# Preliminary Vehicle Mass Estimation Using Empirical Subsystem Influence Coefficients www.a-sp.org

## Report on 

# Preliminary Vehicle Mass Estimation Using Empirical Subsystem Influence Coefficients by Donald E Malen, Adjunct Assistant Professor Kundan Reddy, Masters Candidate InterProfessional Programs

University of Michigan Ann Arbor, MI

Prepared for The FGPC-Mass Compounding Project Team Auto/Steel Partnership 2000 Town Center, Suite 320 Southfield, Michigan May 9, 2007 (Revised June 26, 2007)

# Acknowledgments The authors deeply appreciate the guidance and support provided by the FGPC-Mass Compounding project team: J. R. Shaw, US Steel Corp. (Chairman); H. Ezzat , T. M. Lee, C. C. Leung, J. Polewarczyk, General Motors Corp., V. C. Shah, DaimlerChrysler Corp.; R. Sohmshetty , S. Das, Ford Motor Co.; C. Potter, A.I.S.I.; and R. A. Heimbuch, P. J Villano, Auto/Steel Partnership. Special appreciation is due to the diligent efforts of C. Leung and V. Shah in providing vehicle mass data and their patience in the several iterations of consolidating the data. The authors also appreciate the data provided by L. Pecar of the GM Benchmarking Activity.

# Executive Summary Vehicle design engineers intuitively know that an unplanned mass increase in a component during vehicle design has a ripple effect th roughout the vehicle; other components need to be resized increasing vehicle mass even more. The phrase mass begets mass describes this phenomenon. A more encouraging view of this behavior is considering a reduction in the mass of a component enabled by a new technology resulting in a greater mass saving for the overall vehicle. These secondary mass changes can be considerable—estimated at an additional 0.7 to 1.8 times the initial mass change. This mass compounding behavior may be modeled using subsystem mass influence coefficients—the incremental change in subsystem mass for a unit change in gross vehicle mass. Published data on influence coefficients is sparse, and that published are based on vehicles in the 1975–1981 model years. The purpose of this study is to update influe nce coefficients using contemporary vehicles. In this study, mass data from 35 vehicles have been analyzed to determine mass influence coefficients. The vehicles in the study covered Sedans, SUVs, Pick Ups, and Vans (See Appendix C for the specific models used). Linear regression was used to determine the influence coefficients. The primary results of this study are summarized in the illustration below. The secondary mass change is that additional change due to resizing components when a vehicle mass change occurs during design (the primary change). This secondary change depend s on the vehicle mass influence coefficient—the sum of coefficients for the subsystems. Indicated are resu lts of previous studies from 1975 and 1981, along with results of this study for All vehicles, the SUV group, and the Sedan group. (The Pick Up and Van categories had an insufficient number of vehicles to be represented alone.) When all subsystems can be resized, the secondary mass savings is from 0.8 to 1.5 kg/kg (1.25kg/kg is the estimate for the All vehicles group). When the powertrain has been fixed and is not available for resizing, the secondary mass savings is from 0.4 to 0.5 kg/kg (0.5kg/kg is the estimate for the All vehicles group).

Section 8 provides an in depth example application of this data. 1981 1975 

## 0.0 0.5 1.0 1.5 2.0 2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Vehicle Mass Influence Secondary Mass Savings as Fraction of

Original Change
SUV Sedan All

V



## γ V 

# Γ

All subsystems free to resize All subsystems less powertrain

# Table of Contents 1. Acknowledgements 2 2. Executive Summary 3 3. Preliminary Mass Estimation in Vehicle Design 5 4. Mass Compounding Model 5 5. Previous work on Mass Influence Coefficients 6 6. Description of this study 7 7. Summary of Results 8 8. Example Applications 9 9. Bibliography 14 Appendices Technical Appendix A Derivation of mass model with influence coefficients 15 Technical Appendix B Estimation of subsystem influence coefficients 18 Data Appendix C Vehicles used in analysis 22 Functional Subsystem Mass Categories 23

• Gross Vehicle Mass vs. Plan View Area • Curb Mass vs. Plan View Area • System Mass as a percentage of Curb Mass • Summary of Influence Coefficients • Subsystem Mass vs. Gross Vehicle Mass-Linear • Subsystem Mass vs. Gross Vehicle Mass-Log repeated for 1) All Vehicles 24 2) Sedans 29 3) SUVs 34 4) Pick Ups 39 Tabular Summary of Subsyste m Influence Coefficients 44 Selection of Influence Coefficients for Inclusion in Model 45

## 3. Preliminary Mass Estimation in Vehicle Design Vehicle mass is an important parameter during desi gn. Subsystems are sized based on vehicle mass, and important product characteristics such as acceleration performance and fuel economy depend on vehicle mass. Given this importance of mass in vehicle design, mass estimation becomes a critical activity. The purpose of mass estimation varies with the design stage. During the product planning stage, or pre-configuration stage , the purpose of mass estimation is to determine general feasibility of a program and to set initial mass goals for vehicle subsystems. At this stage, only a broad vehicle mission is identified; for example vehicl e type and number of passengers. Because of this sparse data, mass estimation is of ten based on first order statistical models based on contemporary vehicles. In the next stage of design, the configuration stage, the purpose of mass estima tion is to aid in decision making about which alternative technologies to include in the program, and also to add additional precision to subsystem mass goals. In this stage, mass estimation is based on both semi-empirical models and statistical data. During the detail design stage, post-configuration stage, the goal of mass estimation is monitor mass growth and to control to target. As the vehicle config uration is set, mass estimation is based on actual subsystem designs and prototypes. In this paper, we focus on the pre-configuration and configuration stages. These are particularly significant as lasting decisions are made about which technologies and subsystem will be used. The implications of these decisions shadow all subsequent work. 4. Mass Compounding Model Vehicle design engineers intuitively know that an unplanned mass increase in a component during vehicle design has a ripple effect th roughout the vehicle; other components need to be resized increasing vehicle mass even more. The phrase mass begets mass describes this phenomenon. A more encouraging view of this behavior is considering a reduction in the mass of a component enabled by a new technology resulting in a greater mass saving for the overall vehicle. These secondary mass changes can be considerable—estimated at an additional 0.7 to 1.8 times the initial—primary--mass change. A means to quantify the secondary mass change is with a mass compounding model . In this model, each subsystem (denoted by i) is assigned an influence coefficient , γ i 

## . The influence coefficient is the change in the subsystem mass when gross vehicl e mass undergoes a unit change. The physical interpretation of the influence coefficient is each subsystem is sized to some degree by the mass of the vehicle, and as the vehicle mass changes the subsystem must also be resized. The typical question we are interested in answering is; Given a balanced vehicle under design, a primary mass change now occurs during design. What is the final vehi cle mass after resizing subsystems? The answer depends on the vehicle mass influence coefficient, γ VEH 

## . This the sum of coefficients for all subsystems which may undergo resizing. The resulting vehicle mass is given by Equation 4.1 (see Appendix A for a derivation).V V 

# W W ∆Γ + ∆ + = ∞ 0 

## Equation 4.1 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− = Γ ) 1 ( V V V 

# γ γ Secondary Mass Coefficient for Vehicle Equation 4.2 where 0 

# W is the initial vehicle mass for which the subsystems are sized ∆ is the initial mass change ( primary mass change)

∞ V 

# W is the resized, compounded vehicle mass V 

# ∆Γ is the additional (secondary) mass change γ V 

## is the mass influence coefficient for the vehicle given by 

# ∑

= 

## = n i i V 1 

## γ γ γ I 

## is the mass influence coefficient for subsystem i The resulting mass for subsystem i due to an initial increase of ∆ ;
i i i 

# w w ∆Γ + = ∞ 

## Equation 4.3 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− = Γ ) 1 ( v i i 

# γ γ Secondary Mass Coefficient for Subsystem i Equation 4.4 where i 

# w is the initial subsystem mass

∞ i 

# w is the resized subsystem mass i 

# ∆Γ is the additional secondary change γ V 

## , γ i 

## and ∆ are given above 5. Previous work on Mass Influence Coefficients Published data on influence coefficients is sparse, an d those published are based on vehicles in the 1975– 1981 model years [1, 2, 3]. Figure 5.1 summarizes the subsystem mass influence coefficients for two of these studies. Both studies used linear regression of measured subsystem mass data as described in the next section.

