, or causing a decline in demand despite a

growth forecast (traffic is deterred by congestion and bad pavement, a consequence of

no improvements).

Getting to the Long Run Empirical estimates of the two elasticities depend upon the length of the short-run time

period and the rate of adjustment to changes in price. The length of time between a

change in conditions and a new equilibrium is somewhat arbitrary, because other conditions change before equilibrium is reached; however, the process is one of accelerating

initial response followed by gradual refinement. In the context of highway volume

adjustments in response to changes in the generalized price of travel, the short run is up

to a year. The long run—allowing for changes in residence and workplace locations—

begins within a year but may not run its course for upwards of 20 years. Such changes

are not likely to be motivated solely by changes in transportation prices, but may take

transportation user costs into account when the change is made for other reasons (e.g.,

new job, change in income, change in family).

An approximate adjustment curve is shown in Figure A-7. Although the curve is not fitted to specific data, it reflects the generally observed pattern that roughly half the adjustments take place within about a quarter of the time to long run equilibrium.9 If the full

long-run adjustment period is 10 to 20 years, then half the long-run elasticity occurs

Figure A-7. Path to Long Run Equilibrium.

9 Cambridge Systematics, and JHK Associates (1979), Dowling Associates (1993), Dowling and Colman

(1995), Goodwin (1998). Hansen (1995), Hansen, Gillen, Dobbins, Huang, and Puvathingal (1993), Kroes,

Daly, Gunn, and Van der Hoorn (1996), and Pells (1993) study the time lag in response to highway capacity

increases; Cairns, et al. (1998) study responses to reductions in capacity.

full

equilibrium

50% adjustment

short

run 25% oflong run

50% of

long run longrun

Time

80% adjustment
Induced Demand APPENDIX A

Induced Traffic and Induced Demand A-13

within the first 2.5 to 5 years. There might be some accelerating adjustment in the first

year, as shown, based on the idea that responses don’t occur until consumers become

sure the price change will stick, or until they begin feeling its effects.

Empirical Estimates of 

Short and Long Run 

Elasticities

Many studies have estimated travel-demand elasticities, but one of the difficulties in

interpreting these results is the uncertainty of the time frame that is applicable to the

data. Another confounding problem is the ambiguity of the base of the observed elasticity; because most of the empirical cases observe a change in a small component of the

total price of travel, the base for computing the percentage change in price often is not

obvious and might not be given explicit treatment. The potential differences are large

(e.g., a factor of three or more).10

The parameter sought is the elasticity of vehicle travel with respect to its own price,

including user fees, operating costs, and travel time. Studies undertaken to date suggest

that short-run elasticities tend to fall in a -0.5 to -1.0 range, and long-run elasticities

from -1.0 to -2.0; a within-period short-run elasticity for a 5-year period would thus be

-0.6 to -1.0 and the between-period elasticity from -1.0 to -1.6, yielding an eLRS of

about -0.4 to -1.0.

Interpreting Demand 

Forecasts

Two aspects of the demand forecast are of particular interest. One is how to impute a

presumed price to the baseline forecast. The second is whether long-run feedback of

transportation investments on the demand curve has been incorporated into the forecast.

• Baseline Price. Although the generalized price behind a demand forecast is

seldom made explicit, such attributes as LOS and accident rates may be, and

others can be guessed. Pavement quality is probably assumed to be good, and

operating costs are typical for the conditions (terrain, vehicle type, congestion). The current LOS can be assumed as a default.

• Long-Run Demand Feedback. Constructing or expanding a facility will

induce some travel in the long run even if the price is unchanged from the

baseline. Therefore, the baseline forecast should include growth in travel that

will result from traffic-generating activities that locate to take advantage of

the services provided by the facility at the baseline price. The long-run elasticity amplifies this effect up or down, but does not substitute for it.

If forecasts are based on historical patterns over a time horizon of half a dozen years or

more, then the feedback effect implicitly is built in. Whether it needs to be made explicit

or refined is an open question, but the impacts of errors in out-year forecasts are suppressed somewhat by discounting.

10The empirical evidence and methods for estimating highway travel demand elasticities are covered in

Appendix C.
APPENDIX A Summary

A-14 Induced Traffic and Induced Demand

A.5 Summary

Some of the ambiguity and confusion that surrounds the discussion of induced demand

might be dispelled by applying the following definitions and principles:

(1) The term induced means a movement along a travel demand curve as a result

of changes in endogenous factors, which can be represented as components

(time, running cost, money) of a generalized price.

(2) The measurement of induced travel is dependent upon the market for which

the demand curve is defined; induced travel defined at the facility level will

include traffic diverted from parallel routes, while induced travel at the

regional level will include only trips that are new to the region.

(3) A useful distinction can be made between short-run demand and long-run

demand. Movement along the short-run demand curve amounts to induced

traffic. However, movement along the long-run demand curve constitutes a

shift in the short-run demand; this can be called induced demand.

(4) Benefit-cost evaluation of projects requires that baseline demand forecasts be

adjusted to take into account induced demand, both short and long run; simply stated, improvements that change user costs should be evaluated in the

light of whatever changes in volume will actually occur. Such demand curves

are referred to as general-equilibrium demand curves.

(5) If the short-run elasticity is zero, then traffic volumes are unresponsive to

changes in price within a single demand period, and the demand curve is vertical. If the elasticity of the long-run share (i.e., excluding short-run effects)

is zero, then there are no long-run effects (e.g., no investment in highwayrelated facilities or land-use changes) stimulated by highway pricing and

investment policies. Empirically, neither of these conditions seems to apply.

A.6 References

Brand, Daniel, and Joy L. Benham, “Elasticity-Based Method for Forecasting Travel on

Current Urban Transportation Alternatives,” Transportation Research Record,

895 (1982), pp. 32-37.

Cairns, Sally, Carmen Hass-Klau, and Phil Goodwin, “Traffic Impact of Highway

Capacity Reductions: Assessment of the Evidence,” prepared for London Transport, London, UK: Landor, March 1998.

Cambridge Systematics, and JHK Associates, “The Relationship of Changes in Urban

Highway Supply to Vehicle Miles of Travel,” NCHRP Report 8-19, Washington,

DC: Transportation Research Board, March 1979.
References APPENDIX A

Induced Traffic and Induced Demand A-15

Cohen, Harry S., “Review of Empirical Studies of Induced Traffic,” in Transportation

Research Board (ed.), Expanding Metropolitan Highways: Implications for Air

Quality and Energy Use, Special Report 245, pp. 295-309, Washington, DC:

National Academy Press, 1995.

Coombe, Denvil, “Induced Traffic: What Do Transportation Models Tell Us?,” Transportation, 23, 1 (1996), pp. 83-101.

Dargay, Joyce M., and Phil B. Goodwin, “Evaluation of Consumer Surplus with

Dynamic Demand,” Journal of Transport Economics and Policy, 29, 2 (1995),

pp. 179-193.

DeCorla-Souza, Patrick, and Harry Cohen, “Accounting for Induced Travel in Evaluation of Metropolitan Highway Expansion,” Washington, DC: US DOT/FHWA,

January 1998.

Dowling Associates, “Effects of Increased Highway Capacity on Travel Behavior: Literature Review,” prepared for California Air Resources Board, Oakland, A:

Dowling Associates, July 1993.

Dowling, Richard G., “A Framework for Understanding the Demand Inducing Effects

of Highway Capacity,” paper for TRB, Oakland, CA: Dowling Associates, January 1994.

Dowling, Richard G., and Steven B. Colman, “Effects of Increased Highway Capacity:

Results of Household Travel Behavior Survey,” Transportation Research

Record, 1493 (1995), pp. 143-149.

Dunphy, Robert T., “Transportation and Growth: Myth and Fact,” Washington, DC:

Urban Land Institute 1996.

Economic Research Centre, (ed.) Infrastructure-Induced Mobility, Paris: European Conference of Ministries of Transport, 1998.

Goodwin, Phil B., “Empirical Evidence on Induced Traffic,” Transportation, 23, 1

(1996), pp. 35-54.

Goodwin, Phil B., “Extra Traffic Induced By Road Construction,” in OECD (ed.), Infrastructure Induced Mobility, ECMT Round Table 105, Paris: OECD, 1998.

Goodwin, Phil B., “A Review of New Demand Elasticities with Special Reference to

Short and Long Run Effects of Price Changes,” Journal of Transport Economics

and Policy, 26, 2 (1992), pp. 155-170.

Hansen, Mark, “Do New Highways Generate Traffic?,” Access, 7 (1995), pp. 16-22.

Hansen, Mark, David Gillen, Alison Dobbins, Yuanlin Huang, and M. Puvathingal,

“The Air Quality Impacts of Urban Highway Capacity Expansion: Traffic Generation and Land Use Change,” prepared for California Department of Transportation, Berkeley, CA: Institute of Transportation Studies, University of

California, April 1993.

Heanue, Kevin, “Highway Capacity and Induced Travel: Issues, Evidence and Implications,” paper for TRB, Washington, DC: US DOT/FHWA, January 1997.
APPENDIX A References

A-16 Induced Traffic and Induced Demand

Holder, R. W., and V. G. Stover, “An Evaluation of Induced Traffic on New Highway

Facilities,” College Station, TX: Texas A&M University, March 1972.

Kroes, Eric, Andrew Daly, Hugh Gunn, and Toon Van der Hoorn, “The Opening of the

Amsterdam Ring Road,” Transportation, 23, 1 (1996), pp. 71-82.

Lee, Douglass B., Lisa A. Klein, and Gregorio Camus, “Induced Traffic and Induced

Demand in Benefit-Cost Analysis,” paper for TRB, Cambridge, MA: US DOT/

VNTSC, November 1998.

Mackie, Peter, “Induced Traffic and Economic Appraisal,” Transportation, 23, 1

(1996), pp. 103-119.

Pells, S.R., “User Response to New Road Capacity: A Review of Published Evidence,”

Working Paper 283, Leeds, UK: Institute for Transport Studies, November 1989.

Small, Kenneth A., Urban Transportation Economics, Chur, UK: Harwood Academic,

1992.

Small, Kenneth A., Clifford Winston, and Carol A. Evans, Road Work: A New Highway

Pricing and Investment Policy, Washington, DC: Brookings, 1989.

Standing Advisory Committee on Trunk Road Assessment, “Trunk Roads and the Generation of Traffic,” London: Department of Transport, December 1994.

Taplin, John H.E., “Inferring Ordinary Elasticities From Choice or Mode-Split Elasticities,” Journal of Transport Economics and Policy (1982).

Transportation and Environmental Research and Information Services, “Induced

Demand, Traffic Diversion v. Generation & Related Issues: Annotated Bibliography,” Raleigh, NC: North Carolina State University, September 1996.

Transportation Research Board, “Expanding Metropolitan Highways: Implications for

Air Quality and Energy Use,” Special Report 245, Washington, DC: National

Academy Press 1995.

Williams, Huw C.W.L., and Yaeko Yamashita, “Travel Demand Forecasts and the Evaluation of Highway Schemes Under Congested Conditions,” Journal of Transport

Economics and Policy, 26, 3 (1992), pp. 261-282.
Theory APPENDIX B

Demand Elasticities for Highway Travel B-1

APPENDIX B

Demand Elasticities for Highway 

Travel

Douglass B. Lee, Jr.

An elasticity summarizes a large amount of information in a single number. Levels and

distribution of incomes, price levels of the specific good and of substitute and complementary goods, preferences and tastes, transaction costs, etc., can, ceteris paribus, affect

the measured value of any particular demand-price elasticity. The elasticity concept normalizes for the measurement scales (e.g., pounds or kilograms, dollars or pesos) and

price levels (to the degree that the demand curve is constant elasticity), but other factors

are ignored or implicitly averaged. Although the price elasticity of travel demand is frequently mentioned in discussion, there is no direct empirical measurement of elasticity

with respect to the price of highway travel, and there are several alternatives about even

what that price consists of.

The review and synthesis presented in this Appendix was conducted for the purpose of

establishing values for use in the HERS model to represent the short-run elasticity of

demand on a given highway section, and to estimate the long-run share parameter used

for estimating induced demand, as described in Appendix B. For the 1999 Conditions

and Performance report to Congress, the values selected were -1.0 for short-run elasticity, and -0.6 for the long-run elasticity supplement, giving a full long-run elasticity of

-1.6.

B.1 Theory

As an empirical measure, an elasticity is a microeconomic aggregate: it summarizes The Meaning of Elasticity

demand in a specific market at a point in time, at or near the prevailing price and quantity. A market could be a highway facility, a corridor, or an entire region. A point in time

Acknowledgments: The author thanks E. Ross Crichton, Mark Delucchi, William Goldsmith, and Phil Goodwin for comments on an earlier draft and many helpful suggestions.
APPENDIX B Theory

B-2 Demand Elasticities for Highway Travel

might be a peak hour, or a daily average. The basic concept can be represented as an arc

elasticity between two demand points,

[1]

where v0 = initial traffic volume and p0 = initial price. Elasticity can be thought of as a

measure of slope normalized for the arbitrary measurement scales of p and v, and,

indeed, the form to the right of the second equal sign is a slope multiplied by the initial

demand point. If the derivative of the demand curve is substituted for the slope, the elasticity is instantaneous at the given point, rather than over an arc. For exposition, the arc

form will be used, but the principles apply to either form.

Transferability For a different time point on the same facility, a different group of users may respond

differently to a change in price, because they have different incomes, demographic characteristics, and tastes. Moreover, prices in related markets (e.g., parallel facilities) may

be different. If comparing different facilities, the above may be different, as well as differing substitute alternatives (routes, carpool and transit options, destinations, schedule

options). Different days, seasons, regions, and forms of “price” all limit the transferability of an elasticity measured in one context to another context.

Hence—unlike the speed of light or the age of a rock—there is no underlying true number waiting to be discovered. Similar circumstances are likely to exhibit roughly similar

elasticities, but the most important characteristics of these circumstances need to be

made explicit. Given the nature of the empirical evidence, selecting appropriate values

must rely heavily upon a priori reasoning.

Price, Output, and 

Market

The basic economic model of exchange reconciles supply and demand in a market,

using price. The “price” is the market value of the resources given up by the buyer and

received by the seller, accomplished in modern markets by means of some form of

money that both parties agree to use as representing valuable resources. The market of

interest in the present context is highway travel, measured as vehicle miles of travel

(VMT). A single market has a single price, so a highway market could be a street length

between intersections at a specific time of day. The concept of a market can be applied

more broadly, however, to consist of a facility whose demand is averaged over the day,

or a network of facilities. Elasticities will generally be larger (elastic) the more alternatives (route shift, time of day shift, add or forego trip) are available, and smaller (inelastic) the more broadly the market is defined (e.g., region versus facility). For present

purposes, the focus is on a single facility, and its daily VMT.

Money Price If the price measure were limited to the money price paid by the user to obtain the services of the highway, then such characteristics as travel time, pavement roughness, risk

of accident, scenery, and curves and grades would be attributes of the service. Such a

money price (assuming the user had access to a vehicle) would be a multi-part price

e

%∆v

%∆p ----------- ∆v∆p ------ p0

v0

= = × -----
Theory APPENDIX B

Demand Elasticities for Highway Travel B-3

consisting of vehicle registration fee, drivers’ license fee, excise taxes on fuel and tires,

and tolls.

This formulation of the highway market has limited usefulness for several reasons. Primarily, the fees paid are a small part of the total cost to the user of highway travel, and

attributes of the good (such as travel time) dominate the choice rather than price.

Because travel is a derived demand, at least some of the attributes can be thought of as

part of the cost to be minimized, including time and operating costs as well as user fees.

Generalized Price and Its 

Components

Hence, an alternative formulation is to treat some of the attributes as disutilities, and

translate them into a dollar price. Operation of the vehicle, travel delay, and tolls are

thus all costs to the user, or components of the price. In practice, the only way to estimate the demand elasticity of highway travel is to build up total travel demand elasticity

from elasticities of the components of user costs.

Three relationships are central to estimating total demand elasticities from component

elasticities: the component’s own-price elasticity, the correspondence of a change in the

price of the component to a change in the price of travel, and the expansion from the

component to the total elasticity.

Price Elasticity for a 

Component

If X is a component of the price of travel, and we observe its own price elasticity, then

[2]

where eX is the demand price elasticity of good X, ∆qX is the change in the quantity of X

that is consumed (e.g., gallons of fuel), ∆pX is the change in the price of the good (e.g.,

the price of gasoline at the pump), pX is the initial price of the good, qX is the initial

quantity of the good, and ∆qX/qX is the percent change in the quantity of good X. This is

a relationship between the price of the component and its consumption, not the consumption of the overall good of which X is a component.

Leakage from Component 

to Total

Higher fuel prices, for example, are partly absorbed in improved fuel mileage, so that

the percentage reduction in fuel consumed is greater than the percentage reduction in

VMT. The extent of this “leakage” between the component price elasticity and travel

demand elasticity depends upon the component, and the possibilities for economizing

on the component other than by reducing travel. A change in the price of a component

of travel cost is not exactly an equivalent change in the price of travel, and less so in the

long run. In general,

[3]

where eT,X = elasticity of travel demand with respect to a change in the price of X, and

σ = a shrinkage factor representing the share of a reduction (or change) in consumption

eX

∆qX

∆pX

--------- pX

qX

= × -----

eT X, σ eX = × σ , ≤ 1
APPENDIX B Empirical Estimation of Price Components

B-4 Demand Elasticities for Highway Travel

of X that consists of reduction in travel. A σ = 1 implies that the component and travel

are necessarily consumed in fixed proportions.

Expansion From 

Component to Total

If the elasticity of VMT with respect to a part of the price is known, then the elasticity of

total travel demand is simply an expansion from the part to the whole,

[4]

where eT = demand elasticity for travel (the overall good), pT is the price of travel, and

the component elasticity eX is substituted using [3]. The bottom of the right-hand side is

the share of the component in the total price of travel. For example, if the elasticity of

gasoline consumption with respect to its own price is -0.25, and the shrinkage factor is

0.6 (from changes in fuel efficiency), then the elasticity of travel with respect to

gasoline price is -0.15. If fuel is 20% of the cost of travel, then the implied demand

elasticity is -0.75 with respect to the total price of travel.

B.2 Empirical Estimation of Price Components

From Evidence to 

Application

Because generalized price is being used rather than narrower money price, the analysis

proceeds in two major steps: first, each of the components of generalized price (operating cost, time, etc.) is studied for what the empirical evidence says about the total vehicle price elasticity; and second, the total vehicle price elasticity is applied to specific

contexts where various elasticity components (route change, forgo trip, etc.) may or

may not be available as substitutes. The overall process is represented in Figure B-1.

Empirical studies are mainly oriented toward changes in one component of price; these

studies can be extrapolated to the full price. Once a total price elasticity is determined,

then that value must be adjusted to apply to a specific context such as a highway section. For use in the 1999 Conditions and Performance report, the section-level effects

are assumed to cancel each other, on average, and the overall price elasticity is used for

sections. The evidence and analysis presented here pertain primarily to passenger travel,

although freight movement can be expected to respond in similar ways.

It is important to remember that the analysis concerns vehicle-trips, not person-trips.

Although persons make the decisions for vehicles, vehicle trips are more readily

observed, and the price typically applies to vehicle travel rather than to person trips.

eT

eT X,

pX pT ⁄ --------------- σeXpX pT ⁄ = = ---------------
Empirical Estimation of Price Components APPENDIX B

Demand Elasticities for Highway Travel B-5

Construction of Travel 

Demand Elasticities from 

User Cost Components

The methodological strategy for moving from information about the components of user

cost or “price” to travel demand elasticity is represented in Figure B-2 and described

below:

(1) The first step is an accounting problem to define the user cost categories for

which data have been collected and tabulated, matched with those for which

elasticities have been or could be measured. The units are in dollars per vehicle mile of travel.

(2) Because price per VMT—even by component—is an average of unlike conditions (large and small cars, urban and rural traffic), a more robust result is

obtained by considering several different data sources and reconciling the

numbers. Again, the choice of measure must match whatever is used or

implied in empirical elasticity estimates.

(3) A major source of uncertainty in expanding from component to total price is

which components should be included in the “price” to the user. Possibilities

range from using only short- run variable out-of-pocket costs that the user

“perceives,” to all costs paid by the user including travel time.

(4) Within this range of uncertainty, low and high percentage shares can be calculated for each of the price components.

(5) Empirical estimates of any relevant elasticity estimates can be combed from

the literature, formal or informal. Not all components are suitable for estimating elasticities empirically (e.g., accidents), and some that are suitable

may not have been the subject of published estimates.

Figure B-1. Primary analytical steps in generating project-specific elasticities.

Total

Vehicle-Trip

Price

Elasticity

Fuel

Maintenance

Accidents/

Insurance

Wear and

Ownership

Tolls and Fees

Parking

Travel Time

price components

elasticity components

partial trip

route diversion

occupancy shift

temporal diversion

forgo highway trip
APPENDIX B Empirical Estimation of Price Components

B-6 Demand Elasticities for Highway Travel

Figure B-2. Method For Building Travel Demand Elasticities From Price Components.

Components of travel 

price to user

Component shares of 

total user cost 

Components to be

included in total price

Empirical estimates of 

component magnitudes

Empirical estimates of 

component own-price 

elasticities

Direct empirical

estimates of travel

demand based on 

component

Extent to which

component can be

reduced without

reducing VMT

Interpretation of time 

dimension (short or 

long run) of elasticity

Derived estimates of 

travel demand elasticity

1

2

3

4

5

6 7 8

9
Empirical Estimation of Price Components APPENDIX B

Demand Elasticities for Highway Travel B-7

(6) Given an own-price elasticity estimate for a component, and its share in the

total price, the next problem to be resolved is the extent to which a change in

the consumption of the component results in the same percentage change in

VMT, i.e., the shrinkage factor.

(7) For those instances in which a travel demand elasticity has been estimated

from changes in the price of the component, the component elasticity can be

inflated directly to the total demand elasticity; this information can also be

compared to any own-price elasticities to assess the “leakage” into non-VMT

changes.

(8) All of the empirical elasticity estimates must be interpreted along several

dimensions, the most important being whether it is a short-run or long-run

estimate. Many published estimates are ambiguous regarding the time span

covered.

(9) The above information, subject to its range of uncertainty, can be distilled

into estimates of short-run and long-run travel demand elasticities based on

generalized price.

These steps are explained and implemented in more detail below.

Accounting Framework 

for Price Components

Seven categories of user cost are listed in Table B-1. They are intended to be non-overlapping and exhaustive. Fortunately, this set of categories is generally consistent with

various estimates of user costs. The purpose of these categories is to be able to combine

them in subsets that provide alternative measures of the “price,” to distinguish fixed

from variable costs as a means for defining the relevant costs, to match with empirical

estimates of costs, and to match up with empirical elasticity estimates.

Estimates of Component 

Shares

Estimates of national averages for the cost components of highway travel are provided

in Table B-2. All are intended to cover internal costs borne by users, omitting externalities, since elasticities necessarily must be based on internal costs. Four sources are presented, each of which offers a different orientation:

Table B-1. User Cost Accounting Framework

Category Scope

Fuel gasoline, diesel fuel, or other fuel consumed by motor vehicles, including taxes

Maintenance oil, parts, periodic maintenance, unscheduled maintenance, tires, excise taxes

Accidents and Insurance costs of accidents (internal), insurance administration and profit

Vehicle Wear and Ownership wear and tear, additional depreciation, financing, sales and excise taxes

Tolls and Fees tolls, registration fees, license fees

Parking cost of parking to the user at work, shopping or other

Travel Time dollar value of time spent in traveling
APPENDIX B Empirical Estimation of Price Components

B-8 Demand Elasticities for Highway Travel

(1) Back-of-Envelope: The value for the particular component is estimated from

a few aggregate totals, rates, and averages. This approach provides a reality

check on whether other results are plausible.

(2) Delucchi:1 In his research, Delucchi has made original estimates of national

totals for most of the components for 1991, broken down finely enough to

permit aggregation along several dimensions. For each item, he provides a

low and high estimate, which are averaged here. His estimates are unique for

Table B-2. Estimates of Components of User Cost ($/VMT)

Component Back-of-Envelope Delucchi Runzheimer FHWA

(1) Fuel 0.058 0.069 0.067 0.061

(2) Maintenance 0.087 0.073 0.052 0.053

(3) Accidents and Insurance 0.087 0.133 0.070 0.070

(4) Wear and Ownership 0.125 0.142 0.248 0.127

(5) Tolls, Fees 0.002 0.015 0.003 0.009

(6) Parking 0.022 0.004 0.019 0.013

(7) Time 0.306 0.344 0.344 0.344

Total Variable 0.232 0.275 0.189 0.184

Total Monetized 0.381 0.436 0.459 0.333

Total Variable w/ Time 0.538 0.620 0.495 0.490

Total Internal 0.687 0.780 0.765 0.639

Notes:

(1) Fuel -- BoE assumes $1.15 for fuel (including excise taxes) and 19.7 miles per gallon average fuel economy for all passenger

vehicles (FHWA 1996 Highway Statistics); Delucchi value is sum of fuel costs, oil company producer surplus, and fuel taxes

(Delucchi, 1998), divided by total 1991 US annual VMT of 2,172 billion (Highway Statistics); Runzheimer values are extracted

by applying their 1998 percentage distribution of costs for and intermediate car to their estimates of annual fixed ($6,934) plus

operating costs ($2,240) of a Ford Taurus (Runzheimer, 1997, 1998); FHWA values are for an intermediate sedan, including fuel

taxes, at $1.196 per gallon (Jack Faucett Associates, 1991).

(2) Maintenance -- BoE based on assumed value of $1,000 per year for oil, tires, parts, and maintenance, and an average annual

mileage for passenger vehicles in 1996 of 11,492 (Highway Statistics); Delucchi estimates national expenditures on maintenance, including in-house government and private fleet maintenance, and sales taxes, but excluding external property damage,

divided by national VMT (see Fuel); Runzheimer and FHWA are same as for fuel.

(3) Accidents and Insurance -- BoE assumes $1,000 per year per vehicle for insurance and accidents, divided by average mileage

(see Fuel); Delucchi’s estimates include insurance administration, accidents paid by users, and pain and suffering “inflicted on

oneself,” but not external costs; Runzheimer and FHWA same as for Fuel.

(4) Wear and Ownership -- BoE assumes a capital cost of $12,000 over 5 years, and average passenger car mileage (see Fuel);

Delucchi estimates private ownership costs, excluding sales tax, divided by total US VMT (see Fuel); Runzheimer and FHWA

same as Fuel.

(5) Tolls and Fees -- BoE takes 1996 total toll payments nationally of $4 billion (Highway Statistics) divided by 1996 US VMT of

2,360 (Highway Statistics); Delucchi omits user fees as transfers, so a rate of 1.5 cents per VMT is inserted; Runzheimer estimates registration fees only; FHWA includes parking with tolls, but no adjustment is made here.

(6) Parking -- BoE assumes $1 per day per vehicle for 250 days per year, over 11,492 annual miles (see Maintenance); Delucchi’s

values combine paid private parking and public parking; Runzheimer provides only a residual “Other” category; FHWA includes

tolls with parking.

(7) Time -- BoE uses 60% of US DOT (1997) “personal” wage rate of $17 and 1.2 persons per vehicle at an average speed of 40

mph; Delucchi values time in three categories -- paid time that is delay, paid uncongested time, and unpaid time whether delay or

not; neither Runzheimer nor FHWA include time costs, so the Delucchi value is used.
Empirical Estimation of Price Components APPENDIX B

Demand Elasticities for Highway Travel B-9

including many imputed values, such as travel time, uncompensated accident

costs borne directly by users, and accident costs paid from sources other than

insurance.

(3) Runzheimer:2 The Runzheimer International Corporation is a consulting firm

that collects data on highway vehicle costs and other business expenses, and

compiles these into planning and forecasting estimates for business use.

Their “intermediate vehicle” is a full size sedan used 20,000 miles per year

and traded in after three years.

(4) FHWA:3 Up until 1991, the Federal Highway Administration intermittently

contracted for tabulations of cost components for various types of highway

passenger vehicles, and published the numbers. The most recent set is based

on data collected in Maryland.

The sources and methods for tabulating the various price components are described in

the notes to the table.

Components Included in 

the “Price”

Several criteria might be considered for guiding the definition of total price:

(1) Out-of-pocket costs: These include fuel, maintenance, parking, tolls, vehicle

wear, variable insurance, and other variable costs to the user that are affected

by whether a given trip is taken or not.

(2) Full, average, or long-run costs: Ownership costs and the annual portion of

insurance might be added to out-of-pocket costs.

(3) Generalized cost or generalized price: All variable and fixed costs, plus

travel time, can be included.

(4) Perceived cost: Costs might be limited to those the user explicitly recognizes

in making the decision to take a trip or use a vehicle.

Generalized price is preferred from a theory standpoint, because it allows all components of cost to be fused into a single dimension. Pragmatically, the relevant price is also

affected by (a) how other elasticities have been measured empirically, for comparison,

and (b) how elasticity is used in the model or analytic procedure into which the parameter is inserted.4

 With proper interpretation, different measured elasticities can be used to

estimate a model parameter that is defined or based differently from the empirical

sources.

1 Delucchi (1997).

2 Runzheimer International (199, 1998)

3 Jack Faucett Associates (1991)

4 The HERS model uses a generalized price including time, operating costs, and accidents, but not user fees;

demand is aggregated over peak and off-peak (therefore no time diversion) and applies to a single facility

(therefore the elasticity includes route diversion).
APPENDIX B Empirical Estimation of Price Components

B-10 Demand Elasticities for Highway Travel

Perceived price is an attempt to identify the components of price that are consciously

recognized by the user, as a basis for predicting user behavior. Whether making this

intermediate variable explicit adds anything to predictive accuracy is doubtful, and, in

any event, it does not provide much guidance for which costs to include. Consumers

tend to respond, as a group, to attributes and magnitudes that have some significant

impact on their well-being, whether consciously perceived or not.

This means that the user response depends upon what decisions are at stake. If ownership is not in question, then only variable costs may be considered, and more so in the

short run. Four alternative definitions for total price are given in Table B-2, ranging

from short-run monetary costs to full long-run costs including travel time. The distinction between variable and fixed is not clean: vehicle wear is variable, while ownership is

fixed. Insurance is typically paid annually and has a large fixed component, although

most exposure to risk is from operation.

Component Shares of 

Total User Cost

The several definitions of total cost yield a range of component shares, shown in Table

B-3. Obviously, the range of values is quite large, depending more upon which total is

used than upon the source of data. With travel time being roughly half the cost, its inclusion makes a big difference.

Empirical Estimates of 

Own-Price Elasticities

The number of categories drops when considering which components are suitable for

empirical estimation, and more so when actual estimates are tabulated. The cost of

maintenance is difficult to keep track of, and either controlled or natural experiments are

hard to imagine; no such studies were found. User responses to the risk of accident

based on equipment such as air bags has been used to estimate users’ implicit valuation

of life, but users cannot be observed reducing either their travel or their rate of accidents

in response to changes in risk. Tolls, fees, and parking are clearly candidates, but apply

to very specific circumstances. Direct estimates of time elasticities have been made, and

indirect estimates can be derived from changes in traffic induced by changes in capacity.

Income elasticities are regarded as exogenous for purposes of estimating travel demand

elasticities, by assuming that price changes are not large enough or general enough to

result in a significant change in income for the average traveler.

Table B-3. Component Shares in Total Price.

Component

Low

Share

High

Share

Fuel 8% 36%

Maintenance 9% 48%

Accidents and Insurance 7% 37%

Vehicle Wear and Ownership 18% 54%

Tolls and Fees 0% 10%

Parking 1% 10%

Travel Time 40% 62%
Empirical Estimation of Price Components APPENDIX B

Demand Elasticities for Highway Travel B-11

Magnitudes of the 

Leakages

The size of the shrinkage factor for fuel can be seen in Goodwin’s (1992) review of elasticity estimates. Table B-4 summarizes his result for studies based on fuel price changes.

The numbers are juxtaposed to permit comparison of elasticities of fuel consumption

(average of over 100 separate empirical values) versus elasticities of travel (about a

dozen numbers), stratified by whether a time series model or a cross-sectional model

was used and whether the intent was short term, long term, or ambiguous.

Fuel elasticities are higher than travel demand elasticities, and long term elasticity estimates are at least twice as large as short term values, as might be expected. For fuel, the

shrinkage from fuel consumption to travel consumption seems to be about 0.5 to 0.9,

meaning that half to ninety percent of the reduction in fuel expenditure is the result of

less travel.

For other price components, the shrinkage factor is more speculative. Increases in insurance and vehicle ownership costs might result in fewer vehicles but more mileage per

vehicle, with the latter less than fully offsetting the former. Increases in road roughness

increase wear and tear, reduce fuel mileage, and reduce speeds. Increases in tolls

directly affect the cost per vehicle mile, but, depending upon how the tolls are graduated, could alter the mix of vehicles and the time-of-day distribution.

