EPA-420-P-98-022
 

Calculation of Age Distributions in the Nonroad Model:
 

Growth and Scrappage
 

Report No. NR-007
 

February 19, 1998 

Nonroad Engine Emissions Modeling Team 

Assessment and Modeling Division 

US EPA, Office of Mobile Sources 

Introduction 

The NONROAD model calculates nonroad equipment populations by age (i.e., an age 

distribution) for given equipment types and scenario years. This calculation is necessary for the 

model to account for a number of factors which affect nonroad emissions over time, including 

emissions deterioration, new emissions standards, technology changes, changes in equipment 

sales and total equipment population, and scrappage programs. The NONROAD model 

calculates equipment age distributions for the base year (which in the beta version of the model is 

1996) based on estimated 1996 engine populations and the scrappage function. The model 

calculates age distributions for future years by stepping through each year between the base and 

future years; for each year, the model projects equipment populations, scrappage for each model 

year of equipment still in service, and equipment sales. 

The methods employed for these calculations, the manner in which these methods are 

encoded in the NONROAD model, and the default assumptions and inputs used by the 

NONROAD model are described in this report. The Methodology discussion is divided into 

seven sections. The first section describes the concept of base year populations and its use in 

NONROAD. The second section describes the model’s use of population growth rates to project 

equipment populations in future years. The third section describes the methods used by the 

model to calculate scrappage. The fourth section describes the method used by NONROAD to 

calculate the age distribution in the base year. The fifth section describes the method used by the 

model to calculate annual sales based on estimated scrappage and projected population growth in 

each year. The sixth section brings the methods presented in earlier sections together to describe 

how NONROAD computes the age distribution for all future years. The seventh section 

discusses the implications of and potential drawbacks to the methods used by the NONROAD 

model to calculate age distributions and its relationship to the methods used by the California Air 

Resources Board’s OFFROAD model. 

The Calculations discussion describes the manner in which the methods presented in the 

Methodology discussion are encoded in the NONROAD model. This discussion is divided into 

three sections. The first section describes the calculations used to calculate the growth rate for a 

given equipment population. The second section describes the algorithm used to determine the 

age distribution, equipment population, and equipment sales for the base year. The third section 

1
 
describes the algorithm used to determine the age distribution, equipment population, and 

equipment sales for future years. 

The Inputs discussion describes the information that must be provided to the NONROAD 

model to perform the calculations necessary to determine equipment populations, age 

distributions, and sales. This discussion includes separate sections on equipment populations, 

growth indicators, scrappage functions, and activity data. 

The report ends with a glossary that defines the key terms used in this report. Those 

terms are italicized the first time they appear in this report subsequent to this introduction. 

Methodology 

The NONROAD model calculates equipment populations, the age distribution of those 

populations, annual equipment sales, and equipment scrappage. These calculations are 

performed for the base year, the specified target year for the model run, and for all years 

between the base year and target year. The methods used by the model to perform these 

calculations are described below. In general, the model uses the population growth rate to 

project equipment populations from a base year (in which the equipment population is known) 

through the target year. The model determines equipment sales by adding equipment scrappage 

to the change in equipment population. The model calculates annual equipment sales using the 

following equation: 

Sales(X+1) = [Population(X+1) - Population(X)] + Scrappage(X+1) 

where 

Sales(X+1) = Equipment sales in year X+1
 

Population(X+1) = Equipment population at the end of year X+1
 

Population(X) = Equipment population at the end of year X
 

Scrappage(X+1) = Equipment scrapped during year X+1
 

The model uses a scrappage curve to determine the proportion of equipment of a given age that 

has been removed from service. This proportion can then be multiplied by the annual sales for 

the year in question to determine the accumulated scrappage for equipment of that age. 

Subtracting the accumulated scrappage from initial sales yields the population of equipment still 

in service. With this information, the age distribution of the population can be calculated by 

dividing the population at each age by the total population. The details of these calculations are 

discussed more fully below. 