0 0.05 0.1 0.15 0.2 0.25 0.3

B

o d

y S t r u c t u r e F

r o n t S

u s p e n s i o n R

e a r S

u s p e n s i o n B r a k i n g S

y s t e m P o w

e r t r a i n S t e e r i n g T i r e s & W

h

e e l s E l e c t r i c a l B u m

p e r s 

### 1975-13 vehicles, G M H, X, A, B, C platform s 1981-18 vehicles, range of m anufactures, com pact front wheel drive 

## γ veh 

## =.420 γ veh 

## =.644 0 0.05 0.1 0.15 0.2 0.25 0.3

B

o d

y S t r u c t u r e F

r o n t S

u s p e n s i o n R

e a r S

u s p e n s i o n B r a k i n g S

y s t e m P o w

e r t r a i n S t e e r i n g T i r e s & W

h

e e l s E l e c t r i c a l B u m

p e r s 

### 1975-13 vehicles, G M H, X, A, B, C platform s 1981-18 vehicles, range of m anufactures, com pact front wheel drive 

## γ veh 

## =.420 γ veh 

## =.644 Summary of Previous Mass Influence Coefficients Figure 5.1

## Based on these influence coefficients, the secondary ve hicle mass savings using Equation 4.2 is 1.81 for the 1975 study, and 0.72 for the 1981 study. Note that resizing the body structure and powertrain contribute the most to this secondary mass savings. 6. Description of this study In this study, we identify subsyste m influence coefficients using regressi on. A function is fit relating the mass of subsystem i to gross vehicle mass, Figure 6.1. Th e influence coefficient is th e slope of the fit curve. Data from 32 vehicles were used for the fit. The 32 vehicles were further divided into Sedan, SUV, and Pick up groups. Appendix B desc ribes the model and the method used for estimation. Appendix C shows the scatter plots for each subsystem for each vehicle group.

Influence Coefficient By Linear Regression Figure 6.1 Figure 6.2 shows a comparison of influence coeffici ents by subsystem. Shown are the results for each vehicle group for both a linear func tion and also a power function, Equa tion B.3. A more complete table of results is contained in Appendix C-Tabular Summary of Subsystem Influence Coefficients.

All Vehicles (Linear) All Vehicles (Power @ 3000kg) Sedan (Linear) Sedan (Power @ 3000kg) SUV (Linear) SUV (Power @ 3000kg) N

o n

- s t r u c t u r e
B

o d

y S

t r u c t u r e
F

r o n t S

u s p e n s i o n
R

e a r S

u s p e n s i o n B r a k i n g P

o w e r T

r a i n
F

u e l &

E

x h

a u s t S t e e r i n g
T i r e s &

W

h

e e l s E l e c t r i c a l C o o l i n g

B

u m

p e r s C

l o s u r e s 

### 1975 Study 1981 Study 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Pick Up (Linear) Pick Up (Power @ 3000kg) All Vehicles (Linear) All Vehicles (Power @ 3000kg) Sedan (Linear) Sedan (Power @ 3000kg) SUV (Linear) SUV (Power @ 3000kg) N

o n

- s t r u c t u r e
B

o d

y S

t r u c t u r e
F

r o n t S

u s p e n s i o n
R

e a r S

u s p e n s i o n B r a k i n g P

o w e r T

r a i n
F

u e l &

E

x h

a u s t S t e e r i n g
T i r e s &

W

h

e e l s E l e c t r i c a l C o o l i n g

B

u m

p e r s C

l o s u r e s N

o n

- s t r u c t u r e
B

o d

y S

t r u c t u r e
F

r o n t S

u s p e n s i o n
R

e a r S

u s p e n s i o n B r a k i n g P

o w e r T

r a i n
F

u e l &

E

x h

a u s t S t e e r i n g
T i r e s &

W

h

e e l s E l e c t r i c a l C o o l i n g

B

u m

p e r s C

l o s u r e s 

### 1975 Study 1981 Study 0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Pick Up (Linear) Pick Up (Power @ 3000kg) 

## Subsystem Mass Influence Coefficients Determined in this Study Figure 6.2 Gross Vehicle Mass, W V 

## Subsystem Mass

W

i 

# γ

## An alternative means to estimate the mass influence coefficient is by the Ratio Method [7]. In this method, only the single reference vehicle data is needed. Th e subsystem mass-to-gross vehicle mass relationship is assumed as shown in Figure 6.3. In this case, the influence coefficient is given by Equation 5.1.

Influence Coefficient By Ratio Figure 6.3 Ratio method for influences coefficient determination,

v i i 

# W w = γ Equation 6.1 where i 

# w current subsystem mass W V 

## original gross vehicle mass 7. Summary of Results The results of this study are summarized in Table 7.1 and graphically in Figure 7.1. All Sedan SUV Ratio (sedan) Vehicle Influence Coefficient All subsystems free to resize .562 .599 .463 .532 Vehicle Influence Coefficient All subsystems free to resize Except Powertrain .332 .331 .290 .391 Secondary Mass savings All subsystems free to resize 1.28 Times primary

mass change 1.49 times 0.86 times 1.14 times Secondary Mass Savings All subsystems free to resize Except Powertrain 0.50 times 0.49 times 0.41 times 0.64 times Secondary Mass Savings Table 7.1 Indicated on Figure 7.1 are results of previous studie s from 1975 and 1981, along with results of this study for All vehicles, the SUV group, and the Sedan group. (The Pick Up and Van categories had an insufficient number of vehicles to be represented alone.) When all subsystems can be resized, the secondary mass savings is from 0.8 to 1.5 kg/kg (1.25kg/kg is the estimate for the All vehicles group). When the powertrain is not available for resizing, the secondary mass savings is from 0.4 to 0.5 kg/kg (0.5kg/kg is the estimate for the All vehicles group). Gross Vehicle Mass W V 

# γ = w i 

# / W V 

## Subsystem Mass w

i

## Secondary Mass Savings Figure 7.1 8. Example Application A new vehicle is in the planning stage ( pre-configuration ). It is targeted at 5 passengers with a 120kg cargo capacity. The target test weight class for fuel economy evaluation is 2250Lb (1950Lb or 886kg curb mass). Mass reduction is a primary goal and several techno logies are under investigation for application. The objectives of mass analysis at this stage are to 1) determine an initial mass estimate fo r the vehicle based on conventional design 2) determine the most effective mass reduction technologies to apply 3) estimate the vehicle mass when these technologies are used 4) set subsystem mass goals for the detail design stage which are consistent with 1) , 2), & 3). Step 1: Pre Configuration Mass Estimation From human accommodation and dimensional benchmarki ng, the vehicle length is estimated at 4.732 m and width at 1.815m. From this sparse data, the vehicle curb mass can be estimated given the plan view area (relationship in Appendix C, Sedan section). 

# 1498.55kg mass curb 8.58858m ) 732 . 4 )( 815 . 1 ( 59 . 229 ) ( 75 . 147 (kg) mass curb 2 2



# = = = + = m m A m A Adding passenger mass and cargo mass, the gross ve hicle mass is found. Finally, based on the Subsystem Mass fraction of Curb Mass (Appendix C in the Sedan Section) the mass of each subsystem may be estimated. For example, (Body Non-structure mass) = 0.204 (Curb Mass) (Body Non-structure mass) = 305.70 kg These steps are automated in the spreadsheet provided with this project, Figure 8.1. 1981 1975 

## 0.0 0.5 1.0 1.5 2.0 2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Vehicle Mass Influence Secondary Mass Savings as Fraction of

Original Change
SUV Sedan All 

## 0.9 Pick Up
V 

# γ V 

# Γ

All subsystems free to resize All subsystems less powertrain

## Pre-Configuration Vehicle Mass Estimation Figure 8.1 The above mass estimate is for a nominal vehicle as de fined by the data set used in this paper given the footprint. This estimate is greater than the desired 886kg curb mass by 633kg. Step 2: Identify Mass Reduction Technologies With the nominal vehicle identified, potential mass reduction technologies may be identified for each subsystem. For consistent evaluation of technologies, these steps are suggested; 2a) The initial mass for each subsystem is given by th e nominal vehicle of Step 1 (those identified in Figure 8.1 in this example). Example: Front Suspension subsystem mass=73.43kg 2b) Now for a vehicle of the gross vehicle mass iden tified in Step 1 (1968.55kg) determine the new subsystem mass enabled by a particular technology. Example technology: Shape optimization arms Front Suspension mass with technology=66.09kg >>Note that this new front suspension is sized for the gross mass of the vehicle identified in Step 1. This is required for the later mass compounding analysis.<< 2c) The mass savings is the di fference between 2a) and 2b). Example mass savings=73.43-66.09=7.34kg