The largest user response is likely to come from those users for whom the price change

is relatively largest. A fuel price or tax increase will affect long trips and vehicles with

low fuel efficiency; insurance costs deter ownership in urban areas thereby shifting the

geographic distribution of vehicles; high parking costs deter short trips more than long

ones; high ownership or insurance costs deter vehicles with low annual utilization.

Durations of the Shortand Long-Run 

Adjustment Periods

Some responses occur within days or weeks, while others may take five or ten years to

reach equilibrium. To usefully interpret an empirical elasticity estimate, the time dimension must be known. If the statistical measure for an empirical estimate includes all

VMT or other changes that occurred within a year of the price change, then a short-run

elasticity has been estimated. Longer lag periods for the same price changes yield longer

run elasticities, but separating behavioral responses from background variation gets

harder with longer lags.

Several studies reviewed by Cairns, et al. (1998) reveal the degree to which individuals

change their travel patterns on a daily basis. Two studies, summarized in Table B-5, are

illustrative. Of a group of commuters passing a given point on a road on a given day,

Table B-4. Goodwin’s Review of Fuel Price Elasticities.

Method Fuel or Travel Short Run Long Run Uncertain

Time-series fuel consumption -.27 -.71 -.53

travel demand -.16 -.33 -.46

Cross-section fuel consumption -.28 -.84 -.18

travel demand - .29 -0.5

Source: Goodwin (1992).
APPENDIX B Conversion to Total Price Elasticity

B-12 Demand Elasticities for Highway Travel

60% could be found a week later within the same 2-hour block; the rest were doing

something slightly or completely different. A similar study with a longer time lag

showed a smaller share doing the same thing. Other studies reinforce the same conclusion: individual travel variability is high on a day-to-day basis, and more so over longer

time spans. This is without any significant changes in either exogenous or endogenous

factors.

One implication is that—if stability is much higher in the aggregate than in the microscopic—attempting to predict individual travel behavior is less fruitful than using

aggregate elasticities for endogenous changes. Another is that, with so many individuals

making changes within a short time span, the responses of travelers to changed conditions is likely to be rapid. There is not a lot of inertia in travel patterns. According to

Cairns, et al. (1998), roughly 50% of the response to a change takes place within 1 to 3

years, and 90% within 5 to 10 years. Hence, long-run elasticities tend to be about twice

as large as 1-year or short-run elasticities.

B.3 Conversion to Total Price Elasticity

The results of the above process are displayed in Table B-6, showing empirical estimates of component travel elasticities, along with their implied short- and long-run total

travel demand elasticities. The range of possible values is wide, extending from -0.22 to

-3.7 for short-run demand and -0.57 to -5.1 for long-run demand. The most plausible

numbers, however, lie in the -0.5 to -1.0 range for short-run demand, and -1.0 to -2.0 for

long-run demand. These elasticities apply to vehicle travel, not person travel, which can

be considerably less elastic and still be consistent with these vehicle elasticities due to

changes in vehicle occupancy and other adaptations.5

 The “low” values come from

using the full generalized price, and reinforce the preference for full cost rather than

subsets such as variable costs.

Table B-5. Travel Behavior Variability

Location:

Time Lag:

Type of Travel:

Leeds

1 Week

commuting

Southampton

4 months

regular trips

Same behaviora 60% 49%

Different time 7% 5%

Different route 14% 7%

Different mode 8% 1%

Different destination 5% 13%

No trip/different trip 6% 25%

Source: Cairns, et al. (1998).

a

 travelled the same route by car within the same 2-hour time period.
Conversion to Total Price Elasticity APPENDIX B

Demand Elasticities for Highway Travel B-13

Numerous empirical studies have estimated the price elasticity of gasoline, and a few Fuel Price Elasticities

have measured the travel elasticity with respect to fuel price. The review and summary

by Goodwin described above reflects the results of these studies, and subsequent studies

have tended to confirm his conclusions. Thus a value of -0.16 for short-run travel

impacts and -0.33 for long-run impacts are used, with [4], in Table B-6.

Holding exogenous factors constant, an increase in the real price of vehicles of the same Ownership Elasticity

quality causes a reduction in the purchases of vehicles, especially new ones. The most

likely behavior response is to defer purchase of a new or better vehicle, and keep using

the old one. If, however, the response is measured in the aggregate as total vehicle ownership, then fewer vehicles means less VMT, offset by the extent to which vehicles are

shared.

Dargay (1998) compared several ownership and operation elasticities between the UK

and France, including price elasticity and income elasticity. Converting the price elasticities to VMT elasticities, using a shrinkage factor of 0.9 and the values from Table B-3

in [4], gives the results shown in Table B-6. The source of imprecision in applying ownership elasticities is the uncertain share of total cost per VMT comprised by ownership

and wear-and-tear costs.

Studies based on toll variations are somewhat inconsistent and not easily interpreted. A Toll Elasticities

useful study is one by Gifford and Talkington (1996) that provides elasticity estimates

for the Golden Gate Bridge in San Francisco of -0.187, based on toll variations over the

days of the week as well as changes in the fee structure over several years.6

 They also

review other toll elasticity studies. Because most trips are not tolled, national averages

of tolls per VMT are not useful. Of trips that are tolled, $1.25 might be about average,

5 Cairns, et al. (1998) provide an illuminating list of examples that illustrate the many ways in which individuals and households can satisfy their travel requirements while reducing vehicle miles of travel.

Table B-6. Component and Total Travel Demand Elasticities

Component Implicit Total Travel Elasticities

Elasticities Low High

User Cost Component SRE LRE SRE LRE SRE LRE

Fuel -0.17 -0.33 -0.48 -0.93 -2.0 -3.9

Wear and Ownership -0.12 -0.31 -0.22 -0.57 -0.6 -1.7

Tolls -0.10 -0.19 -0.33 -0.63 -1.0 -1.9

Parking -0.15 -1.17 -1.61 -3.7 -5.1

Time -0.38 -0.68 -0.60 -1.07 -0.9 -1.7

6 Harvey (1994) provides examples that are roughly consistent with Gifford and Talkington’s. Peter Samuel

uses a phased-in toll increase on the Ohio Turnpike to make a back-of-the envelope calculation of trip elasticity of -0.23 and VMT elasticity of -0.15, in his Toll Roads Newsletter for February, 2000.
APPENDIX B Conversion to Total Price Elasticity

B-14 Demand Elasticities for Highway Travel

yielding a share of total costs on a 15-mile trip ranging from 10-30%. This range is used

in Table B-6 instead of the range shown in Table B-3.

Elasticities in response to tolls are difficult to impute because the quality of travel, in

delay time, often changes when the toll changes. For measuring elasticity, an ideal

experiment is one in which travel time is constant while tolls change. Under even moderately congested conditions, a toll change results in trade-offs between money and time

(value of time) as well as money and travel (price elasticity), not to mention time and

travel (time elasticity). Separating these seems difficult.

Parking Price Elasticities Shoup (1994), and Willson and Shoup (1990) review more than a dozen studies of parking pricing, including their own as well as Shoup and Pickrell (1980). From these studies it is possible to extract five case studies that provide sufficient data to construct

ordinary price elasticities. In all of these examples, the price of parking was zero for the

base alternative in the comparison, so the calculations in Table B-7 base the elasticity

estimates on an assumed total price for travel, rather than for parking alone. The elasticity magnitudes are large even when the price change is measured against only a small

share of long-run cost.

In the before/after cases, the price of parking changed at a particular work site, and the

behavior responses were tracked for up to a year after parking became priced. Some of

the employers had ridesharing incentive programs, which were ineffective so long as

parking was free. These examples are interpreted as representative of short-run demand

elasticities. The with/without cases compare similar work sites, one priced and one not.

These are interpreted here as long-run elasticities, on the rationale that commuters had

sufficient time to make long run adjustments. These elasticities would be higher if all

Table B-7. Parking Total Price Elasticities

Trip Ratea Parking Priceb Total Price Elasticityc

Before/After Case Studies: Free Priced Free Priced Low High

Mid Wilshire, LA 48 30 0 58 -1.05 -3.33

Warner Center, LA 92 64 0 30 -1.65 -5.23

Ottawa CBD, Canada 94 80 0 30 -0.81 -2.56

Average -1.17 -3.70

With/Without Case Studies:

Century City, LA 39 32 0 23 -1.27 -4.02

Civic Center, LA 78 50 0 30 -1.95 -6.16

Average -1.61 -5.09

Notes:

a Autos driven per 100 employees.

b Price in dollars per month.

c Full vehicle “backward” arc (low price to high) price elasticity based on 35-mile round trip average for LA reported in Willson and Shoup

(1990), at an average user cost of $.22 per VMT for variable costs only (=$163 per month for the Low estimate) or $.70 for all costs including

time but excluding parking (=$515 for the High estimate). Backward elasticities are lower than midpoint or forward arc elasticities for downward-sloping demand curves.
Conversion to Total Price Elasticity APPENDIX B

Demand Elasticities for Highway Travel B-15

employee parking were priced, because more people at more sites would be seeking

ridesharing or transit arrangements.

Because parking is free to the user for 99% of all trips (over 90% of urban work trips),

the average share of parking in the cost of travel to the user is not a valid base value for

these elasticities. As Shoup (1994) states,

“It is important to remember that the elasticity estimates [average 0.15] refer to commuter response to changes in only the parking price of their trip and are therefore 

smaller than the elasticity of demand with respect to changes in the full price of automobile trips.”(p. 159)

He gives other reasons why these estimates are low, including the likely availability of

cheaper parking nearby and the inelasticity of work trip demand.7

Several studies have tabulated traffic volumes subsequent to an increase in capacity, or Time Cost Elasticities

occasionally in response to a decrease in capacity or change in travel time. For those

based on change in capacity, the measure of elasticity is

[5]

where %∆cap = percent change in capacity, with capacity measured in lane miles.

Hansen et al. (1993) estimate this elasticity for eighteen highway sections in California,

and include controls for trend VMT. To transform this measure into a price elasticity

requires substituting a price measure for the capacity measure, such that

[6]

i.e., a conversion factor is needed from the Hansen elasticity to a price elasticity, consisting of the ratio of an increase in capacity to its corresponding reduction in price. Taking time as the only component affected, the question is what are the time savings from

a given added capacity? Most of Hansen’s expansions are from four to six lanes or six to

eight lanes; if it is assumed that two lanes in the same direction are congested, and that

adding a third will increase average speed from 40 to 60 mph8

 for at least a few years,

then a 50% capacity increase is equivalent to a 33% time savings (neither the value of

time nor occupancy affect this result), for a conversion factor of -1.5. Thus Hansen’s

7 Harvey (1994) offers examples from San Francisco and Boston airport parking, which are consistent with

Shoup’s summary if Harvey’s elasticities measure the number of vehicles parking. This does not necessarily

equate, however, to the same percentage reduction in VMT, because some of the deterred parking is shifted

to taxi trips.

8 This speed change implies an average savings of 0.50 minutes per VMT. Using the HERS (Chapter 6) delay

equations for expressways, which model average daily delay per VMT as a function of AADT/c(apacity), a

50% increase in capacity at an AADT/c of 15 (fairly high) results in delay savings of 0.855 minutes per

mile, whereas an initial AADT/c of 12 yields a savings of 0.255 per mile.

eT capacity ,

%∆VMT

%∆cap = ---------------------

eT

%∆VMT

%∆p --------------------- %∆VMT%∆cap --------------------- %∆cap%∆p × ------------------ eT capacity ,

%∆cap

%∆p == = × ------------------
APPENDIX B Conclusions

B-16 Demand Elasticities for Highway Travel

low or short-run value of about 0.25 becomes -0.375 and his high or long-run value of

0.45 becomes -0.675.

Cohen (1995) reviews several time-travel elasticity studies. The results are somewhat

erratic, but generally consistent with the above. Often, some types of induced traffic are

counted (e.g., new travel by users already in the market) and others omitted (e.g., route

diversions). Unlike other components of user price, time cannot be economized by sharing the cost among additional vehicle occupants. Therefore, elasticity with respect to

time cost should be lower than for the other components.

B.4 Conclusions

Despite the widely varying orientations, data sources, and scope of applicable empirical

studies, and the fact that none was attempting to estimate total travel elasticity, the

results are roughly consistent. Users respond to changes in any of the components of

travel cost that are measurable, and the response starts immediately and continues over

many years.

Taking the short run to be approximately a year or less, vehicle demand-price elasticity

tends to fall in the range of -0.5 to -1.0, with -0.7 to -0.8 being the most likely for typical

conditions. The long run may occur over twenty years, but five years is enough to cover

most of the effects. long-run elasticities are about twice as high as short-run, with a

range of about -1.0 to -2.0. Response to variable and obvious money costs such as parking and fuel show higher elasticities than for fixed and more hidden costs. These elasticities apply to vehicle-trips, not person-trips.

B.5 References

Cairns, Sally, Carmen Hass-Klau, and Phil Goodwin, “Traffic Impact of Highway

Capacity Reductions: Assessment of the Evidence,” prepared for London Transport, London, UK: Landor, March 1998.

Chan, Yupo, and F.L. Ou, “A Tabulation of Demand Elasticities for Urban Travel Forecasting,” paper for TRB, Washington, DC, January 1978.

Cohen, Harry S., “Review of Empirical Studies of Induced Traffic,” in Transportation

Research Board (ed.), Expanding Metropolitan Highways: Implications for Air

Quality and Energy Use, Special Report 245, pp. 295-309, Washington, DC:

National Academy Press, 1995.

Dahl, Carol A., and Thomas Sterner, “Analyzing Gasoline Demand Elasticities,”

Energy Economics (1991), pp. 203-210.
References APPENDIX B

Demand Elasticities for Highway Travel B-17

Dahl, Carol A., and Thomas Sterner, “A Survey of Econometric Gasoline Demand Elasticities,” International Journal of Energy Systems, 11, 2 (1991).

Dargay, Joyce M., “Demand Elasticities: A Comment,” Journal of Transport Economics

and Policy, 27, 1 (1993), pp. 87-90.

Dargay, Joyce M., “Estimation of Dynamic Car Ownership Model for France Using a

Pseudo-Panel Approach,” prepared for INRETS, London: ESRC Transport Studies Unit, University College London, January 1998.

Dargay, Joyce M., and Dermot Gately, “The Demand for Transportation Fuels,” Transportation Research (B), 31B, 1 (1997).

Dehgani, Youssef, and Antti Talvitie, “Model Specification, Modal Aggregation, and

Market Segmentation in Mode-Choice Models: Some Empirical Evidence,”

Transportation Research Record, 775 (1980), pp. 28-34.

DeJong, John G. J., “Estimation of Gasoline Price Elasticities for New Jersey,” Transportation Research Record, 812 (1981), pp. 64-67.

Delucchi, Mark A., “The Annualized Social Cost of Motor-Vehicle Use in the U. S.,

1990-1991: Summary of Theory, Methods, and Results,” Vol. 1 of 20, The Annualized Social Cost of Motor-Vehicle Use in the United States, based on 1990-

1991 Data, Davis, CA: Institute of Transportation Studies, University of California, June 1997.

Federal Highway Administration, “1990 Nationwide Personal Transportation Survey:

Summary of Trends,” Washington, DC: US DOT/FHWA, March 1992.

Federal Highway Administration, “Cost of Owning and Operating Automobiles and

Vans 1984,” Washington, DC: FHWA, 1984.

Federal Highway Administration, “Highway Statistics 1996,” Washington, DC: US

DOT/FHWA, November 1997.

Gifford, Jonathan L., and Scott W. Talkington, “Demand Elasticity Under Time-Varying

Prices: Case Study of Day-of-Week Varying Tolls on Golden Gate Bridge,”

Transportation Research Record, 1558 (1996), pp. 55-59.

Goodwin, Phil B., “Empirical Evidence on Induced Traffic,” Transportation, 23, 1

(1996), pp. 35-54.

Goodwin, Phil B., “Extra Traffic Induced By Road Construction,” in OECD (ed.), Infrastructure Induced Mobility, ECMT Round Table 105, Paris: OECD, 1998.

Goodwin, Phil B., “A Review of New Demand Elasticities with Special Reference to

Short and Long Run Effects of Price Changes,” Journal of Transport Economics

and Policy, 26, 2 (1992), pp. 155-170.

Hall, Jane V., “The Role of Transport Control Measures in Jointly Reducing Congestion

and Air Pollution,” Journal of Transport Economics and Policy, 29, 1 (1995), pp.

93-103.

Hansen, Mark, David Gillen, Alison Dobbins, Yuanlin Huang, and M. Puvathingal,

“The Air Quality Impacts of Urban Highway Capacity Expansion: Traffic Gen-
APPENDIX B References

B-18 Demand Elasticities for Highway Travel

eration and Land Use Change,” prepared for California Department of Transportation, Berkeley, CA: Institute of Transportation Studies, University of

California, April 1993.

Harvey, Greig W., “Transportation Pricing and Travel Behavior,” in Transportation

Research Board (ed.), Curbing Gridlock: Peak-Period Fees To Relieve Traffic

Congestion, Special Report 242, pp. 89-114, Washington, DC: National Academy Press, 1994.

Jack Faucett Associates, “Cost of Owning and Operating Automobiles and Vans 1991,”

prepared for Federal Highway Administration, Washington, DC: FHWA, 1992.

Luk, James, and Stephen Hepburn, “New Review of Australian Travel Demand Elasticities,” Research Report ARR No. 249, Victoria, Australia: Australian Road

Research Board, December 1993.

Metropolitan Transportation Commission, “Travel Forecasting Assumptions '98 Summary,” Oakland, CA: MTC, August 1998.

Meyer, Michael D., and Eric J. Miller, Urban Transportation Planning: A Decision-Oriented Approach, New York: McGraw-Hill, 1984.

Oum, Tae Hoon, II W. G. Waters, and Jong-Say Tong, “Concepts of Price Elasticities of

Transport Demand and Recent Empirical Estimates,” Journal of Transport Economics and Policy, 26, 2 (1992), pp. 139-154.

Pritchard, Tim, and Larry DeBoer, “The Effect of Taxes and Insurance Costs on Automobile Registrations in the United States,” Public Finance Quarterly, 23, 3

(1995), pp. 283-304.

Runzheimer International, “Runzheimer Analyzes 1998 Car, Van, and Light Truck

Costs,” news release, Rochester, WI: Runzheimer, November 3 1997.

Runzheimer International, “Runzheimer Analyzes Typical Vehicle Costs: Where Does

Your Automotive Dollar Go?,” news release, Rochester, WI: Runzheimer, June 1

1997.

Schimek, Paul, “Gasoline and Travel Demand Models Using Time Series and CrossSection Data from United States,” Transportation Research Record, 1558

(1996), pp. 83-89.

Shoup, Donald C., “Cashing Out Employer-Paid Parking: A Precedent for Congestion

Pricing?,” in Transportation Research Board (ed.), Curbing Gridlock: PeakPeriod Fees To Relieve Traffic Congestion, Special Report 242, pp. 152-199,

Washington, DC: National Academy Press, 1994.

Shoup, Donald C., and Don H. Pickrell, “Free Parking as a Transportation Problem,”

prepared for US DOT, Los Angeles, CA: University of California, 1980.

Small, Kenneth A., Urban Transportation Economics, Chur, UK: Harwood Academic,

1992.

Sterner, Thomas, and Carol A. Dahl, “Gasoline Demand Modeling: Theory and Application,” in Thomas Sterner (ed.), International Energy Modeling, London, UK:

Chapman and Hall, 1992.
References APPENDIX B

Demand Elasticities for Highway Travel B-19

Sterner, Thomas, Carol A. Dahl, and Mikael Frazen, “Gasoline Tax Policy, Carbon

Emissions and the Global Environment,” Journal of Transport Economics and

Policy, 26, 2 (1992), pp. 109-120.

Strathman, James G., and Kenneth J. Dueker, “Transit Service, Parking Charges and

Mode Choice for the Journey-to-Work: Analysis of the 1990 NPTS,” Portland,

OR: Center for Urban Studies, Portland State University, January 1996.

Symons, N. R., J. R. K. Standingford, and R. B. Jones, “Sensitivity of Travel Demand to

Toll Charges: Experience at West Gate,” Hobart, Australia: Australian Road

Research Board, August 1984.

Taplin, John H.E., “Inferring Ordinary Elasticities From Choice or Mode-Split Elasticities,” Journal of Transport Economics and Policy (1982).

US Department of Transportation, “The Value of Saving Travel Time: Departmental

Guidance for Conducting Economic Evaluations,” Washington, DC: US DOT/

OST, April 9 1997.

Willson, Richard W., and Donald C. Shoup, “Parking Subsidies and Travel Choices:

Assessing the Evidence,” Transportation, 17, 2 (1990), pp. 141-157.
APPENDIX B References

B-20 Demand Elasticities for Highway Travel
APPENDIX C

Basic Theory of Highway Project Evaluation C-1

APPENDIX C

Basic Theory of Highway Project 

Evaluation

Douglass B. Lee, Jr.

The criterion for making good investments is to select projects for which the net benefits are positive, i.e., incremental benefits exceed incremental costs. The major analytic

steps are: define alternatives, evaluate impacts, and select the project with highest net

benefits. If pricing is determined independently of marginal cost, however, pricing is

exogenous and the investment evaluation is necessarily in a second-best mode.

The HERS model incorporates demand elasticity and benefit-cost evaluation principles The HERS Model

that are specific to the investment and policy alternatives typically considered at

national and local levels. As highway investment concerns shift, the HERS model

attempts to adapt by making explicit the variables and relationships that will permit the

model to realistically address the new concerns. In doing so, the model becomes more

general in its scope and more flexible in its application to questions of interest.

For the 1997 Conditions and Performance report to Congress, the HERS model was

extended to utilize demand elasticities, such that highway improvements that lowered or

raised user costs could lead to changes in travel volumes, and that over the long run the

effects of improvements could be to shift the demand curve from where it might have

been placed in initial forecasts (See Appendices B and C). Also, HERS was modified to

estimate and take into account emissions of air pollutants, although the feature was not

turned on until the 1999 report to Congress.

While HERS recognizes a “price” to the user, it does not incorporate a money price that

is separate from user time and operating costs. Fuel taxes and tolls are therefore ignored,

both in estimating demand and as potential policy instruments such as for congestion

pricing.

This appendix presents the principles that apply generally to evaluating highway

improvements, under conditions of exogenously-determined arbitrary pricing. The

HERS model implements a subset of these principles. The purpose of displaying a

Acknowledgments: The author thanks E. Ross Crichton and Anthony Rufolo for helpful comments on a previous draft.
APPENDIX C Project Description

C-2 Basic Theory of Highway Project Evaluation

broader scope is to illuminate the capabilities of the HERS model in the context of the

more general theory, and to indicate the directions in which the model might be modified to extend its applicability.

C.1 Project Description

A physical facility can be represented for evaluation purposes by its unit costs with

respect to traffic volume, measured as vehicle trips per hour. Three functions of volume

provide the information necessary for calculating net operating benefits: average variable cost (AVC), marginal cost (MC), and price. Assuming a base alternative and one

project alternative, the physical characteristics of each alternative are given by their

variable cost curves, while the price curve constitutes the policies affecting how the

facility is operated. All variable costs, whether monetized or not, are included. Cost and

price components are assumed to be converted into a common numeraire (dollars),

referred to as generalized cost or generalized price, meaning that it combines money and

in-kind components on the same scale. Neither fixed costs nor fixed charges (e.g.,

annual vehicle license) are represented in the diagrams. 

In general, at any given volume, marginal cost, average variable cost, and price to the

user are all different. MC and AVC are mathematically related, and will diverge if any

component of cost varies with volume (or v/c), i.e., MC is unequal to AVC if unit cost

(AVC) goes up or down with volume. Because unit travel time costs rise with congestion, for most volume levels marginal cost lies above average cost. Price includes user

charges, which are transfers and not costs, and excludes externalities and agency costs

(facility wear, maintenance, and operation), which are costs that are not part of the price.

Marginal Cost The marginal social cost curve is the guide for efficient pricing, so if p = MC at all volumes, then net benefits in the short run are maximized for the facility. In this special

(first-best) case, price and marginal cost are the same. As shown more generally in Figure C-1, price, represented by the price function, is not directly tied to marginal cost,

labeled MC. Since the price function determines the quantity demanded by its intersection with the demand curve, actual volume is q0 at a price of p, with a marginal cost of

mc and an average cost of ac. The inefficiency from not pricing at marginal cost is given

by the triangular area bounded by pmc, mc, and p.

1

Average Cost Variable social costs include travel time, fuel, accidents, other vehicle wear and operating costs, damage from emissions and noise, and facility wear, maintenance, and operation (agency costs), but not fuel taxes or tolls. They are variable because they increase

1 The welfare loss from inefficient pricing does not enter in to the measurement of second-best benefits, but

recognition of the inefficiency provides some insights when comparing second-best benefits to first-best

pricing.
Project Description APPENDIX C

Basic Theory of Highway Project Evaluation C-3

with vehicle miles traveled. Their combined average unit cost per vehicle mile (AVC)

might rise, decline, or remain constant with volume, which is a rate of flow. In fact,

most of the components of variable cost vary slightly with volume, due to congestion,

but the one that varies by far the most is travel time.

Because users are faced with the average rather than the marginal cost of travel time, it

is frequently assumed that price and average cost are the same, but this usually is not

true because of user charges, agency costs, and externalities. The AVC and MC functions are mathematically related, such that either one could be derived from the other,

but it is the components of average cost that can be observed empirically.

Total variable cost can be measured either as the area under the marginal cost curve

(e.g., up to q0) or as the average variable cost (ac) times the volume (q0), the latter being

a rectangle, as shown in Figure C-1. This relationship will be used later.

Price is the cost to the user, and includes travel time, accidents, and operating costs as Price

well as money payments that vary with usage. The price function in Figure C-1 assumes

that travel time is the main reason the generalized price varies with volume; user

charges are approximately constant per vehicle mile, such as through a fuel tax.

The price function in this diagram is shown as lying above average cost. This might be

the case if variable user charges exceed variable externalities and agency costs. If the

reverse is true, then the price function lies below AVC, as shown in Figure C-2. The

same relationships hold as before, although the inefficiency triangle is relatively larger.

For congested conditions, it is unlikely that price will be above MC without a congestion-related toll, but price could be above AVC. Whether price is above or below AC

Figure C-1. Three Functions of Trip Volume.

MC

AVC

ac

p

qo vehicle volume

generalized

cost,

price

price function

pac

pmc

mc

demand
APPENDIX C Project Description

C-4 Basic Theory of Highway Project Evaluation

depends upon the magnitude and valuation of externalities and agency costs relative to

user charges.

Thus volume could be determined by any of the three functions, shown at the circled

points in Figure C-1 or Figure C-2: by marginal cost at pmc, for efficient pricing and

first-best evaluation; by average variable cost at pac, which ignores actual user charges,

agency costs, and externalities; or by the price function at p, which is the most general

case.

Constructing the Demand 

Curve

The demand curve shows the quantity that will be taken by consumers across a range of

prices, generalized to include time and running costs. In reality, this demand curve is

constantly shifting, affected by user preferences as well as their knowledge of what conditions will actually pertain at their time of usage. For analytic purposes, the demand

curve is assumed to be fixed—or represented by some average—for some period of

time. An example of a demand period is the AM peak period, lasting several hours in

larger urban areas. A single demand curve might represent the AM peak, or the AM and

PM peaks combined; time periods do not need to be contiguous to be treated as a single

demand period.

The minimum information needed to construct a demand curve is a price, a quantity,

and an elasticity at that point. The price could be the average generalized price during

peak periods, namely, the sum of travel time, running costs, and user fees representative

of peak times.2

 The quantity is the average traffic volume for the peak, in vehicles per

hour. An elasticity can be selected by comparing the project to other facilities with

Figure C-2. Three Functions with Price Below AC.

MC

AVC

ac

p

qo vehicle volume

generalized

cost,

price

price function pac

pmc

mc

demand

2 See Table C-1 below, page 10.
Single-Period Evaluation APPENDIX C

Basic Theory of Highway Project Evaluation C-5

respect to the mix of components of price, the substitutes available, and the types of

vehicles and trip purposes. Ideally, the elasticity should be compatible with the nature of

the project, e.g., include diversions if the project is a single facility. The demand curve

could be disaggregated into separate analyses for each market segment (e.g., trucks,

commuters, recreational travelers), but some averaging is always necessary. A single

demand curve for all users is assumed here.

With a single elasticity value, the functional form of the demand curve can be either

straight line or constant elasticity. Given the demand point (p, q0) in Figure C-2, only

one demand curve of each type passes through that point with the given elasticity at that

point. A straight line is used here.

To evaluate a project, a set of curves is needed for each of the base and the project alter- Project Alternatives

natives, as shown in Figure C-3. Data for the base alternative are designated with a “0”

subscript, and with a “1” for the project alternative.

The marginal and average cost functions are characteristics of the facility, resulting

from its capacity, geometrics, terrain, pavement condition, and so forth. The price function is partly endogenous to the facility in that it includes some variable costs, and partly

exogenous in the form of user charges and regulation. The price function could be made

to go through the point pmc by the correct congestion toll, in which case the facility

would be operating efficiently. Another possibility is that externalities (except delay)

and agency costs are exactly offset by user charges, such that the price function follows

the AC curve. These are special cases of the general case presented here.

C.2 Single-Period Evaluation

A highway improvement—resurfacing, reconstruction, additional lanes—will change

user costs by some amount, resulting in operating benefits. Reductions in running costs,

travel time, and accidents are both reductions in price and real benefits. Savings in

agency costs and externalities are real benefits but not included in the price, whereas

savings in user fees are not real benefits. The impacts of each improvement can be estimated from its induced traffic volume (based on the price and demand curve) and variable cost savings. These net operating benefits (NOB) are estimated for the current

period, and subsequent periods, over the lifetime of the improvements. Any improvement whose NOB over its lifetime exceeds its capital costs is considered feasible;

among feasible improvement projects, the one generating the highest net benefits is preferred.

Short-Run Effects of 

Improvements

Highway improvements that reduce congestion (by expanding capacity), or reduce vehicle wear and fuel consumption, or reduce accidents, have the effect of lowering the

price to the user and stimulating greater volumes, depending upon the elasticity of
APPENDIX C Single-Period Evaluation

C-6 Basic Theory of Highway Project Evaluation

demand. If the short-run price elasticity is non-zero, changes in the generalized price

will cause changes in volume, within the same period, by movement along the demand

curve.

To some extent, capacity expansions are self-limiting, in that induced traffic reintroduces congestion, which offsets some of the initial time savings from expansion. This

supply-demand equilibrium may not result in as high a volume as would be the case if

there were no congestion, but congestion will remain below the original congestion

level before the capacity expansion. It is not possible for the same level of congestion to

return after the expansion as before, because the short-run demand curve slopes downward to the right, and demand in the short run stays on the same demand curve. In subsequent demand periods, shifts in the demand curve might lead to higher congestion

than in the current period, but such demand growth would be at least partly exogenous.3

Incremental Net Benefits Benefits of the project are generally a combination of cost savings and additional travel.

The net of such operating benefits is compared to the net or sum or fixed costs, with all

Figure C-3. Net Operating Benefit (NOB) for a Project.

cost savings additional costs

MCo

MC1

AVCo

aco

ac1

po

p1

AVC1

qo q1 vehicle volume

generalized

cost,

price

price function (1)

price function (0)

mco

mc1

D

3 This effect of exogenous growth overtaking short-run improvements is observed in TRB Special Report 245

(1995).
Single-Period Evaluation APPENDIX C

Basic Theory of Highway Project Evaluation C-7

values discounted or annualized as appropriate. Figure C-3 can be used to illustrate the

net operating benefit (NOB) of the project. This diagram assumes price lies above AVC;

the (minor) consequences of changing this assumption will be shown subsequently. The

measurement of NOB can be defined in two ways, using different combinations of the

variable cost and pricing functions and the demand curve.

NOB Based on Marginal 

Cost

Total variable costs for the base alternative are represented by the area under the MC

curve up to the existing volume q0. For the project alternative, the corresponding area is

lower but extends out to q1. The cost difference is an area of cost savings between the

two curves up to q0, and an area of additional costs under MC1 from q0 to q1. The latter

is offset by the (not necessarily equal) incremental benefits from the additional trips,

represented by the area under the demand curve from q0 to q1. The resulting NOB is the

area outlined by the dot-dash line. It can be described as the area between the two MC

curves and under the demand curve.

Where MC crosses above the demand curve, the area—marked “additional costs”—is

negative; these disbenefits are a consequence of underpricing the project alternative, relative to marginal cost pricing. NOB could be increased by this amount if the new project

were efficiently priced, but this is not an option with exogenous pricing. Correspondingly, NOB would be smaller if it did not include the inefficiency from underpricing the

base alternative.