Base Year Populations 

Estimates of the base year equipment populations are contained in the NONROAD 

model’s input files. The basis for these estimates is discussed at length in the Population 

2
 
Estimates Technical Report (NR-006). The beta version of the NONROAD model uses 1996 as 

its base year. 

Population Growth: Growth Rates and Projected Populations 

The NONROAD model projects equipment populations in future (post-base year) years 

by applying a growth rate to the base year equipment population. This growth rate is calculated 

by determining the compound annual growth rate (CAGR) in equipment population between 

1989 and 1996, as reported by PSR. This approach is discussed more fully in the Growth 

Technical Report (NR-008). The model assumes that the population growth rate remains 

constant during the years between the base and target years. EPA’s Nonroad Engine Emissions 

Modeling Team (NEEMT) has chosen this approach, instead of relying on economic indicator 

variables, for the reasons discussed in NR-008. Once the CAGR has been calculated, the model 

uses this growth rate to project the total equipment population in each future year up to and 

including the target year using the following equation: 

Total population in year X+1 = [1+(CAGR/100)] * [Total population in year X] 

Scrappage 

The NONROAD model uses a scrappage curve to determine the proportion of equipment 

that has been scrapped as a function of equipment age. The model uses the scrappage curve 

originally developed for the EPA NEVES project as its default scrappage curve for all equipment 

types; the curve is scaled to the average lifetime of the equipment such that half of the units sold 

in a given year will be scrapped by the time those units reach the average expected lifetime and 

all units will be scrapped at twice the average lifetime. The average lifetime (in years) is 

calculated as the average life (in hours at full load) divided by the activity level (hours/year) and 

the load factor. The default scrappage curve is shown in Figure 1 (the data plotted in Figure 1 

are also provided in Table 1, located on p. 16 of this document). In Figure 1, age has been 

transformed to a dimensionless quantity by dividing by the average lifetime for the type of 

equipment under consideration. Note that in Figure 1, the proportion of equipment that has been 

scrapped represents the accumulated scrappage since the equipment was placed in service. 

The default scrappage curve used in the NONROAD model is based on a normal 

distribution of accumulated scrappage versus age. Other distributions can be used; for example, 

EPA’s proposed standards for small spark-ignited engines uses a Weibull distribution to project 

fleet turnover. This distribution results in reduced scrappage in the first few years and increased 

scrappage in later years than is the case for a normal distribution. The NONROAD model allows 

a user-specified curve to be substituted for the default curve for any or all equipment types. A 

user-specified curve can vary the rate of scrappage with age (the shape of the curve) but must 

conform to the assumption that all units are scrapped within twice the average lifetime. 

3
 
Default Scrappage Curve 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 0.5 1 1.5 2 

Age / Average Lifetime 

Figure 1. The default scrappage curve relating percent of units removed from 

service to age. 

The scrappage rate is defined as the percentage of equipment of a given age removed 

from service in a given year. The scrappage rate can be derived from the scrappage curve by 

determining the slope of the scrappage curve at the age in question. Note that for the default 

scrappage curve, the scrappage rate changes as the equipment age changes: the scrappage rate is 

low when units are new, reaches a maximum when unit age is equal to the average lifetime, and 

then declines again for units that are older than the average lifetime. 

Age Distribution in the Base Year 

To determine the equipment population’s actual age distribution as of the base year, one 

would need to know past equipment sales and scrappage. However, estimates of past equipment 

sales suffer from missing or incomplete data, are of poor quality, or are based on estimation 

methods that are incompatible with the methods used to estimate the base year equipment 

populations used in the NONROAD model. Given these uncertainties, the NEEMT has elected 

to determine the age distribution as of the base year by assuming constant equipment sales over 

the (N) years preceding the base year, where N is two times the average lifetime for the 

equipment type (in other words, the model does not backcast the effects of growth). Under this 

assumption, the base year age distribution can be determined directly from the scrappage curve. 