## These steps are summarized for several hypothetical technologies in Table 8.1 Columns 1, 2, 3. subsystem mass reduction tech nology mass savings cost cost/unit mass (mc) kg $ $/kg Tires & Wheels Minimum capacity wheels and tires 20.00 -20 -1.000 non structure reduced sound treatment with 19.45 -5 -0.257 Braking optimized pedal bracket 3.00 0 0.000 rear suspension shape optimization 6.59 0 0.000 body structure joint improvements 15.00 0 0.000 closures hardware: optimization for bar 10.00 0.1 0.010 front suspension shape optimization 7.34 0.2 0.027 body structure AHSS optimization 70.00 3 0.043 non structure reduce glass thickness 5.00 0.3 0.060 non structure IP substrate optimization 21.43 2 0.093 Braking tubular pedals 4.00 0.4 0.100 non structure seat frame shape optimization 40.00 5 0.125 closures AHSS optimization 12.46 2 0.161 Fuel and Exhaust lower gage of exhaust 5.99 1 0.167 bumper shape optimization 4.95 1 0.202 steering tubular rack 2.00 0.5 0.250 powertrain reduce wall thickness 27.72 7 0.253 non structure carpet material 15.00 5 0.333 non structure new seat system technology 5.00 5 1.000 Fuel and Exhaust New muffler technology 10.00 50 5.000 body structure carbon fiber underbody 60.00 500 8.333 Potential Mass Reduction Technologies (Hypothetical Examples) Table 8.1 It is important to note again that the mass reduction in Column 3 must be based on the vehicle mass identified in Step 1 to meet the assu mptions of the mass compounding model. Step 3: Sort Mass Reduction Technologies by Cost This marginal cost of mass, mc , (cost per unit mass reduction) may be used to sort which technologies to include in the new vehicle program. 3a) Identify the cost difference to pr ovide this technology in this specific vehicle. (Note, this may be a cost reduction and a negative value) Example technology: Shape optimization arms Front Suspension cost increase with technology=$0.20 3b) Identify the marginal cost to provide the technology. Example: marginal cost=mc=($0.20)/(7.34kg reduction)=0.027$/kg 3c) From all identified mass reduction technologies, sort by increasing marginal cost Example: Table 8.1 is sorted for 21 potential technologies 3d) Filter technologies using marginal cost for inclusion in the vehicle configuration Example: Include all technologies with mc 

## ≤ 0.4 $/kg The 18 technologies at the top of Table 8.1 are carried forward.

## 3e) For those technologies passing the filter, su m the total mass reduction for each subsystem. Example; Subsystem Mass reduction using technologies passing mc filter Non Structure 19.45+5+21.43+40+15=100.88kg Body Structure 15+70=85kg Front Suspension 7.34kg Rear Suspension 6.59kg Braking 3+4=7.00kg Powertrain 27.72kg Fuel and exhaust 5.99kg Steering 2.00kg Tire & Wheels 20kg Bumper 4.95kg Closures 10.0+12.46=22.46kg These technologies provide a primary mass reduction total of 289.93kg. Step 4: Estimate Vehicle Mass Using Mass Compounding The mass savings opportunities found in Step 3, are primary mass reductions. They are sized for the vehicle mass found in Step 1; 1500kg curb mass. Now as each technology is applied to the vehicle, the curb mass is reduced. Due to this reduction, the subsystems may be re sized. This resizing results in a secondary mass savings given by Equation 4.2, Primary mass savings 

# ∆ = 289.93kg Secondary mass savings = 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− ∆ ) 1 ( V V 

# γ γ , where the vehicle influence coefficient, 

# γ V



## , may be based on the results of this study shown in Figure 7.1. Taking a nominal value for the vehicle influence coefficient; 

# γ V 

## = 0.532 gives 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− ) 1 ( V V 

# γ γ = 1.1368 or a secondary mass savings=329.61kg. Thus the total mass reduction when the mass reduction technologies are applied is the compounded vehicle mass which is the sum of the primary reduction (289.93kg) and the secondary reduction (329.61kg) due to the subsystems being resized for the new reduced vehicle mass; 289.93kg + 329.61kg=619.54kg. To see how this compounded reduction is distributed across the subsystems, Equation 4.3 and 4.4 may be used. These steps are automated in the spreadsheet provided with this project, Figure 8.2. The spreadsheet of Figure 8.2 applies the mass influence coefficients found in this work to arrive at the compounded masses. The user may select from the All Vehicles , Sedan , SUV groups, use the Ratio method, Equation 6.1, or input a User Defined set of coefficients. Selection of which to use is based on the subject vehicle type and the predicted gross vehicle mass. The predicted mass should be within the range of data used to estimate the influence coefficients. Interp olation limits for the infl uence coefficients are; All Vehicles group 1600<GVM<3150kg Sedan group 1600<GVM<2225kg SUV group 1920<GVM<3150kg If a prediction beyond these ranges is necessary, the Ratio method is recommended.

## Compounded Mass Estimation (including powertrain resizing) Figure 8.2 Step 5: Adjust Subsystem Mass to arrive at Design Targets In Steps 1-4, we have used a rational procedure to estimate a vehicle's mass based on current practice, and then to estimate the influence of mass reduction technologies using a mass compounding model. It is important during this stage to investigate altern ative configurations. For example, below is the compounding model as in Figure 8.2 except the powe rtrain has not been allowed to resize, Figure 8.2.

Compounded Mass Estimation (powertrain not resized) Figure 8.2 These mass estimation tools are intended to be highly iterative allowing rapid sensitivity studies to arrive at robust design targets for vehicle and subsystem mass.

# Bibliography Past Influence Coefficient Studies 1. Internal GM communication, Report of the Cost of Weight Task Force , January, 1975 2. Internal GM communication, Weight Influence Coefficients , November, 1981. 3. Anderson, M., Engine and Transmission Mass as a Fraction of Vehicle Mass , Integrated Vehicle System Design Course Notes , University of Michigan, January, 2007. Independent Mass Data Sources 4. www.autobytel.com, Autobytel, 18872 MacArthu r Boulevard, Irvine, California 92612-1400. 5. www.cars.com, Classified Ventures, LLC, 175 W. Jackson Blvd., Suite 800, Chicago, IL 60604. 6. www.internetautoguide.com, Internet Auto Guide. Methodology for Mass Analysis 7. Society of Allied Weight Engineers, Aircraft Weight Engineering , 1996 8. Tornbeek, E., Synthesis of Subsonic Airplane Design , Delft University Press, Boston, 1988 9. de Weck, O. L., A Systems Approach To Mass Budget Management , Paper AIAA 2006-7055, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference , September 2006 . 10. Spacecraft Preliminary Mass Estimation & Allocation , Technical University of Delft, http://www.lr.tudelft.nl/ live/pagina.jsp?id=10d 9b8b2-e85b-4 8e7-94f2- 462356f1d730&lang=en 11. Piano Software For Preliminary Design Of Commercial Aircraft Including Mass Estimation , http://www.lissys.demon.co.uk/ Statistical Methods 12. Box, G., and Draper, N., Empirical Model-Building and Response Surfaces , Wiley & Sons, NY, 1987 13. Mendenhall, W., et al, Mathematical Statistics with Applications , Duxbury Press, Boston, 1986. 14. Neter, J., et al., Applied Linear Statistical Models , IRWIN Publishing, Boston, 1990

# Technical Appendix A Derivation of mass model and influence coefficients Vehicle mass is the sum of the masses for n subsystems,

n i V 

# w w w w W + + + + + = ... ... 2 1 

## Equation A.1 Where W V 

## is the vehicle mass w i 

## is the mass of subsystem i For convenience, we include as subsystems the passengers, and cargo, so W V 

## represents the maximum vehicle mass (gross vehicle mass). The mass of each subsystem depend s upon the mass of the vehicle an d other functional parameters. 