Because areas under the marginal cost curve can also be represented by rectangles con- NOB Based on AVC

structed from the AVC curve, using the relation,

[1]

the area under MC0 up to q0 is equal to the rectangle whose length is q0 and whose

height is ac0 (read from AVC0), as shown in Figure C-4. Similarly, the area under MC1

up to q1 is equal to the rectangle q1 by ac1. The difference between these two rectangles

is the shaded area labeled “delay and cost savings,” minus the additional costs from q0

to q1, plus the area under the demand curve from q0 to q1. This shaded area is exactly

equal to the outlined area derived from the MC curves.

In practice, a distinction is made between trips that are already being made in the base “Old” versus “New” Trips

case (up to q0), or “old” trips, on the one hand, and additional trips (from q0 up to q1)

generated by the reduction in price (from p0 to p1), or “new” trips, on the other.4 A reason for making this distinction is the nature of the benefits to the two groups: old users

have “demonstrated” or “revealed” (even if the demand curve is estimated or forecast)

MC

0

q

∫ q AVCq = ×

4 It is likely, though not necessary, that most previous users of the base facility remain on the new facility to

become “old” users, since they obtain what they had previously but now at a lower generalized price. The

old-new distinction, however, is heuristic, rather than defining a fixed set of vehicles.
APPENDIX C Single-Period Evaluation

C-8 Basic Theory of Highway Project Evaluation

their willingness to pay for their travel, and so the benefits to them are the cost savings

over their previous generalized cost. New trip makers on this facility, in contrast, have

not shown any willingness-to-pay, so their benefits must be estimated from the demand

curve as consumer surplus over what they actually pay when using the new project.

Although the total NOB areas are the same whether defined by MC or AVC, the way

they partition the benefits between old and new users is not. The area under MC1 up to

q0 indicates the total average cost if volume on the new facility were held at the volume

on the base facility, but that is not what will happen; the new volume will be q1, and

costs for “old” users will be higher than if volume were held to q0. At a volume of q0,

ac1 would occur where AVC1 crosses the vertical at q0, but none of the old users actually

faces this hypothetical cost on the new facility; instead they all pay the actual ac1 at q1.

The shaded area representation based on AVC provides a more useful interpretation with

respect to old and new users, and also allows for direct empirical estimation of the benefit components.

NOB with Price Below 

AVC

With price above AVC, the NOB diagram looks similar in shape to the first best case.

This is because with price being above AVC there is at least a partial “toll” even if it is

Figure C-4. NOB Measured from AVC.

∆ producer

surplus

delay and cost savings ∆ consumer

surplus

MCo

MC1

AVCo

aco

ac1

po

p1

AVC1

qo q1 vehicle volume

generalized

cost,

price

price function (1)

price function (0)

mco

mc1

D

"old" trips "new" trips
Single-Period Evaluation APPENDIX C

Basic Theory of Highway Project Evaluation C-9

below marginal cost. If it is assumed that p < AVC, the diagram is slightly different. Figure C-5 shows such a situation, in which price is below AVC for both the base and

project alternatives.

This diagram can be compared to Figure C-4. The outline of NOB based on MC is

essentially the same, but the area defined by AVC curves has a somewhat different

shape. Savings on old trips start above the current price, because the elimination of

externalities in the base case is a benefit. Correspondingly, the benefits stop farther up,

because some of the travel time and cost savings are offset by agency costs or externalities in the project alternative; cost savings would come down to p1 were it not for the

new externalities. Consumer surplus is the same in both diagrams, but a share of incremental consumer surplus in Figure C-5 is offset by additional agency costs or externalities from new trips, which might be thought of as negative producer surplus.

Figure C-5. NOB with Price Below AVC.

delay and cost savings

negative

benefits

∆ consumer surplus

MCo

MC1

AVCo

aco

ac1

po

p1

AVC1

qo q1 vehicle volume

generalized

cost,

price

price function (1)

price function (0)

D

mco

mc1

"old" trips "new" trips
APPENDIX C Components of Net Operating Benefit

C-10 Basic Theory of Highway Project Evaluation

C.3 Components of Net Operating Benefit

Breaking NOB into components is useful for several reasons:

(1) Most of the components can be estimated directly, whereas the NOB defined

by MC curves can only be estimated by estimating the functional form of

total variable costs.

(2) Valuation can be done separately for each component, e.g., value of travel

time, cost per accident.

Table C-1. Price and Cost Components

Marginal 

Cost

Average 

Cost Price HERS

Travel Time

Uncongested Time y y y y

Excess Delay MT AD AD AD

Operating Cost

Fuel y y y y

Vehicle Maintenance y y y y

Vehicle Wear y y y y

Accidents (internal) y y y y

Parking (internal)

Vehicle Ownership

Infrastructure

Pavement Wear y y y

Maintenance and Operation y y y

Fixed Capital

Parking (unpriced)

Externalities

Air Pollution y y y

Water Pollution y y

Noise and Vibration y y

User Charges

Tolls y

Excise Taxes y

Other Variable Fees y

y = cost component is included in the total for the column category

MT = marginal time cost is included

AD = average delay cost is included
Components of Net Operating Benefit APPENDIX C

Basic Theory of Highway Project Evaluation C-11

(3) The magnitudes of the components can be interpreted in meaningful terms

and their relative magnitudes compared.

Most of the components can be disaggregated further than the major categories shown

in Figures C-4 and C-5 and described below. A more detailed breakdown is provided in

Table C-1. The first three columns refer to the three functions of volume previously

described. Travel time is divided into normal travel time and delay, which can be anything above free-flow speed or above a v/c of, say, 0.8 of capacity. Some operating and

infrastructure costs (vehicle ownership and pavement) are divided into variable and

fixed as well as internal (paid by the user) and external (paid or suffered by others).

Parking cost is excluded for purposes of project evaluation of highway facilities,

although it may be relevant to other purposes such as price elasticities.

The fourth column notes those components included in the HERS model. Travel time

and operating cost components are included in both price and cost, while infrastructure

costs (agency costs) and externalities are included in cost only. HERS does not include

user fees such as fuel taxes or tolls. Neither HERS nor the general theory deal with fixed

user fees, such as annual fees not based on miles traveled.

Most of the major components are shown again in Figure C-6, which is similar to (and a

blend of) Figures C-4 and C-5 but with the MC outline of NOB and the MC lines themselves omitted.

Trips being taken on the base facility before the improvement and remaining on the new Savings on Old Trips

facility receive benefits in the form of reduced delay and operating costs. In Figure C-6,

the average cost with no improvement is AVC0 and yields an average cost of ac0 for the

base or “unimproved” volume q0. With the improvement, ac1 is the cost as read off the

AVC1 curve.

Savings on old trips, then, is the difference in average cost (a0-a1) times the unimproved

volume q0, indicated by the shaded rectangle. All costs listed in the “Average Cost” column of Table C-1 are included. For example, fuel savings, highway maintenance cost

savings, and pollution reduction are included, but fuel tax savings are ignored.

Incremental Consumer 

Surplus

Consumer surplus is the amount users would be willing to pay above what they actually

pay; it is measured as an area under the demand curve between the “with” and “without”

volumes, and above the price. Because incremental consumer surplus applies to induced

or “new” trips, the relevant volumes in Figure C-6 are q0 (with no improvement) and q1

(with improvement). Data required consist of two prices and the demand curve. This

consumer surplus is a triangular area whose hypotenuse is the demand curve between p0

and p1, and whose legs are formed by q0 and p1 (only the top of this triangle is shown,

because the bottom is offset by external costs). Both fuel costs and fuel taxes, for example, are included in the measurement.
APPENDIX C Components of Net Operating Benefit

C-12 Basic Theory of Highway Project Evaluation

Producer Surplus on New 

Trips

Producer surplus is an area under the demand curve that is below what users pay but

above short-run variable cost. Normally, user fees are regarded as transfers and therefore ignored in estimating benefits, but here it is simply a part of the means for valuing

induced travel. Like consumer surplus, it indicates a willingness to pay for new trips. A

congestion toll generates producer surplus, but only the portion on new trips is counted

as a benefit; the portion applying to old trips is already counted in the time and cost savings on old trips. The net of revenues above incremental agency costs and externalities

is producer surplus.

Producer surplus can be negative if payments are less than average cost. Although not

comprised of revenues, users create negative externalities that are omitted from the

price, so these costs can be treated symmetrically to positive producer surplus. Negative

producer surplus is shown in Figures C-5 and C-6, while Figure C-4 shows positive producer surplus. In Figure C-7, the surplus of revenues over short-run cost is the rectangle

with a height of (p0-ac0) and a length of q0; this area is excluded from NOB of the

project because it occurs in the base case.

External Costs Negative externalities shift the marginal and average social cost curves upward, but not

the price function. External costs are included in the average variable cost (AVC) curves

Figure C-6. Components of Net Operating Benefit (NOB).

delay and cost savings

negative

producer

surplus

∆ consumer

surplus

AVCo

aco

ac1

po

p1

AVC1

qo q1 vehicle volume

generalized

cost,

price

price function (1)

price function (0)

D

"old" trips "new" trips
Components of Net Operating Benefit APPENDIX C

Basic Theory of Highway Project Evaluation C-13

in Figure C-6. Thus the MC and AVC curves in the diagram include both externality as

well as time costs.

A negative externality has the opposite effect as a user charge. If the user charge and the

externality happened to be equal in value (at all volume levels), then there would be no

externality. In outlining the incremental NOB area, external costs are rectangles taken

from the average cost curves, and are negative in sign. In Figure C-7, for example, the

net of external and agency costs over user payments in the project alternative has a

height of (ac1-p1) and a length of q1. Subtracting this area from consumer surplus (for

new trips) and user cost savings (on old trips) leaves the small triangle above the

demand curve at the outer end in Figure C-6 as a negative benefit (i.e., traffic induced

by underpricing produces costs that exceed internal benefits).

Externalities in Related 

Markets

Externalities caused by induced trips diverted from other facilities may not be adding to

the total emissions of pollutants, but this is irrelevant to the present project. The only

way to incorporate changes in externalities in related markets (e.g, parallel facilities) is

to measure the difference in the total inefficiency with and without the improvement

project; it cannot be done one item (e.g., pollution or congestion) at a time.

It seems conceptually plausible to sum up the net change in air pollution caused by a

project for a region, say, and count that as the project’s pollution benefit or disbenefit;

then do the same for travel time, accidents, and running costs. While certainly a chore to

Figure C-7. Positive and Negative Producer Surplus.

externalities and agency costs in excess of user fees

revenues in excess of

short run variable cost

MCo

MC1

AVCo

aco

ac1

po

p1

AVC1

qo q1 vehicle volume

generalized

cost,

price

price function (1)

price function (0)

Demand
APPENDIX C Multi-Period Evaluation

C-14 Basic Theory of Highway Project Evaluation

detect the thousands of microscopic impacts occurring throughout the region, the task

might be accomplished with regional simulation models.

The real problem, however, is that all of these calculations are meaningless without also

calculating and summing all of the changes in consumer utility occurring at the same

time, each of them the result of a shift in the demand curve in the relevant market. The

likely error in such an estimate would greatly exceed the magnitude of the impact being

estimated. Total air pollution in the region may be a performance measure of important

policy concern, but the change in that index is not a basis for evaluating individual

projects. The practical solution is to ignore what happens in related markets, except perhaps to trace out the efficiency changes for a few externalities in a few closely-related

markets. The magnitude of such differences in related markets is generally small relative to benefits in the primary market.

C.4 Multi-Period Evaluation

The above steps describe a static equilibrium analysis conducted within a single shortrun demand period. For each improvement alternative, the steps are repeated for each

demand period over the lifetime of the improvement. Once the lifetime NOB is accumulated for each alternative and compared to costs, the investment choice can be made for

that project.

Breaking the Project Life 

Into Discrete Demand 

Periods

The demand curve shifts over time in two primary patterns: 

(1) Periodic Daily Peaks. Demand fluctuates with time of day, typically reaching

peaks in the morning and afternoon, and lows in the small hours of the night.

(2) Secular Growth Trend. Average daily traffic may be growing, declining, or

remaining stable over the course of years.

There are also periodic fluctuations over days of the week, and days or seasons of the

year. Daily commuting peaks may be unimportant on some facilities. For evaluation,

however, it is usually sufficient to recognize 1-3 daily demand period “types” and 1-4

demand periods over the investment lifetime, depending upon the rate of traffic growth.

The overall analysis period (e.g., twenty years) can be broken into shorter demand periods (e.g. 1-5 years), depending upon how rapidly exogenous demand factors are changing. Each demand period embodies a short run during which demand is assumed to be

fixed, meaning that a single short-run demand curve applies for the duration of the

period. This “single” demand can still be composed of several periodic demand curves,

such as peak and off-peak, or it could be a daily average.

Once the overall analysis period is broken into demand periods, the secular or trend

forecast becomes a series of discrete points representing the midpoints of demand peri-
Multi-Period Evaluation APPENDIX C

Basic Theory of Highway Project Evaluation C-15

ods. These points provide the origins or calibration points for the associated short-run

demand curves.

Even in the short run, demand stimulated by reduction in the generalized price generates Growth in Demand

enough traffic to partly offset the gains from increased capacity. In the long run, this

effect can be exaggerated, when general growth in demand and highway improvements

reinforce each other to increase traffic volumes. A casual observer of this process can

easily come to the conclusion that building more road capacity is self-defeating, because

congestion is soon back to where it was. For those trying to carry out benefit-cost analysis, the benefits seem to disappear. The reality, however, is a bit different.

The simplest case is shown in Figure C-8, in which a base alternative and a project alternative are represented by their AVC curves, and these also give the price to the user

under each alternative. Two demand curves are included, D1 for the first period of time

and D2 for the next period. The curves are drawn such that, by coincidence, the cost to

the user in the first demand period under the no-build alternative is the same as the price

in the second period under the project alternative. In other words, users are individually

no better off after the improvement than before.

This does not mean, however, that there are no benefits. First, there is more travel than

was the case under the base alternative. Second, the relevant comparison is not to the

Figure C-8. Benefits From a Project in Two Demand Periods.

AVCalt = price

p2,base

p1,alt

p2,alt

= p1,base

AVCbase = price

v2,base v2,alt v1,base v1,alt vehicle

volume

generalized

cost,

price

D2

D1

benefits in demand

period 2

benefits in demand

period 1
APPENDIX C Multi-Period Evaluation

C-16 Basic Theory of Highway Project Evaluation

price and volume in period one, but to the period two base case—i.e., the conditions that

would have occurred in period two if the improvement had not been made. With an

exogenous growth in demand, congestion would have been much worse without the

improvement, and less travel would have been served. Hence, there is positive incremental NOB in the first period, and additional (and larger) NOB in the second demand

period. Together (assuming only two periods) these account for project benefits, to be

compared against incremental capital costs.

A more general case is illustrated in Figure C-9, in which user price does not follow the

average cost curve. In this case, price is above average cost (compare this to Figure C-4,

the single-period case with price above AVC). The MC curve is omitted because pricing

inefficiency is ignored, i.e., a second-best investment comparison is assumed. Price is

again arbitrarily set so as to equate base alternative price in the first period to the price

with the improvement in the second period. Again, the areas of NOB are outlined and

shaded, and together form the NOB for the project alternative. Because price is above

AVC for the project alternative, NOB includes some producer surplus on new trips, in

addition to consumers surplus.

A final configuration, shown in Figure C-10 illustrates the case when price is below

social cost for both alternatives. The two demand periods are independent of each other.

Each of these periods is similar to Figure C-5.

Figure C-9. NOB For Two Demand Periods with Pricing Above AVC.

AVCalt

AVCbase

vehicle

volume

generalized

cost,

price

price function (base)

price function (project alternative)

v2,base v2,alt v1,base v1,alt

benefits in demand

period 2

benefits in demand

period 1

D2

D1

p2,alt = p1,base
Multi-Period Evaluation APPENDIX C

Basic Theory of Highway Project Evaluation C-17

In summary, each demand period is handled as a single period, in which the short-run

demand curve is fixed to a point based on the actual or forecast traffic at an associated

price. Within the demand period, volume can move along the demand curve depending

upon reductions in generalized price resulting from improvements being evaluated.

Between demand periods, demand can shift and facilities wear out, resulting in a new

set of cost and demand curves. The sum of the discounted benefits in each demand

period is the present value of project benefits. This is true whether pricing is efficient at

p = MC, price follows AC, or pricing follows neither of the above.

The HERS model produces results like those shown in Figure C-10 because agency

costs and air pollution (if the module is enabled) are included. If other negative externalities (e.g., noise, water pollution, external costs of accidents) were modeled in HERS,

the gap between average variable cost and the price function would be wider. The model

cannot produce results of the type shown in Figure C-9 because there is no price in the

model that is separate from other user costs.

Figure C-10. NOB for Two Demand Periods with Price Below AVC.

AVCalt

AVCbase

vehicle

volume

generalized

cost,

price

price function

(base)

price function (project alternative)

v2,base v2,alt v1,base v1,alt

benefits in demand

period 2

benefits in demand

period 1

D2

D1

negative

benefits
APPENDIX C Summary

C-18 Basic Theory of Highway Project Evaluation

C.5 Summary

(1) Three functions (or selected points along them) are needed to define the base

and project alternatives for evaluation: marginal cost, average cost, and price,

as enumerated in Table C-1.

(2) For benefit-cost analysis, changes in costs determine incremental benefits,

whereas changes in the generalized price lead to induced travel.

(3) Incremental net operating benefit (NOB) of a project alternative relative to

the base alternative can be defined using marginal or average cost curves, but

the latter is ultimately more practical.

(4) The primary components of NOB are delay and cost savings on old trips,

consumer surplus on new trips, and producer surplus on new trips. The latter

may be negative if agency costs and environmental externalities exceed user

payments.

(5) Each demand period is a single evaluation of NOB. Demand periods can be

periodic, such as peak and off-peak, as well as discrete intervals on a secular

growth trend.

(6) Changes in user costs (time, running costs, accidents, user charges) cause

changes in traffic volumes, referred to as induced traffic or induced demand.

These effects should be incorporated into benefit-cost evaluation of improvement projects.

(7) Multiple demand periods (periodic and secular) are discounted and accumulated for comparison to fixed costs to assess the net benefits of an improvement project.

These concepts are readily made operational, and can be implemented in spreadsheet or

other models.

C.6 A Numerical Example

Table C-2 shows some hypothetical data for a single demand period for one project

alternative versus the base case. All of the data are converted from whatever natural

units (e.g., minutes, crashes, grams) they might have been generated in to dollars per

vehicle trip over the facility. All of the bolded numbers are required input data about

costs and pricing that must be estimated for the specific conditions of the project,

including the volumes that will occur at the relevant prices. Capacities of the existing

and expanded facilities are also required.
A Numerical Example APPENDIX C

Basic Theory of Highway Project Evaluation C-19

Calculations are done on the basis of two contrasting assumptions:

(1) First-best pricing and investment, assuming that price can be set so as to

maximize net benefits of both operation and investment. Numerical values

for prices and volumes, and the outlines for NOB, are shown in Figure C-11.

(2) Second-best pricing, assuming that user fees are determined exogenously and

cannot be changed. Prices and volumes are shown in Figure C-12, which is

similar to Figure C-5.

Table C-2. Input Data for Example Project Evaluation

Marginal Average

$ per trip BASE PROJECT Cost Price Cost

RUNNING COSTS 2.80 1.75 1 11

Vehicle Wear 0.90 0.60

Fuel 0.80 0.55

Maintenance 0.50 0.30

Insurance/Accidents 0.60 0.30

Parking (internal) 0.00 0.00

Other 0.00 0.00

HIGHWAY COSTS 0.50 0.40 1 1

Pavement Wear 0.30 0.30

Administration 0.20 0.10

Parking (unpriced) 0.00 0.00

Other 0.00 0.00

USER CHARGES 0.15 0.15 1

EXTERNALITIES 1.10 1.10 1 1

Pollution 0.50 0.60

Noise 0.40 0.40

Accidents (external) 0.20 0.10

Other 0.00 0.00

TRAVEL TIME COST 6.80 3.40

Free Flow 1.80 1.40 1 11

Excess Delay 5.00 2.00 1 1

MARGINAL COST 6.20 4.65 <----

PRICE 9.75 5.30 <----

AVERAGE COST 11.20 6.65 <----

efficient price 12.19 7.31

efficient toll 5.99 2.66

efficient volume 4,000 6,000

OTHER DATA AND PARAMETERS

Capacity (veh/hr) 4,000 6,000

Volume (act/est) 5,000 6,826

elasticity -0.80
APPENDIX C A Numerical Example

C-20 Basic Theory of Highway Project Evaluation

Figure C-11. First-best Net Operating Benefit (NOB).

Figure C-12. Second-best Net Operating Benefit (NOB).

$12.19

6.20

MC1

4.65

MC2

incremental 

consumer 

surplus on new 

trips

4,000 6,000

7.31

0

2

4

6

8

10

12

14

16

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

MC1 MC2

5,000 6,826

9.75

11.20

5.30

6.65

0

2

4

6

8

10

12

14

16

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000
References APPENDIX C

Basic Theory of Highway Project Evaluation C-21

Total NOB as well as the major components under each of the two assumptions are

shown in Table C-3. Areas in the diagrams correspond to components of NOB in the

table. For example, savings on old trips in the first-best evaluation are measured by the

rectangle

[2]

which is composed of normal running time savings = (1.80-1.40) x 4000 = 1,600, plus

running cost savings = , plus delay savings = zero with

efficient pricing, plus highway operating cost savings .

Numbers for the “Existing” facility show the net benefits of operating the facility efficiently (i.e., correctly priced) or inefficiently, and do not enter into the benefit-cost evaluation of the expansion project.

C.7 References

AASHTO, A Manual on User Benefit Analysis of Highway and Bus-Transit Improvements—1977, Washington, DC: American Association of State Highway and

Transportation Officials, 1978.

Adler, Hans A., Economic Appraisal of Transport Projects: A Manual With Case Studies, Baltimore, MD: Johns Hopkins, 1987.

Anderson, Lee G., and Russell Settle, Benefit-Cost Analysis: A Practical Guide, Lexington, MA: DC Heath, 1977.

Beesley, Michael E., and Alan A. Walters, “Some Problems in the Evaluation of Road

Investments,” Applied Economics, 1 (1970), pp. 241-259.

SOT = ( ) 6.20 4.65 – × 4000

= 6,200

( ) 2.80 1.75 – × 4 000 , = 4 200 ,

( ) 0.50 0.40 – × 4 000 , = 400

Table C-3. First-Best and Second-Best NOB for the Example Project

NET OPERATING BENEFITS efficient inefficient 1stB 2ndB

normal running time savings on old trips 1,600 2,000

running cost savings on old trips 4,200 5,250

delay savings on old trips 15,000

externality cost savings on old trips 0 0

highway operating cost savings on old trips 400 500

incremental consumer surplus on new trips 19,500 30,469 4,875 4,062

producer surplus on new trips 23,950 750 5,325 274

externality costs on new trips (5,500) (2,008)

highway operating costs on new trips (2,500) (730)

Total NOB 43,450 23,219 16,400 24,347

Existing Expansion
APPENDIX C References

C-22 Basic Theory of Highway Project Evaluation

Boardman, Anthony E., David H. Greenberg, Aidan R. Vining, and David Weimer,

Cost-Benefit Analysis: Concepts and Practice, Upper Saddle River, NJ: Prentice

Hall, 1996.

Brent, Robert J., Applied Cost-Benefit Analysis, Cheltenham, UK: Edward Elgar, 1996.

Button, Kenneth, Transport, the Environment and Economic Policy, Aldershot, UK:

Edward Elgar, 1993.

Davis, Otto A., and A.B. Whinston, “Piecemeal Policy in the Theory of Second Best,”

Review of Economic Studies, 34 (1967), pp. 323-331.

DeCorla-Souza, Patrick, Brian Gardner, M. Culp, Jerry Everett, Chimai Ngo, and J.

Hunt, “Estimating the Costs and Benefits of Transportation Corridor Alternatives,” paper for TRB, Washington, DC: US DOT/FHWA, January 1997.

Dreze, Jean, and Nicholas Stern, “The Theory of Cost-Benefit Analysis,” in Alan J.

Auerbach and Martin Feldstein (eds.), Handbook of Public Economics: Volume

II, pp. 909-989, Amsterdam, The Netherlands: North-Holland, 1985.

Dusansky, R., and J. Walsh, “Separability, Welfare Economics, and the Theory of Second Best,” Review of Economic Studies, 43, 1 (1976), pp. 49-51.

Gramlich, Edward M., A Guide to Benefit-Cost Analysis, 2nd ed., Englewood Cliffs, NJ:

Prentice-Hall, 1990.

Gramlich, Edward M., “Infrastructure Investment: A Review Essay,” Journal of Economic Literature, 32 (1994), pp. 1176-1196.

Greene, David L., Donald W. Jones, and Mark A. Delucchi, (eds.) The Full Costs and

Benefits of Transportation: Contributions to Theory, Method, and Measurement,

Berlin: Springer, 1997.

Harberger, Arnold C., Project Evaluation: Collected Papers, Chicago: Markham, 1974.

Keeler, Theodore E., and Kenneth A. Small, “Optimal Peak-Load Pricing, Investment,

and Service Levels on Urban Expressways,” Journal of Political Economy, 85, 1

(1977), pp. 1-25.

Layard, Richard, and Stephen Glaister, (eds.) Cost-Benefit Analysis, Cambridge, UK:

Cambridge University Press, 1994.

McFarland, William F., Jeffrey L. Memmott, and Margaret L. Chui, “Microcomputer

Evaluation of Highway User Benefits,” NCHRP Project 7-12, College Station,

TX: Texas Transportation Institute, October 1993.

Ng, Yew-Kwang, “Rents and Pecuniary Externalities in Cost-Benefit Analysis: Comment,” American Economic Review, 73, 5 (1983), pp. 1163-1170.

Transportation Research Board, Curbing Gridlock: Peak-Period Fees To Relieve Traffic

Congestion, 2 vols, Vol. 2, Washington, DC: National Academy Press, 1994.

U.S. Department of Transportation, “1997 Status of the Nation's Surface Transportation

System: Condition and Performance,” Report to Congress, Washington, DC: US

DOT/FHWA/FTA 1997.
References APPENDIX C

Basic Theory of Highway Project Evaluation C-23

Walters, Alan A., The Economics of Road User Charges, Washington, DC: International

Bank for Reconstruction and Development, 1968.

Williams, Alan, and Emilio Giardina, (eds.) Efficiency in the Public Sector: The Theory

and Practice of Cost-Benefit Analysis, Aldershot, UK: Edward Elgar, 1993.

Wohl, Martin, and Chris Hendrickson, Transportation Investment and Pricing Principles, New York: John Wiley, 1984.
APPENDIX C References

C-24 Basic Theory of Highway Project Evaluation
D-1

Appendix D: Operating Cost Equations

Vehicle operating cost equations have been revised in HERS v3.54 to eliminate discontinuities

within some of the constant-speed operating cost equations used in previous versions, as well as

to establish complete coverage of the equations for excess cost due to curvature.

D.1 Source of HERS Operating Cost Equations

The computations for the operating cost components in HERS are based on the report “Vehicle

Operating Costs, Fuel Consumption, and Pavement Type and Condition Factors”, by J.P. Zaniewski,

et.al., Texas Research and Development Foundation, June 1982. This report was prepared for the

U. S. Department of Transportation, Federal Highways Administration.

In the Zaniewski report, operating costs are listed in tables in Appendix B. There are three categories of tables matching the HERS categories: constant-speed operating costs; excess cost due to

speed change cycles; and excess costs due to horizontal curvature. Of these, only constant-speed

operating cost and excess cost due to horizontal curvature are addressed in this document.

In two cases, data from the Zaniewski report demonstrated constant-speed fuel consumption of

0.0 over a broad range of gradient and speed. The data from the table was compared to other

sources: P. J. Claffey and Associates, “Running Costs of Motor Vehicles as Affected by Road

Design and Traffic,” NCHRP Report 111, Highway Research Board, National Research Council,

Division of Engineering, 1971; and Daniels, C. Vehicle Operating Costs in Transportation Studies, E.S.U Technical Series No. 1, London: Spencer House, 1974. Both these sources were referenced by the Zaniewski report. Source Data Organization

The tables for constant-speed operating costs are given as a matrix of speed in miles per hour

and gradient. The miles per hour are given from 5 to 70 in increments of 5-m.p.h. The gradient is

given from -8% to 8% in increments of 1%.

The tables for excess cost due to horizontal curvature are organized as a matrix of degrees of curvature (1°, 2°... 6°, 8°, 10°... 20°, 25°, 30°) and speed in miles per hour (5 to 70 in 5-m.p.h. increments).

The Zaniewski data was scanned and converted to spreadsheet form. Certain corrections were

applied where it was apparent that the original data were in error.

D.1.1 Region of Interest

For constant-speed operating costs, the data between gradients of -3% and 3% (inclusive) are

considered important. Speeds of up to 90 miles per hour are also important, and are extrapolated

from existing data. Data for speeds of 2 miles per hour are also extrapolated.

For excess cost due to curvature, only speed/curvature settings below the value of vcurve (equation 6.2 of HERS Technical Report V3.26) are considered important. In some cases, at a low

degree of curvature, data must be extrapolated to 90-m.p.h.
Operating Cost Equations

D-2

D.2 Generation of New Operating Cost Equations

D.2.1 Determining Which Equations Require Updating

Existing constant-speed operating costs equations are examined graphically within the region of

interest (-3% to 3% gradient, 2–90 m.p.h.) to look for discontinuity or other form of error (e.g. values less than 0; arcing towards infinity, especially in the extremes). The results are also compared, graphically, to the source data. If the results show a noticeable discontinuity or a poor

resemblance to the source data, then the equations for that component are updated and the

results are given below.

The examination uses gradient increments of 0.25% between the range of -3% to 3%, and increments of 1-m.p.h. between 2- and 90-m.p.h.

It should be noted that the gradient ranges of between -8% to -3% and 3% to 8% are also examined for erratic behavior, though this examination is not as exacting as within the region of interest. For this case, gradient increments of 1% and speed increments of 5-m.p.h. and range starting

at 5-m.p.h. are used.

In the case of excess operating costs due to curvature, the previously equations applied to cases

of speeds of greater than or equal to 55-m.p.h. New equations were generated to the complete

region of interest.

D.2.2 Method and Tools Employed

Microsoft Excel is used for the initial examination and comparison. The existing equations were

entered in spreadsheet form, and a script is used to gather the matrix of data for a given operating cost component and vehicle type. Excel is also used to give a graphic display of the data to

examine for discontinuity and to compare, graphically, against the original data.

When an equation is found to require updating, Excel is used to render the data into segments.

This data is then read by a software package called ‘TableCurve 3D’, by SPSS. Often there is an

iteration of segmenting the data, examining the results with TableCurve, resegmenting the data

(either dividing the current segment further still, or going back a step and segmenting along different boundaries), and examine the results with TableCurve.

TableCurve produces a list of equations to predict the output based on the two input variables

(gradient and speed). The equations are ranked by adjusted r2

 score. The first pass attempts to

find a reasonable fit with a maximum of five terms. If a good fit is not found, then the term count

is stepped until either a reasonable fit is found or that it becomes apparent that resegmenting is

necessary.

When complete, the new equations are entered into a test version of the spreadsheet to be examined for discontinuity, other errors, and comparison with the source data.

D.2.3 Notable Exception: 3-4 Axle Combination Unit Trucks
HERS Technical Report v3.54

September 2002

D-3

For reasons noted above, the data from the Zaniewski report was not used directly for constantspeed fuel consumption (CSFC) for 3-4 axle combination unit trucks and 5+ axle combination

unit trucks. Data from the Claffey study, adjusted to scale, was used for 3-4 axle CU trucks. It

should be noted that the Zaniewski data is consistent with the Claffey data at steep uphill gradients (GR >= 3) across the range of speed, and at lesser gradients up to 30 m.p.h.

D.2.4 Notable Exception: 5+ Axle Combination Unit Trucks

The Zaniewski report states that the data for 3-S2 semi (5+ axle CU) trucks was extrapolated

from 2-S2 semi (3+ axle CU) trucks, yet the report does not state the method applied for this

extrapolation. For the new HERS equations, the following method was applied to obtain constant-speed fuel consumption equations for 5+ axle CU trucks: 

• The percentage difference of fuel consumption rates from 2-S2 semi (3-4 Axle CU truck)

and 3-S2 semi (5+ axle CU truck) from the Zaniewski report was derived for all gradient/

speed points.

• The average percentage difference for each gradient was then generated. For gradients

less than(-1), where the data becomes zero for both vehicle types, the percentage difference from gradient of (-1) is used. This created an asymptote on the consumption curve

as the gradient gets steeper downhill, consistent with both the Claffey and Daniels findings.