4
 
The NEEMT recognizes that the assumption of constant sales for the years up to and 

including the base year may introduce inaccuracies in estimating the rate at which existing 

equipment is scrapped. For example, to the extent that annual equipment sales increased during 

the years preceding the base year, the model would overestimate the population of equipment 

produced between N and N/2 years prior to the base year and would underestimate the population 

of equipment produced between the base year and N/2 years prior to the base year. As a result, 

the model would tend to overestimate the rate of scrappage of existing engines for the first N/2 

years after the base year and then underestimate the rate of scrappage for the subsequent N/2 

years. Furthermore, overestimating scrappage rates during the first N/2 years would tend to result 

in overestimates of sales and the benefits of lower emission standards during those years. The 

NEEMT plans to minimize these problems by updating its base year population estimates 

periodically as new information becomes available, thereby helping to compensate for any 

discrepancies between modeled and actual scrappage. These updates would take the form of new 

default population input files. The NEEMT continues to investigate these issues and welcomes 

suggestions regarding alternative sources of information about the age distribution in the base 

year, scrappage rates, and other model inputs. 

Annual Sales for Future Years 

As the model steps through each year from the base year to the target year, it estimates the 

sales expected to take place during each year. As discussed above, annual sales are determined 

by adding the scrappage projected to occur during the year to the increase in equipment 

population projected for that year: 

Sales(X+1) = [Population(X+1) - Population(X)] + Scrappage(X+1) 

where 

Sales(X+1) = Equipment sales in year X+1
 

Population(X+1) = Equipment population at the end of year X+1
 

Population(X) = Equipment population at the end of year X
 

Scrappage(X+1) = Equipment scrapped during year X+1
 

The scrappage projected for equipment sold in the target year depends on the type of scenario 

being modeled. For end-of-year scenarios, the projected scrappage of newly-sold equipment is 

based on an average equipment age of 6 months. For mid-year scenarios, the projected scrappage 

of newly-sold equipment is based on an average equipment age of 3 months. 

For a mid-year scenario, the target year sales estimated using the equation presented 

above represent only one-half year of sales, including one-half year of equipment population 

growth and one-half year of scrappage replacement. To determine projected full-year sales 

during the target year, the NONROAD model multiplies the calculated sales by two. 

5
 
Age Distribution for Future Years 

To calculate age distributions for future years, the NONROAD model steps through each 

year between the base and target years, calculating the effects of growth and scrappage during 

each step. As the model steps through each year, it estimates the equipment population of each 

age expected to remain in service using the scrappage curve mentioned above. The age 

distribution is determined by dividing the equipment population of each age by the total 

equipment population. 

Discussion 

The methods used in the NONROAD model have considerable similarity to the methods 

used in the CARB OFFROAD model. Both models use the same default scrappage curve and 

similar methods for calculating an age distribution; both models also assume that equipment 

durability remains constant over time. At the present time, the NEEMT is aware of two major 

differences between the models. First, the CARB model is only capable of calculating year-end 

age distributions, whereas NONROAD can calculate either a year-end or mid-year distribution. 

Second, the CARB model appears to use a different method to adjust age distributions for 

growth. This method is not fully understood by the NEEMT at this time but will be described in 

a future technical report. 

Calculations 

Calculation of Equipment Population Growth Rate 

The NONROAD model uses an exponential growth model to project equipment sales 

over time, a model that is analogous to compound interest. The subroutine GRWFAC computes 

the Compound Annual Growth Rate (CAGR) from default or user-specified indicator data. 

CAGR is expressed as percent growth in total equipment population per year. It is calculated by 

fitting an exponential function to indicator data for 2 years that best match the time period of the 

base and scenario years. Thus, at least 2 years of data are required for every growth indicator 

used by the model. 