# ) , ( parameters functional W f w V

i 

# = Equation A.2 Note that some subsystems will have a strong vehi cle mass dependence—for example, the powertrain subsystem—while for others the dependence on vehicle mass will be weak—for example, interior ventilation. Mass Influences Coefficients Imagine subsystem i is designed to function within a vehicle mass of W V 

## with the resulting subsystem mass of w i 

## . Now imagine a second vehicle which is slightly heavier at mass W V 

## +dW V 

## . Subsystem i is now sized for this slightly larger mass with the resulting subsystem mass of w i 

## +dw i 

## . We define the subsystem mass influence, γ i 

## , as the change in subsystem mass required when the vehicle mass is increased by one unit;

V i i 

# W w ∂ ∂ = γ Equation A.3 Consider a vehicle design with initial mass W 0 

## and all subsystems sized for this mass. Now during preliminary design, an unexpected small mass increase of δ occurs in a subsystem. All subsystems must now be resized for this mass increase. The resulting change in vehicle mass is d W which we would like to determine. This can be quantified using su bsystem mass influence coefficients;



# ) ... ... ( ) ... ... ( ... ...

2 1 2

1 2 1

n i n

i V n V i V V 

# dW dW W w W w W w W w dW
γ γ γ γ δ γ γ γ γ δ δ δ δ δ

+ + + + + = + + + + + = ∂ ∂ + + ∂ ∂ + + ∂ ∂ + ∂ ∂ = Equations A.4
The vehicle mass influence coefficient, γ V 

## , is defined as the change in mass of the vehicle, dW, due to a resizing of all the subsystems for a unit increase in mass. 

# δ γ dW

V 

# = Equation A.5

## Comparing the last of Equations A.4 with A.5, we see that the vehicle mass influence coefficient, γ V 

## , is the sum of the influence coefficients for all subsystems. 

# ∑

= 

# = n i i V 1 

# γ γ Equation A.6 Mass Change during the Configuration Design Stage Now consider a balanced vehicle design with initial mass W 0 

## . It is now learned that the mass of a subsystem has changed by an amount ∆ for a new vehicle mass of W 0 

## + ∆ . Since the subsystems were sized for vehicle mass W 0 

## , they must be redesigned to function with the additional mass ∆ : Resizing 1

V V 

# W W γ γ ∆ + ∆ + = ∆ ∆ ) ( mass vehicle new : mass additional causes change mass to due subsystems resize : change mass

0 1 

## But now the subsystems are sized for vehicle mass (W 0 

## + ∆ ), and they must be resized for the additional mass ∆γ V 

## : Resizing 2

2 0 2 2 

# ) ( : mass additional causes change mass to due subsystems resize : change mass

V V V V 

# W W γ γ γ γ ∆ + ∆ + ∆ + = ∆ ∆
In a similar way, the subsystems are sized for vehicle mass (W 0 

## + ∆+∆γ V 

## ), and they must be resized for the additional mass ∆γ V 2 

## : Resizing 3

3 2 0 3 3 2 

# ) ( : mass additional causes change mass to due subsystems resize : change mass

V V V V V 

# W W γ γ γ γ γ ∆ + ∆ + ∆ + ∆ + = ∆ ∆
This resizing continues until we have: Resizing m



# ∞ → + + + + + + ∆ + ∆ + = ∞ → ∆ + + ∆ + + ∆ + ∆ + ∆ + ∆ + =
m

W W m W W

m V j V V V V m m V j V V V V m 

# ), ... ... ( , ... ...
3 2 0 3 2 0 

# γ γ γ γ γ γ γ γ γ γ Equations A.7 Recognizing the sum in the parentheses is a geometric series we have;

# 1 0 when , ) 1 ( ) 1 ( ) 1 ( ), ... ... 1 ( ), ... ... (

V 3 2 3 2



# < <

− = =

− + = ∞ → + + + + + + + = ∞ → + + + + + + =

γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ

V V V V V m V j V V V V V m V j V V V V



# S S S S m S m S Equations A.8

Substituting the last of Equations A.8 into A.7 gives the mass of the vehicle after all resizing; 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− ∆ + ∆ + = ∞ → 

# ) 1 ( 0 V V m 

# W W 

# γ γ Equations A.9 Where ∆ is the original mass change 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− ∆ ) 1 ( V V 

# γ γ is the secondary mass change due to resizing subsystems. We define the Secondary mass coefficient for the vehicle, Γ V 

## ; 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− = Γ ) 1 ( V V V 

# γ γ Equation A.10 and for each subsystem, Γ i 

## , as; 

# ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− = Γ ) 1 ( v i i 

# γ γ Equation A.11 So the final vehicle mass due to an unexpected mass increase of ∆ is
V V 

# W W ∆ Γ + ∆ + = ∞ 0 

## Equation A.12 and the final mass for subsystem i is; i i i 

# w w ∆ Γ + = ∞ 

## Equation A.13 To prove that the sum of subsystem influence coefficien ts is the vehicle influence coefficient, begin with Equation A.12;

n i V V n V i V V V V n i V n i m n i n i m n n i i m n i V V m



# W W w w w w W w w w w W w w w w W W W

γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ
+ + + + + = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− + +

− + +

− +

− ∆ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− ∆ Γ + + Γ + + Γ + Γ ∆ = ∆Γ Γ + + Γ + + Γ + Γ ∆ + + ∆ = Γ + + Γ + + Γ + Γ ∆ + + + + + + + ∆ = ∆Γ + + ∆Γ + + + ∆Γ + + ∆Γ + + ∆ = + + + + + = ∆Γ + ∆ + =

∞ → ∞ → ∞ → ∞ →



# ... ... ) 1 ( ... ) 1 ( ... ) 1 ( ) 1 ( ) 1 ( ) ... ... ( ) ... ... ( ) ... ... ( ) ... ... ( ) ...( ) ( ... ) ( ) ( ... ...

2 1 2 1 2 1 2 1 0 2 1 2 1 2 2 1 1 2 1 0


## Equation A.14

# Technical Appendix B Modeling Subsystem Mass We assume that the mass of each subsystem depends on the gross vehicle mass and on other functional parameters [8]; 

# ) ... ( ) , (

r b a r b a V i i V i 

# P P P W C w parameters functional W f w β β β α 

# = = Equation B.1 Where w i 

## is a subsystem mass W V 

## is the gross vehicle mass P a,b,..r 

## are functional parameters some of which are performance measures For example, consider the powertrain subsystem mass, w i 

## . Its mass depends on the overall vehicle mass, α V i 

# W C
. The mass also depends on vehicle acceleration performance; a a 

# P β 

## , where Pa is the required 0- 60mph acceleration time. It also depends on the powertrain layout; TFWD, LRWD, AWD; P b 

## . Here P b 

## is an indicator variable: P b 

## =+1 for TFWD, P b 

## =0 for LWD, P b 

## =-1 for AWD. This relationship may be visualized graphically;

Subsystem Mass Relationship Figure B.1 With the model defined by Equation B.1, the subsystem influence coefficient is given by;

V W V i i 

# W w ∂ ∂ = γ Equation B.2 Estimation of subsystem influence coefficients To estimate the relationship between subsystem mass and vehicle mass, we fit observed data with both a linear and power model. In both cases, the fit was made using linear regression. 

# linear ˆ power ˆ 1 0 V i V i i 

# W w W C w 

# β β α 

# + = = Equations B.3 Log Subsystem Wei g ht

Log Gross Vehicle Wei g ht Log Functional Parameter

Surface defined by Equation B.1

## In this study, we have not accounted for the subsys tem mass dependence on functional parameters and have only considered the dependence on gross vehicle mass. Thus we are looking at a projection of the true relationship onto an x-y plane, Figure B.2.

Projection of data on to x-y plane for curve fitting Figure B.2 This necessity, has the practical effect of increasing the apparent lack of fit (measured by smaller R 2 

## values). Figure B.3 illustrates this by showing a ty pical residual error—the difference between a data point and the fit function. In our case, this residual is comprised of both pure error—randomness, along with the ignored dependence on functional parameters. Despite this assumption, the data fit is deemed to be satisfactory even though the R 2 

## values are somewhat low due to this effect.

Components of Residual Error Figure B.3 For all fit equations, the R 2 

## values are reported. Below is a brief summary of the meaning of this coefficient [12, 14]. The variation of the un-fit data is measured by the sum of the squared deviations from the average value, Figure B.4. This sum is the total sum of squares, SSTO. Subsystem mass w

i



## GVM W V 

## residual 

# r Variation in subsystem Performanc 

## e Pure Error ε actual data

prediction Pure Error, ε , due to 

# • Misclassification of parts 

# • Incorrect vehicle model used 

# • Clerical: recording 

# • Weighing parts Log Subsystem mass w

i



### Log Gross Vehicle Mass W

V 

### Log Functional Performance Surface defined by

Projection of data when functional performance not accounted for 1 

## ) ) ( β α 

## p erformance (f

unctiona l CW w V

i 

## =

## Total Sum of Squares Figure B.4 Now a function is fit to the data as illustrated in Figure B.5. The remaining variation in the data is measured by the sum of the squared deviations from the function . This sum is the error sum of squares, SSE.