• The 3-4 axle CU truck CSFC data (generated from Claffey) was incremented by the average percentage differences, along gradients, from the Zaniewski report, to create CSFC

data points for 5+ axle CU trucks.

The new data tables for both 3-4 Axle CU trucks and 5+ axle CU trucks were then rendered using

Microsoft Excel and processed using TableCurve, as shown above.

D.3 Roster of Updates

Not all equations required updating. Table D-1 summarizes which constant-speed and excess

cost due to curvature equations were updated.

The equations below are grouped by vehicle type, then by component. If the equations for a

given component for a given vehicle did not require updating, it will not be included below.

Equations are typically segmented, and the conditions to define the range of the segments are

given along with the equation for that segment. In the cases where an equation has been

updated, all segments (conditions and equations) for that vehicle/component combination will

be shown, even if not all segments for that vehicle/component changed. 

The list below summarizes the terms used in the equations:

AES average Effective Speed (m.p.h.)

GR gradient (%)

DCA degree of Curvature

CSFC constant-speed fuel consumption (gallons/1000 miles)

CSOC constant-speed oil consumption (quarts/1000 miles)

CSTW constant-speed tire wear (% worn/1000 miles)
Operating Cost Equations

D-4

CSMR constant-speed maintenance and repair (%avg. cost/1000 miles)

CFC excess fuel consumption due to curves (gallons/1000 vehicle miles)

CTW excess tire wear due to curves (% worn/1000 vehicle miles)

CMR excess maintenance and repair due to curves (% avg. cost/1000 vehicle

miles)

Table D-1. Equation Update Summary

Component

Vehicle Type

Small 

Auto

Med/

Large 

Auto

4-Tire 

Truck

6-Tire 

Truck

3+ 

Axle 

Single

-Unit 

Truck

3-4 

Axle 

Combo 

Unit 

Truck

5+ 

Axle 

Combo 

Unit 

Truck

Constant-Speed Fuel Consumption ♦♦ ♦ ♦ ♦ ♦ ♦

Constant-Speed Oil Consumption ♦♦ ♦

Constant-Speed Tire Wear ♦ ♦

Constant-Speed Maintenance and Repair ♦♦♦

Constant-Speed Depreciation

Curvature Fuel Consumption ♦♦ ♦ ♦ ♦ ♦ ♦

Curvature Tire Wear ♦♦ ♦ ♦ ♦ ♦ ♦

Curvature Maintenance and Repair ♦♦ ♦ ♦ ♦ ♦ ♦

♦ = equation updated
HERS Technical Report v3.54

September 2002

D-5

D.4 Small Automobile

D.4.1 Constant-Speed Fuel Consumption (CSFC)

D.4.2 Constant-Speed Oil Consumption (CSOC)

Table D-2. Small Automobile Constant-Speed Fuel Consumption

1

Condition GR ≥ 0

Equation CSFC = 100.82 - 4.9713*AES + 0.11148*AES2

-0.0011161*AES3 + 5.1089e06*AES4 + 3.0947*GR

2

Condition GR < 0 AND AES ≤ 40

Equation

CSFC = (91.045 - 4.0552*AES + 0.060972*AES2

 + 4.0504*GR + 

0.4227*GR2

) / (1 - 0.014068*AES + 0.0004774*AES2 -0.045957*GR + 

0.0054245*GR2

)

3

Condition GR < 0 AND AES > 40

Equation CSFC = 23.373 + 3.6374*GR + 0.21681*GR2 + (72.562 / (1 + exp(-((AES - 

81.639) / 7.4605))))

Table D-3. Small Automobile Constant-Speed Oil Consumption

1

Condition GR > 0 AND AES < 55

Equation CSOC = exp(2.7835 - 0.79034*ln(AES) - 1.1346 / (AES(1.5)) + 

0.65342*(GR(0.5)))

2

Condition GR ≥ 0 AND 55 ≤ AES ≤ 70

Equation CSOC = -170.4 + 34.02*ln(AES) + 1939/AES + 0.4747*GR - 

0.003296*AES*GR

3

Condition GR ≥ 0 AND AES ≥ 70

Equation CSOC = -170.4 + 34.02*ln(AES) + 1939/AES+0.27*GR

4

Condition GR ≤ 0 AND AES < 55

Equation CSOC = 1.0435 + (327.89/((1 + (((AES + 7.1977)/3.0141)2)) * 

(1 + (((GR + 8.0484)/2.8984)2))))

5

Condition Otherwise

Equation CSOC = -170.4+34.02*ln(AES)+1939/AES
Operating Cost Equations

D-6

D.4.3 Excess Fuel Consumption due to Curves (CFC)

D.4.4 Excess Tire Wear Due to Curves (CTW)

Table D-4. Small Automobile Excess Fuel Consumption Due to Curves

1

Condition AES ≥ (1/(0.001147 + 0.008062*DCA(0.5) + 0.008862/DCA))

Equation CFC = MAX(0, 18387.7115*(1 / (1 + (DCA/39.459)(-3.0419)))*1 / (1 + 

(AES/104.38)(-6.2768)))

2

Condition DCA ≥ 6 AND AES > 10 AND AES ≤ (-0.6807*DCA + 30.944)

Equation CFC = MAX(0, -0.046905 + 0.95904*LN(DCA) - 0.02218*AES - 

0.17662*(LN(DCA))2

 + 0.000957*AES2 - 0.021388*AES*LN(DCA))

3

Condition (DCA ≥ 6 AND AES ≤ 10) OR (DCA < 6 AND AES ≤ 25)

Equation CFC = MAX(0, -1.9503 + 1.0112*LN(DCA) + 0.31328*AES - 

0.16763*(LN(DCA))2

 - 0.012903*AES2 - 0.031507*AES*LN(DCA))

4

Condition Otherwise

Equation CFC = 0

Table D-5. Small Automobile Excess Tire Wear Due to Curves

1

Condition

(DCA≥16 AND AES ≥ (-0.031746*DCA2 + 0.74603*DCA + 21.19))

OR (16 > DCA ≥ 6 AND AES ≥ (45 - 1.9167*DCA + 0.041667*DCA2

))

OR (DCA < 6 AND AES ≥ (-442.3 + 2959.4/DCA(0.5) - 6735.1/DCA + 

6810.6/DCA(1.5) - 2582.5/DCA2))

Equation

CTW = MAX(0, 351887 * EXP(-EXP(-(DCA - 51.408)/19.756) - (DCA51.408)/19.756 + 1) * EXP(-EXP(-(AES - 122.22)/38.201) - (AES-122.22)/

38.201 + 1))

2

Condition (DCA ≥ 16 AND AES < (-0.031746*DCA2

 +0.74603*DCA + 21.19))

OR (16 > DCA ≥ 8 AND AES < (45 - 1.9167*DCA + 0.041667*DCA2))

Equation CTW = MAX(0, -21.508 + 13.474*LN(DCA) + 19.67*LN(AES) - 

1.5206*(LN(DCA))2 - 3.5315*(LN(AES))2 - 3.6298*LN(DCA)*LN(AES))

3

Condition

(8 > DCA ≥ 6 AND AES < (45 - 1.9167*DCA + 0.041667*DCA2))

OR (DCA < 6 AND AES < (-442.3 + 2959.4/DCA(0.5) - 6735.1/DCA + 

6810.6/DCA(1.5) - 2582.5/DCA2

)

Equation CTW = MAX(0, -3.3578 + 3.5095*DCA + 0.080638*AES - 0.18665*DCA2

 - 

0.00054297*AES2 - 0.061173*DCA*AES)
HERS Technical Report v3.54

September 2002

D-7

D.4.5 Excess Maintenance and Repair Due to Curves

D.5 Medium/Large Automobile

D.5.1 Constant-Speed Fuel Consumption (CSFC)

Table D-6. Small Automobile Excess Maintenance and Repair Due to Curves

1

Condition (DCA > 10 AND AES ≥ -0.65*DCA + 34.5)

OR (DCA < 10 AND AES ≥ -2.4444*DCA + 52.444)

Equation CMR = MAX(0, EXP(-19.624 - 1.0614*DCA(0.5)*LN(DCA) + 

6.4853*DCA(0.5) + 0.033374*AES(1.5) - 0.00046284*AES2

*LN(AES)))

2

Condition 5 ≤ DCA ≤ 10 AND (-1*DCA + 20) ≤ AES ≤ (-1*DCA + 25)

Equation CMR = 0.1

3

Condition Otherwise

Equation CMR = 0

Table D-7. Medium/Large Automobile Constant-Speed Fuel 

Consumption

1

Condition AES ≤ 40

Equation

CSFC = 88.556 - 3.384*AES + 1.7375*GR + 

0.053161*AES2 + 0.18052*GR2 + 0.076354*AES*GR

2

Condition AES > 40

Equation

CSFC = 85.255 - 2.2399*AES + 2.7478*GR + 

0.028615*AES2

 + 0.041389*GR2 + 0.046242*AES*GR
Operating Cost Equations

D-8

D.5.2 Constant-Speed Oil Consumption (CSOC)

D.5.3 Excess Fuel Consumption due to Curves (CFC)

Table D-8. Medium/Large Automobile Constant-Speed Oil Consumption

1

Condition GR > 0 AND AES < 55

Equation CSOC = exp(-1.5698 + 9.8768/AES(0.5) - 7.6187 /AES + 0.70702*GR(0.5))

2

Condition GR ≥ 0 AND 55 ≤ AES < 70

Equation CSFC = 9.5234-0.29873*AES +0.0026913*AES2

 + 0.28997*GR1.00129

3

Condition GR ≥ 0 AND AES ≥ 70

Equation CSFC = -173.3 + 34.6*ln(AES) + 1973/AES + 0.29*GR

4

Condition -3 ≤ GR ≤ 0 AND 15 ≤ AES < 55

Equation CSOC = 0.42295 + 0.35839*AES - 0.029984*AES2

 + 0.0010392*AES3 -

0.000016196*AES4

 + 9.3539e-08*AES5 - 0.0024*GR

5

Condition GR < -3 AND 15 ≤ AES < 55

Equation CSOC = 1/(-0.18739 + 0.0014953*AES(1.5) - 1.7461/GR)

6

Condition GR ≤ 0 AND AES < 15

Equation CSOC = exp(1.7713 - 0.12178*AES(0.5)*ln(AES) + 0.14636*GR + 

0.11002*GR2 + 0.0082804*GR3)

7

Condition Otherwise

Equation CSOC = -173.3 + 34.6*ln(AES) + 1973/AES

Table D-9. Medium/Large Automobile Excess Fuel Consumption Due to Curves

1

Condition DCA ≤ 5 AND AES ≤ 1/(-0.0137 + 0.0123*DCA0.5 + 0.0299/DCA0.5)

Equation CFC = MAX(0, -0.34211 + 0.28291*DCA + 0.014828*AES - 

0.016971*DCA2 - 0.00024465*AES2

 - 0.0047869*DCA*AES)

2

Condition DCA > 5 AND AES ≤ 1/(-0.0137 + 0.0123*DCA0.5 + 0.0299/DCA0.5)

Equation CFC = MAX(0, -0.79434 + 1.1403*LN(DCA) + 0.052408*AES - 

0.1933*(LN(DCA))2

 - 0.00060403*AES2 - 0.028889*AES*LN(DCA))

3

Condition AES > 1/(-0.0137 + 0.0123*DCA0.5 + 0.0299/DCA0.5)

Equation CFC = MAX(0, EXP(-18.864 - 0.02183*DCA(1.5) + 2.6113*DCA(0.5) + 

1.80792*AES(0.5)))
HERS Technical Report v3.54

September 2002

D-9

D.5.4 Excess Tire Wear Due to Curves (CTW)

D.5.5 Excess Maintenance and Repair Due to Curves

Table D-10. Medium/Large Automobile Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (-0.031746*DCA2 +0.74603*DCA +21.19))

OR (6 ≤ DCA < 16 AND AES ≥(45 - 1.9167*DCA + 0.041667*DCA2

))

OR (DCA < 6 AND AES ≥ (-442.3 + 2959.4/DCA(0.5) - 6735.1/DCA + 

6810.6/DCA(1.5) - 2582.5/DCA2

))

Equation

CTW = MAX(0, 519464*EXP( -EXP( -(DCA - 48.665)/18.647) - (DCA - 

48.665)/18.647 + 1) * EXP( -EXP( -(AES - 127.84)/39.862) - (AES - 

127.84)/39.862 + 1))

2

Condition (DCA ≥ 16 AND AES < (-0.031746*DCA2

 +0.74603*DCA +21.19))

OR (6 ≤ DCA < 16 AND AES < (45 - 1.9167*DCA + 0.041667*DCA2

))

Equation CTW = MAX(0, -31.7 + 20.767*LN(DCA) + 22.783*LN(AES) - 

2.5841*(LN(DCA))2

 - 3.9522*(LN(AES))2 - 4.4831*LN(DCA)*LN(AES))

3

Condition DCA < 6 AND AES < (-442.3 + 2959.4/DCA(0.5) - 6735.1/DCA + 6810.6/

DCA(1.5) - 2582.5/DCA2

)

Equation CTW = MAX(0, -4.4955 + 4.542*DCA + 0.088792*AES - 0.27253*DCA2 - 

0.00042329*AES2

 - 0.07399*DCA*AES)

Table D-11. Medium/Large Automobile Excess Maintenance and Repair Due to 

Curves

1

Condition (DCA > 12 AND AES ≥ (-0.5*DCA + 30))

OR (DCA < 12 AND AES ≥ (-2.3636*DCA + 52.364))

Equation CMR = MAX(0, EXP(-37.927 + 3.2935*LN(DCA) + 1.8096/DCA + 

7.8477*LN(AES)))

2

Condition 5 ≤ DCA ≤ 10 AND (-1*DCA + 20) ≤ AES ≤ (-1*DCA - 25)

Equation CMR = 0.1

3

Condition Otherwise

Equation CMR = 0
Operating Cost Equations

D-10

D.6 4-Tire Trucks

D.6.1 Constant-Speed Fuel Consumption (CSFC)

Table D-12. 4-Tire Truck Constant-Speed Fuel Consumption

1

Condition GR ≥ 0 AND 20 < AES < 55

Equation CSFC = 115.41 - 3.6397*AES + 7.0832*GR + 0.050662*AES2

 - 0.34401*GR2

+ 0.096956*AES*GR

2

Condition GR ≥ 0 AND AES ≤ 20

Equation CSFC = 120.7 + -5.0201*AES + 0.1088*AES2 + 9.8816*GR - 1.3755*GR2

 + 

0.11582*GR3

3

Condition GR < 0 AND AES ≤ 10

Equation CSFC = 161.2 - 6.622*AES - 87.758*ln(AES)/AES - 1.0889*GR2

 - 

0.13217*GR3

4

Condition GR < 0 AND 10 < AES ≤ 20

Equation CSFC = 106.31 - 2.7456*AES + 5.0147*GR - 0.001281*AES2

 + 0.94555*GR2

+ 0.19499*AES*GR

5

Condition GR < 0 AND 20 < AES < 55

Equation CSFC = 351.5 - 184.42*ln(AES) + 0.71838*GR + 28.297*(ln(AES))2

 + 

1.0105*GR2

 + 2.8947*GR*ln(AES)

6

Condition GR ≥ 1.5 AND AES ≥ 55

Equation CSFC = 110.4 + 0.000249*AES3 - 18.93*ln(AES) + 8.06*GR

7

Condition -2.5 ≤ GR < 1.5 AND AES ≥ 55

Equation CSFC = (28.77 + 0.183655*AES + 3.34032*GR) / 

(1 - 0.0074966*AES - 0.049703*GR)

8

Condition Otherwise

Equation CSFC = exp(2.784 + 0.02014*AES + 0.06881*GR)
HERS Technical Report v3.54

September 2002

D-11

D.6.2 Constant-Speed Tire Wear

Table D-13. 4-Tire Truck Constant-Speed Tire Wear

1

Condition GR ≥ 2.5 AND AES < 55

Equation CSTW = EXP(-2.08 + 0.0001517*AES2

 + 0.012*AES + 1.367*LN(GR) - 

0.001389*AES*GR)

2

Condition (0 < GR < 2.5 AND AES < 15)

OR (-AES/20 < GR < 2.5 AND 15 ≤ AES < 55)

Equation CSTW = 0.297 + 2.9*10(-6)*AES3

 - 0.0421*LN(AES) + 0.0234*GR2 + 

0.00429*AES*GR

3

Condition (-2.5 < GR ≤ 0 AND AES < 15)

OR (-AES/10 < GR ≤ -AES/20 AND 15 ≤ AES < 55)

Equation CSTW = 0.1294 + 3.64*10(-6)*AES3

 + 0.0324*GR2 + 0.1085*GR + 

0.0000631*AES2

*GR

4

Condition (GR ≤ -2.5 AND AES < 15)

OR (GR < -AES/10 AND 15 ≤ AES < 55)

Equation CSTW = EXP(-5.45 - 4.13*10(-6)*AES3 - 0.01377*AES 

+ 2.79*LN(-GR))

5

Condition GR ≥ 0.5 AND AES ≥ 55

Equation CSTW = 1.365 + 0.000736*AES2 - 0.05471*AES + 0.0197*GR2 + 

0.004395*AES*GR

6

Condition ((-AES/10+1) < GR < 0.5 AND AES ≥ 55)

OR (GR < 0.5 AND AES ≥ 80)

Equation CSTW = ABS(-0.1554 + 0.000258*AES2

 + 0.0205*GR2 - 0.05138*GR + 

0.005058*AES*GR)

7

Condition Otherwise

Equation CSTW = MAX(0.01, -0.2177 + 0.000208*AES2

 + 0.02376*GR2 + 

0.005895*AES*GR - 0.03288*LN(AES)*GR)
Operating Cost Equations

D-12

D.6.3 Excess Fuel Consumption due to Curves (CFC)

Table D-14. 4-Tire Truck Excess Fuel Consumption Due to Curves

1

Condition (DCA < 6 AND AES ≥ (-0.5682*DCA2 + 0.75*DCA + 55.818)) 

OR (DCA ≥ 6 AND AES ≥ (-0.0055*DCA2

 - 0.7634*DCA + 43.597))

Equation

CFC = MAX(0, EXP(779.63 - 1.2743*DCA + 

3.1889*DCA(0.5)*LN(DCA) - 2.9306*DCA(0.5) - 25.106*AES(0.5) - 

10108.5/AES(0.5) + 10588.5*LN(AES)/AES))

2

Condition (DCA ≥ 10 AND AES ≤ (57.993 + 1.1162*DCA - 13.963*DCA0.5)) 

OR (8 ≤ DCA < 10 AND AES ≤ 25)

Equation CFC = MAX(0, -0.45381 + 0.98231*LN(DCA) + 0.10049*AES - 

0.15*(LN(DCA))2

 - 0.0011603*AES2 - 0.046122*AES*LN(DCA))

3

Condition 4 ≤ DCA < 8 AND AES ≤ (-2.5*DCA + 45)

Equation CFC = MAX(0, -2.0296 + 2.4402*LN(DCA) + 0.087398*AES - 

0.50234*(LN(DCA))2

 - 0.0012841*AES2 - 0.036879*AES*LN(DCA))

4

Condition (2 ≤ DCA < 4 AND AES ≤ 35) 

OR (DCA < 2 AND AES ≤ (2.5*DCA + 30))

Equation CFC = MAX(0, EXP(0.0010091 - 5.4673/DCA2

 - 0.082805*AES + 

0.011991*AES2

 - 0.0018375*AES(2.5)))

5

Condition Otherwise

Equation CFC = 0
HERS Technical Report v3.54

September 2002

D-13

D.6.4 Excess Tire Wear Due to Curves (CTW)

D.6.5 Excess Maintenance and Repair Due to Curves

Table D-15. 4-Tire Truck Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (0.02381*DCA2

 - 1.4524*DCA + 42.143))

OR (6 ≤ DCA < 16 AND AES ≥ (35 - 125/DCA + 750/DCA2

))

OR (DCA < 6 AND 

AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2 + 25/DCA3))

Equation

CTW = MAX(0, 450515*EXP( -EXP( -(DCA - 49.07)/18.816) - (DCA - 

49.07)/18.816 + 1) * EXP( -EXP( -(AES - 124.84)/38.88) - (AES - 124.84)/

38.89 + 1))

2

Condition DCA ≤ 16 AND AES < (0.02381*DCA2

 - 1.4524*DCA + 42.143)

Equation CTW = MAX(0, -13.126 + 79.095/DCA + 254.26/AES - 39.567/DCA2

 - 

694.97/AES2

 - 217.62/(DCA*AES))

3

Condition

(6 ≤ DCA < 16 AND AES < (35 - 125/DCA + 750/DCA2))

OR (DCA < 6 AND 

AES < (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/DCA3)

Equation CTW = MAX(0, -2.743 + 3.5215*DCA + 0.077273*AES - 0.16376*DCA2

 - 

0.00069592*AES2

 - 0.064592*DCA*AES)

Table D-16. 4-Tire Truck Excess Maintenance and Repair Due to Curves

1

Condition (DCA ≥ 12 AND AES ≥ (-0.45*DCA + 30.4))

OR (DCA < 12 AND AES ≥ (-2.2727*DCA + 52.273))

Equation CMR = MAX(0, EXP(594.56 - 0.021279*DCA(1.5) + 2.6656*DCA(0.5) - 

19.444*AES(0.5) - 7777/AES(0.5) + 8121.8*LN(AES)/AES))

2

Condition

(3.5 < DCA < 8.5 AND 17.5 ≤ AES < 22.5) 

 OR (4.5 < DCA < 10.5 AND 12.5 ≤ AES ≤ 17.5)

 OR (7.5 < DCA < 12.5 AND 7.5 < AES <= 12.5)

Equation CMR = 0.1

3

Condition Otherwise

Equation CMR = 0
Operating Cost Equations

D-14

D.7 6-Tire Truck

D.7.1 Constant-Speed Fuel Consumption (CSFC)

D.7.2 Constant-Speed Oil Consumption (CSOC)

Table D-17. 6-Tire Truck Constant-Speed Fuel Consumption

1

Condition GR ≥ 0 AND AES < 55

Equation

CSFC = 298.60 - 13.131*AES + 53.987*GR + 0.30096*AES2

 - 4.7321*GR2 - 

0.88407*AES*GR - 0.0020906*AES3

 + 0.22739*GR3 + 0.02875*AES*GR2 + 

0.0045428*AES2

*GR

2

Condition GR < 0 AND AES < 55

Equation

CSFC = 273.05 - 9.2427*AES +58.195*GR + 0.14718*AES2

 + 6.7665*GR2 - 

1.3785*AES*GR - 0.00046068*AES3

 + 0.13884*GR3 - 0.079555*AES*GR2 + 

0.012622*AES2

*GR

3

Condition GR ≥ 1.5 AND AES ≥ 55

Equation CSFC = 361.11 - 8.1978*AES + 11.186*GR + 0.077607*AES2

-0.27665*GR2

- 0.035211*AES*GR

4

Condition GR < 1.5 AND AES ≥ 55

Equation CSFC = 101.5 + 0.000186*AES3 + 1.102*GR2 + 18.22*GR

Table D-18. 6-Tire Truck Constant-Speed Oil Consumption

1

Condition GR > 0 AND AES < 55

Equation CSOC = exp(3.8424 - 0.93964*ln(AES) - 1.7418/AES + 0.80327*GR(0.5))

2

Condition GR > 0 AND AES ≥ 55

Equation CSOC = 51.76 + 0.002513*AES2

 - 14.29*ln(AES)+ 0.7485*GR

3

Condition

(-1.5 < GR ≤ 0 AND AES < 55) 

OR

(-AES/10 ≤ GR ≤ 0 AND AES < 55)

Equation CSOC = 13.98 + 0.0000603*AES3

 - 0.00857*AES2 + 0.523*AES - 

6.17*ln(AES)

4

Condition GR < -AES/10 AND AES ≥ 70

Equation CSOC = exp(1.41 + 0.000519*AES2 - 0.0845*AES - 0.0344*GR2 - 0.649*GR)

5

Condition Otherwise

Equation CSOC = 51.76 + 0.002513*AES2

 - 14.29*ln(AES)
HERS Technical Report v3.54

September 2002

D-15

D.7.3 Constant-Speed Maintenance and Repair (CSMR)

D.7.4 Excess Fuel Consumption due to Curves (CFC)

Table D-19. 6-Tire Truck Constant-Speed Maintenance and Repair

1

Condition -4 ≤ GR ≤ -1 AND AES > (-1.6667*GR3 - 17.5*GR2 -70.833*GR -45) AND 

AES < (-1.6667 *GR3

 - 17.5*GR2 -70.833*GR -40)

Equation CSMR = 1/(0.96223 + 2.3017e-06*AES3 - 0.33129*exp(AES/44.4878) + 

0.48203/GR - 0.00029083*exp(-GR))

2

Condition (GR ≥ -1) OR (GR < -1 AND AES ≥ (-1.6667 *GR3

 - 17.5*GR2 -70.833*GR -

40))

Equation CSMR = 44.2 + 0.01147*AES2 + 0.1462*AES*GR

3

Condition Otherwise

Equation CSMR = -0.722 - 0.00697*AES2 - 15.9*GR

Table D-20. 6-Tire Truck Excess Fuel Consumption Due to Curves

1

Condition

(DCA ≥ 10 AND AES >= (27.9 - 0.0144*DCA2

 + 300/DCA2)) 

OR (2 ≤ DCA < 10 AND AES ≥ (1/(0.0127 + 0.00484*DCA - 

0.000675*DCA2

 + 3.97e-05 * DCA3)))

OR (DCA < 2 AND AES ≥ (1/(0.0286 + 0.00429*DCA - 0.00429*DCA2

)))

Equation CFC = MAX(0, EXP(-50.349 - 0.98363*DCA - 0.05974*DCA2 + 

59.476*EXP(DCA/31.649) - 90.158/AES(0.5)))

2

Condition DCA ≥ 5 AND AES ≤ (27.9 - 0.0144 * DCA2 + 300/DCA2

)

Equation CFC = MAX(0, -9.7649 + 7.88*LN(DCA) + 6.036*LN(AES) - 

1.0423*(LN(DCA))2 - 1.053*(LN(AES))2 - 1.464*LN(DCA)*LN(AES))

3

Condition 1 < DCA < 5 AND AES ≤ (30 + 70/DCA - 100/DCA2

)

Equation CFC = MAX(0, EXP(1.604 - 4.6423/DCA(1.5) - 0.000062414*AES3

))

4

Condition Otherwise

Equation CFC = 0
Operating Cost Equations

D-16

D.7.5 Excess Tire Wear Due to Curves (CTW)

D.7.6 Excess Maintenance and Repair Due to Curves

The fourth equation for 6-Tire Truck excess maintenance and repair due to curves is incremental

- the condition is true when certain other conditions are true and the equation adds value to the

existing CMR value.

Table D-21. 6-Tire Truck Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (0.02381*DCA2 - 1.4524*DCA + 42.143))

OR (6 ≤ DCA < 16 AND AES ≥ (35 - 125/DCA + 750/DCA2

))

OR (DCA < 6 AND AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/

DCA3))

Equation

CTW = MAX(0, 377675*EXP( -EXP( -(DCA - 51.703)/19.791) -( DCA - 

51.703)/19.791 + 1) * EXP( -EXP( -(AES - 120.93)/37.611) - (AES - 120.93)/

37.611 + 1))

2

Condition (DCA ≥ 16 AND AES < (0.02381*DCA2

 - 1.4524*DCA + 42.143))

OR (6 ≤ DCA < 16 AND AES < (35 - 125/DCA + 750/DCA2))

Equation CTW = MAX(0, -26.586 + 17.42*LN(DCA) + 19.303*LN(AES) - 

2.1482*(LN(DCA))2

 - 3.3487*(LN(AES))2 - 3.81*LN(DCA)*LN(AES))

3

Condition DCA < 6 AND 

AES < (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/DCA3)

Equation CTW = MAX(0, -4.0066 + 3.8372*DCA + 0.11043*AES - 0.2262*DCA2

 - 

0.0011358*AES2

 - 0.064529*DCA*AES)
HERS Technical Report v3.54

September 2002

D-17

Table D-22. 6-Tire Truck Excess Maintenance and Repair Due to Curves

1

Condition DCA ≥ 8 AND AES ≥ (-0.0038*DCA2 - 0.3106*DCA + 27.272)

Equation CMR = MAX(0, EXP(9.6157 + 0.12975*DCA - 157.95/DCA2

 + 

7095.5*EXP(-DCA) - 106.49*LN(AES)/AES))

2

Condition DCA < 8 AND AES ≥ (-0.625*DCA2 + 3.125*DCA + 40)

Equation

CMR = MAX(0, EXP(-314.6 + 2.5973*DCA*LN(DCA) - 1.4569*DCA2 + 

0.30227*DCA(2.5) + 2642/LN(AES) - 

2565.9/AES(0.5)))

3

Condition

(1 ≤ DCA ≤ 3 AND (-10*DCA + 37.5) < AES < (10*DCA + 2.5))

OR (3 < DCA ≤ 5 AND AES < 32.5)

OR (5 < DCA < 8 AND AES < (0.8333*DCA2

 - 14.167*DCA +85)) 

OR (DCA ≥ 8 AND AES < (-0.0038*DCA2 - 0.3106*DCA + 24.5))

Equation CMR = 0.1

4

Condition DCA > 4.5 AND 12.5 < AES < (-0.35*DCA2

 + 3.85*DCA + 12)

Equation CMR = CMR + 0.1

5

Condition Otherwise

Equation CMR = 0
Operating Cost Equations

D-18

D.8 3+ Axle Single-Unit Truck

D.8.1 Constant-Speed Fuel Consumption (CSFC)

Table D-23. 3+ Axle Single Unit Truck Constant-Speed Fuel Consumption

1

Condition GR ≥ 3 AND AES ≤ 20

Equation CSFC = 68.536 + 12.823*AES + 122.45*GR + 0.023896*AES2

 + 

0.36758*GR2

 - 6.2014*AES*GR

2

Condition 3 ≥ GR ≥ 0 AND AES ≤ 20

Equation

CSFC = 254 - 3.0854*AES - 2.177*GR - 0.063346*AES2

 + 24.848*GR2 + 

4.3101*AES*GR + 0.0012816*AES3

 - 1.2432*GR3 - 1.6437*AES*GR2 + 

0.0013556*AES2*GR

3

Condition GR < 0 AND AES ≤ 20

Equation

CSFC = (259.66 - 19.925*AES+ 0.49931*AES2 - 0.0045651*AES3 - 

1.5876*GR) / (1 - 0.058535*AES + 0.00077356*AES2 - 0.14916*GR + 

0.024241*GR2)

4

Condition GR > 3 AND AES > 20

Equation CSFC = 290.45 - 2.598*AES + 25.823*GR + 0.024983*AES2 - 2.2654*GR2 + 

0.21897*AES*GR

5

Condition 3 ≥ GR ≥ 0 AND AES > 20

Equation CSFC = 1208.8 - 586.87*LN(AES) + 80.955*(ln(AES))2

+ 93.99*GR - 

13.477*GR2

6

Condition 0 > GR ≥ -3 AND AES > 20

Equation CSFC = exp(6.0673 - 0.1139*AES + 0.023622*AES*ln(AES) + 0.79191*GR - 

0.022171*GR3)

7

Condition GR < -3 AND AES > 20

Equation

CSFC = (-1.3978 / (1 + (((AES - 40.215) / -11.403)2

))) + 

(47.024 / (1 + (((GR + 0.01611)/5.4338)2))) + 

(-26.724 / (1 + (((AES - 40.215) / -11.403)2

))) * 

(1 / (1 + (((GR + 0.01611) / 5.4338)2

)))
HERS Technical Report v3.54

September 2002

D-19

D.8.2 Constant-Speed Maintenance and Repair (CSMR)

D.8.3 Excess Fuel Consumption due to Curves (CFC)

Table D-24. 3+ Axle Single Unit Truck Constant-Speed Maintenance and Repair

1

Condition -4 ≤ GR ≤ -1 AND AES > (-1.6667*GR3 - 17.5*GR2 -75.833*GR -45) AND 

AES < (-1.6667 *GR3

 - 17.5*GR2 -75.833*GR -40)

Equation CSMR = 1046.8 - 499.21*ln(AES) + 106.76*(ln(AES))2 + 601.98*GR + 

154.36*GR2 + 15.039*GR3

2

Condition (GR ≥ -1) OR (GR < -1 AND AES ≥ (-1.6667 *GR3

 - 17.5*GR2 -75.833*GR 

-40))

Equation CSMR = 46 + 0.008*AES2

 + 0.146*AES*GR

3

Condition Otherwise

Equation CSMR = 1.6996 + 0.094776*AES - 0.016324*AES2 + 0.00037673*AES3

 - 

4.0767e-06*AES4 + 1.4984e-08*AES5 - 14.684*GR

Table D-25. 3+ Axle Single Unit Truck Excess Fuel Consumption Due to Curves

1

Condition

(DCA ≥ 6 AND AES ≥ (44.375 - 1.8236*DCA + 0.02044*DCA2

 + 

0.0018571*DCA2 - 0.000053954*DCA2

))

OR (6 > DCA ≥ 2 AND AES ≥ (39.5 + 4.1667*DCA - 0.83333*DCA2))

Equation CFC = EXP(371.346 + 5.1878*LN(DCA) + 10.1521/DCA(0.5) - 

12.1424*AES(0.5) - 4915.79/AES(0.5) + 5093.19*LN(AES)/AES))

2

Condition DCA < 2 AND AES ≥ (24.5 - 10*DCA + 10*DCA2)

Equation CFC = MAX(0, 1.3873+ 38.977*EXP( -0.5*(((DCA-2.2124)/1.071)2 + 

((AES-102.44)/16.633)2)))

3

Condition 2 ≤ DCA ≤ 16 AND AES < 10

Equation CFC = MAX(0, -4.0824 + 1.833*DCA - 0.15946*DCA2

 + 

0.0044245*DCA3

 + 0.56919*AES - 0.038513*AES2 + 0.00079158*AES3)

4

Condition DCA ≤ 1 AND AES < 25

Equation CFC = 0

5

Condition Otherwise

Equation CFC = MAX(0, -8.9743 - 0.099969*DCA +16.366*LN(AES)+ 

0.0052265*DCA2

 - 3.6805*(LN(AES))2 - 0.11371*DCA*LN(AES))
Operating Cost Equations

D-20

D.8.4 Excess Tire Wear Due to Curves (CTW)

D.8.5 Excess Maintenance and Repair Due to Curves

The third equation for 3+ Axle Single Unit Truck excess maintenance and repair due to curves is

used to increment the value for CMR derived from the second equation under certain conditions.