Calculation of the Age Distribution and Equipment Population for the Base Year 

and Prior Years 

The calculation of the age distribution of engines for the base year and any previous year 

is performed in the MODYR subroutine. The steps employed are: 

1.	 Calculate the hours accumulated in service for units of each model year using 

activity data for each year. NONROAD assumes that all engines of a given 

application, size, and engine type which are still in service operate for the same 

number of hours during any given time period. Note that the hours accumulated 

by units sold in the base year must be adjusted downward to reflect the units’ 

6
 
average age at the time of evaluation. For an end-of-year scenario, base year units 

were on average sold in June and therefore have accumulated only half a year’s 

activity. For a mid-year scenario, base year units have accumulated only a quarter 

of a year’s activity, on average. A mid-year scenario is defined as spring or 

summer season scenario, or a monthly scenario earlier than October. All other 

scenarios are defined as end-of-year scenarios. 

2.	 Calculate the average equipment lifetime (in years) as the number of years at 

which the accumulated hours of service equal the average equipment life (in 

hours), adjusted for the average load that the equipment’s engine experiences, 

using the following equation: 

Average Life (hrs) Average Lifetime (years) = Activity (hrs/yr) * Load Factor 

where the average life is expressed in terms of hours of operation at full load and 

the load factor is expressed in terms of the average fraction of available power 

that is used by the equipment during operation. 

3.	 Use the average equipment lifetime to transform the dimensionless scrappage 

curve (Figure 1) to an annualized scrappage curve. 

4.	 Use the annualized scrappage curve to estimate the in-service fraction for each 

model year, which is the fraction of units that were produced in each year from the 

base year back to twice the average equipment lifetime and which are still in 

service as of the base year. The NONROAD model calls this fraction modfrc; the 

fraction for a specific year M is called modfrc(M). Figure 2 shows an example for 

equipment with a ten-year life. 

5.	 Calculate the base year age distribution. Assume that the sales in each year were 

the same so that the population of units still in service during the base year for a 

given model year (M) is proportional to modfrc(M). The model year fraction is 

the proportion of in-service equipment of a specific model year M and is called 

modscp(M); as of the base year, it is given by: 

modscp(M) = modfrc(M) / I modfrc(L) 

where Imodfrc(L) is summed over the N years between the base year and (N-1) 

years prior to the base year (N = twice the average equipment lifetime). 

6.	 To calculate a given model year’s equipment population as of the base year, the 

model year fraction is multiplied by the application’s total base year equipment 

population. 

7
 
Note that step 5 calculates an age distribution based on the assumption that sales did not 

vary over the N years prior to and including the base year. This assumption is equivalent to 

assuming that total equipment populations did not vary over those years. The age distribution 

for later model years can be adjusted to account for changes in population, as discussed below. 

Figure 2. Fraction of equipment still in service versus equipment age,
 

assuming an average equipment lifetime of ten years.
 

Calculation of the Age Distribution and Equipment Population for Future Years 

The key difference between base year and future year age distributions, equipment 

population, and equipment sales is that future year calculations are adjusted to account for 

growth in equipment populations and sales. The adjustment of age distributions to account for 

population and sales growth is performed in the GRWCLC subroutine. The steps employed are: 

1.	 Calculate populations of each model year back to twice the average equipment 

lifetime prior to the base year by multiplying the base year population by the 

model year fractions as of the base year (i.e., by the base year age distribution). 

Save these populations for use in future calculations. 

8
 
2.	 Step from the base year out to the target year in one year increments and perform 

the following steps at each year until the target year is reached: 

A.	 Grow the total population by multiplying the previous year’s population by 

(1 + CAGR/100), where CAGR is the compound annual growth rate. 

B.	 For all model years prior to the current year, recalculate the model year 

populations. Conceptually, this calculation is performed by multiplying 

the sales for each model year by the fraction of equipment projected to 

remain in use in the current year based on the scrappage curve. For model 

years prior to or including the base year, the NONROAD model uses a 

computational shortcut to calculate populations: the model re-uses the set 

of base year populations by model year shifted by a year. This approach is 

mathematically equivalent to direct calculation of model year populations 

for these years because the model assumes that sales were constant for all 

years up to and including the base year. 