Error Sum of Squares Figure B.5 The R 2 

## coefficient of determination is the fraction of variation explained beyond that using the average value only, and is given by; 

# SSTO SSE SSTO R 

# ) ( 2 

# −

= Equation B.4 Thus any non-zero R 2 

## indicates a reduction in variation provided by the fit function. Again in our case, the residual error, r i 

## , contained in the SSE contains both pure error as well as the variation due to functional performance differences between the various ve hicles as shown in Figure B.3. While R 2 

## measures the overall goodness of fit of the model, we are interested in the in fluence coefficient. For a linear model, the influence coefficient is the slope of the fit line, β 1 

## . We can place a confidence interval around this parameter using Equation B.5 [13]; 

# [ ] ∑ ∑

= 

## − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛

− = + =

n i n n



## x x y y n Var Var N x y y y y y x x x x data

, 1 2 2 1 1 1 1 1 0 3 2 1 3 2 1


## ) ( )

ˆ ( 2 1 ) ( ) ( , ~ ˆ ; ,... , , ; ,... , , :
β β β β β β Equations B.5 For example, looking at the All Vehicles group and the Body Structure subsystem, we have an influence coefficient β 1 

## =0.1758 and R 2 

## =0.4542. Applying Equations B.5,

Subsystem mass w

i 

## GVM W

V 

## ρ

i 2 

# ∑ = i 

# SSTO ρ

Sum of squares; total ρ i 

## is residual from mean

Subsystem mass w

i 

## GVM W

V 2 

# ∑ = i 

# r SSE Sum of squares; error r i 

## is residual from model r i

## 001198 . ) ( 33 1758 . 0 5294 . 1 ˆ ˆ

1 1 0



## = = +

− = + = β β

β
Var n x y x y Equation B.6 The 90% confidence interval is shown in Figure B.6.

Confidence Interval for an Influence Coefficient Figure B.6 

## 90% confidence interval for influence coefficient 0.0 0.1 0.2 0.3 Body Structure Mass Influence

# Data Appendix C Vehicles used in analysis Mass data were collected for 35 ve hicles representing Sedans, SUVs, Pickups and Vans. For each vehicle, the mass of each functional subsystem (see next page for subsystem defini tions) was calculated. Considerable effort was placed on consistency of the component masses contained in each subsystem across all vehicle sources. In addition to the subsystem mass, Gross Vehicle Mass , Curb Mass , and Number of Passengers were identified for each vehicle using independent sources [4, 5, 6]. The vehicles in this study are shown below. Due to th e propriety nature of subs ystem mass data, specific numerical values are not provided. Sedans: 15 (of which there is 1 duplicate) SUV: 12 Pick Up: 5 Note: Due to the small sample size, Pick Up results are less reliable than for Sedans and SUVs. Van: 3 (of which there is 1 duplicate) Note: Due to the insufficient sample size, vans were not included as a vehicle group. 35 (33 vehicles used in study) Note: For the 'All Vehicles' group, all non- duplicate vehicles were included 2004 VW Touareg (SUV) 2004 Mazda 3 (Sedan) 2004 Nissan Murado (SUV) 2004 Toyota Sienna (Van) (Dup.) 2004 Hundai XG350 (Sedan) 2004 Toyota Prius (Sedan) 2003 Lexus ES300 (Sedan) 2003 Toyota Camry (US) (Sedan) 2003 BMW 330i (Sedan) 2003 Infiniti G35 (Sedan) 2003 Honda Accord (Sedan)(Dup.) 2003 Toyota Corolla Sedan (Sedan) 2002 Audi A4 (Sedan) 2007 Model Year Cadillac SRX (SUV) Chevrolet HHR (SUV) Saturn Outlook (SUV) GMC Denali Sierra Crew Cab (Pick Up) Chevrolet Colorado (Pick Up) Chevrolet Impala (Sedan) Pontiac G6 SE1 (Sedan) Cadillac STS (Sedan) GMC Yukon (SUV) Saturn Vue (SUV) 2002 Honda Civic LX (Sedan) 2003 Honda Accord EX (Sedan) 2003 PT Cruiser (SUV) 2003 Toyota Matrix XRS (SUV) 2003 Toyota Tacoma 4x2 (Pick Up) 2004 Dodge Ram 4x4 Light Duty (Pick Up) 2004 Nissan Titan LE (Pick Up) 2004 Toyota Highlander Premium (SUV) 2004 Toyota Sienna (Van) 2005 Honda Odyssey Touring (Van) 2005 Jeep Liberty (SUV) 2005 Jeep Wrangler (SUV)

## Functional Subsystem Mass Categories Each category below contains the set of components which provide a specific vehicle function. The assumption is that the mass required to provide that function varies in part with the gross vehicle mass. 1. Body Non-structural Sheet Metal Glass Seats Insulation Trim Heating and Ventilation Exterior Lighting Wiper 2. Body Structure Body Shell (Body-in-White less closures) Frame (if present) Engine Cradle (if present) 3. Front Suspension Spring Control Arms Knuckle Stabilizer Bar 4. Rear Suspension 5. Braking Disc/Drum Caliper Hydraulic cylinder 6a. Engine Engine Engine Cooling Starting System 6b. Transmission Transmission Note: Engine and Transmission subsystems were combined to Drive Shafts form the Powertrain Subsystem used in the final analysis. 7. Fuel System and Exhaust 8. Steering Rack Column Tie rods Power assist 9. Tires & Wheels 10. Electrical Entertainment, navigation Lighting Wiring 11. Cooling Air Conditioning components 12. Bumpers Note: Closures include hardware and door trim, with the 13. Body Closures exception of the GM Benchmark data where it is the door shell only. These cases are noted on the graphs.

# ALL VEHICLES
GVM / PLAN VIEW AREA y = 202.34x + 371.22 R 2 = 0.6309 y = 326.15x 0.8647 R 2 = 0.6338

0 1000 2000 3000 4000

5 10 15 Plan View Area (m 2 )GVM (Kg) Sedan SUV Pick Up Linear Power CURB / PLAN VIEW AREA y = 169.07x + 143.61 R 2 = 0.5544 y = 213.66x 0.9299 R 2 = 0.5488

0 1000 2000 3000

5 10 15 Plan View Area (m 2 )Curb Mass (Kg) Sedan SUV Pick Up Linear Power

Cargo Mass (kg) GVM / Cargo Mass

0 1000 2000 3000 4000

1000 2000 3000 4000 Sum of Subsystem + Passenger MassReported GVM 500 250 125 0

Closures Bumpers Cooling Electrical Tires & Wheels Steering Fuel and Exhaust Power Train Transmission Engine Braking Rear Suspension Front Suspension Body Structure Body Non-structural Subsystem Mass as a Fraction of Curb Mass

All Vehicles

0.064 0.020 0.024 0.037 0.067 0.013 0.039 0.205 0.079 0.126 0.029 0.039 0.047 0.231 0.185

0 0.1 0.2 0.3

T ir e s & W h e e ls N o n s t r u c t u r a l
B o d y S t r u c t u r e
F r o n t S u s p e n s io n
R e a r S u s p e n s i o n B r a k in g E n g in e T r a n s m is s io n P o w e r T r a in
F u e l & E x h a u s t S t e e r in g

E l e c t r i c a l C o o l in g B u m p e r s C l o s u r e s

Body Non structural y = 0.1445x - 8.4657 R 2 = 0.3637

0 200 400 600 800

1000 2000 3000 4000 GVMBody Non structural Mass Body Non structural y = 0.1988x 0.9507 R 2 = 0.2974

100 1000

1000 10000 GVMBody Non structural Mass

# ALL VEHICLES Body structural y = 0.1758x - 1.5294 R 2 = 0.4542

0 200 400 600 800

1000 2000 3000 4000 GVMBody Structural Mass Body structural y = 0.325x 0.9176 R 2 = 0.4672

100 1000

1000 10000 GVMBody Structural Mass

Front Suspension y = 0.0454x - 21.537 R 2 = 0.4096

0 40 80 120 160

1000 2000 3000 4000 GVMFront Suspension Mass Front Suspension y = 0.0137x 1.1176 R 2 = 0.3067