These conditions for this may be true when the condition for equation two is true.

Table D-26. 3+ Axle Single Unit Truck Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (0.02381*DCA2 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES ≥ (35 - 125/DCA + 750/DCA2

))

OR (DCA < 6 AND AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/

DCA2))

Equation

CTW = MAX(0, 707192*EXP( -EXP( -(DCA - 44.524)/16.77) - (DCA - 

44.524)/16.77 + 1) * EXP( -EXP( -(AES - 132.23)/40.729) - (AES - 

132.23)/40.729 + 1))

2

Condition (DCA ≥ 16 AND AES < (0.02381*DCA2

 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES < (35 - 125/DCA + 750/DCA2

))

Equation CTW = MAX(0, 7.4369 + 29.473/DCA + 6.5816*LN(AES) - 541.46/DCA2

 - 

3.8133*(LN(AES))2 + 45.797*(LN(AES))/DCA)

3

Condition DCA < 6 AND AES < (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/

DCA3)

Equation CTW = MAX(0, -4.6194 + 4.5401*DCA + 0.10837*AES - 0.26588*DCA2

 - 

0.00099725*AES2

 - 0.076619*DCA*AES)
HERS Technical Report v3.54

September 2002

D-21

D.9 3-4 Axle Combination Unit Truck

D.9.1 Constant-Speed Fuel Consumption (CSFC)

Table D-27. 3+ Axle Single Unit Truck Excess Maintenance and Repair Due to 

Curves

1

Condition

(DCA ≥ 10 AND AES ≥ (-0.75*DCA + 40)) 

OR (10 > DCA ≥ 2 AND AES ≥ (-2.1875*DCA + 54.375))

OR (DCA < 2 AND AES ≥ (5*DCA2

-2.5*DCA+35))

Equation CMR = MAX(0, EXP(-50.038+ 0.71092*(LN(DCA))2 + 0.50522*LN(DCA) - 

0.08522*AES + 13.02*LN(AES)))

2

Condition

(1 ≤ DCA ≤ 3 AND (10*DCA + 2.5) ≥ AES ≥ (-10*DCA + 37.5))

OR (3 < DCA ≤ 5 AND AES ≤ 32.5)

OR (DCA ≥ 14 AND AES ≤ (-0.3125*DCA + 21.875)) 

OR (5 < DCA < 14 AND AES ≤ (-1.66667*DCA + 40.8333))

Equation CMR = 0.1

3

Condition

4.5 ≤ DCA ≤ 10.5 AND AES > (39.3 - 13.497*DCA + 2.215*DCA2 - 

0.11833*DCA3) AND AES < (17.5 + 5/(1 + exp( -((DCA - 7.0222)/-

0.07845))))

Equation CMR = CMR + 0.1

4

Condition Otherwise

Equation CMR = 0

Table D-28. 3-4 Axle Combination Unit Truck Constant-Speed Fuel Consumption

1

Condition (AES > 20 AND 3 ≥ GR ≥ -3) OR (AES ≤ 20 AND GR ≥ -3)

Equation CSFC = (1087.9 - 576.71*LN(AES) 82.039*(LN(AES))2 + 22.325*GR) / (1-

0.17121*LN(AES) - 0.035147*GR)

2

Condition GR < -3

Equation CSFC = -239.17 + 61.115*LN(AES) + 2221.9/AES -

 4411.6*EXP(-AES)

3

Condition AES > 20 AND GR > 3

Equation CSFC = EXP(4.5952 + 0.0049349*AES*LN(AES) + 0.31272*GR)
Operating Cost Equations

D-22

D.9.2 Constant-Speed Tire Wear (CSTW)

D.9.3 Constant-Speed Maintenance and Repair (CSMR)

Table D-29. 3-4 Axle Combination Unit Truck Constant-Speed Tire Wear

1

Condition GR > 3

Equation CSTW = 0.27453 - 0.016411*AES +0.090845*GR+ 0.00035502*AES2

 + 

0.047978*GR2 + 0.0042709*AES*GR

2

Condition GR < −3

Equation CSTW = ABS(-0.14758 + 0.01337*AES + 0.0040158*GR - 

0.000053182*AES2

 + 0.052391*GR2 + 0.0044432*AES*GR)

3

Condition -3 ≤ GR ≤ 3

Equation CSTW = 0.15566 - 0.0058457*AES + 0.041763*GR + 0.00021374*AES2 + 

0.056992*GR2 + 0.0050156*AES*GR

Table D-30. 3-4 Axle Combination Unit Truck Constant-Speed Maintenance and 

Repair

1

Condition -3 ≤ GR ≤ -1 AND AES ≥ (-7.5*GR2 - 52.5*GR - 25) AND 

AES < (-7.5*GR2 - 52.5*GR - 20)

Equation CSMR = 169.6 + 6.4867*AES + 333.98*GR + 48.825*GR2

2

Condition (GR > -1) OR 

(GR < -1 AND GR ≥ -3 AND AES ≥ (-7.5*GR2-52.5*GR-20)

Equation CSMR= 46 + 0.008*AES2

 + 0.146*AES*GR

3

Condition Otherwise

Equation CSMR = 2.44881 - 0.0404901*AES(1.5) - 15.8112*GR
HERS Technical Report v3.54

September 2002

D-23

D.9.4 Excess Fuel Consumption due to Curves (CFC)

Table D-31. 3-4 Axle Combination Unit Truck Excess Fuel Consumption Due to 

Curves

1

Condition DCA < 6 AND AES ≤ 20

Equation

CFC = MAX(0,( -0.069855 + 0.4852*LN(DCA) + 0.029223*LN(AES))/(1-

0.30752*LN(DCA) + 0.10364*(LN(DCA))2

 - 0.52169*LN(AES) + 

0.10545*(LN(AES))2

))

2

Condition 20 < AES ≤ (64 + 0.93749*DCA - 13.928 * DCA(0.5)) AND DCA < 6

Equation CFC = MAX(0, -36.549 + 8.3919*DCA + 19.444*LN(AES) - 0.19172*DCA2

 - 

2.6623*(LN(AES))2

 - 1.9932*DCA*LN(AES))

3

Condition 20 < AES ≤ (64 + 0.93749*DCA - 13.928 * DCA(0.5)) AND DCA ≥ 6

Equation CFC = MAX(0, -44.639 + 15.079*LN(DCA) + 31.738*LN(AES) - 

1.734*(LN(DCA))2

 - 5.305*(LN(AES))2 - 3.6061*LN(DCA)*LN(AES))

4

Condition DCA > 1 AND AES ≥ (67 + 0.93749*DCA - 13.928 * DCA(0.5))

Equation

CFC = MAX(0, EXP(948774.18 + 1.056802*(LN(DCA))2

 + 

11715.15*AES(0.5)*LN(AES) + 54041.58*(LN(AES))2

 - 133443.12*AES(0.5) - 

268395.66*LN(AES) + 309522.12/LN(AES) - 1311374.33/(AES(0.5))))

5

Condition DCA ≤ 1 AND AES ≥ (67 + 0.93749*DCA - 13.928 * DCA(0.5))

Equation CFC = MAX(0, (-13.559 - 1.1956*DCA + 0.37772*DCA2

 + 

3.5166*LN(AES))/(1 - 0.37771*DCA + 0.1152*DCA2

 - 0.1529*LN(AES)))

6

Condition Otherwise

Equation CFC = 0
Operating Cost Equations

D-24

D.9.5 Excess Tire Wear Due to Curves (CTW)

Table D-32. 3-4 Axle Combination Unit Truck Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (0.02381*DCA2 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES ≥ (35 - 125/DCA + 750/DCA2

))

OR (DCA < 6 AND

 AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2 + 25/DCA3))

Equation

CTW = MAX(0, 578653*EXP( -EXP( -(DCA - 54.618)/20.44) - (DCA - 

54.618)/20.44 + 1) * EXP( -EXP( -(AES - 120.41)/37.427) - (AES - 120.41)/

37.427 + 1))

2

Condition (DCA ≥ 16 AND AES < (0.02381*DCA2

 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES < (35 - 125/DCA + 750/DCA2

))

Equation CTW = MAX(0, -26.305 + 16.264*LN(DCA) + 20.114*LN(AES) - 

1.7217*(LN(DCA))2 - 3.4077*(LN(AES))2 - 4.0945*LN(DCA)*LN(AES))

3

Condition DCA < 6 AND AES < (23.334 + 112.5/DCA - 150.83/DCA2 + 25/DCA3

)

Equation CTW = MAX(0, -3.8937 + 3.8291*DCA + 0.092128*AES - 0.22412*DCA2 - 

0.00082522*AES2 - 0.064764*DCA*AES)
HERS Technical Report v3.54

September 2002

D-25

D.9.6 Excess Maintenance and Repair Due to Curves

* The third equation for 3-4 Axle Combination Unit Truck excess maintenance and repair due to curves is, under certain conditions, used to increment the CMR value derived from the second equation. Under some circumstances, the conditions for both equation two and equation three will be true.

Table D-33. 3-4 Axle Combination Unit Truck Excess Maintenance and Repair Due 

to Curves

1

Condition

(DCA ≥ 17.5 AND AES ≥ (-0.4*DCA + 29.5))

OR (17.5 > DCA ≥ 2.5 AND AES ≥ (-1.5*DCA + 48.75))

OR (DCA < 2.5 AND AES ≥ (4*DCA + 35)

Equation

CMR = MAX(0, EXP(304.96 - 0.90108*DCA + 

2.0321*DCA(0.5)*LN(DCA) - 0.70003*LN(DCA) - 41.773*LN(AES) - 

1312.1/AES(0.5) + 2080.7/AES))

2

Condition

(DCA ≤ 3 AND (-6.667*DCA2 + 38.33*DCA + -22.5) ≥ AES ≥

(6.667*DCA2

 - 38.33*DCA + 62.5))

OR (3 < DCA ≤ 6 AND AES ≤ 32.5)

OR (6 < DCA < 10 AND AES ≤ (-2.5*DCA + 47.5))

OR ((DCA ≥ 10 AND AES ≤ (-0.5*DCA + 27.5))

Equation CMR = 0.1

3*

Condition (3.5 < DCA < 6.5 AND 12.5 < AES < 22.5)

OR (5.5 < DCA < 12.5 AND 7.5 < AES < 17.5)

Equation CMR = CMR + 0.1

4

Condition Otherwise

Equation CMR = 0
Operating Cost Equations

D-26

D.10 5+ Axle Combination Unit Truck

D.10.1 Constant-Speed Fuel Consumption (CSFC)

Table D-34. 5+ Axle Combination Unit Truck Constant-Speed Fuel Consumption

1

Condition 3 ≥ GR ≥ -3

Equation CSFC = (1618.8 - 864.83*LN(AES) + 124.88*(LN(AES))2

 + 32.087*GR) / 

(1 - 0.16247*LN(AES) - 0.07074*GR + 0.011717*GR2

 - 0.0011606*GR3)

2

Condition GR < -3

Equation CSFC = -305.94 + 76.547*LN(AES) + 2737.7/AES - 

5493.1*EXP(-AES)

3

Condition GR > 3

Equation CSFC = (1607 - 986.23*LN(AES) + 149.01*(LN(AES))2

 + 84.747*GR) / (1 - 

0.17168*LN(AES) - 0.021455*GR)
HERS Technical Report v3.54

September 2002

D-27

D.10.2 Excess Fuel Consumption due to Curves (CFC)

Table D-35. 5+ Axle Combination Unit Truck Excess Fuel Consumption Due to 

Curves

1

Condition DCA < 6 AND AES ≤ 20

Equation CFC = MAX(0, EXP(4.892 - 5.8015/DCA2

 - 0.070341*AES 

- 6.612/AES(0.5)))

2

Condition 20 < AES ≤ (64 + 0.93749*DCA - 13.928 * DCA(0.5)) 

AND DCA < 6

Equation CFC = MAX(0, -0.76579 + 9.3637*LN(DCA) + 0.025171*AES - 

0.75491*(LN(DCA))2 + 0.00010068*AES2

 - 0.22116*AES*LN(DCA))

3

Condition AES ≤ (64 + 0.93749*DCA - 13.928 * DCA(0.5)) AND DCA ≥ 6

Equation CFC = MAX(0, -44.672 + 15.308*LN(DCA) + 31.804*LN(AES) - 

1.8472*(LN(DCA))2

 - 5.3075*(LN(AES))2 - 3.5085*LN(DCA)*LN(AES))

4

Condition DCA > 1 AND AES ≥ (67 + 0.93749*DCA - 13.928 * DCA(0.5))

Equation CFC = MAX(0, EXP(-37.185 - 0.0034062*DCA2

 + 1.262*(LN(DCA))2 - 

0.00000046205*AES3 + 8.9915*LN(AES)))

5

Condition DCA ≤ 1 AND AES ≥ (67 + 0.93749*DCA - 13.928 * DCA(0.5))

Equation CFC = MAX(0, -3.3518 + 58.52/((1 + ((DCA - 3.8448)/3.142)2

) 

* (1+ ((AES - 99.792)/14.486)2

)))

6

Condition Otherwise

Equation CFC = 0
Operating Cost Equations

D-28

D.10.3 Excess Tire Wear Due to Curves (CTW)

Table D-36. 5+ Axle Combination Unit Truck Excess Tire Wear Due to Curves

1

Condition

(DCA ≥ 16 AND AES ≥ (0.02381*DCA2 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES ≥ (35 - 125/DCA + 750/DCA2

))

OR (1 ≤ DCA < 6 

AND AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2 + 25/DCA3))

Equation CTW = MAX(0, EXP(-40.193 + 14.371*EXP(DCA/-53.803) + 

1.2303*(LN(DCA))2 - 1.8886*AES/LN(AES) + 7.0737*AES(0.5)))

2

Condition DCA < 1 

AND AES ≥ (23.334 + 112.5/DCA - 150.83/DCA2

 + 25/DCA3)

Equation CTW = MAX(0, 1/(1.1442 - 0.015388*DCA3

 - 9704.3/AES(1.5) + 

27917*LN(AES)/AES2

 - 42372/AES2))

3

Condition (DCA ≥ 16 AND AES < (0.02381*DCA2 - 1.4524*DCA + 42.143))

OR (16 > DCA ≥ 6 AND AES < (35 - 125/DCA + 750/DCA2

))

Equation CTW = MAX(0, -27.686 + 18.235*LN(DCA) + 24.103*LN(AES) - 

2.2305*(LN(DCA))2 - 4.3932*(LN(AES))2

 - 4.4593*LN(DCA)*LN(AES))

4

Condition

 DCA < 6 

AND AES < (23.334 + 112.5/DCA - 150.83/DCA2 + 25/DCA3)

Equation CTW = MAX(0, -4.9124 + 4.8372*DCA + 0.12051*AES - 0.2845*DCA2

 - 

0.0011691*AES2

 - 0.08169*DCA*AES)
HERS Technical Report v3.54

September 2002

D-29

D.10.4 Excess Maintenance and Repair Due to Curves

* The third and fourth equations for 5+ Axle Combination Unit Truck excess maintenance and repair due to curves are, under certain conditions, used to increment the CMR value derived from the second equation. These conditions for one or both of these equations may be true when the condition for equation two is true.

Table D-37. 5+ Axle Combination Unit Truck Excess Maintenance and Repair Due 

to Curves

1

Condition

(DCA ≥ 10 AND AES ≥ (-0.5*DCA + 32.5))

OR (10 > DCA ≥ 3 AND AES ≥ (-2.8571*DCA + 56.071))

OR (DCA < 3 AND AES ≥ (6.6667*DCA + 27.5)

Equation CMR = EXP(703.2 + 0.75135*(LN(DCA))2

 - 1.3433/DCA(0.5) - 

62.464*LN(AES) - 2045.3/LN(AES) + 3128.1/AES))

2

Condition

(1.5 ≤ DCA ≤ 3 AND (5*DCA + 22.5) > AES > (-5*DCA + 17.5))

OR (16 ≤ DCA ≤ 25 AND AES ≤ 17.5)

OR (DCA > 25 AND AES <= (-1*DCA + 42.5))

OR (3 < DCA < 16 AND AES ≤ (-1.5385*DCA + 42.115))

Equation CMR = 0.1

3*

Condition

(2.5 < DCA ≤ 6.5 AND 12.5 ≤ AES ≤ 27.5)

OR (3.5 < DCA ≤ 10.5 AND 7.5 ≤ AES < 22.5)

OR (9.5 ≤ DCA ≤ 15 AND 2.5 < AES ≤ 17.5)

OR (15 ≤ DCA ≤ 17 AND 7.5 ≤ AES ≤ 17.5)

OR (17 ≤ DCA < 22.5 AND 7.5 ≤ AES ≤ 12.5)

Equation CMR = CMR + 0.1

4*

Condition

(3.5 < DCA < 6.5 AND 17.5 ≤ AES < 22.5)

OR (4.5 < DCA < 10.5 AND 12.5 ≤ AES ≤ 17.5)

OR (7.5 < DCA < 10.5 AND 7.5 < AES ≤ 12.5)

Equation CMR = CMR + 0.1

5

Condition Otherwise

Equation CMR = 0
Operating Cost Equations

D-30
E-1

Appendix E: Detailed Description of Procedures for Incorporating Air Pollution Costs in 

HERS

E.1 Overview

HERS calculates the monetary value of damages from air pollution generated by motor vehicles

using a sample section under “baseline” conditions during each funding period, and with each

candidate improvement to that sample section. Air pollution costs under baseline or improved

travel conditions on a section depend upon three factors: (1) HERS’ estimates of average daily

traffic volume on the section during each funding period; (2) the mix of vehicle classes that typically use facilities of the type represented by the sample section; and (3) HERS’ estimates of the

average effective speed (AES) of travel on the section during each future funding period. Figure

E-1 illustrates the process used to calculate air pollution costs for a sample section under each set

of travel conditions.1

Differences in air pollution costs between baseline or unimproved travel conditions – including

daily traffic volume and average effective speed – and conditions with an improvement in place

are included in HERS’ calculation of the net benefits from implementing that improvement.

Reductions in air pollution costs increase the net benefits from an improvement, while an increase

in the air pollution costs generated by the travel volume and speed estimated to result from an

improvement reduce its net benefits. Changes in air pollution costs resulting from an improvement’s effect on travel conditions on a sample section increase or reduce the benefits from making that improvement during all funding periods comprising its lifetime.

E.1.1 How Improvements Affect Air Pollution Costs 

Differences between baseline travel conditions and conditions with an improvement in place can

cause total air pollutant emissions from vehicles traveling on a section to change for two reasons.

First, the per-mile rates at which motor vehicles emit some pollutants vary with travel speed, and

can rise or decline in response to the increase in average speed on a sample section that results

from an improvement. Second, average daily traffic and thus total vehicle-miles of travel on a

section increases from its baseline level under improved conditions due to the response of travel

demand to the increase in average travel speed on the section. 

By increasing the volume of travel on a section, a candidate improvement increases air pollutant

emissions and their resulting costs, since these costs are assumed to depend directly on total

emissions. At the same time, the increase in average travel speed on the segment can reduce

emissions per vehicle-mile of some pollutants, thus offsetting some or all of the effect of higher

travel volumes on total air pollution costs. However, particularly large speed increases can actu1. The broad outline for these procedures was developed by Apogee Research under contract to the Federal Highway

Administration, and is documented in the report Procedures for Incorporating Air Pollution Effects in the HERS Model

for National Highway Investment Analysis, September 1996. 
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-2

ally cause per-mile emission rates of some pollutants to rise, thereby “magnifying” the increase

in air pollution costs from higher travel volumes. Thus total air pollution costs resulting from

travel on a HERS sample section can either rise or fall as the result of an improvement.

Figure E-1. Overview of HERS Procedure for Estimating Air Pollution Costs

Vehicle Mix

Segment Type

MOBILE 5a, 

PART 5

Emissions/

VMT

Pollution 

Costs/ VMT

Annual Pollution Costs

Improvement 

Benefits or 

Disbenefits

Damage

Costs/ Ton

Location

Adjustment

Factors

Average

Effective

Speed

Annual VMT

HERS
HERS Technical Report v3.54

September 2002

E-3

E.1.2 Critical Assumptions

Differences in air pollutant emissions generated by changes between baseline and improved

travel conditions are assumed to contribute directly to changes in atmospheric concentrations of

those pollutants. In turn, the total costs of damages to human health and property from air pollution are assumed to vary in response to changes in these atmospheric concentrations. Thus

potential improvements to a HERS sample section are assumed to alter total air pollution damage costs in exact proportion to any change in pollutant emissions generated by vehicles traveling on the section that results from an improvement. HERS uses widely-accepted estimates of

the dollar value of health and property damages caused per ton of each major pollutant to calculate air pollution costs from travel on sample sections under baseline and improved conditions.

Because the air pollution cost estimates used by HERS represent nationwide averages for dollar

damages to human health and property caused by individual pollutants, they reflect the exposure of residents and property to air pollution that occurs at typical U.S. population and development densities. For pollutants that tend to remain concentrated near their original source,

HERS scales these average per-ton damage costs upward to reflect the greater population and

property exposure to emissions of those pollutants from vehicles using sample sections located

in urban areas. Conversely, HERS scales these nationwide average damage costs downward to

reflect the lower population and development densities that typically surround sample sections

located outside urban areas. For pollutants that tend to disperse widely, HERS applies nationwide average damage costs per ton of emissions generated by travel on both urban and nonurban sample sections.

HERS estimates the changes in costs from air pollution damages that would result from all candidate improvements to a sample section during the current and each future funding period.

Because the per-mile rates at which motor vehicles emit most air pollutants are expected to

decline throughout the time horizon considered by HERS, air pollution costs on most sample

sections are expected to fall throughout the foreseeable future under both baseline and improved

travel conditions. As a result, differences in air pollution costs between baseline and improved

conditions – and thus the changes in air pollution costs that HERS includes among the benefits or

disbenefits resulting from candidate improvements – are expected to decline during each successive future funding period considered by the model. 

E.2 Estimating Air Pollutant Emissions

E.2.1 Specific Pollutants Considered

Motor vehicles’ contribution to air pollution consists partly of tailpipe emissions of four commonplace pollutants that can accumulate in unhealthful concentrations in the earth’s atmosphere: carbon monoxide (usually abbreviated CO), sulfur oxides (SOx), nitrogen oxides (NOx),

and particulate matter less than 2.5 microns in diameter (PM2.5). Under certain conditions, nitrogen oxides also combine in the atmosphere with other chemical compounds emitted by motor

vehicles (among other sources) to form ground-level ozone.2 Atmospheric levels of airborne

2. These “volatile organic compounds” (VOC) are emitted from the tailpipes of gasoline-powered vehicles, as well as

by the evaporation of gasoline during vehicle refueling, storage, and operation.
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-4

dust, another pollutant that can be harmful to human health and property when it reaches certain concentrations, are also increased as moving vehicles’ tires contact road pavement surfaces. 

E.2.2 Emission Rates for HERS Vehicle Classes and Section Types

Different types of motor vehicles emit each of these six pollutants at varying rates per mile of

travel. Vehicles’ emission rates depend on the type of fuel used (gasoline or diesel), engine size,

and vehicle weight, as well as on operating conditions such as ambient temperature, road grade,

and altitude. Emission rates for some pollutants - principally carbon monoxide, volatile organic

compounds, and nitrogen oxides – also vary with vehicles’ average operating speeds, while others (sulfur oxides, particulate matter, and road dust) are approximately constant regardless of

speed. In addition, emission rates for individual vehicle classes can vary among different roadway types even for travel at the same average speed, because the characteristic patterns of acceleration, braking, and cruising that produce a given average speed differ among major roadway

classes, such as freeways, arterials, and collectors. 

Each of the nine section types utilized by HERS, which are differentiated by location (urban vs.

rural) and functional class (expressway, arterial, collector) tends to be used by a characteristic

mix of vehicle types. Differing vehicle mixes reflect the varying combinations of travel purposes

served by different road and highway facilities, together with the common use of specific types

of vehicles to provide different types of transportation services. Table E-1 reports the characteristic distribution of total vehicle-miles traveled among the seven detailed vehicle classes employed

by HERS for each of its nine different roadway section types. 

Emission rates for each HERS vehicle class operating on different types of roadways were first

estimated for the various pollutants using models developed by the U.S. Environmental Protection Agency (EPA). These rates measure average emissions per vehicle-mile of travel on freeway,

arterial, and collector sections for each of the six air pollutants whose damage costs are considered by HERS. The MOBILE6 motor vehicle emission factor model was used to estimate average

emissions per vehicle-mile of travel at different average speeds for carbon monoxide (CO), volatile organic compounds (VOCs), and oxides of nitrogen (NOx) as functions of average travel

speed and roadway type.3 The EPA’s vehicle emission factor model for particulate pollutants,

PART5, was used to estimate average emissions per vehicle-mile of sulfur oxides (SOx), small

particulate matter (PM-10), and road dust generated by individual vehicle classes operating on

each HERS section type.4 Emissions of these pollutants are assumed by PART5 to be independent of vehicle operating speeds. Both emission models’ “default” assumptions regarding the

age distribution of the U.S. vehicle fleet and operating conditions such as typical fuel composition, ambient temperatures, and altitude were employed in developing these estimates. 

3. For a brief description of the structure of the MOBILE model, see The MOBILE Model and Transportation Planning, Report FHWA-PD-96-005, Federal Highway Administration, September 1995. Complete documentation of

MOBILE is available at http://www.epa.gov/otaq/m6.htm

4. The PART5 model is described in An Overview of PM-10 Base Year Emission Inventories, Report FHWA-PD-98-

002, Federal Highway Administration, November 1997.
HERS Technical Report v3.54

September 2002

E-5

Developing these emission rates required detailed “mapping” of the distribution of vehicle

travel among the seven detailed vehicle classes employed by HERS into the different vehicle

classification systems employed by MOBILE6 (which employs 16 separate vehicle types) and

PART5 (12 vehicle types). This was accomplished using extremely detailed data on travel by

vehicle type, weight, and roadway class derived from the HPMS system, which were provided

by FHWA’s Office of Highway Policy Information. These data were employed as an intermediate or “translating” stage between the vehicle classification systems used by HERS and each of

the two emission factor models, in conjunction with detailed descriptions of the weight ranges

and physical characteristics of vehicles used by HERS, MOBILE6, and PART5 to classify vehicles.

Tables E-2 and E-3 show the relationships between HERS’ seven detailed vehicle classes and the

vehicle classes employed by the MOBILE6 and PART5 emission factor models. 

For the three speed-sensitive pollutants, emission rates for each of the seven detailed vehicle

classes and nine section types employed by HERS were estimated at speeds ranging from 5 to 70

mph in 5-mph increments. The measure used by the MOBILE6 emissions factor model to adjust

individual vehicle types’ emission rates for speed variation represents the average operating

speeds for several different “driving cycles” that combine different phases of vehicle operation

Small 

Autos

Med/Lg 

Autos

Pickups 

& Vans

All Four 

Tire 

Vehicles

Six-Tire 

Trucks

3 + Axle 

SUTs

All 

Single 

Unit 

Trucks

3 - 4 

Axles

5 or 

More 

Axles

All 

Combination 

Trucks

Rural 

Interstate 28.4% 34.2% 37.3% 100.0% 83.9% 16.1% 100.0% 7.4% 92.6% 100.0%

Rural OPA* 26.9% 32.4% 40.8% 100.0% 79.6% 20.4% 100.0% 9.4% 90.6% 100.0%

Rural Minor 

Arterial 26.7% 32.2% 41.1% 100.0% 79.2% 20.8% 100.0% 11.7% 88.3% 100.0%

Rural Major 

Collector 25.7% 31.0% 43.3% 100.0% 77.5% 22.5% 100.0% 12.3% 87.7% 100.0%

Urban 

Interstate 30.4% 36.9% 32.7% 100.0% 81.5% 18.5% 100.0% 9.2% 90.8% 100.0%

Urban Other 

Fwy/ Exwy 31.4% 38.1% 30.5% 100.0% 82.1% 17.9% 100.0% 12.4% 87.6% 100.0%

Urban OPA* 29.5% 35.7% 34.7% 100.0% 80.8% 19.2% 100.0% 16.6% 83.4% 100.0%

Urban Minor 

Arterial 30.1% 36.4% 33.6% 100.0% 73.5% 26.5% 100.0% 26.5% 73.5% 100.0%

Section Type

Four Tire Vehicles Single Unit Trucks Combination Trucks

Table E-1. Distribution of Travel Among HERS Vehicle Classes by Section Type

* OPA indicates Other Principal Arterials.

Source: Estimated by Volpe Center from 1999 HPMS data on VMT by vehicle type and functional class supplied by FHWA Office of Highway Policy Information. 
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-6

(acceleration, cruising, braking, and idling) in varying proportions.5 The specific driving cycles

used to test variation in different vehicle classes’ emission rates are intended to represent typical

trips that specific types of vehicles are commonly used to make, and that result in different overall average speeds. This measure of travel speed is broadly consistent with the average effective

speed (AES) measure employed by HERS, which is intended to represent the average speed of

travel on a section associated with its predicted daily travel volume, assuming a characteristic

mix of vehicle classes and distribution of travel between peak and off-peak periods for that section type. 

5. Emissions for a sample of vehicles are measured on each of these driving cycles, and expressed relative to those

measured for the test cycle used to certify their compliance with prevailing federal emission standards. The resulting “speed correction factors” are used to estimate vehicles’ emissions when driven at speeds other than the

approximately 20 mph average of the certification test cycle.

Small 

Autos

Medium/ 

Large 

Autos

Pickups 

& Vans

Six-Tire 

Trucks

3+ Axle 

SUTs

3-4 Axle 

Combos

5+ Axle 

Combos

LDGV 0.9991 0.9179

LDDV 0.0009 0.0008

LDGT1 0.0813

LDGT2 0.6835

LDGT3 0.2142

LDGT4 0.0984

LDDT34 0.0040

HDGV2B 0.8002

HDDV2B 0.1998

HDGV3 0.1778

HDDV3 0.3733

HDGV4 0.0284

HDDV4 0.1756

HDGV5 0.1311

HDDV5 0.1138

HDGV6 0.1689

HDDV6 0.2876

HDGV7 0.0781

HDDV7 0.4654

HDGV8A 0.0001

HDDV8A 0.1606

Table _-2. Relationship of MOBILE6 Vehicle Classes to HERS Vehicle Classes

MOBILE6 

Vehicle 

Class

Proportion of MOBILE6 Vehicle Class Included in HERS Vehicle Class:

Table E-2. Relationship of MOBILE6 Vehicle Classes to HERS Vehicle Classes

Source: Estimated by Volpe Center from 1999 HPMS data on VMT by vehicle type and functional class supplied by FHWA Office of Highway Policy Information.
HERS Technical Report v3.54

September 2002

E-7

E.2.3 Future Trends in Emission Rates

In response to the progressive tightening of federal regulations on new motor vehicles’ emission

rates, the vehicles added to the U.S. fleet each year are significantly less polluting than those they

replace.6

 The downward trend in average emission rates resulting from such “turnover” of the

vehicle fleet is reflected in the estimates of future emission rates for individual vehicle classes

produced by the MOBILE6 and PART5 models.7

 Thus the average emissions rates by vehicle

class and speed for each pollutant and section type calculated by HERS will reflect this projected

downward trend in future emission rates. 