C.	 Sum the populations for all model years up to the current year minus one. 

Subtract this sum from the total population to get the current model year 

population. 

D.	 Calculate the number of engines scrapped during the current year by 

summing the scrappage for each model year. For model years prior to the 

current year, scrappage amounts to one full year of scrappage. For the 

current model year, scrappage equals 1/2 year’s worth of scrappage for an 

end-of-year scenario and 1/4 year’s worth of scrappage for a mid-year 

scenario. Scrappage for a given model year is calculated by subtracting 

the model year’s accumulated scrappage as of the year prior to the current 

year from the model year’s accumulated scrappage as of the current year. 

E.	 Calculate the the current model year sales and save this value to use in 

subsequent calculations. For end-of-year scenarios, sales for the current 

model year are calculated by adding the total scrappage calculated in step 

2D to the current model year population calculated in step 2C. For midyear scenarios, the sum of total scrappage and current model year 

population must be multiplied by two in order to place the current model 

year sales on a full-year basis. 

3. Step 2 gives populations by model year for the future year scenario. To convert to 

model year fractions, divide by the total population. Note that in GRWCLC, the 

base year population is used as the divisor to give model year fractions relative to 

the base year population (i.e., the fractions do not sum to one). 

9
 
An example calculation using this algorithm is shown in Figure 3. Figure 3 shows the 

age distribution in the base year for equipment with a life of ten years. Also shown are the age 

distributions incorporating 2 percent per annum growth in population for 5, 10 and 20 years after 

the base year. Since the model year fractions in Figure 3 are shown relative to the base year 

population, the divisor in each curve is the same and the curves are effectively a direct measure 

of population by model year, making it easier to compare curves. Note that after 5 years of 

growth, the populations for the first 5 years have risen above the base year curve, but for years 6-

20 the populations remain the same as for the base year. This makes clear the point that the 

growth algorithm does not perform any backcasting; thus, populations for model years prior to 

the base year are always assumed to be based on sales at the base year level. After 10 years of 

growth, effects have propagated into model years 1-10. After 20 years of growth, effects have 

propagated through the entire distribution. 

Age Distributions Adjusted for 2% Growth 

0.18 

0.16 

0.14 

0.12 

0.10 

0.08 

0.06 

0.04 

0.02 

0.00 

base year 

base + 5 yr 

base + 10 yr 

base + 20 yr 

0 5 10 15 20 

Age 

Figure 3. Model year fractions after adjustment for 2% annual growth 

beginning in the base year, shown for the base year, base + 5 years, and 

base + 10 years. Model year populations are expressed as fractions 

relative to the total equipment population in the base year. 

Growth may be negative. Equipment populations may decrease due to economic factors 

or because of changes in technology (e.g., shift from 2-cycle to 4-cycle engines). Figure 4 shows 

the effects of negative 2% per annum growth for the same example as used in Figure 3. Note that 

the 5, 10 and 20 year curves drop below the base year curve. 

10
 
If population data predict a strongly negative growth rate, the population could drop faster 

than the rate of attrition, resulting in a prediction of negative sales and therefore negative model 

year fractions. Figure 5 shows that such a situation occurs if negative 15% growth is assumed for 

the scenario used in Figures 3 and 4. The GRWCLC subroutine traps negative sales to zero 

which effectively limits the rate of population decrease to be no greater than the rate of attrition. 

Figure 4. Model year fractions after adjustment for negative 2% annual 

growth beginning in the base year, for the base year, base + 5 years, and 

base + 10 years. Populations are expressed in terms of fractions of the 

total equipment population in the base year. 

11
 
Figure 5. Model year fractions after adjustment for negative 15% annual 

growth beginning in the base year, for the base year, base + 5 years, and 

base + 10 years. Populations are expressed as fractions of the total 

equipment population in the base year. 