10 100 1000

1000 10000 GVMFront Suspension Mass

Rear Suspension y = 0.0354x - 12.061 R 2 = 0.1912

0 50 100 150 200

1000 2000 3000 4000 GVMRear Suspension Mass Rear Suspension

10 100 1000

1000 10000 GVMRear Suspension Mass y = 0.0072x 1.172 R 2 = 0.2062

# ALL VEHICLES Braking System y = 0.0077x + 30.355 R 2 = 0.0311

0 20 40 60 80 100

1000 2000 3000 4000 GVMBraking System Mass Braking System y = 1.421x 0.4422 R 2 = 0.0269

10 100

1000 10000 GVMBraking System Mass

Powertrain y = 0.2302x - 162.07 R 2 = 0.6687

0 200 400 600 800

1000 2000 3000 4000 GVMPowertrain Mass Powertrain y = 0.004x 1.4741 R 2 = 0.7265

100 1000

1000 10000 GVMPowertrain Mass

Fuel & Exhaust System y = 0.0332x - 7.612 R 2 = 0.3357

0 40 80 120 160

1000 2000 3000 4000 GVMFuel & Exhaust System Mass Fuel & Exhaust System y = 0.0103x 1.1318 R 2 = 0.3723

10 100 1000

1000 10000 GVMFuel & Exhaust System Mass

# ALL VEHICLES Steering y = 0.0056x + 8.8642 R 2 = 0.1418

0 10 20 30 40

1000 2000 3000 4000 GVMSteering Mass Steering y = 0.1265x 0.6583 R 2 = 0.0961

10 100

1000 10000 GVMSteering Mass

Tires & Wheels y = 0.0488x + 4.2581 R 2 = 0.7106

0 50 100 150 200

1000 2000 3000 4000 GVMTires & Wheels Mass Tires & Wheels y = 0.058x 0.9818 R 2 = 0.7354

10 100 1000

1000 10000 GVMTires & Wheels Mass

Electrical y = 0.0143x + 30.235 R 2 = 0.0688

0 40 80 120 160

1000 2000 3000 4000 GVMElectrical Mass Electrical y = 0.7054x 0.5751 R 2 = 0.1142

10 100 1000

1000 10000 GVMElectrical Mass

# ALL VEHICLES Cooling y = 0.0206x - 5.7438 R 2 = 0.2651

0 25 50 75 100

1000 2000 3000 4000 GVMCooling Mass Cooling y = 0.0225x 0.9627 R 2 = 0.2013

10 100

1000 10000 GVMCooling Mass

Bumpers y = 0.0129x + 3.9693 R 2 = 0.2139

0 20 40 60 80

1000 2000 3000 4000 GVMBumpers Mass Bumpers y = 0.2118x 0.6462 R 2 = 0.0918

10 100

1000 10000 GVMBumpers Mass

Closures y = 0.0867x - 82.945 R 2 = 0.3037

Doors in white Doors with components

0 50 100 150 200 250

1000 2000 3000 4000 GVMClosures Mass Closures y = 8 x 10 -6 x 2.1099 R 2 = 0.2438

10 100 1000

1000 10000 GVMClosures Mass

# SEDAN
GVM / PLAN VIEW AREA y = 163.14x + 561.69 R 2 = 0.5502 y = 376.41x 0.7676 R 2 = 0.5545

0 500 1000 1500 2000 2500

2 4 6 8 10 12 Plan View Area (m 2 )GVM (kg) CURB MASS / PLAN VIEW AREA y = 147.75x + 229.59 R 2 = 0.5128 y = 206.11x 0.9212 R 2 = 0.5034

0 400 800 1200 1600 2000

2 4 6 8 10 12 Plan View Area (m 2 )Curb Mass (kg)

0.046 0.022 0.027 0.046 0.065 0.014 0.040 0.185 0.067 0.118 0.032 0.044 0.049 0.227 0.204

Closures Bumpers Cooling Electrical Tires & Wheels Steering Fuel and Exhaust Power Train Transmission Engine Braking Rear Suspension Front Suspension Body Structure Body Non-structural
Sedan

0 0.1 0.2 0.3 Subsystem Mass as a Fraction of Curb Mass

T ir e s & W h e e ls N o n s t r u c t u r a l
B o d y S t r u c t u r e
F r o n t S u s p e n s io n
R e a r S u s p e n s i o n B r a k in g E n g in e T r a n s m is s io n P o w e r T r a in
F u e l & E x h a u s t S t e e r in g

E le c t r i c a l C o o lin

g B u m p e r s C l o s u r e s Influence Coefficient Summary

Sedan (Linear) Sedan (Power @ 3000kg) 0.0 0.1 0.2 0.3 0.4 0.5 0.6

1975 Study 1981 Study Sedans

N o n - s t r u c t u r e
B o d y S t r u c t u r e
F r o n t S u s p e n s i o n
R e a r S u s p e n s i o n

B r a k i n g P o w e r T r a i n
F u e l & E x h a u s t S

t e e r i n g T i r e s & W h e e l s E l e c t r i c a l C o o l i n g

B u m p e r s C l o s u r e s

Body Non Structural y = 0.1419x + 26.297 R 2 = 0.2058

0 200 400 600

1000 2000 3000 GVMBody Non structuralMass Body Non Structural y = 0.1465x 1.0054 R 2 = 0.2263

100 1000

1000 10000 GVMBody Non structural Mass

# SEDAN Body Structural y = 0.1317x + 78.114 R 2 = 0.6626

0 100 200 300 400 500

1000 2000 3000 GVMBody Structural Mass Body Structural y = 0.8247x 0.7928 R 2 = 0.6934

100 1000

1000 10000 GVMBody Structural Mass

Front Suspension y = 0.0333x + 8.0864 R 2 = 0.1057

0 30 60 90 120

1000 2000 3000 GVMFront Suspension Mass Front Suspension y = 0.631x 0.622 R 2 = 0.0488

10 100 1000

1000 10000 GVMFront Suspension Mass

Rear Suspension y = 0.0894x - 108.43 R 2 = 0.337

0 40 80 120 160

1000 2000 3000 GVMRear Suspension Mass Rear Suspension y = 2 x 10 -7 x 2.5895 R 2 = 0.3659

10 100 1000

1000 10000 GVMRear Suspension Mass

# SEDAN Braking System y = 0.0177x + 12.206 R 2 = 0.0378

0 20 40 60 80

1000 2000 3000 GVMBraking System Mass Braking System y = 0.5579x 0.5719 R 2 = 0.0154

10 100

1000 10000 GVMBraking System Mass

Powertrain y = 0.2703x - 249.45 R 2 = 0.8126

0 100 200 300 400 500

1000 2000 3000 GVMPowertrain Mass Powertrain y = 0.0002x 1.8598 R 2 = 0.8586

100 1000

1000 10000 GVMPowertrain Mass

Fuel and Exhaust System y = 0.0272x + 6.3007 R 2 = 0.0835

0 30 60 90 120

1000 2000 3000 GVMFuel and Exhaust System Mass Fuel and Exhaust System y = 0.0197x 1.0525 R 2 = 0.1445

10 100 1000

1000 10000 GVMFuel and Exhaust System Mass

# SEDAN Steering y = -0.0023x + 25.304 R 2 = 0.0084

0 10 20 30

1000 2000 3000 GVMSteering Mass Steering y = 373.16x -0.3868 R 2 = 0.0179

10 100

1000 10000 GVMSteering Mass

Tires & Wheels y = 0.0395x + 18.528 R 2 = 0.4535

0 30 60 90 120 150

1000 2000 3000 GVMTires & Wheels Mass Tires & Wheels y = 0.1496x 0.8524 R 2 = 0.5074

10 100 1000

1000 10000 GVMTires & Wheels Mass

Electrical y = 0.0139x + 40.455 R 2 = 0.0115

0 40 80 120 160

1000 2000 3000 GVMElectrical Mass Electrical y = 0.0276x 1.0228 R 2 = 0.1023

10 100 1000

1000 10000 GVMElectrical Mass

# SEDAN Cooling y = 0.0446x - 46.748 R 2 = 0.5784

0 20 40 60 80

1000 2000 3000 GVMCooling Mass Cooling y = 3 x 10 -6 x 2.1611 R 2 = 0.5661

10 100

1000 10000 GVMCooling Mass

Bumpers y = 0.0174x - 0.9741 R 2 = 0.2799

0 10 20 30 40 50

1000 2000 3000 GVMBumpers Mass Bumpers y = 0.015x 1.0134 R 2 = 0.2845

10 100

1000 10000 GVMBumpers Mass

Closures y = 0.1028x - 131.1 R 2 = 0.1394

0 50 100 150 200

1000 2000 3000 GVMClosures Mass

Doors in white Doors with components Closures y = 5 x 10 -9 x 3.0387 R 2 = 0.1636