As a consequence, estimated air pollution costs under baseline and improved travel conditions

on each sample section are predicted to decline over successive future funding periods. HERS’

estimates of differences in air pollution costs between baseline and improved travel conditions

on each section — which the model includes in its estimates of the benefits from potential

improvements to the section – are also expected to narrow during each successive future funding

6. The effect on average emissions of adding new, cleaner vehicles to the fleet has been partly offset by the tendency

for aging vehicles - most of which met less stringent emission standards when new – to be kept in service for

longer periods and to be used more intensively than has historically been the case. Shifts toward heavier vehicles

that are subject to less stringent emission standard, particularly the increasing substitution of light trucks (pickups,

vans, and sport/utility vehicles) for automobiles as passenger vehicles, have also offset some of the effect of new

vehicles’ progressively lower emission rates. On balance, however, individual vehicle classes’ and fleet-wide average emission rates for most pollutants have declined significantly in recent years, and are expected to decline significantly over the foreseeable future.

7. Both models also assume continued increases in the number of light- duty trucks used as passenger vehicles and in

the average weight of heavy-duty trucks over the future, which slightly slow the decline in fleet-wide average

emissions rates resulting from a progressively “cleaner” fleet.

Small 

Autos

Medium/ 

Large 

Autos

Pickups & 

Vans

Six-Tire 

Trucks

3+ Axle 

SUTs

3-4 Axle 

Combos

5+ Axle 

Combos

LDGV 0.9991 0.9991

LDGT1 0.7303

LDGT2 0.2571

HDGV 0.8002 0.3373 0.2470 0.0001

MC

LDDV 0.0009 0.0009

LDDT 0.0126

2BHDDV 0.1998

LHDDV 0.6627

MHDDV 0.7530

HHDDV 0.9999

BUSES

All Classes 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Proportion of PART5 Vehicle Class Included in HERS Vehicle Class: PART5 

Vehicle 

Class

Table E-3. Relationship of PART5 Vehicle Classes to HERS Vehicle Classes.

Source: Estimated by Volpe Center from 1999 HPMS data on VMT by vehicle type and functional class supplied by FHWA Office of Highway Policy Information. 
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-8

period considered by HERS. Thus the effect of considering air pollution costs on the likelihood

that HERS will select candidate improvements to a sample section also diminishes during each

successive future funding period. 

E.2.4 Final Emission Rates

This process produced a set of tables showing emissions of a single pollutant per vehicle-mile of

travel at different average speeds by each of HERS’ seven detailed vehicle classes, for one of its

nine roadway section types. Table E-4 provides one example: it shows average carbon monoxide emissions (in grams per vehicle-mile traveled) at speeds from 5 to 50 mph for each of HERS’

seven detailed vehicle classes operating on Rural Major Arterials, one of HERS’ nine roadway

section types, for the year 2000. In order to ensure that the projected decline in future emission

rates is accurately reflected in the estimates of future air pollution damage costs – and in HERS’

estimates of benefits or disbenefits from improvements proposed during future years – emission

rates for each pollutant, vehicle class, and section type were also estimated for the year 2015. This

represents approximately the outer time horizon recommended for use with the MOBILE6 and

PART5 emissions models. 

Average emissions rates for each pollutant and HERS vehicle class differ among the nine section

types even at the same average speed, partly because the representation of the 16 different

MOBILE6 vehicle classes and the 12 PART5 vehicle classes in each HERS vehicle class differs

very slightly among section types. In addition, the typical driving cycles and resulting emissions

rates that are associated with the same average speed differ among roadway types. For three of

the six pollutants – carbon monoxide, volatile organic compounds, and nitrogen oxides – average emissions rates by individual HERS vehicle classes on each section type vary in response to

changes in the average effective speed of travel. Thus the emission rates calculated by HERS for

Small 

Autos

Medium/ 

Large 

Autos

Pickups 

& Vans

Six-Tire 

Trucks

3+ Axle 

SUTs

3-4 Axle 

Combos

5+ Axle 

Combos

5 41.82 41.70 56.11 71.74 71.89 59.90 20.94

10 29.02 28.77 38.87 47.79 47.90 40.01 14.44

15 25.62 25.33 34.35 33.60 33.71 28.21 10.42

20 23.93 23.62 32.08 24.96 25.05 20.99 7.87

25 23.02 22.70 30.87 19.58 19.66 16.48 6.22

30 22.62 22.29 30.29 16.24 16.30 13.66 5.14

35 22.73 22.40 30.37 14.22 14.27 11.95 4.45

40 23.57 23.25 31.36 13.16 13.19 11.03 4.03

45 24.42 24.11 32.35 12.86 12.88 10.75 3.83

50 25.27 24.97 33.34 13.28 13.29 11.06 3.80

55 26.11 25.82 34.32 14.48 14.47 12.01 3.94

60 26.96 26.68 35.31 16.70 16.66 13.75 4.29

65 27.80 27.52 36.30 20.33 20.24 16.66 4.88

HERS Vehicle Class:

Speed 

(mph)

Source: estimated by Volpe Center using Table 2 and EPA MOBILE6 motor vehicle emission factor model. 

Table E-4. Carbon Monoxide (CO) Emission Rates by HERS Vehicle Class for Urban

Other Principal Arterials (grams/mile)
HERS Technical Report v3.54

September 2002

E-9

these three pollutants will differ between baseline conditions and those with each candidate

improvement in place. In contrast, average emission rates for the three remaining pollutants –

sulfur oxides, particulate matter, and road dust – do not vary significantly with travel speed, and

will thus be identical under baseline and improved conditions within a funding period. Finally,

average emission rates for all six pollutants generated by all vehicle classes on all section types

will decline across the entire range of travel speeds during future years. 

E.3 Air Pollution Damage Costs

E.3.1 Damage Costs for Individual Air Pollutants

The estimated costs of human health and property damage per ton of each pollutant that are

employed in HERS were derived from a widely cited recent study.8 These values are derived

by dividing the study’s estimate of total annual costs from health and property damages caused

by highway vehicles’ contribution to atmospheric levels of each individual pollutant by the total

number of tons of that pollutant emitted annually by highway vehicles. Thus they represent estimates of nationwide average damage costs per ton of each pollutant, given the typical atmospheric levels of those pollutants that prevailed at the time the study was conducted (1995).

These values are assumed to represent acceptable estimates of the changes in total health and

property damage costs that would result if emissions of each pollutant changed by one ton.

HERS provides the option of using either the midpoint or the upper limit of the range for costs

per ton of each pollutant implied by the study’s reported range of estimates for total annual economic costs attributable to each pollutant. These dollar-denominated damage costs per ton of

each pollutant are assumed to remain constant over all future funding periods considered by

HERS. 

E.3.2 Adjustments to Per-Ton Damage Costs

The cost per ton estimates derived from this study represent average damage costs from exposure to prevailing air pollution levels that occurs at typical U.S. population and development

densities. For pollutants that remain concentrated near their original sources, these average costs

should be scaled up or down to reflect local variation in damage costs resulting from differences

in population and property exposure to air pollution caused by higher or lower population and

development density surrounding those sources. Unfortunately, however, usable information on

the location of each sample sections is limited to whether it is located within an urbanized area or

not; in the absence of more detailed data, HERS uses each sample section’s urban or non-urban

location to adjust the nationwide average costs per ton of each individual pollutant generated by

vehicles traveling on it. 

Specifically, HERS scales costs for the three pollutants that tend to remain localized (carbon

monoxide, particulate matter, and road dust) downward from their national average values for

sections located outside urbanized areas to reflect the lower density of rural populations located

adjacent to highways and thus exposed to these pollutants. Damage costs per ton of these three

pollutants emitted by vehicles using sample sections located in urban areas are assumed to equal

8. McCubbin, D. and M. Delucchi. Health Effects of Motor Vehicle Air Pollution. Institute for Transportation Studies,

University of California, Davis, 1996.
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-10

their nationwide average values. In contrast, average damage costs for the three more widely

dispersed pollutants - ozone, nitrogen oxides, and sulfur oxides – are scaled upward from their

national averages for sample sections within urbanized areas in order to reflect the larger populations exposed to them. The scaling factors used in this process were developed by examining

county-level population and population density data for the 100 largest U.S. metropolitan areas

and comparing them to corresponding figures for all non-urbanized counties in the nation. Table

E-5 summarizes the moderate and high estimates of per-ton damage costs for each pollutant, as

well as the factors used by HERS to make these locational adjustments. 

E.3.3 Air Pollution Costs per Vehicle-Mile

These damage costs per ton of each pollutant were multiplied by the previously-developed estimates of emissions per mile by vehicle class and speed for each HERS section type during the

year 2000, with the per-ton damage cost for each pollutant adjusted appropriately to reflect its

urban or rural location. The resulting values for each of the six pollutants were then summed to

determine total air pollution damage costs per vehicle-mile of travel for each roadway type and

location, vehicle class, and average speed at 5-mph intervals. Damage costs for 1-mph increments were interpolated from the surrounding values for 5-mph increments. 

Values for the seven detailed vehicle classes used by HERS were then consolidated to the three

aggregate vehicle classes for which the HPMS data records for individual sample sections provide estimated shares of travel (Four-Tire Vehicles, Single-Unit Trucks, and Combination

Trucks), using the distributions of the seven detailed vehicle classes within each of these three

broader classes on individual roadway types (reported previously in Table _-1); Table _-6 provides an example of the resulting values. Finally, this entire process was repeated for the year

2015, and annual rates of decline in emissions damage costs were estimated from their 2000 and

2015 values for each combination of vehicle class and roadway type. The annual percentage rates

at which emission costs decline were assumed to be constant throughout this period (and

beyond). 

Adjustment Factor:

Urban Rural

Carbon Monoxide $100 1.0 0.5

Volatile Organic Compounds $2,750 1.5 1.0

Nirtogen Oxides $3,625 1.5 1.0

Sulfur Dioxide $8,400 1.5 1.0

Fine Particulate Matter (PM2.5) $4,825 1.0 0.5

Road Dust $4,825 1.0 0.5

Damage Costs 

($/ton) Pollutant

Table E-5. Air Pollutant Damage Costs 

and Adjustment Factors Used in HERS (2000 $)

Sources:

McCubbin and DeLucchi, 1995, and Volpe Center analysis of county population density data from U.S. Census Bu- reau, 2000 Census of the United States.
HERS Technical Report v3.54

September 2002

E-11

E.3.4 Assessing the Effect of Proposed Improvements on Air Pollution Costs 

HERS calculates the economic costs of air pollution generated by annual travel on a sample section by multiplying its estimates of total annual vehicle-miles traveled by each vehicle class

(Four-Tire Vehicles, Single-Unit Trucks, and Combination Trucks) by the value of air pollution

damage costs per vehicle-mile for the appropriate vehicle class, roadway section type, average

travel speed, and calendar year. Air pollution costs per vehicle-mile for the calendar year in

which a proposed improvement is being evaluated are calculated by applying the average

annual rate of decline over the appropriate number of years to the year-2000 cost estimates. 

By repeating this procedure under the baseline and hypothetically improved travel conditions,

HERS calculates the change in total air pollution costs generated by travel on the section that

would result from implementing each proposed improvement. The change or difference in total

air pollution costs between baseline and improved conditions increases or reduces net benefits

from the improvement under consideration, depending on whether the changes in average effective speed and annual travel volume by each vehicle class resulting from that improvement

cause air pollution costs to rise or decline. This process is repeated to evaluate the effect on net

benefits from the candidate improvement from including air pollution costs during each future

year making up the expected lifetime of that improvement. HERS then applies the usual process

of discounting the stream of future net benefits from each candidate improvement – including its

effect on air pollution costs – to its present value in order to evaluate the desirability of selecting

that improvement during the current funding period. 

E.3.5 Likely Effects of Including Air Pollution Costs

As indicated previously, proposed improvements to a sample section tend to increase air pollution costs by making travel on it less costly and thus raising the level of travel on the section.

Thus if air pollutant emissions per vehicle-mile were unaffected by the changes in travel conditions that occur when sample sections are improved, air pollution costs would normally rise,

thereby reducing the net benefits from typical improvements. At the same time, however,

increases in the average effective speed of travel that result from an improvement can reduce

average emissions per vehicle-mile for certain pollutants. By doing so, an improvement can thus

reduce average air pollution costs per vehicle-mile traveled on the section, thereby offsetting

some or all of the effect of higher travel volumes on total air pollution costs. 

As Tables E-6 through E-14 suggests, per-mile air pollution costs on most facility types fall significantly as speeds increase up to about 40 mph, so benefits from improvements that increase

speeds over this range are likely to be reduced only modestly - and may actually be increased in

some cases – by including air pollution costs. Because per-mile emission rates and thus air pollution costs for most vehicle classes and roadway types begin to rise gradually above about 40

mph, however, large speed increases resulting from an improvement can accentuate the increase

in air pollution costs caused by higher travel volumes. 

Thus where travel speeds on sample sections under baseline or unimproved conditions are

already above about 40 mph, the increase in air pollution costs resulting from the higher travel

volumes produced by most improvements will be reinforced by an increase in per-mile air pollution costs. This same effect may also occur where baseline travel speeds are below the 45 mph
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-12

threshold, but where candidate improvements to a sample section produce very large increases

in travel speeds. In these cases, including air pollution costs may significantly reduce the net

benefits from many potential improvements considered by HERS, making them less likely to be

selected. 

Air pollution damage costs per vehicle-mile differ considerably among the various section types

considered by HERS across the entire range of travel speeds. Air pollution costs imposed by

travel on facilities located in urban areas are significantly higher than those for identical facility

types in rural areas because of the increased exposure to air pollution experienced by residents

and properties surrounding sample sections located in urbanized areas. Average costs per vehicle-mile are also higher for facilities that carry larger shares of heavy vehicle travel (Interstate

highways and other major arterials), since the per-mile rates at which trucks and other heavy

vehicles emit some pollutants are much higher than those for light-duty vehicles. Thus considering air pollution costs is more likely to result in significant reductions in net benefits from candidate improvements to higher-order facilities (Interstate highways and other major arterials) and

sample sections in urbanized locations. 

On balance, the increase in air pollution costs from higher travel volumes seems likely to outweigh the effect of any decline in per-mile pollution costs for most proposed improvements.

Thus considering air pollution costs will make most improvements slightly less likely to meet the

benefit-cost criterion used by HERS to select improvements for adoption. Across the very large

number of sample sections analyzed by HERS, the result seems likely to be a reduction in the

number and value of improvement projects that are selected by HERS when the economic efficiency criterion is employed. Where projects are selected on a different basis, including air pollution costs is likely to reduce the net benefits generated by any selected set of improvements. 

 

Table E-6. Emission Damage Costs by HERS Vehicle Class: Rural Interstatea

Speed

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.03283 $0.05347 $0.14932

6 $0.02902 $0.04925 $0.14350

7 $0.02630 $0.04623 $0.13935

8 $0.02426 $0.04397 $0.13623

9 $0.02267 $0.04221 $0.13380

10 $0.02140 $0.04081 $0.13186

11 $0.02031 $0.03930 $0.12864

12 $0.01940 $0.03805 $0.12595

13 $0.01863 $0.03699 $0.12368

14 $0.01797 $0.03608 $0.12173

15 $0.01740 $0.03529 $0.12004
HERS Technical Report v3.54

September 2002

E-13

16 $0.01708 $0.03448 $0.11805

17 $0.01680 $0.03376 $0.11630

18 $0.01655 $0.03312 $0.11474

19 $0.01633 $0.03255 $0.11334

20 $0.01613 $0.03204 $0.11209

21 $0.01576 $0.03162 $0.11088

22 $0.01543 $0.03125 $0.10978

23 $0.01512 $0.03091 $0.10877

24 $0.01484 $0.03060 $0.10785

25 $0.01459 $0.03031 $0.10701

26 $0.01477 $0.03010 $0.10636

27 $0.01493 $0.02991 $0.10575

28 $0.01509 $0.02973 $0.10520

29 $0.01523 $0.02956 $0.10468

30 $0.01537 $0.02941 $0.10419

31 $0.01530 $0.02933 $0.10400

32 $0.01523 $0.02926 $0.10381

33 $0.01517 $0.02919 $0.10364

34 $0.01511 $0.02913 $0.10348

35 $0.01506 $0.02907 $0.10333

36 $0.01506 $0.02909 $0.10355

37 $0.01506 $0.02910 $0.10376

38 $0.01505 $0.02912 $0.10395

39 $0.01505 $0.02914 $0.10414

40 $0.01505 $0.02915 $0.10432

41 $0.01506 $0.02925 $0.10497

42 $0.01506 $0.02934 $0.10559

43 $0.01507 $0.02943 $0.10618

44 $0.01507 $0.02951 $0.10674

45 $0.01508 $0.02959 $0.10727

Table E-6. Emission Damage Costs by HERS Vehicle Class: Rural Interstatea

Speed

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-14

46 $0.01509 $0.02977 $0.10842

47 $0.01510 $0.02994 $0.10951

48 $0.01511 $0.03010 $0.11056

49 $0.01511 $0.03026 $0.11157

50 $0.01512 $0.03041 $0.11254

51 $0.01514 $0.03068 $0.11430

52 $0.01515 $0.03093 $0.11600

53 $0.01516 $0.03117 $0.11763

54 $0.01518 $0.03140 $0.11920

55 $0.01519 $0.03163 $0.12072

56 $0.01521 $0.03200 $0.12332

57 $0.01523 $0.03236 $0.12584

58 $0.01525 $0.03271 $0.12826

59 $0.01527 $0.03304 $0.13061

60 $0.01529 $0.03336 $0.13287

61 $0.01531 $0.03389 $0.13667

62 $0.01533 $0.03439 $0.14034

63 $0.01536 $0.03488 $0.14390

64 $0.01538 $0.03535 $0.14734

65 $0.01540 $0.03581 $0.15068

66 $0.01542 $0.03627 $0.15410

67 $0.01544 $0.03675 $0.15759

68 $0.01546 $0.03722 $0.16116

69 $0.01548 $0.03771 $0.16481

70 $0.01550 $0.03820 $0.16855

rb 6.27% 7.79% 12.17%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-6. Emission Damage Costs by HERS Vehicle Class: Rural Interstatea

Speed

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-15

Table E-7. Emission Damage Costs by HERS Vehicle Class: Rural Other Principal 

Arteriala

Average 

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.03584 $0.05605 $0.12750

6 $0.03169 $0.05145 $0.12117

7 $0.02872 $0.04816 $0.11665

8 $0.02649 $0.04570 $0.11326

9 $0.02476 $0.04378 $0.11062

10 $0.02338 $0.04224 $0.10851

11 $0.02228 $0.04059 $0.10504

12 $0.02136 $0.03921 $0.10214

13 $0.02059 $0.03804 $0.09969

14 $0.01993 $0.03704 $0.09759

15 $0.01935 $0.03617 $0.09577

16 $0.01880 $0.03527 $0.09362

17 $0.01831 $0.03448 $0.09172

18 $0.01787 $0.03377 $0.09004

19 $0.01748 $0.03314 $0.08853

20 $0.01713 $0.03257 $0.08717

21 $0.01687 $0.03212 $0.08587

22 $0.01663 $0.03170 $0.08468

23 $0.01641 $0.03132 $0.08360

24 $0.01621 $0.03098 $0.08260

25 $0.01602 $0.03066 $0.08169

26 $0.01586 $0.03042 $0.08099

27 $0.01571 $0.03021 $0.08034

28 $0.01558 $0.03000 $0.07974

29 $0.01545 $0.02982 $0.07917

30 $0.01533 $0.02964 $0.07865

31 $0.01523 $0.02956 $0.07844

32 $0.01514 $0.02948 $0.07824

33 $0.01506 $0.02941 $0.07805
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-16

34 $0.01498 $0.02934 $0.07788

35 $0.01490 $0.02927 $0.07771

36 $0.01490 $0.02929 $0.07863

37 $0.01490 $0.02931 $0.07949

38 $0.01489 $0.02933 $0.08030

39 $0.01489 $0.02934 $0.08108

40 $0.01489 $0.02936 $0.08181

41 $0.01489 $0.02947 $0.08185

42 $0.01490 $0.02957 $0.08188

43 $0.01491 $0.02967 $0.08191

44 $0.01492 $0.02977 $0.08194

45 $0.01492 $0.02986 $0.08196

46 $0.01493 $0.03006 $0.08319

47 $0.01494 $0.03025 $0.08437

48 $0.01495 $0.03043 $0.08550

49 $0.01496 $0.03060 $0.08658

50 $0.01497 $0.03077 $0.08762

51 $0.01499 $0.03107 $0.08952

52 $0.01500 $0.03136 $0.09135

53 $0.01502 $0.03163 $0.09311

54 $0.01503 $0.03190 $0.09480

55 $0.01505 $0.03215 $0.09643

56 $0.01507 $0.03258 $0.09924

57 $0.01509 $0.03298 $0.10194

58 $0.01511 $0.03338 $0.10456

59 $0.01513 $0.03376 $0.10708

60 $0.01515 $0.03413 $0.10952

61 $0.01516 $0.03473 $0.11360

62 $0.01517 $0.03530 $0.11755

Table E-7. Emission Damage Costs by HERS Vehicle Class: Rural Other Principal 

Arteriala

Average 

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-17

63 $0.01518 $0.03586 $0.12138

64 $0.01519 $0.03640 $0.12508

65 $0.01520 $0.03693 $0.12868

66 $0.01520 $0.03746 $0.13237

67 $0.01521 $0.03800 $0.13617

68 $0.01522 $0.03855 $0.14008

69 $0.01523 $0.03911 $0.14411

70 $0.01524 $0.03967 $0.14825

rb 6.06% 7.79% 11.30%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-8. Emission Damage Costs by HERS Vehicle Class: Rural Minor Arteriala

Speed 

(mph)

Emissions Damage Cost

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.03586 $0.05609 $0.12643

6 $0.03170 $0.05149 $0.12011

7 $0.02873 $0.04820 $0.11560

8 $0.02651 $0.04573 $0.11221

9 $0.02477 $0.04381 $0.10958

10 $0.02339 $0.04228 $0.10747

11 $0.02229 $0.04062 $0.10402

12 $0.02138 $0.03924 $0.10114

13 $0.02060 $0.03807 $0.09871

14 $0.01994 $0.03707 $0.09662

15 $0.01936 $0.03620 $0.09482

16 $0.01881 $0.03530 $0.09268

Table E-7. Emission Damage Costs by HERS Vehicle Class: Rural Other Principal 

Arteriala

Average 

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-18

17 $0.01832 $0.03450 $0.09080

18 $0.01788 $0.03380 $0.08913

19 $0.01749 $0.03317 $0.08763

20 $0.01714 $0.03260 $0.08628

21 $0.01688 $0.03214 $0.08499

22 $0.01664 $0.03172 $0.08381

23 $0.01642 $0.03134 $0.08273

24 $0.01622 $0.03100 $0.08175

25 $0.01603 $0.03068 $0.08084

26 $0.01587 $0.03044 $0.08014

27 $0.01573 $0.03022 $0.07950

28 $0.01559 $0.03002 $0.07890

29 $0.01546 $0.02984 $0.07834

30 $0.01534 $0.02966 $0.07782

31 $0.01524 $0.02958 $0.07761

32 $0.01515 $0.02950 $0.07741

33 $0.01507 $0.02942 $0.07723

34 $0.01499 $0.02936 $0.07705

35 $0.01491 $0.02929 $0.07689

36 $0.01491 $0.02931 $0.07778

37 $0.01491 $0.02933 $0.07862

38 $0.01490 $0.02934 $0.07942

39 $0.01490 $0.02936 $0.08017

40 $0.01490 $0.02937 $0.08089

41 $0.01490 $0.02948 $0.08094

42 $0.01491 $0.02959 $0.08097

43 $0.01492 $0.02969 $0.08101

44 $0.01493 $0.02979 $0.08105

45 $0.01493 $0.02988 $0.08108

46 $0.01494 $0.03008 $0.08230

Table E-8. Emission Damage Costs by HERS Vehicle Class: Rural Minor Arteriala

Speed 

(mph)

Emissions Damage Cost

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-19

47 $0.01495 $0.03027 $0.08346

48 $0.01496 $0.03045 $0.08458

49 $0.01497 $0.03063 $0.08565

50 $0.01498 $0.03079 $0.08667

51 $0.01500 $0.03109 $0.08855

52 $0.01501 $0.03138 $0.09036

53 $0.01503 $0.03165 $0.09210

54 $0.01504 $0.03192 $0.09377

55 $0.01506 $0.03218 $0.09538

56 $0.01508 $0.03260 $0.09815

57 $0.01510 $0.03301 $0.10083

58 $0.01512 $0.03341 $0.10341

59 $0.01514 $0.03379 $0.10590

60 $0.01516 $0.03416 $0.10831

61 $0.01517 $0.03476 $0.11235

62 $0.01518 $0.03534 $0.11625

63 $0.01519 $0.03590 $0.12003

64 $0.01520 $0.03644 $0.12369

65 $0.01521 $0.03697 $0.12724

66 $0.01521 $0.03750 $0.13090

67 $0.01522 $0.03805 $0.13465

68 $0.01523 $0.03860 $0.13852

69 $0.01524 $0.03916 $0.14249

70 $0.01525 $0.03973 $0.14658

rb 6.06% 7.79% 11.25%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-8. Emission Damage Costs by HERS Vehicle Class: Rural Minor Arteriala

Speed 

(mph)

Emissions Damage Cost

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-20

Table E-9. Emission Damage Costs by HERS Vehicle Class: Rural Major Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.03599 $0.05627 $0.12618

6 $0.03182 $0.05166 $0.11986

7 $0.02885 $0.04837 $0.11535

8 $0.02662 $0.04590 $0.11197

9 $0.02488 $0.04398 $0.10934

10 $0.02349 $0.04244 $0.10723

11 $0.02239 $0.04077 $0.10379

12 $0.02147 $0.03938 $0.10092

13 $0.02070 $0.03821 $0.09849

14 $0.02003 $0.03720 $0.09640

15 $0.01946 $0.03633 $0.09460

16 $0.01890 $0.03542 $0.09247

17 $0.01841 $0.03462 $0.09059

18 $0.01797 $0.03391 $0.08892

19 $0.01758 $0.03328 $0.08742

20 $0.01723 $0.03271 $0.08608

21 $0.01697 $0.03224 $0.08478

22 $0.01673 $0.03182 $0.08361

23 $0.01651 $0.03144 $0.08253

24 $0.01630 $0.03109 $0.08155

25 $0.01612 $0.03077 $0.08064

26 $0.01596 $0.03053 $0.07995

27 $0.01581 $0.03031 $0.07930

28 $0.01567 $0.03011 $0.07871

29 $0.01554 $0.02992 $0.07815

30 $0.01542 $0.02974 $0.07763

31 $0.01533 $0.02966 $0.07742

32 $0.01524 $0.02958 $0.07722

33 $0.01515 $0.02950 $0.07704

34 $0.01507 $0.02943 $0.07686
HERS Technical Report v3.54

September 2002

E-21

35 $0.01500 $0.02937 $0.07670

36 $0.01499 $0.02938 $0.07759

37 $0.01499 $0.02940 $0.07842

38 $0.01499 $0.02942 $0.07922

39 $0.01498 $0.02943 $0.07997

40 $0.01498 $0.02945 $0.08068

41 $0.01499 $0.02956 $0.08073

42 $0.01500 $0.02967 $0.08077

43 $0.01501 $0.02977 $0.08081

44 $0.01501 $0.02987 $0.08085

45 $0.01502 $0.02996 $0.08088

46 $0.01503 $0.03016 $0.08209

47 $0.01504 $0.03036 $0.08325

48 $0.01505 $0.03054 $0.08437

49 $0.01506 $0.03072 $0.08543

50 $0.01507 $0.03089 $0.08646

51 $0.01509 $0.03119 $0.08833

52 $0.01510 $0.03148 $0.09013

53 $0.01512 $0.03176 $0.09186

54 $0.01513 $0.03203 $0.09353

55 $0.01515 $0.03229 $0.09514

56 $0.01517 $0.03273 $0.09790

57 $0.01519 $0.03315 $0.10057

58 $0.01521 $0.03355 $0.10315

59 $0.01523 $0.03394 $0.10563

60 $0.01525 $0.03432 $0.10804

61 $0.01526 $0.03492 $0.11206

62 $0.01527 $0.03551 $0.11595

63 $0.01527 $0.03609 $0.11972

64 $0.01528 $0.03664 $0.12338

Table E-9. Emission Damage Costs by HERS Vehicle Class: Rural Major Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-22

65 $0.01529 $0.03718 $0.12692

66 $0.01530 $0.03772 $0.13056

67 $0.01530 $0.03827 $0.13430

68 $0.01531 $0.03884 $0.13816

69 $0.01532 $0.03941 $0.14212

70 $0.01533 $0.03999 $0.14620

r

b 6.05% 7.80% 11.24%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-10. Emission Damage Costs by HERS Vehicle Class: Urban Interstatea

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck

5 $0.02562 $0.04511 $0.14771

6 $0.02256 $0.04200 $0.14188

7 $0.02038 $0.03978 $0.13772

8 $0.01875 $0.03811 $0.13460

9 $0.01747 $0.03681 $0.13217

10 $0.01646 $0.03578 $0.13023

11 $0.01566 $0.03454 $0.12709

12 $0.01499 $0.03351 $0.12447

13 $0.01443 $0.03264 $0.12225

14 $0.01395 $0.03189 $0.12035

15 $0.01353 $0.03124 $0.11871

16 $0.01338 $0.03058 $0.11674

17 $0.01324 $0.03000 $0.11500

18 $0.01312 $0.02949 $0.11345

19 $0.01301 $0.02902 $0.11207

Table E-9. Emission Damage Costs by HERS Vehicle Class: Rural Major Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-23

20 $0.01291 $0.02861 $0.11083

21 $0.01283 $0.02826 $0.10963

22 $0.01275 $0.02794 $0.10854

23 $0.01268 $0.02765 $0.10754

24 $0.01262 $0.02739 $0.10663

25 $0.01256 $0.02714 $0.10579

26 $0.01250 $0.02697 $0.10515

27 $0.01245 $0.02682 $0.10455

28 $0.01240 $0.02667 $0.10400

29 $0.01235 $0.02654 $0.10349

30 $0.01231 $0.02641 $0.10301

31 $0.01226 $0.02636 $0.10281

32 $0.01221 $0.02632 $0.10263

33 $0.01217 $0.02627 $0.10246

34 $0.01213 $0.02623 $0.10230

35 $0.01209 $0.02619 $0.10215

36 $0.01209 $0.02623 $0.10237

37 $0.01209 $0.02627 $0.10258

38 $0.01209 $0.02630 $0.10277

39 $0.01209 $0.02634 $0.10296

40 $0.01209 $0.02637 $0.10314

41 $0.01211 $0.02648 $0.10378

42 $0.01212 $0.02659 $0.10439

43 $0.01214 $0.02670 $0.10498

44 $0.01215 $0.02680 $0.10553

45 $0.01216 $0.02689 $0.10607

46 $0.01217 $0.02708 $0.10720

47 $0.01219 $0.02726 $0.10829

48 $0.01220 $0.02743 $0.10933

49 $0.01221 $0.02759 $0.11032

Table E-10. Emission Damage Costs by HERS Vehicle Class: Urban Interstatea

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-24

50 $0.01222 $0.02775 $0.11128

51 $0.01224 $0.02802 $0.11303

52 $0.01225 $0.02828 $0.11471

53 $0.01227 $0.02853 $0.11633

54 $0.01228 $0.02877 $0.11789

55 $0.01229 $0.02901 $0.11940

56 $0.01231 $0.02938 $0.12198

57 $0.01233 $0.02975 $0.12447

58 $0.01235 $0.03010 $0.12687

59 $0.01237 $0.03044 $0.12919

60 $0.01239 $0.03077 $0.13144

61 $0.01241 $0.03129 $0.13520

62 $0.01243 $0.03180 $0.13883

63 $0.01245 $0.03229 $0.14236

64 $0.01247 $0.03276 $0.14577

65 $0.01249 $0.03322 $0.14908

66 $0.01251 $0.03369 $0.15246

67 $0.01253 $0.03416 $0.15592

68 $0.01255 $0.03465 $0.15945

69 $0.01256 $0.03514 $0.16307

70 $0.01258 $0.03563 $0.16677

rb 6.77% 8.07% 12.15%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-10. Emission Damage Costs by HERS Vehicle Class: Urban Interstatea