12
 
 

 

 

 

 

 

 

 

Inputs 

The calculation of age distributions requires the following data to be supplied to the 

NONROAD model: 

� Equipment Populations 

� Growth Indicators 

� Scrappage Curve 

� Activity Data 

These data are input to the model using data files. The format of the data files is 

described below, examples of data are given, and the location of the data is specified. 

Equipment Populations 

Equipment population data for each state are provided in the directory “data/pop.” If 

estimates are provided for more than one year, the NONROAD model will use the closest year 

which comes before the target year. 

The format of the data in the /POPULATION/ packet is as follows: 

1 - 5 FIPS code
 

7 - 11 Subregion code (used for subcounty estimates)
 

13 - 16 Year of population estimates
 

18 - 27 SCC code (no globals accepted)
 

29 - 68 Equipment description (ignored)
 

70 - 74 Minimum HP range
 

76 - 80 Maximum HP range (ranges must match those internal to model)
 

82 - 86 Expected average life (in hours of use)
 

87 - 96 Flag for scrappage distribution curve (DEFAULT = standard curve)
 

100 - 116 Population estimate
 

An example of data from a /POPULATION/ packet is given below (note that lines are 

wrapped to fit the page). 

02000 1990 2260001010 2-Stroke Motorcycles: Off-Road 

16 25 750 DEFAULT 7
 

02000 1990 2260001010 2-Stroke Motorcycles: Off-Road 

25 40 1500 DEFAULT 525
 

02000 1990 2260001010 2-Stroke Motorcycles: Off-Road 

40 50 1500 DEFAULT 131
 

02000 1990 2260001010 2-Stroke Motorcycles: Off-Road 

50 100 3000 DEFAULT 482
 

13
 
 

Growth Indicators 

The default data are based on national growth estimates for the various source category 

groups. Data are located in the “data/growth” directory in a single file that contains both data 

packets: 

/INDICATORS/ Cross reference between SCC code and growth indicator code. 

/GROWTH/ Numerical values for different growth indicator codes. 

An indicator code is an alphanumerical code used to identify an actual growth indicator, 

such as population or employment growth. The growth indicator codes used in the 

/INDICATORS/ packet must match one of the codes provided in the /GROWTH/ packet. Cross 

referencing between the /INDICATORS/ and /GROWTH/ packets is based on FIPS code, SCC 

code, horsepower (HP) range, and technology type. The model uses the best match to the codes 

provided, falling back on global values if a unique match is not found. 

The format of the data in the /INDICATORS/ packet is as follows: 

1- 5 FIPS code (00000 = applies to entire nation) 

(ss000 = applies to all of state ss) 

7-10 Indicator code (arbitrary alphanumeric code) 

12-21 SCC code (2260004000 = applies to all 2-stroke lawn and garden) 

(2600000000 = applies to all 2-stroke) 

23-27 Beginning of HP range 

28-32 Ending of HP range 

34-43 Technology type (ALL = applies to all tech types) 

An example data record from the /INDICATORS/ packet is given below. 

00000 001 2260001000 0 9999 ALL 2-Stroke Recreational Vehicles
 

The format of the data in the /GROWTH/ packet is as follows: 

1- 5 FIPS code (00000 = applies to entire nation) 

(ss000 = applies to all of state ss) 

6-10 Subregion code (blank = applies to all subregions) 

11-15 Year of estimate (4-digit year) 

17-20 Indicator code (arbitrary alphanumeric code) 

26-45 Indicator value 

14
 
 

 

 

 

An example data record from the /GROWTH/ packet is given below. 

02000 1992 001 15.8
 

02000 2000 001 20.4
 

02000 2005 001 22.7
 

02000 2010 001 24.7
 

Scrappage Curve 

A single default scrappage curve is used by the NONROAD model. The scrappage curve 

is read in from the same data file as the growth data in the “data/growth” directory. 

15
 
Table 1. Default Scrappage Curve. 