10 100 1000

1000 10000 GVMClosures Mass

# SUV GVM / PLAN VIEW AREA y = 205.28x + 489.31 R 2 = 0.5458 y = 402.26x 0.7981 R 2 = 0.544

0 1000 2000 3000 4000

3 6 9 12 15 Plan View Area (m 2 )GVM (kg) CURB MASS / PLAN VIEW AREA y = 150.16x + 417.36 R 2 = 0.3965 y = 324.28x 0.767 R 2 = 0.3978

0 1000 2000 3000

3 6 9 12 15 Plan View Area (m 2 )Curb Mass (kg)

SUV

0 0.1 0.2 0.3

Closures Bumpers Cooling Electrical Tires & Wheels Steering Fuel and Exhaust Power Train Transmission Engine Braking Rear Suspension Front Suspension Body Structure Body Non-structural

0.077 0.017 0.024 0.033 0.067 0.011 0.035 0.215 0.077 0.138 0.027 0.040 0.048 0.229 0.177 Subsystem Mass as a Fraction of Curb Mass

T ir e s & W h e e ls N o n s t r u c t u r a l
B o d y S t r u c t u r e
F r o n t S u s p e n s io n
R e a r S u s p e n s i o n B r a k in g E n g in e T r a n s m is s io n P o w e r T r a in
F u e l & E x h a u s t S t e e r in g

E le c t r i c a l C o o lin

g B u m p e r s C l o s u r e s Influence Coefficient Summary

SUV (Linear) SUV (Power @ 3000kg) 0.0 0.1 0.2 0.3 0.4 0.5 0.6

1975 Study 1981 Study SUV

N o n - s t r u c t u r e
B o d y S t r u c t u r e
F r o n t S u s p e n s i o n
R e a r S u s p e n s i o n

B r a k i n g P o w e r T r a i n
F u e l & E x h a u s t S

t e e r i n g T i r e s & W h e e l s E l e c t r i c a l C o o l i n g

B u m p e r s C l o s u r e s

Body Non Structural y = 0.2373x - 236.91 R 2 = 0.6766

0 200 400 600 800

1000 2000 3000 4000 GVMBody Non Structural Mass Body Non Structural y = 0.0008x 1.6506 R 2 = 0.7013

100 1000

1000 10000 GVMBody Non Structural Mass

# SUV Body Structural y = 0.0765x + 218.34 R 2 = 0.33

0 150 300 450 600

1000 2000 3000 4000 GVMBody Structural Mass Body Structural y = 12.215x 0.4485 R 2 = 0.3319

100 1000

1000 10000 GVMBody Structural Mass

Front Suspension y = 0.0787x - 96.804 R 2 = 0.8176

0 50 100 150 200

1000 2000 3000 4000 GVMFront Suspension Mass Front Suspension y = 7 x 10 -6 x 2.1045 R 2 = 0.7236

10 100 1000

1000 10000 GVMFront Suspension Mass

Rear Suspension y = 0.0645x - 78.811 R 2 = 0.4068

0 50 100 150 200

1000 2000 3000 4000 GVMRear Suspension Mass Rear Suspension y = 1 x 10 -5 x 1.9817 R 2 = 0.3817

10 100 1000

1000 10000 GVMRear Suspension Mass

# SUV Braking System y = 0.0036x + 38.73 R 2 = 0.0075

0 20 40 60 80

1000 2000 3000 4000 GVMBraking System Mass y = 2.2981x 0.3756 R 2 = 0.0188

10 100

1000 10000 GVMBraking System Mass Braking System

y = 0.173x - 22.151 R 2 = 0.4237

0 200 400 600 800

1000 2000 3000 4000 GVMPowertrain Mass Powertrain y = 0.0549x 1.1371 R 2 = 0.4822

100 1000

1000 10000 GVMPowertrain Mass Powertrain

Fuel and Exhaust System y = 0.0254x + 2.0453 R 2 = 0.3483

0 20 40 60 80 100

1000 2000 3000 4000 GVMFuel and Exhaust System Mass y = 0.0175x 1.0487 R 2 = 0.432

10 100

1000 10000 GVMFuel and Exhaust System Mass Fuel and Exhaust System

# SUV

y = 0.0085x + 0.0729 R 2 = 0.2486

0 10 20 30 40

1000 2000 3000 4000 GVMSteering Mass Steering y = 0.001x 1.2618 R 2 = 0.2185

10 100

1000 10000 GVMSteering Mass Steering

y = 0.0374x + 30.485 R 2 = 0.7306

0 40 80 120 160

1000 2000 3000 4000 GVMTires & Wheels Mass Tires & Wheels y = 0.3292x 0.7581 R 2 = 0.7207

10 100 1000

1000 10000 GVMTires & Wheels Mass Tires & Wheels

y = 0.0455x - 47.102 R 2 = 0.6354

0 40 80 120 160

1000 2000 3000 4000 GVMElectrical Mass Electrical y = 0.0004x 1.5455 R 2 = 0.7031

10 100 1000

1000 10000 GVMElectrical Mass Electrical

# SUV

y = 0.0401x - 50.975 R 2 = 0.7354

0 25 50 75 100

1000 2000 3000 4000 GVMCooling Mass Cooling y = 5 x 10 -6 x 2.0598 R 2 = 0.6324

10 100

1000 10000 GVMCooling Mass Cooling

y = 0.0193x - 15.349 R 2 = 0.3833

0 20 40 60 80

1000 2000 3000 4000 GVMBumpers Mass Bumpers y = 0.0018x 1.2394 R 2 = 0.2462

10 100

1000 10000 GVMBumpers Mass Bumpers

y = 0.0204x + 84.476 R 2 = 0.0246

0 50 100 150 200 250

1000 2000 3000 4000 GVMClosures Mass Closures

Doors in white Doors with components y = 453.49x -0.1772 R 2 = 0.0031

10 100 1000

1000 10000 GVMClosures Mass Closures

# Pick Up
y = 155.34x + 869.82 R 2 = 0.6882 y = 478.35x 0.702 R 2 = 0.7078

0 1000 2000 3000 4000

4 8 12 16 Plan View Area (m 2 )GVM (kg) GVM / PLAN VIEW AREA y = 194.79x - 218.79 y = 98.88x 1.2301 R 2 = 0.585 R 2 = 0.6458

0 1000 2000 3000

4 8 12 16 Plan View Area (m 2 )Curb Mass (kg) CURB MASS / PLAN VIEW AREA

0.072 0.023 0.019 0.027 0.075 0.012 0.046 0.247 0.122 0.124 0.021 0.031 0.047 0.223 0.156

Closures Bumpers Cooling Electrical Tires & Wheels Steering Fuel and Exhaust Power Train Transmission Engine Braking Rear Suspension Front Suspension Body Structure Body Non-structural Pick up

T ir e s & W h e e ls N o n s t r u c t u r a l
B o d y S t r u c t u r e
F r o n t S u s p e n s io n
R e a r S u s p e n s i o n B r a k in g E n g in e T r a n s m is s io n P o w e r T r a in
F u e l & E x h a u s t S t e e r in g

E le c t r i c a l C o o lin

g B u m p e r s C l o s u r e s 0 0.1 0.2 0.3 Subsystem Mass as a Fraction of Curb Mass Influence Coefficient Summary

Pick Up (Linear) Pick Up (Power @ 3000kg) 0.0 0.1 0.2 0.3 0.4 0.5 0.6

1975 Study 1981 Study Pick Ups

N o n - s t r u c t u r e
B o d y S t r u c t u r e
F r o n t S u s p e n s i o n
R e a r S u s p e n s i o n

B r a k i n g P o w e r T r a i n
F u e l & E x h a u s t S

t e e r i n g T i r e s & W h e e l s E l e c t r i c a l C o o l i n g

B u m p e r s C l o s u r e s

y = 0.2124x - 248.57 R 2 = 0.3014

0 150 300 450 600

1000 2000 3000 4000 GVMBody Non structural Mass Body Non Structural y = 4 x 10 -5 x 2.0202 R 2 = 0.3321

100 1000

1000 10000 GVMBody Non structural Mass Body Non Structural

# Pick Up

y = 0.4453x - 719 R 2 = 0.5678

0 200 400 600 800

1000 2000 3000 4000 GVMBody Structural Mass Body Structural y = 3 x 10 -7 x 2.6754 R 2 = 0.6374