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck
HERS Technical Report v3.54

September 2002

E-25

Table E-11. Emission Damage Costs by HERS Vehicle Class: Urban Other Freeway/

Expresswaya

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck

5 $0.02550 $0.04503 $0.14537

6 $0.02246 $0.04192 $0.13959

7 $0.02028 $0.03970 $0.13546

8 $0.01865 $0.03804 $0.13236

9 $0.01739 $0.03674 $0.12995

10 $0.01637 $0.03571 $0.12802

11 $0.01558 $0.03447 $0.12491

12 $0.01492 $0.03344 $0.12231

13 $0.01436 $0.03258 $0.12011

14 $0.01388 $0.03183 $0.11823

15 $0.01346 $0.03118 $0.11660

16 $0.01331 $0.03053 $0.11465

17 $0.01317 $0.02995 $0.11293

18 $0.01305 $0.02943 $0.11140

19 $0.01294 $0.02897 $0.11003

20 $0.01284 $0.02856 $0.10880

21 $0.01276 $0.02821 $0.10762

22 $0.01268 $0.02790 $0.10654

23 $0.01261 $0.02761 $0.10556

24 $0.01255 $0.02734 $0.10465

25 $0.01249 $0.02710 $0.10383

26 $0.01244 $0.02693 $0.10319

27 $0.01238 $0.02678 $0.10260

28 $0.01233 $0.02663 $0.10205

29 $0.01229 $0.02650 $0.10154

30 $0.01224 $0.02637 $0.10107

31 $0.01219 $0.02632 $0.10088

32 $0.01215 $0.02628 $0.10070

33 $0.01210 $0.02624 $0.10053
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-26

34 $0.01206 $0.02619 $0.10037

35 $0.01202 $0.02616 $0.10022

36 $0.01202 $0.02620 $0.10044

37 $0.01202 $0.02623 $0.10064

38 $0.01202 $0.02627 $0.10083

39 $0.01202 $0.02630 $0.10102

40 $0.01203 $0.02633 $0.10119

41 $0.01204 $0.02645 $0.10182

42 $0.01205 $0.02655 $0.10242

43 $0.01207 $0.02666 $0.10300

44 $0.01208 $0.02676 $0.10355

45 $0.01209 $0.02685 $0.10407

46 $0.01211 $0.02704 $0.10519

47 $0.01212 $0.02722 $0.10626

48 $0.01213 $0.02739 $0.10728

49 $0.01214 $0.02755 $0.10826

50 $0.01215 $0.02771 $0.10920

51 $0.01217 $0.02798 $0.11093

52 $0.01218 $0.02824 $0.11258

53 $0.01220 $0.02849 $0.11417

54 $0.01221 $0.02873 $0.11571

55 $0.01223 $0.02896 $0.11719

56 $0.01225 $0.02933 $0.11973

57 $0.01227 $0.02969 $0.12218

58 $0.01229 $0.03004 $0.12454

59 $0.01230 $0.03038 $0.12683

60 $0.01232 $0.03071 $0.12904

61 $0.01234 $0.03123 $0.13273

62 $0.01236 $0.03173 $0.13631

Table E-11. Emission Damage Costs by HERS Vehicle Class: Urban Other Freeway/

Expresswaya

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck
HERS Technical Report v3.54

September 2002

E-27

63 $0.01238 $0.03222 $0.13978

64 $0.01240 $0.03269 $0.14313

65 $0.01242 $0.03314 $0.14639

66 $0.01244 $0.03361 $0.14972

67 $0.01246 $0.03408 $0.15312

68 $0.01248 $0.03456 $0.15660

69 $0.01250 $0.03504 $0.16016

70 $0.01251 $0.03553 $0.16380

rb 6.77% 8.07% 12.15%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-12. Emission Damage Costs by HERS Vehicle Class: Urban Other Principal 

Arterialsa

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.02669 $0.04726 $0.12349

6 $0.02369 $0.04387 $0.11733

7 $0.02155 $0.04145 $0.11293

8 $0.01994 $0.03964 $0.10963

9 $0.01869 $0.03823 $0.10706

10 $0.01769 $0.03710 $0.10501

11 $0.01700 $0.03575 $0.10161

12 $0.01643 $0.03462 $0.09877

13 $0.01594 $0.03367 $0.09637

14 $0.01553 $0.03286 $0.09432

15 $0.01517 $0.03215 $0.09254

Table E-11. Emission Damage Costs by HERS Vehicle Class: Urban Other Freeway/

Expresswaya

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicle

Single-Unit 

Truck

Combination 

Truck
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-28

16 $0.01479 $0.03143 $0.09045

17 $0.01446 $0.03080 $0.08860

18 $0.01416 $0.03024 $0.08697

19 $0.01390 $0.02973 $0.08550

20 $0.01366 $0.02928 $0.08418

21 $0.01345 $0.02890 $0.08291

22 $0.01327 $0.02855 $0.08176

23 $0.01310 $0.02824 $0.08071

24 $0.01294 $0.02795 $0.07974

25 $0.01280 $0.02768 $0.07885

26 $0.01267 $0.02749 $0.07817

27 $0.01256 $0.02732 $0.07754

28 $0.01245 $0.02716 $0.07695

29 $0.01236 $0.02702 $0.07641

30 $0.01226 $0.02688 $0.07590

31 $0.01219 $0.02682 $0.07569

32 $0.01212 $0.02677 $0.07550

33 $0.01206 $0.02673 $0.07532

34 $0.01199 $0.02668 $0.07515

35 $0.01194 $0.02664 $0.07499

36 $0.01194 $0.02668 $0.07522

37 $0.01194 $0.02672 $0.07543

38 $0.01195 $0.02675 $0.07564

39 $0.01195 $0.02678 $0.07583

40 $0.01195 $0.02681 $0.07601

41 $0.01197 $0.02694 $0.07669

42 $0.01198 $0.02706 $0.07733

43 $0.01199 $0.02718 $0.07794

44 $0.01200 $0.02729 $0.07853

Table E-12. Emission Damage Costs by HERS Vehicle Class: Urban Other Principal 

Arterialsa

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-29

45 $0.01201 $0.02740 $0.07908

46 $0.01202 $0.02760 $0.08027

47 $0.01204 $0.02780 $0.08141

48 $0.01205 $0.02799 $0.08249

49 $0.01206 $0.02817 $0.08354

50 $0.01207 $0.02834 $0.08454

51 $0.01209 $0.02864 $0.08637

52 $0.01211 $0.02892 $0.08813

53 $0.01213 $0.02920 $0.08983

54 $0.01214 $0.02946 $0.09146

55 $0.01216 $0.02972 $0.09304

56 $0.01218 $0.03013 $0.09574

57 $0.01220 $0.03053 $0.09835

58 $0.01222 $0.03091 $0.10086

59 $0.01224 $0.03128 $0.10329

60 $0.01226 $0.03164 $0.10565

61 $0.01228 $0.03222 $0.10958

62 $0.01231 $0.03277 $0.11339

63 $0.01233 $0.03331 $0.11707

64 $0.01235 $0.03383 $0.12064

65 $0.01237 $0.03434 $0.12410

66 $0.01239 $0.03485 $0.12766

67 $0.01241 $0.03537 $0.13133

68 $0.01243 $0.03590 $0.13509

69 $0.01246 $0.03644 $0.13897

70 $0.01248 $0.03699 $0.14296

r

b 6.72% 8.16% 11.19%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-12. Emission Damage Costs by HERS Vehicle Class: Urban Other Principal 

Arterialsa

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-30

Table E-13. Table _-13. Emission Damage Costs by HERS Vehicle Class: Urban Minor 

Arteriala

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.02662 $0.04827 $0.11858

6 $0.02363 $0.04482 $0.11254

7 $0.02150 $0.04236 $0.10823

8 $0.01990 $0.04052 $0.10500

9 $0.01865 $0.03908 $0.10249

10 $0.01765 $0.03793 $0.10047

11 $0.01696 $0.03654 $0.09717

12 $0.01639 $0.03538 $0.09442

13 $0.01590 $0.03440 $0.09210

14 $0.01548 $0.03356 $0.09010

15 $0.01512 $0.03283 $0.08837

16 $0.01475 $0.03209 $0.08635

17 $0.01441 $0.03143 $0.08457

18 $0.01412 $0.03084 $0.08299

19 $0.01386 $0.03032 $0.08157

20 $0.01362 $0.02984 $0.08030

21 $0.01341 $0.02944 $0.07907

22 $0.01323 $0.02908 $0.07796

23 $0.01306 $0.02875 $0.07694

24 $0.01290 $0.02845 $0.07601

25 $0.01276 $0.02817 $0.07516

26 $0.01264 $0.02797 $0.07450

27 $0.01252 $0.02779 $0.07389

28 $0.01242 $0.02762 $0.07333

29 $0.01232 $0.02746 $0.07280

30 $0.01223 $0.02731 $0.07231

31 $0.01215 $0.02725 $0.07211

32 $0.01208 $0.02720 $0.07192

33 $0.01202 $0.02714 $0.07175
HERS Technical Report v3.54

September 2002

E-31

34 $0.01196 $0.02710 $0.07158

35 $0.01190 $0.02705 $0.07142

36 $0.01190 $0.02709 $0.07164

37 $0.01191 $0.02712 $0.07184

38 $0.01191 $0.02715 $0.07203

39 $0.01191 $0.02719 $0.07221

40 $0.01192 $0.02722 $0.07239

41 $0.01193 $0.02735 $0.07303

42 $0.01194 $0.02748 $0.07363

43 $0.01195 $0.02760 $0.07421

44 $0.01196 $0.02772 $0.07477

45 $0.01197 $0.02783 $0.07530

46 $0.01199 $0.02805 $0.07642

47 $0.01200 $0.02826 $0.07750

48 $0.01201 $0.02846 $0.07853

49 $0.01202 $0.02865 $0.07953

50 $0.01204 $0.02883 $0.08048

51 $0.01205 $0.02915 $0.08222

52 $0.01207 $0.02945 $0.08389

53 $0.01209 $0.02975 $0.08550

54 $0.01210 $0.03003 $0.08705

55 $0.01212 $0.03030 $0.08854

56 $0.01214 $0.03075 $0.09110

57 $0.01216 $0.03118 $0.09358

58 $0.01218 $0.03159 $0.09596

59 $0.01220 $0.03199 $0.09827

60 $0.01222 $0.03238 $0.10050

61 $0.01225 $0.03300 $0.10423

62 $0.01227 $0.03360 $0.10784

Table E-13. Table _-13. Emission Damage Costs by HERS Vehicle Class: Urban Minor 

Arteriala

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-32

63 $0.01229 $0.03419 $0.11134

64 $0.01231 $0.03475 $0.11473

65 $0.01233 $0.03530 $0.11801

66 $0.01236 $0.03586 $0.12139

67 $0.01238 $0.03642 $0.12486

68 $0.01240 $0.03700 $0.12844

69 $0.01242 $0.03758 $0.13211

70 $0.01244 $0.03818 $0.13589

rb 6.73% 8.17% 11.01%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected annual rate of decline after year 2000.

Table E-14. Emission Damage Costs by HERS Vehicle Class: Urban Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks

5 $0.02662 $0.04779 $0.11686

6 $0.02363 $0.04437 $0.11087

7 $0.02150 $0.04193 $0.10659

8 $0.01989 $0.04010 $0.10338

9 $0.01865 $0.03868 $0.10088

10 $0.01765 $0.03754 $0.09889

11 $0.01696 $0.03617 $0.09562

12 $0.01639 $0.03502 $0.09290

13 $0.01590 $0.03406 $0.09060

14 $0.01548 $0.03323 $0.08863

15 $0.01512 $0.03251 $0.08692

16 $0.01475 $0.03178 $0.08492

Table E-13. Table _-13. Emission Damage Costs by HERS Vehicle Class: Urban Minor 

Arteriala

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

E-33

17 $0.01441 $0.03113 $0.08316

18 $0.01412 $0.03055 $0.08160

19 $0.01385 $0.03004 $0.08020

20 $0.01362 $0.02958 $0.07894

21 $0.01341 $0.02918 $0.07773

22 $0.01323 $0.02883 $0.07663

23 $0.01306 $0.02851 $0.07563

24 $0.01290 $0.02821 $0.07471

25 $0.01276 $0.02793 $0.07386

26 $0.01264 $0.02774 $0.07322

27 $0.01252 $0.02757 $0.07261

28 $0.01242 $0.02740 $0.07206

29 $0.01232 $0.02725 $0.07154

30 $0.01223 $0.02711 $0.07105

31 $0.01215 $0.02705 $0.07086

32 $0.01208 $0.02700 $0.07067

33 $0.01202 $0.02695 $0.07050

34 $0.01196 $0.02690 $0.07033

35 $0.01190 $0.02685 $0.07018

36 $0.01190 $0.02689 $0.07039

37 $0.01191 $0.02693 $0.07058

38 $0.01191 $0.02696 $0.07077

39 $0.01191 $0.02700 $0.07095

40 $0.01192 $0.02703 $0.07112

41 $0.01193 $0.02716 $0.07174

42 $0.01194 $0.02728 $0.07234

43 $0.01195 $0.02740 $0.07291

44 $0.01196 $0.02752 $0.07345

45 $0.01197 $0.02763 $0.07397

46 $0.01199 $0.02784 $0.07508

Table E-14. Emission Damage Costs by HERS Vehicle Class: Urban Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
Detailed Description of Procedures for Incorporating Air Pollution Costs in HERS

E-34

47 $0.01200 $0.02804 $0.07614

48 $0.01201 $0.02823 $0.07715

49 $0.01202 $0.02842 $0.07812

50 $0.01204 $0.02860 $0.07905

51 $0.01205 $0.02891 $0.08076

52 $0.01207 $0.02920 $0.08240

53 $0.01209 $0.02949 $0.08398

54 $0.01210 $0.02976 $0.08550

55 $0.01212 $0.03002 $0.08697

56 $0.01214 $0.03045 $0.08948

57 $0.01216 $0.03087 $0.09191

58 $0.01218 $0.03127 $0.09425

59 $0.01220 $0.03166 $0.09651

60 $0.01222 $0.03203 $0.09870

61 $0.01225 $0.03263 $0.10236

62 $0.01227 $0.03321 $0.10591

63 $0.01229 $0.03377 $0.10934

64 $0.01231 $0.03431 $0.11266

65 $0.01233 $0.03484 $0.11588

66 $0.01235 $0.03538 $0.11919

67 $0.01238 $0.03592 $0.12260

68 $0.01240 $0.03648 $0.12610

69 $0.01242 $0.03704 $0.12971

70 $0.01244 $0.03761 $0.13342

rb 6.73% 8.17% 10.95%

a. Source: estimated by Volpe Center using procedure described in text.

b. Projected Annual Rate of Decline after year 2000.

Table E-14. Emission Damage Costs by HERS Vehicle Class: Urban Collectora

Speed 

(mph)

Emission Damage Cost 

(2000 $ per vehicle-mile)

Four-Tire 

Vehicles

Single-Unit 

Trucks

Combination 

Trucks
HERS Technical Report v3.54

September 2002

F-1

Appendix F: Delay Estimation for Sections 

with Traffic Signals and for Free-Flow Sections with Two or More Lanes per Direction

The second section of this appendix presents the procedure used for estimating incident delay

and other congestion delay for free-flow sections with two or more lanes per direction. The third

section presents the procedure used for estimating zero-volume delay, incident delay, and other

congestion delay for sections with traffic signals.1

 The first section presents definitions of all variables used by the two procedures.

F.1 Definitions

The following definitions are used in the equations below.

F.1.1 Input Variables

ACR = ratio of AADT to two-way capacity during the off-peak period

BPM = bottlenecks per mile (set to 0.083 for multi-lane free-flow sections

and 0.5 for sections with traffic signals)

CPCAP = capacity during peak periods in the counter-peak direction (one

way)

CPLANES = through lanes in peak period, counter-peak direction

DFAC = directional (“D”) factor

FFS = free-flow speed (mph)

NSIG = number of signalized intersections per mile (average)

OP2WCAP = two-way capacity during off-peak period

PKCAP = capacity during peak period in peak direction (one way)

PLANES = through lanes in peak period, peak direction

F.1.2 Intermediate and Output Variables

Index K, K = 1, 2, or 3

1 = peak period, peak direction

2 = peak period, counter-peak direction

3 = off-peak period

1. Both procedures were developed in Cambridge Systematics, Inc., 2000 Revisions to HERS, prepared for the U.S.

Department of Transportation, Federal Highway Administration, Washington, D.C., August 2002. The procedures

are based on relationships developed in Cambridge Systematics, Inc., Harry Cohen, and Science Applications

International Corp., Sketch Methods for Estimating Incident-Related Impacts, prepared for the U.S. Department of

Transportation, Federal Highway Administration, Washington, D.C., December 1998, Section 2.3.
Delay Estimation for Sections with Traffic Signals and for Free-Flow Sections with Two or More Lanes per Direction

F-2

DINC(K) = incident-related delay (hours per million vehicle-miles) in period/

direction K (K = 1, 2, 3)

NITR(K) = travel rate (hours per vehicle-mile) without incidents in period/

direction K (K = 1, 2, 3)

SHFAC = shoulder factor (based on left and right shoulder widths, see Table

F-1)

TRAVF(K) = fraction of annual travel in period/direction K (K = 1, 2, 3)

VCRPP(K) = peak-period volume/capacity ratio – average hourly volume in

the indicated direction during a three-hour peak period divided by

capacity (K = 1 for peak direction, 2 for counter-peak direction)

ZVDSIG = zero-volume delay due to traffic signals (hours per vehicle-mile)

F.2 Free-Flow Sections with Two or More Lanes per 

Direction

F.2.1 Fractions of Travel for Free-Flow Sections.

The equations for fraction of travel for free-flow sections with two or more lanes per direction are

defined in Table F-2.

Table F-1. Shoulder Factors (SHFAC)

Number of Lanes per 

Direction

Number of Six Foot (or wider) Shoulders in Each Direction

012

2 5.22 3.04 1.00

3 4.77 2.83 1.00

4 or more 4.45 2.68 1.00

Table F-2. Fractions of Travel by Peak/Off-peak Phase for Free-Flow Sections

Peak/Off-Peak Condition Fraction of Travel

Off-Peak 

Period

ACR ≤ 7

ACR > 7 and ACR ≤ 9

ACR > 9 and ACR ≤ 12

ACR > 12

TRAVF( ) 3 = 0.6970

TRAVF( ) 3 0.6970 0.00085 – ( ) ACR – 7

0.00212( ) ACR – 7 1.39 e

–0.00798( ) ACR – 7 ) ×

= +

TRAVF( ) 3 0.6953 0.00187 – ( ) ACR – 9

0.00212( ) ACR – 7 1.39 e

–0.00798( ) ACR – 7 ) ×

= +

TRAVF( ) 3 0.6897 0.00408 – ( ) ACR – 12

0.00212( ) ACR – 7 1.39 e

–0.00798( ) ACR – 7 ) ×

= +
HERS Technical Report v3.54

September 2002

F-3

F.2.2 Volume-to-Capacity Ratios for Peak Period on Free-Flow Sections.

The equations for volume-to-capacity for free-flow sections with two or more lanes per direction

are defined in Table F-3.

F.2.3 Travel Rate Without Incidents for Free-Flow Sections.

The equations for travel rate for free-flow sections with two or more lanes per direction are

defined in Table F-4

Peak Period

Peak Direction

Counter-peak Direction

Table F-3. Volume-to-Capacity Ratios for Peak Periods for Free-Flow Sections

Direction Volume-to-Capacity Ratio

Peak Direction

Counter-peak 

Direction

Table F-4. Travel Rate Without Incidents for Free-Flow Sections

Peak/OffPeak Condition Travel Rate (hours per vehicle-mile)

Off-Peak 

Period

ACR ≤ 7

ACR > 7 and 

ACR ≤ 11

ACR > 11

Peak 

Period

VCRPP(K) ≤ 0.5995

VCRPP(K) > 0.5995

Table F-2. Fractions of Travel by Peak/Off-peak Phase for Free-Flow Sections

Peak/Off-Peak Condition Fraction of Travel

TRAVF( ) 1 = DFAC × ( ) 1 – TRAVF( ) 3

TRAVF( ) 2 = ( ) 1 – DFAC × ( ) 1 – TRAVF( ) 3

VCRPP( ) 1 = 0.243 × ACR TRAVF × ( ) 1 × OP2WCAP PKCAP ⁄

VCRPP( ) 2 = 0.243 × ACR TRAVF × ( ) 2 × OP2WCAP PKCAP ⁄

NITR( ) 3 ( ) 1 ⁄ FFS 1 9.19 –11 ×10 ACR7.71 = × ( ) + ×

NITR( ) 3 ( ) 1 ⁄ FFS 1 9.19 –11 ×10 ACR7.71 × ( ) + ×

0.00000133 × BPM ACR × ( ) – 7 6.97 e

–0.356 × ( ) ACR – 7 + ×

=

NITR( ) 3 ( ) 1 ⁄ FFS 1.0367294 0.0169 ACR

0.00177 ACR2 0.0000407 ACR3 × – ×

( – × +

)

×

0.00000133 × BPM ACR × ( ) – 7 6.97 e

–0.356 × ( ) ACR – 7 + ×

=

NITR K( ) ( ) 1 ⁄ FFS 1 0.388 VCRPP K( )7.27 = × ( ) + ×

NITR K( ) ( ) 1 ⁄ FFS 1.4060195 1.84 × VCRPP K( )

2.54 VCRPP K( )2 × 0.958 VCRPP K( )3 – ×

( – +

)

×

1.69 × BPM ( ) VCRPP K( ) – 0.5995 2.54 e

1.94 × ( ) VCRPP K( ) – 5.995 × ×

+

=
Delay Estimation for Sections with Traffic Signals and for Free-Flow Sections with Two or More Lanes per Direction

F-4

F.2.4 Incident Delay for Free-Flow Sections.

The equations for incident delay2 for free-flow sections with two or more lanes per direction are

defined in Table F-5.

2. These equations produce values of DINC in hours per vehicle-mile for consistency with the corresponding equations for sections with traffic signals (in Section I.3). The equations in the HERS code for multi-lane free-flow sections (but not those for sections with traffic signals) actually produce values in hours per million vehicle-miles that

are subsequently converted to hours per thousand vehicle-miles and hours per vehicle-mile as needed.

Table F-5. Incident Delay for Free-Flow Sections

Peak/OffPeak

Number of 

Lanes per 

Direction Condition Incident Delay (hours per vehicle-mile)

Off-Peak 

Period

2

ACR ≤ 11

ACR > 11

3

ACR ≤ 11

ACR > 11

4 or more

ACR ≤ 11

ACR > 11

Peak 

Period

2

VCRPP(K) ≤

0.5995

VCRPP(K) >

0.5995

3

VCRPP(K) ≤

0.5995

VCRPP(K) >

0.5995

4 or more

VCRPP(K) ≤

0.5995

VCRPP(K) >

0.5995

DINC( ) 3 4.05 ACR–0.251 × e

( ) 0.603 × ACR = × × SHFAC

DINC( ) 3 3.55826 10–11 × ACR17.1 × e

–0.865 × ACR = × × SHFAC

DINC( ) 3 0.789 ACR–0.834 e

0.854 × ACR = × × × SHFAC

DINC( ) 3 3.5131342 10–11 × ACR16.9 e

–0.847 × ACR = × × × SHFAC

DINC( ) 3 0.153 ACR–0.881 × e

1.01 × ACR = × × SHFAC

DINC( ) 3 3.2672 10–11 × ACR16.8 × e

–0.82 × ACR = × × SHFAC

DINC K( ) 4.6 VCRPP K( )–0.247 × e

9.2 × VCRPP K( ) = × × SHFAC

DINC K( ) 29173.1 VCRPP K( )5.16 × e

–0.789 × VCRPP K( ) = × × SHFAC

DINC K( ) 0.011 VCRPP K( )–2.3 × e

16.9 × VCRPP K( ) = × × SHFAC

DINC K( ) 560567 VCRPP K( )7.99 × e

–3.92 × VCRPP K( ) = × × SHFAC

DINC K( ) 0.00035 VCRPP K( )3.19 × e

21.8 × VCRPP K( ) = × × SHFAC

DINC K( ) 5841010 VCRPP K( )10.1 × e

–6.12 × VCRPP K( ) = × × SHFAC
HERS Technical Report v3.54

September 2002

F-5

F.3 Signalized Arterials

F.3.1 Fractions of Travel for Signalized Arterials.

The equations for fraction of travel for signalized arterials are defined in Table F-6.

F.3.2 Volume-to-Capacity Ratios for Peak Period on Signalized 

Arterials.

The equations for volume-to-capacity for signalized arterials are defined in Table F-7.

F.3.3 Zero-volume Delay Due to Traffic Signals for Signalized Arterials.

Zero-volume delay is delay associated with traffic control signals. The equation for zero-volume

delay is:

ZVDSIG = 0.0687 ( 1 – e-NSIG / 24.4 )

Table F-6. Fraction of Travel for Signalized Arterials

Peak/OffPeak Condition Fraction of Travel

Off-Peak

ACR ≤ 7 TRAVF(3) = 0.7106

ACR > 7 and 

ACR ≤ 9

TRAVF(3) = 0.7106 - 0.00160 (ACR-7) 

+ 0.00240 (ACR-7) 1.48 e –0.0431(ACR-7)

ACR > 9 and 

ACR ≤ 12

TRAVF(3) = 0.7074 - 0.00227 (ACR-9) 

+ 0.00240 (ACR-7) 1.48 e –0.0431(ACR-7)

ACR > 12 TRAVF(3) = 0.7006 + 0.00373 (ACR-12) + 0.00240 (ACR-7) 1.48 e –

0.0431(ACR-7)

Peak

Peak Direction TRAVF(1) = DFAC * ( 1 – TRAVF(3) )

Counter-peak Direction TRAVF(2) = ( 1 – DFAC ) * ( 1 – TRAVF(3) )

Table F-7. Volume-to-Capacity Ratios for Peak Periods on Signalized Arterials

Direction Volume-to-Capacity Ratio

Peak Direction

Counter-peak 

Direction

VCRPP( ) 1 = 0.243 × ACR TRAVF × ( ) 1 × OP2WCAP PKCAP ⁄

VCRPP( ) 2 = 0.243 × ACR TRAVF × ( ) 2 × OP2WCAP PKCAP ⁄
Delay Estimation for Sections with Traffic Signals and for Free-Flow Sections with Two or More Lanes per Direction

F-6

F.3.4 Travel Rate Without Incidents for Signalized Arterials.

The equations for travel rate for signalized arterials are defined in Table F-8.

F.3.5 Incident Delay for Signalized Arterials.

The equations for incident delay for signalized arterials are defined in Table F-9.

Table F-8. Travel Rate Without Incidents for Signalized Arterials

Peak/OffPeak Condition Travel Rate (hours per vehicle-mile)

Off-Peak 

Period

ACR ≤ 7 NITR(3) = (1/FFS+ZVDSIG) (1 + 0.0213 ACR1.05 )

ACR > 7 and 

ACR ≤ 11

NITR(3) = (1/FFS+ZVDSIG)(1 + 0.0213 ACR1.05 ) + 4.56E-08 BPM 

(ACR-7) 8.25 e –0.561 (ACR-7)

ACR > 11

NITR(3) = (1/FFS+ZVDSIG) (1.05 + 0.0247 ACR 

– 0.000504 ACR2 + 2.68E-06 ACR3) 

+ 4.56E-08 x BPM x (ACR-7) 8.25 e –0.561 (ACR-7)

Peak 

Period

VCRPP(K) ≤ 0.5767 NITR(K) = (1/FFS+ZVDSIG) (1 + 0.455 VCRPP(K)1.02 )

VCRPP(K) > 0.5767

NITR(K) = (1/FFS + ZVDSIG)(0.889 + 

0.680 x VCRPP(K) + 0.0423 VCRPP(K)2 – 0.182 VCRPP(K)3

) 

+ 0.228 BPM (VCRPP(K) - 0.5767) 2.66 e 3.61 (VCRPP(K)-0.5767

Table F-9. Incident Delay for Signalized Arterials

Peak/OffPeak Condition Incident Delay (hours per vehicle-mile)

Off-Peak 

Period

ACR ≤ 11 DINC(3) = 7.52E-06 (ACR) 1.11 e 0.132 ACR

ACR > 11 DINC(3) = 7.74E-09 (ACR) 5.20 e –0.135 ACR

Peak 

Period

VCRPP(K) ≤ 0.5767 DINC(K) = 0.000111 (VCRPP(K)) –0.828 e 2.83 VCRPP(K)

VCRPP(K) > 0.5767 DINC(K)= 1.34E-06 (VCRPP(K)) –2.05 e 7.74 VCRPP(K)
G-1

Appendix G: Unique Features of HERS-ST

The first three sections of this appendix describe three differences between HERS-ST 2.0 and

HERS 3.54. The fourth section describes the section-level files produced by HERS-ST 2.0.

Section G.5 provides guidance for providing HERS or HERS-ST with a state’s own estimates of

the capital cost of highway improvements. And the concluding section describes the HERS-ST

feature that allows the user to override HERS decisions relating to improvement selection and

the capital costs and capacity effects of improvements.

G.1 Rural Minor Collectors and Functionally Local 

Roads

HERS is not designed to handle rural minor collectors or sections on the two local functional

systems. To allow states to analyze sections on these three systems, HERS-ST treats all sections

on these systems as if they were rural major collectors or urban collectors, as appropriate.

Accordingly, statistics printed by HERS-ST for rural major collectors actually include

information for any rural minor collectors and rural local roads analyzed; and statistics for urban

collectors similarly include information for any urban streets analyzed.

G.2 Widening Feasibility Overrides

In HERS-ST, the user may specify separate widening feasibility overrides (see 4.5, “The Widening Feasibility Model”) for each functional system instead of being limited to a single override

value for the entire system being analyzed.

G.3 Initial Pavement Condition

For sections for which both International Roughness Index (IRI) and present serviceability rating

(PSR) are coded, HERS 3.54 uses the coded value of IRI as the condition of the pavement at the

beginning of the run. For these sections, HERS-ST 2.0 allows the user to request that the coded

value of PSR be used instead. (This request can be made on the Run Specifications screen of the

HERS GUI Control Model or in the preprocessor control file, PPSPEC.DAT.)

G.4 Section Output Files

In addition to the conventional HERS output, for each funding period (FP), HERS-ST produces a

comma-delimited ASCII file describing the condition of each section at the end of the FP along

with information about all improvements that have been selected and the effects of these

improvements. The file describing conditions at the end of FP nn is called SECNSnn.OUT. The

first record of the file contains the final year of the FP. The second contains the user’s description
Unique Features of HERS-ST

G-2

of the run. The third record contains a set of column headings shown in Table G-1; and the

remaining records contain descriptions of all sections, in comma-delimited format, as listed in

Table G-1 and described below.

The first data item in each record contains the record number of the HPMS file containing the

original description of the section. This number may be useful in locating the record.

Items 2 - 7 contain additional identification of the section being improved. These items are

obtained from the corresponding HPMS record.

Items 8 - 14 identify deficiencies that will exist by the end of the FP if the section is not improved.

Four of these items (PSR, lane width, shoulder type, and right shoulder width) correspond to

items in the HPMS file. Volume/capacity (v/c) ratio (Item 8) is HERS’ estimate of the ratio of

design-hour volume to peak-period hourly capacity. Horizontal and vertical alignment adequacy (Items 12 and 13) are either derived from information supplied on curves and grades by

class, or they are obtained from the input values for horizontal and vertical alignment adequacy.

In both cases, they use the HPMS codes for alignment adequacy. A simplified description of

these codes1 is:

1. All curves (or grades) meet design standards.

2. Some curves (or grades) do not meet design standards, but they do not affect speed or

safety.

3. Infrequent curves (or grades) affect speed or safety.

4. Several curves (or grades) affect speed or safety.

The next five items describe the improvement that is finally selected for the section, if any. If one

or more potential improvements are identified but none are selected, these items describe the

rejected improvement with the highest BCR. If no potential improvement is evaluated in this FP,

these items are blank. The use of these items when an improvement is selected is described

below:

15. Improvement type. A code identifying the type of improvement. The codes used for the 

improvement types that can be generated in basic runs are shown in the last two columns of 

Table G-2. As discussed in Section G.6, in override runs, the HERS-ST user may introduce 

additional codes to represent other types of (user-specified) improvements. The improvement types shown in Table G-2 are the only ones analyzed by the National HERS system. In 

Section G.6, these improvement types are referred to as “HERS-type” improvements.

16. Lanes added is the number of lanes added by the improvement (if any).

17. Increase in capacity. The increase in peak-period peak-direction capacity (if any) produced by 

this improvement.