Age/ 

Average 

Life 

Percent 

Scrapped 

Age/ 

Average 

Life 

Percent 

Scrapped 

0 0 1.05 69 

0.06 1 1.1 75 

0.12 2 1.15 76 

0.17 3 1.2 79 

0.22 4 1.25 81 

0.24 4.5 1.3 82 

0.26 5 1.35 85 

0.3 6 1.4 86 

0.4 8 1.45 87 

0.45 10 1.5 89 

0.5 11 1.55 90 

0.55 13 1.6 92 

0.6 14 1.7 94 

0.65 15 1.72 95 

0.7 18 1.74 95.5 

0.75 19 1.78 96 

0.8 21 1.83 97 

0.85 24 1.88 98 

0.9 25 1.94 99 

0.95 31 2 100 

1 50 

Activity 

The /ACTIVITY/ packet defines how often a piece of equipment is used in a year. The 

file also contains some other information about the equipment, such as average load factor and 

tank volume. 

The format of the /ACTIVITY/ packet is as follows: 

1-10 SCC code 

12-51 Equipment description (not used) 

16
 
 

52-56 Region code 

57-66 Technology type 

67-71 Minimum HP 

72-76 Maximum HP 

77-81 Load factor 

82-86 Tank volume (gallons) 

87-96 Activity level units 

97-106 Activity level 

An example data record from the /ACTIVITY/ packet is (note that lines are wrapped to fit 

on page): 

2260001010 2-Stroke Motorcycles: Off-Road 

ALL 0 9999 76 0.5 Hrs/Yr 120 0.0
 

For more information on equipment populations and equipment activity, load factors and average 

life, see EPA’s technical reports on these subjects, NR-006 and NR-005. 

17
 
Glossary of Terms 

Term Definition 

Accumulated scrappage The total amount of scrappage that has occurred for 

equipment of a given model year since its introduction into 

service 

Activity level The number of hours per year that the equipment in 

question operates 

Age distribution The function that describes the proportion of in-service 

equipment by age; consists of the full set of model year 

fractions for a given year 

Annual equipment sales Total sales during a given calendar year 

Annualized scrappage curve The result of scaling the scrappage curve by the average 

lifetime of the equipment in question 

Average life The average number of hours that a given type of 

equipment operates at full load 

Average lifetime The age (in years) at which half of the equipment will have 

been removed from service; one-half the age at which all of 

the equipment will have been scrapped 

Base year The year for which the population of equipment in service 

is known 

Compound Annual Growth Rate 

 (CAGR) 

The rate at which the population is projected to grow each

year in order to reach a specified level 

Current year The year for which the model is currently calculating 

quantities such as population, sales, scrappage, and 

emissions 

End-of-year Refers to model runs for which the target date is October 1 

or later 

18
 
Term 

Glossary of Terms 

Definition 

In-service fraction The fraction of the engines originally sold in a given year 

which are still in service; the inverse of accumulated 

scrappage 

Load factor The average power level at which the engine operates 

divided by the maximum available power 

Mid-year Refers to model runs for which the target date is September 

30 or earlier 

Model year Refers to the year in which equipment was produced. 

Equipment of the same model year was produced in the 

same year. To clarify the relationship between age and 

model year, consider the following example: 1990-model 

year equipment is (on average) six years old in 1996 and 

ten years old in 2000.

 Model year fraction The fraction of the total equipment population represented 

by a given model year at a given point in time 

Population growth rate The rate at which the equipment population increases each 

year 

Scrappage curve A graphical representation of the scrappage function 

Scrappage function The relationship between equipment age (expressed in 

terms of the fraction of average lifetime) and the proportion 

of equipment that has been removed from service, i.e., 

scrapped 

Scrappage rate The percentage of equipment of a given age removed from 

service in a given year 

Target year The year for which the NONROAD model’s user wishes to 

estimate emissions and other quantities 

19
 
Glossary of Terms 

Term Definition 

Total equipment population The total number of pieces of equipment in service at a 

given point in time; the sum of the populations of each 

model year still in service 

20