100 1000

1000 10000 GVMBody Structural Mass Body Structural

Front Suspension y = 0.0354x - 1.6075 R 2 = 0.2669

0 30 60 90 120 150

1000 2000 3000 4000 GVMFront Suspension Mass y = 0.0315x 1.0098 R 2 = 0.2636

10 100 1000

1000 10000 GVMFront Suspension Mass Front Suspension

y = 0.0287x - 15.192 R 2 = 0.9861

0 20 40 60 80

1000 2000 3000 4000 GVMRear Suspension Mass Rear Suspension y = 0.003x 1.2584 R 2 = 0.9853

10 100

1000 10000 GVMRear Suspension Mass Rear Suspension

# Pick Up

y = 0.0339x - 46.856 R 2 = 0.3216

0 20 40 60 80

1000 2000 3000 4000 GVMBraking System Mass Braking System y = 6 x 10 -7 x 2.2871 R 2 = 0.3138

10 100

1000 10000 GVMBraking System Mass Braking System

y = 0.2953x - 289.5 R 2 = 0.7712

0 200 400 600 800

1000 2000 3000 4000 GVMPowertrain Mass Powertrain y = 0.0022x 1.5596 R 2 = 0.8142

100 1000

1000 10000 GVMPowertrain Mass Powertrain

y = 0.0621x - 71.059 R 2 = 0.5274

0 40 80 120 160

1000 2000 3000 4000 GVMFuel and Exhaust System Mass Fuel and Exhaust System y = 2 x 10 -5 x 1.9676 R 2 = 0.536

10 100 1000

1000 10000 GVMFuel and Exhaust System Mass Fuel and Exhaust System

# Pick Up

y = 0.0056x + 8.8616 R 2 = 0.1363

0 10 20 30 40

1000 2000 3000 4000 GVMSteering Mass Steering y = 0.0309x 0.8408 R 2 = 0.207

10 100

1000 10000 GVMSteering Mass Steering

y = 0.0356x + 52.678 R 2 = 0.2622

0 50 100 150 200

1000 2000 3000 4000 GVMTires & Wheels Mass Tires and Wheels y = 0.3396x 0.7689 R 2 = 0.3161

10 100 1000

1000 10000 GVMTires & Wheels Mass Tires and Wheels

y = 0.0189x + 3.8375 R 2 = 0.4488

0 20 40 60 80

1000 2000 3000 4000 GVMElectrical Mass Electrical y = 0.0376x 0.9209 R 2 = 0.4722

10 100

1000 10000 GVMElectrical Mass Electrical

# Pick Up

y = 0.0181x - 10.62 R 2 = 0.0829

0 25 50 75 100

1000 2000 3000 4000 GVMCooling Mass Cooling y = 0.0312x 0.8853 R 2 = 0.0662

10 100

1000 10000 GVMCooling Mass Cooling

y = 0.0198x - 7.7917 R 2 = 0.4043

0 20 40 60 80

1000 2000 3000 4000 GVMBumpers Mass Bumpers y = 0.0067x 1.1153 R 2 = 0.3722

10 100

1000 10000 GVMBumpers Mass Bumpers

y = 0.1276x - 190.53 R 2 = 0.701

0 50 100 150 200 250

1000 2000 3000 4000 GVMClosures Mass Closures y = 5 x 10 -7 x 2.4574 R 2 = 0.6981

10 100 1000

1000 10000 GVMClosures Mass ClosuresClosuresBumpersCoolingElectricalTires &WheelsSteeringFuel andExhaustPowertrainBrakingSystemRearSuspensionFrontSuspensionBodyStructureBody Nonstructuralc=5E-09
α=3.03870.0450.103c=8E-06
α=2.10990.1220.0690.087c=0.015 α=1.01340.0170.017c=0.2118 α=0.64620.0080.0100.013c=3E-06 α=2.16110.0320.045c=0.0225 α=0.96270.0160.0160.021c=0.0276 α=1.02280.0330.014c=0.7054 α=0.57510.0140.0170.014c=0.1496 α=0.85240.0430.040c=0.058 α=0.98180.0490.0500.049c=373.16
α=-0.3959-0.006(0)-0.002(0)c=0.1265 α=0.65830.0050.0060.006c=0.0197 α=1.05250.0300.027c=0.0103 α=1.13180.0330.0310.033c= 0.0002 α=1.85980.2000.270c= 0.004 α=1.47410.2620.2060.230c=0.5579 α=0.57190.0140.018c=1.421 α=0.44220.0070.0100.008c=2E-07 α=2.58950.0580.089c=0.0072 α=1.1720.0330.0310.035c=0.631 α=0.6220.0250.033c=0.0137 α=1.11760.0390.0370.045c=0.8247 α=0.79280.1440.132c=0.325 α=0.91760.1540.1610.176c=0.1465 α=1.00540.1530.142c=0.1988 α=0.95070.1270.1310.145PowerEquationY=C X αPower@ 1800kgLinearPowerEquationY=C XαPower@ 3000kgPower@ 1800kgLinearSedanAll Vehicles0.0060.0480.0060.0220.0360.0310.0110.1310.1830.0160.0380.0120.0130.0290.0210.1660.29419811975c=5E-07
α=2.45740.1440.128c=453.49
α=-0.1772-0.0060.020c=0.0067 α=1.11530.0190.020c=0.0018 α=1.23940.0150.019c=0.0312 α=0.88530.0110.018c=5E-06 α=2.05980.0500.040c=0.0376 α=0.92090.0180.019c=0.0004α=1.54550.0490.046c=0.3396 α=0.76890.0410.036c=0.3292 α=0.75810.0360.037c=0.0309 α=0.84080.0070.006c=0.001 α=1.26180.0100.009c=2E-05 α=1.96760.0910.062c=0.0175α=1.04870.0270.025c= 0.0022 α=1.55960.3030.295c= 0.0549 α=1.13710.1870.173c=6E-07 α=2.28710.0410.034c=2.2981 α=0.01880.0060.004c=0.003 α=1.25840.0300.029c=1E-05 α=1.98170.0510.065c=0.0315 α=1.00980.0340.035c=7E-06 α=2.10450.1020.079c=3E-07 α=2.67540.5370.445c=12.215 α=0.44850.0660.077c=4E-05 α=2.02020.2850.212c=0.0008 α=1.65060.2420.237LinearPower@ 3000kgLinearPick Up(Not signifcant as a group)SUVHistoricalPowerEquationY=C X αPowerEquationY=C X αPower@ 3000kgInfluence CoefficientsSum ofrecommendedcoefficients0.644 0.413 0.562 0.599 0.9000.463Recommended subsystem coefficientsshown in bold with border

## Selection of Influence Coefficients for Inclusion in Model

1.00 0.50-1.00 0.50 0.25 -0.50 0.25 00-0.25 No 0.09 Little 0.30 0.70 0.02 0.16 0.30 Closures Yes 0.01 Stron g 0.32 0.40 0.38 0.28 0.21 Bumpers No 0.02 Moderate 0.41 0.08 0.74 0.57 0.27 Cooling No 0.02 Little 0.35 0.47 0.70 0.10 0.11 Electrical Yes 0.04 Stron g 0.57 0.32 0.73 0.51 0.74 Tire & wheels ( Yes ) <0.01 Moderate 0.15 0.21 0.25 0.02 0.14 Steering No 0.03 Little 0.37 0.54 0.43 0.14 0.37 Fuel & exhaus t Yes 0.20 Stron g 0.72 0.81 0.48 0.86 0.73 Powertrain Yes 0.02 Stron g 0.10 0.32 0.02 0.04 0.03 Braking Yes 0.03 Stron g 0.49 0.99 0.41 0.37 0.21 Rear Yes 0.03 Stron g 0.40 0.27 0.82 0.11 0.41 Front Yes 0.15 Stron g 0.53 0.64 0.33 0.69 0.47 Body structure No 0.20 Little 0.41* 0.33 0.70 0.23 0.36 Non structure γ Magnitude Average Pick SUVs Sedan All Regression Coefficient R 2



## Key *note: High R 2 

## coefficient for Non-structure subsystem assumed to be due to co linearity of plan view area with GVM: w non structure 

## → (interior space) → (plan view area) → (GVM) Inclusion Criteria Physical link with

vehicle

mass Included in prior

work

No Yes No Yes/No

Yes Yes No Yes Yes Yes Yes Yes No Include

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