1. More formal descriptions of the alignment adequacy codes are contained in FHWA, Highway Performance Monitoring System Field Manual, December 1999, pp. IV-31 and IV-32.
HERS Technical Report v3.54

September 2002

G-3

Table G-1. Record Format and Column Headings of SECNSnn.OUT Files

Field Column 

Heading Data Type

Section Identification

1. Record number RECNO I

2. County code CNTY I

3. Section identification SECID A

4. Sample identifier SAMPID A

5. LRS identification LRSID A

6. LRS beginning point BEGMP F

7. LRS ending point ENDMP F

Deficiencies

8. PSR PSR0 F

9. Volume/Capacity ratio VCR0 F

10. Lane width LW0 I

11. Shoulder type SHLT0 I

12. Right shoulder width RSHLW0 I

13. Horizontal alignment adequacy HORA0 I

14. Vertical alignment adequacy VERA0 I

Improvement

15. Improvement type ITYPE I

16. Lanes added LADD I

17. Increase in capacity CAPINC F

18. Type of selection TYPSEL I

19. BCR BCR F

Characteristics at End of FP

20. Volume/Capacity ratio VCR F

21. Average speed SPD F

22. PSR PSR F

23. IRI (inches/mile) IRI F

24. Total lanes TLAN I

25. Peak lanes, peak direction PLAN I

26. Peak lanes, opposite direction CPLAN I
Unique Features of HERS-ST

G-4

27. Peak capacity, peak direction PCAP F

28. Peak capacity, opposite direction CPCAP F

29. Off-peak capacity OPCAP F

30. Access control ACCESS I

31. Lane width LWID I

32. Shoulder type SHLT I

33. Right shoulder width RSHLW I

34. Median type MEDT I

35. Median width MEDW I

36. Widening feasibility WFEAS I

37. Horizontal alignment adequacy HORA I

38. Vertical alignment adequacy VERA I

39. AADT AADT F

40. Emissions costs EMC F

Costs and Benefits

41. Improvement cost IMPC F

42. Emissions benefits EMB F

43. Travel-time benefits TTB F

44. Operating-cost benefits OPCB F

45. Safety benefits SAFB F

46. Total benefits TOTB F

State Control Field

47. State control field SCF A

Table G-2. Codes for “HERS-Type” Improvements

Improvement Code

IMPRCOST Code

Without

Alignment

Improvement

With 

Alignment

Improvement

Rs Resurface 1 11

RsSh Resurface and improve shoulders 2 12

MinW Resurface and widen lanes (minor widening) 3 13

Table G-1. Record Format and Column Headings of SECNSnn.OUT Files
HERS Technical Report v3.54

September 2002

G-5

18. Type of selection. This field identifies the roles played by HERS-ST and the user in the 

improvement selection process. The codes used by HERS-ST 2.0 are:

0. Improvement was evaluated by HERS-ST but not selected.

1. Improvement was selected by HERS-ST.

2. Improvement was specified by user. (User requested HERS-ST not to add additional

options).

3. Improvement was requested by user; HERS-ST did not find any cost-effective options to

add.

4. Improvement combines options requested by user with options added by HERS.

5. Improvement combines a HERS-ST selection for this FP with a Table G-2 Type 1, 2, or 6

improvement requested by the user for a subsequent FP.

It should be noted that HERS-ST 2.0 produces information about some improvements

that were not selected.

19. BCR. Normally, the BCR of the improvement is the discounted present value (at the time of 

improvement implementation) of the sum of the user and agency benefits of the improvement divided by the implementation costs. An exception occurs when the system is operating under a funding constraint or with a performance goal (i.e., when objective type is 1 or 

2) and two (or more) alternative improvements are provisionally selected for a section in 

sequence. In this case, the BCR of the improvement is an incremental BCR; i.e., it is derived 

from the incremental benefits and costs of choosing the improvement that is finally selected 

to replace the last previous improvement that had been provisionally selected.

The next 21 items describe the section at the end of the FP. Items 22 - 25, 27, 30 - 36, and 39 correspond to items in the HPMS file. Items 20, 37, and 38 correspond to Items 9, 13, and 14 of the

SECNSnn file and are described above. Items 21 and 40 are the program’s estimates of: the overall average speed on the section (in mph); and the external costs of emissions in the last year of

the FP generated by vehicles using the section (in thousands of dollars). Item 39 is HERS’ estimate of AADT at the end of the FP.

Item 26 is the number of “counter-peak” lanes; i.e., the number of peak-period lanes in the “nonpeak” direction. This value is usually obtained by subtracting the number of peak lanes in the

peak direction (Item 25) from the total number of (off-peak) through lanes (Item 24). However,

MWNC Resurface and add normal-cost lanes (major widening) 4 14

MWHC Resurface and add high-cost lanes 5 15

RC Pavement reconstruction 6 16

RCWL Pavement reconstruction with wider lanes 7 17

RCNC Pavement reconstruction and add normal-cost lanes 8 18

RCHC Pavement reconstruction and add high-cost lanes 9 19

Table G-2. Codes for “HERS-Type” Improvements
Unique Features of HERS-ST

G-6

for some sections, HERS infers the likely existence of extra peak-period lanes resulting from

parking restrictions or use of shoulders as travel lanes during the peak period. For these sections,

total peak lanes (Items 25 and 26) will exceed (off-peak) through lanes (Item 24). For rural sections with less than four lanes, “peak” lanes represent the total number of lanes in both directions, and counter-peak lanes equals zero.

Corresponding to peak, counter-peak, and through lanes are three values of capacity: peak,

counter-peak, and off-peak capacity (Items 27 - 29). For rural roads with less than four lanes, the

peak and off-peak capacities are two-way capacity, and counter-peak capacity is zero. For all

other roads, the three capacities are one-way capacities. Peak capacity is the capacity coded in

the HPMS record. Off-peak and counter-peak capacities may be equal to or smaller than peak

capacity.

The next part of the record contains information about the costs and benefits of any improvement. The first of these fields contains improvement costs (in thousands of dollars) supplied by

the user (see Section G.5) and/or estimated by the program (see Section G.3).

When section-specific estimates of improvement costs for a specific improvement are supplied

by the user, these costs are used for that improvement. If the program chooses to combine this

improvement with an additional widening option and/or an alignment improvement, the incremental cost of these options are estimated and added to the total.

The next five fields are the program’s estimates of the user and external benefits of the improvement in the last year of the FP, in thousands of dollars. Separate estimates are provided of the

benefits of reductions in emissions costs, travel time, operating costs, and crash costs, along with

the sum of all four types of benefits. Negative values in the fields for emissions benefits or safety

benefits indicate an estimated increase in emissions or safety costs. For improvements that are

estimated by the program to result in increased use of the section, estimated benefits include the

benefits to new users of the section (estimated per new vehicle to equal half the per-vehicle benefits to old users). If no potential improvement is evaluated in the FP, these fields are blank.

The final field of the record reproduces the contents of the State Control Field (Field 8 of the

HPMS record).

The system user may find it useful to read the SECNSnn.OUT files into Excel. Attempting to

open any of these files in Excel results in entering Excel’s Text Import Wizard. After entering this

subsystem, the user should choose “Delimited” in Step 1, and choose only “Comma” in Step 2. In

Step 3, the Format should be set to “Text” for Columns 3 - 5 and 472

 and left as “General” for all

other columns.3

 The imported file will contain: the final year of the FP on Line 1; the user’s

description of the run on Line 2; and a set of column headings (from Table G-1) on Line 3. To

adjust all spreadsheet columns to the appropriate widths, the user should highlight the entire

spreadsheet except Rows 1 and 2 and then ask Excel to select the appropriate column widths

(Format, Column, AutoFit Selection).

2. Scrolling down two lines will cause Columns 1 - 6 to appear in the Data Preview. Column 47 can be reached by

scrolling to the right.

3. The Text Import Wizard can be bypassed by changing the file type to CSV before reading the file into Excel. This

alternative is simpler, but it assigns “General” format to all columns. If Columns 3, 4, or 46 have any cells that contain only numeric characters, “General” format will result in interpreting the contents of these cells as numbers, an

interpretation that may not always be desirable.
HERS Technical Report v3.54

September 2002

G-7

An example of the first several rows and columns of the resulting spreadsheet is shown in

Exhibit G-1.

G.5 Capital Cost of Improvements

The improvement cost file (IMPRCOST.DAT) contains FHWA’s estimates of national unit costs

for highway improvements in thousands of 2000 dollars per lane-mile. The system adjusts these

costs to state values using a set of State Cost Factors developed by FHWA. State users may wish

to incorporate their own estimates of pavement and widening costs into the system. This section

discusses how to incorporate these estimates.

The first 36 lines of IMPRCOST.DAT contain unit costs for all pavement and widening improvements. The codes used in this part of the file are mnemonics for the nine types of pavement and

widening improvements distinguished by the National HERS system. These codes are listed and

described in Table G-2.4 These costs are also accessible via the Improvement Cost screen of the

GUI Parameter Model.

For rural areas, the costs are specified separately by functional system and terrain (flat, rolling, or

mountainous). For urban areas, they are specified separately by facility type (freeways and

expressways, other divided roads, and undivided roads). There are 135 unit costs in this part of

the file. With a few exceptions, the costs are specified in thousands of 2000 dollars per lane-mile.

The exceptions are resurfacing or reconstruction with additional high-cost lanes and also, for

urban sections, resurfacing with additional normal-cost lanes; for these improvement types the

costs are specified in thousands of 2000 dollars per added lane-mile.

States that wish to use their own cost data are likely to have information for some of the 135 unit

costs in this part of the file, but not for all of them. However, it is important that reasonable relationships be maintained between the various unit costs. Thus, if significant changes are made to

any of the unit costs, all of the costs will require some adjustment. These adjustments may be

made either judgmentally or by scaling the remaining costs (or appropriate subsets of these

costs) uniformly. States that use their own cost estimates should change the State Cost Factor for

their state to 1.0. This factor is located near the end of PARAMS.DAT and is also accessible via

the Improvement Cost screen of the GUI Parameter Model.

When changing the unit costs for pavement and widening improvements, it is not necessary to

continue to express these costs in 2000 dollars. However, if dollars of another year are used, it is

important to replace the price indexes (on Lines 52 and 53 of PARAMS.DAT) with values that

will result in converting the costs to 2000 dollars. Values for converting rural and urban

improvement costs expressed in dollars of any year between 1995 and 2001 to 2000 dollars are

shown in Table G-3.

4. The table also shows numeric codes (discussed in Section G.4) for these improvement types with and without

additional alignment improvements. When pavement and/or widening improvements are combined with alignment improvements, HERS combines its estimate of the cost of the pavement and/or widening improvement with

an estimate of the incremental costs of the alignment improvement obtained using a procedure described in

Section 7.4.2. Unit costs used in the alignment-cost procedure are specified on Lines 39 - 129 of IMPRCOST.DAT in

1988 dollars (and indexed to 2000 dollars using price indexes on Lines 56 - 58 of PARAMS.DAT).
Unique Features of HERS-ST

G-8

2005

The Highway Economic Requirements System - State Version 2.0 - Min. BCR = 1.0 

 RECN

O CNT

Y SECID SAMPID LRSID BEGMP ENDMP PSR0 VCR0 LW0 SHLT0 RSHLW0 HORA0

1 1 FU7811001910 FU7811001910 000000000000 0 0 2.3 0.01 12 1 4 02 1 FU7804000000 AUTAPRAA1002 000000000000 0 0 3.5 0.01 12 1 3 03 1 001065188360 I65186989 000I00106500 188.36 195.48 3.98 0.78 12 1 10 14 1 C01400001061 AUTA 1061 000000000000 0 0 1 0.78 9 3 2 05 1 FU7797000000 FU7797000000 000000000000 0 0 3.46 0.78 10 1 4 06 1 FU7798000000 FU7798000000 000000000000 0 0 3.45 0.78 11 1 4 07 1 FU7798001050 AUTAPRA 1075 000000000000 0 0 3.5 0.78 11 1 6 08 1 FU7799000000 AUTAPRA 1089 000000000000 0 0 3.5 0.78 10 1 4 09 1 FU7802000000 FU7802000000 000000000000 0 0 3.45 0.78 12 1 4 0

10 1 FU7802000980 FU7802001580 000000000000 0 0 2.3 0.1 10 1 8 011 1 FU7804001720 AUTAPRAB1002 000000000000 0 0 4.5 0.1 12 1 4 012 1 FU7806000000 AUTAPRA 5161 000000000000 0 0 3.3 0.1 15 4 0 013 1 FU7810000000 FU7810000000 000000000000 0 0 3.45 0.1 16 4 0 014 1 FU7810001230 AUTAPRA 1210 000000000000 0 0 3.8 0.1 12 1 4 015 1 FU7811000750 AUTAPRA 1132 000000000000 0 0 2.3 0.36 12 1 3 016 1 S00003000700 3188755 000S00100300 0.7 3.5 3.63 0.36 12 1 10 017 1 S00003004090 3191521 000000000000 0 0 2.3 0.52 12 1 10 018 1 S00006000350 6116720 000S00100600 0.35 3.4 3.86 0.52 12 1 6 119 1 S00006005950 6122211 000S00100600 5.95 8.15 3.97 0.52 12 1 6 120 1 S00006011940 6128312 000S00100600 11.94 15.97 4.13 0.52 12 1 6 121 1 S00006017010 6133589 000S00100600 17.01 21.33 4.17 0.36 12 1 10 122 1 S00006021330 S00006021330 000S00100600 21.33 21.65 3.15 0.39 12 1 10 023 1 S00006021650 500006034840 000S00100600 21.65 22.51 3.97 0.39 12 1 8 024 1 S00006022510 6138967 000S00100600 22.51 22.91 4.21 0.12 12 1 10 025 1 S00006024360 6140827 000S00100600 24.36 25.02 3.46 0.47 12 1 10 026 1 S00014000000 14126525 000S00101400 0 4.55 3.29 0.47 12 1 6 127 1 S00014006210 14132766 000S00101400 6.21 10.21 3.43 0.47 12 1 8 128 1 S00014015170 14141907 000S00101400 15.17 20.82 3.47 0.22 12 1 6 2

Exhibit G-1. Excerpt from SECNS01.OUT After Reading File Into Excel
HERS Technical Report v3.54

September 2002

G-9

Source:Derived from FHWA, “Price Trends for Federal-Aid Highway Construction,” quarterly.

G.6 Override Runs

In override runs, the HERS-ST user has the ability to override some (or all) of the decisions HERS

makes regarding the selection of improvements, the initial cost of these improvements, and their

effects on capacity. In particular, for any section, the user can specify:

• That a particular type of improvement is to be made in a particular FP;

• The initial cost of such an improvement;

• Its effect on capacity; or

• That improvements are to be made only in specified FPs.

Override runs make it possible to override HERS-ST decisions on the basis of specific knowledge

of the feasibility of particular improvements selected by HERS-ST or knowledge of unusual costs

(e.g., for replacing bridges) that would be incurred in implementing these projects. These runs

also make it possible to require that several related improvements (such as widening a given

highway) be scheduled for the same FP or in consecutive FPs. (Because HERS analyzes individual sections in isolation, it is not currently capable of recognizing the relationship between such

improvements.)

Override runs also make it possible for HERS-ST users to specify improvements not selected by

HERS. These improvements can be either HERS-type improvements (pavement, widening, or

alignment improvements) or other types of projects (such as intersection modification or grade

separation). In the latter case, the user must specify both the initial cost of the project and its

effect on capacity. For HERS-type improvements, the user has the choice of providing cost and/

or capacity specifications or allowing HERS to estimate these quantities.

Section G.6.1 describes how users can specify improvements that should or should not be made

and, optionally, specify the initial costs of these improvements and/or their effects on capacity.

Sections G.6.2 and G.6.3 describe some of the output describing the effects of such user-specified

improvements. Finally, Section G.6.4 provides details about how HERS-ST estimates the costs

and benefits of user-specified improvements as well as the incremental costs and incremental

benefits of substituting a more aggressive improvement for a user-specified improvement.

G.6.1 User-Specified Improvements

Table G-3. Price Index Values for Converting Improvement Costs to 2000 Dollars

Convert From Rural Urban

1995 123.8 118.5

1996 115.7 130.2

1997 113.7 111.0

1998 111.2 117.1

1999 105.7 108.9

2000 100.0 100.0

2001 102.4 96.8
Unique Features of HERS-ST

G-10

For a given section, user-specified improvements are described in an optional “State Improvements,” or “StateImp” file. The name of this file is entered on the File Specifications screen of the

HERS GUI Control Model or on Line 56 of PPSPEC.DAT. The HERS preprocessor reads this file

and writes a binary version that is passed to the main HERS program.5

Each record of the StateImp file describes one or more improvements for a single highway section in chronological order. This information can be entered using the State Improvements data

window of the HERS GUI, or it can be entered directly into the StateImp file using a commadelimited format. Each record of the file contains 6n+3 fields, where n is the number of improvements described. The contents of the first 10 fields of this file are shown in Table G-4.

The first field of each record specifies the number of improvements described. A maximum of 10

improvements can be described in any record.

The next two fields contain the county code and the Sample Identifier (from HPMS Field 47).

These fields are used to match the StateImps record with the corresponding HPMS record

describing the section in question.6

User-specified improvements are entered in chronological order in sets of six fields (Fields 4 - 9,

10 - 15, etc.).

For the first improvement, a particular type of improvement is specified for a particular FP by

setting the year (Field 4) to any year in that FP and identifying the improvement type in Field 5.

For HERS-type improvements, the improvement type is specified using the codes in Table G-2.7

Other types of improvements (such as intersection modification or grade separation) should be

assigned codes that are divisible by 20 when they are not combined with pavement, widening, or

alignment improvements. The combination of a non-HERS-type improvement with pavement,

widening, and/or alignment improvements should be assigned a code that is the sum of a code

5. The GUI handles the passing of the binary file automatically. If the GUI is not being used, the name of the file to be

created is entered on Line 60 of PPSPEC.DAT and name of the file to be read by the main HERS program is entered

on Line 19 of RUNSPEC.DAT.

Table G-4. Record Format of State Improvements File

Field Format

1. Number of improvements I

2. County Code I

3. Sample Identifier A

4. Year of First Improvement (four digits) I

5. Type of improvement I

6. Override Flag I

7. Cost of Improvement F

8. Lanes Added I

9. Increase in Capacity I

10. Year of Second Improvement I

Continue for up to 10 improvements

6. The match will be unique if all HPMS records are from a single state. If data from multiple states are used in a single run, there is a small probability that the same County/Sample-ID pair will be used to identify sections in more

than one state. In this case HERS-ST 2.0 will arbitrarily match the StateImps record to the first HPMS record that it

finds.

7. For unpaved sections, all improvements should entail pavement reconstruction. User-specified improvements

that do not entail pavement reconstruction are treated as entailing reconstruction and a warning message is

printed.
HERS Technical Report v3.54

September 2002

G-11

that is divisible by 20 and the appropriate code from Table G-2.8 Improvements that are not

HERS-type or are combinations of HERS-type and non-HERS-type are called special improvements

by HERS-ST.

If the first improvement involves adding lanes, the number of lanes to be added is specified in

Field 8. An entry in this field is required for improvement types that end in 4, 5, 8, or 9; and this

field only has an effect for improvement types that end in 4, 5, 8, or 9 (i.e., the lanes specified in

Field 8 are added only if an “add lanes” improvement is specified). On two-way roads,

HERS-ST 2.0 normally assumes that, after the addition of lanes, the number of travel lanes will

be even, and the current system does not have procedures for estimating capacity if the number

of travel lanes will be odd. Accordingly, if the resulting number of lanes will be odd, the

increase in capacity must be specified by the user in the last of the fields describing the improvement (Field 9 for the first improvement). Otherwise, a message is printed and the number of

added lanes is adjusted appropriately. (If an odd number of added lanes is specified, the number is increased by one; otherwise, the number of added lanes is reduced by one.) If lanes are to

be added but the lanes-added field is zero, HERS-ST adds either one lane (on one-way facilities)

or the minimum number of additional lanes that will produce an even number of lanes (on twoway facilities), and a message to this effect is printed.

The initial costs of a user-specified improvement may be provided (in thousands of dollars), and

the change in peak-hour capacity may be provided (in passenger-car equivalents per hour). For

the first user-specified improvement, Fields 7 and 9 are used. For rural two- and three-lane

roads, capacity changes should be specified as changes in two-way capacity; for all other roads

they should be specified as changes in peak-period, peak-direction capacity. For HERS-type

improvements, if these fields are blank or zero, the HERS-ST estimates of improvement costs

and/or new capacity will be used. For all special improvements, these fields must contain nonzero values.

The override flag (Field 6 for the first user-specified improvement) is used to indicate whether

HERS-ST has any leeway in modifying a user-specified improvement. For HERS-type improvements (Types < 20) and pure non-HERS-type improvements (Types divisible by 20), this flag

may be set to either zero or one. For improvements that are combinations of HERS-type and

non-HERS-type improvements (Type greater than 20 and not divisible by 20), this flag must be

set to one.

If the override flag is set to one, the project is selected just as described in the set of six fields. If it

is set to zero, these fields describe the minimum improvement that will be selected. In this case,

HERS-ST may identify a “more aggressive” improvement that warrants evaluation; i.e., an

improvement that incorporates more widening than requested and/or also improves the section’s alignment. If any more aggressive improvements are identified, the incremental benefits

and costs of these improvements are estimated and used for determining whether any of the

additional options should be implemented.

In addition to controlling whether HERS-ST can modify a user-specified improvement, the override flag controls the insertion by HERS-ST of improvements prior to the implementation of a

user-specified improvement. If the override flag for the next user-specified improvement is one,

HERS-ST does not consider any improvements until after the corresponding FP. On the other

8. For example, the user might use an improvement type of 20 (or 40) to represent construction of an overpass. The

construction of an overpass combined with resurfacing the entire section would then be represented by Type 21

(or 41).
Unique Features of HERS-ST

G-12

hand, if it is zero, HERS-ST considers the possibility that a pavement or widening improvement

may be warranted in an earlier FP and, if so, an appropriate improvement is selected for the earlier period. In this case, if the user-specified improvement is of Type 1, 2, or 6 (i.e., the kind of

improvement that can be analyzed by a Pavement Management System), the two improvements

are combined and assigned to the earlier FP (but only if the user-specified improvement would

otherwise be implemented prior to the end of the last FP to be analyzed during the run). When

two improvements are combined in this way, any subsequent user-specified improvements with

override flags of zero are advanced appropriately. If the user-specified improvement is not of

Type 1, 2, or 6, its timing is not adjusted, but HERS-ST prints a message to alert the user to the

possibility that the number of improvements selected for the section may be more than are warranted.

As implied in the preceding paragraph, the override flag can be used to prevent HERS-ST from

selecting improvements for a section in one or more FPs. For this purpose, a set of six user-specified improvement fields is used with an appropriate year in the year field, an improvement code

of zero, and an override flag of one. If these fields represent the first user-specified “improvement” to be implemented (i.e., if they are Fields 4 - 9), no improvements will be considered by

HERS-ST until after the FP corresponding to the coded year. If there are one or more earlier userspecified improvements coded, the period when no improvements are considered starts after the

last of the user-specified improvements. For example, if the first user-specified improvement is

requested for FP 1, the second set of improvement fields can be used in this way to specify that

no subsequent improvements be considered until FP 4 (by setting the year in the second set of

improvement fields to a year that falls in FP 3). Similarly, if the first set of improvement fields

contains an improvement code of zero, an override flag of one, and the same year (in FP 3) in the

year field, no improvement will be considered until FP 4.

In each FP, HERS-ST automatically selects all user-specified improvements for implementation

regardless of their benefit/cost ratios (BCR). If a funding constraint is in effect, the cost of these

improvements is subtracted from the budget for the FP before any consideration is given to

selecting other improvements or choosing to go beyond the user-specified minimum improvement for any section for which such an improvement is specified. If the cost of implementing all

user-specified improvements exceeds the funding constraint for the FP, a message is printed and

the funding constraint for the next FP is reduced accordingly. Similarly, if a performance goal is

in effect, the benefits of user-specified improvements are taken into account before considering

any improvements or improvement options that are not user specified.

G.6.2 Tabular Output

As described in Section 8.2, the effects of selected improvements are summarized, by improvement type, on several pages of optional tabular output. In HERS-ST, two lines have been added

to this output to provide information about special improvements (i.e., all improvements of

Type ≥ 20). The first of these lines, labeled “Special imprs.” provides summary statistics for all

such improvements. The second of these lines has the same label but is in a portion of the output

headed “With improved alignment only” this line provides summary statistics for any special

improvements that are coded as incorporating an alignment improvement.9

 A sample page of

9. Such improvements have types that are the sum of any alignment improvement type (Types 11 - 19) and any userdefined special-improvement type (which must be divisible by 20).
HERS Technical Report v3.54

September 2002

G-13

optional output (showing the initial cost of all selected improvements) is reproduced as Exhibit

G-2.

G.6.3 Evaluations of Individual Improvements

Descriptions and evaluations of all improvements selected for a particular FP are contained in

the section file (SECNSnn.OUT) produced for that FP. The contents of this file are described in

Section G.4. For any section, comparisons of the benefits and costs of alternative improvements

can be obtained by specifying each alternative in a separate override run and comparing the

resulting evaluations in the improvement files that are produced.

G.6.4 Benefits and Costs

This section provides details of how HERS-ST estimates the user benefits and improvement costs

of user-specified improvements and also the corresponding incremental benefits and incremental costs of replacing a user-specified improvement by a more aggressive improvement.

G.6.4.1 Improvement Costs

If the cost of any user-specified improvement is specified, HERS-ST uses that cost as the cost of

the improvement. Otherwise, if the improvement is a HERS-type improvement, the cost is estimated using the HERS procedure for estimating improvement costs (as described in Section 5.4).

If no cost is provided for a special improvement, HERS-ST prints a warning message and sets the

improvement cost to a default value.10

When evaluating the possibility of replacing a HERS-type user-specified improvement (e.g.,

resurfacing, as identified by a State’s Pavement Management System) by a more aggressive

improvement (e.g., resurface and add lanes), HERS estimates the incremental cost of replacing the

former improvement by the latter one. This incremental cost is estimated as the difference

between estimates of the costs of the two improvements that are both obtained using HERS’ procedure for estimating improvement costs (regardless of whether the user has provided an exogenous cost estimate for the user-specified improvement).

Consider the possibility of replacing a non-HERS-type user-specified improvement (Type divisible by 20) by a combination of that improvement and a HERS-type of improvement. The cost of

the combined improvement is estimated by using the HERS procedure for estimating improvement costs to estimate the cost of the HERS-type of improvement, and adding this cost to the cost

of the original user-specified improvement. Thus, the resulting estimate of the incremental cost

of adding the HERS-type improvement ignores any efficiencies obtained by implementing both

improvements simultaneously; and so there may be a tendency to overestimate the incremental

cost. If the first improvement applies only to an intersection or interchange and the second

applies to an entire section, this effect is likely to be fairly small11 and so may be ignored. How10. When the special improvement combines a non-HERS-type improvement with a HERS-type improvement, the

default cost is the cost of the HERS-type improvement. Otherwise, it is one dollar per section.

11. One potential efficiency is a reduction in the disruptive effects of highway construction. However, because the

costs of such disruption are not currently estimated by either HERS or HERS-ST, there is no need to adjust for the

reduction in disruption.
Unique Features of HERS-ST

G-14

ever, if both improvements apply to the entire section, the effect may be more significant. For

this reason, HERS-ST will tend to overestimate the incremental cost of adding a HERS-type

improvement to a user-specified improvement that affects an entire section. Also for this reason,

HERS-ST requires that the override flag be set to one for user-specified improvements that combine HERS-type and non-HERS-type improvements.

RUN NUMBER: Test 1 1000 sections; Economic Efficiency Run 

 OVERALL ANALYIS PERIOD

 TOTAL INITIAL COST OF SELECTED IMPROVEMENTS 

 (IN MILLIONS OF DOLLARS) 

 RURAL URBAN TOTAL

 Int. OPA MA Maj. C. TOTAL Int. OFE OPA MA Coll. TOTAL 

 All improvements: 

 Reconst w/ more 

 high cost lanes 0 0 0 0 0 0 0 0 0 0 0 0

 Reconst w/ more 

 avg. cost lanes 0 0 0 0 0 0 0 0 0 0 0 0

 Reconstruction 

 with wider lanes 0 0 0 90 90 0 0 82 0 0 82 173

 

 Reconstruction 0 9 0 0 9 0 0 0 0 0 0 9

 Maj. widening w/

 high cost lanes 0 0 0 13 13 0 483 2459 539 178 3660 3674

 Maj. widening w/

 avg. cost lanes 468 152 165 12 797 4879 29 666 62 141 5778 6576

 

 Minor widening 0 10 141 996 1148 0 0 178 688 828 1696 2844

 Resurfacing 

 + shoulder imp's 0 213 270 7 492 0 2 35 98 79 216 708

 

 Resurfacing 338 335 97 200 971 920 50 347 200 104 1624 2595

 

 Special imprs. 0 0 0 0 0 0 0 0 0 0 0 0

 Total 806 721 673 1320 3522 5799 566 3771 1589 1332 13059 16582

 Mandatory 0 0 0 0 0 0 0 0 0 0 0 0

 Nonmandatory 806 721 673 1320 3522 5799 566 3771 1589 1332 13059 16582

 With improved alignment only: 

 Reconst w/ more 

 high cost lanes 0 0 0 0 0 0 0 0 0 0 0 0

 Reconst w/ more 

 avg. cost lanes 0 0 0 0 0 0 0 0 0 0 0 0

 Reconstruction 

 with wider lanes 0 0 0 0 0 0 0 0 0 0 0 0

 

 Reconstruction 0 9 0 0 9 0 0 0 0 0 0 9

 Maj. widening w/

 high cost lanes 0 0 0 0 0 0 0 0 0 0 0 0

 Maj. widening w/

 avg. cost lanes 0 4 49 0 53 0 0 0 0 0 0 53

 

 Minor widening 0 0 76 463 539 0 0 0 0 0 0 539

 Resurfacing 

 + shoulder imp's 0 111 187 0 298 0 0 0 0 0 0 298

 

 Resurfacing 8 113 48 128 299 0 0 0 0 0 0 299

 

 Special imprs. 0 0 0 0 0 0 0 0 0 0 0 0

 Total 8 238 361 591 1200 0 0 0 0 0 0 1200

Exhibit G-2. Sample Output Page Showing Initial Costs of Selected 

Improvements
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G-15

G.6.4.2 User Benefits

HERS-ST estimates the user benefits of an improvement as the net reduction in user costs resulting from changes in the physical characteristics of the improved section (including increases in

the number of lanes) and from the resulting increases in capacity and average speed.

In the case of user-specified improvements, any increase in the number of lanes must be specified

by the user and any increase in capacity may be specified. The user benefits of a non-HERS-type

improvement (Type divisible by 20) are estimated entirely from these two increases. For such

improvements, if both fields are zero, estimated benefits will be zero. (However, if only the second field is zero, increased capacity will be estimated from the increase in the number of lanes.)

User-specified improvements that either are purely HERS-type (Type < 20) or are a combination

of HERS-type and non-HERS-type (Type not divisible by 20), may produce other changes in the

physical characteristics of the section. These are simulated by HERS-ST, and thus they provide

another potential source of information for estimating user benefits. For these sections, the estimates of user benefits reflect any non-capacity effects of these changes plus either the user-coded

change in capacity or, if the capacity change is not coded, the HERS-ST estimate of change in

capacity.

When evaluating the possibility of replacing a user-specified improvement by a more aggressive

improvement, HERS-ST estimates the incremental user benefits of the replacement by analyzing

the effects of the replacement on the physical characteristics of the section and the resulting

effects on user benefits. This process is straightforward when the user does not specify the

capacity effects of the user-specified improvement, but it requires some clarification for the case

in which the user does specify these effects. In the latter case, we distinguish several different

estimates of capacity:

a. Estimated capacity before implementation of the user-specified improvement;

b. Estimated capacity after implementation of this improvement – obtained by adding the 

user-coded capacity effect of the improvement to (a);

c. A separate estimate of capacity after implementation of the improvement that is produced 

by HERS-ST entirely from the physical characteristics of the section after improvement 

(ignoring the user-coded capacity effect); and

d. HERS-ST’s estimate of capacity after implementation of the more aggressive improvement (obtained entirely from the physical characteristics of the section without reference 

to the user-specified capacity effect of the original improvement).

The benefits of the replacement are then estimated by using (b) as estimated capacity without the

replacement, and (b) + (d) – (c) as estimated capacity with the replacement.12

12. A similar process is used to estimate the capacity effects of any improvement that is designated or considered for

implementation in subsequent FPs.


FHWA-IF-02-060