What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

Table of Contents 

CHAPTER 2: WHAT ARE THE ATTRIBUTE-BASED CURVES THE AGENCIES 

ARE USING, AND HOW WERE THEY DEVELOPED?

2.1 Standards are attribute-based and defined by a mathematical function ....... 22-22-1

2.2 What attribute do the agencies use, and why? .................................................. 52-22-4

2.3 What mathematical function do the agencies use, and why?........................... 62-22-5

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CHAPTER 2: What are the Attribute-Based Curves the Agencies 

are Using, and How Were They Developed? 

2.1 Standards are attribute-based and defined by a mathematical function 

As discussed in Section II.B of the NPRM, NHTSA and EPA are setting attributebased CAFE and CO2 standards for MYs 2012-2016 passenger cars and light trucks which 

standards are expressed by a mathematical function. EPCA, as amended by EISA, expressly 

requires that CAFE standards for passenger cars and light trucks be based on one or more 

vehicle attributes related to fuel economy, and be expressed in the form of a mathematical 

function.1 The CAA has no such requirement, although such an approach is permissible 

under section 202 (a) and EPA has used the attribute-based approach in issuing standards 

under analogous provisions of the CAA (e.g., standards for non-road diesel engines using 

engine size as the attribute). Given the advantages of using attribute-based standards for light 

duty vehicles and given the goal of coordinating and harmonizing CO2 standards promulgated 

under the CAA and CAFE standards promulgated under EPCA, as expressed by President 

Obama in his announcement of the new National Program and by the agencies in the joint 

NOI, EPA is also proposing standards that are attribute-based and expressed as mathematical 

functions. 

Under an attribute-based standard approach, each vehicle model has a fuel economy or 

CO2 target, the stringency of which depends of the value of the attribute for the vehicle 

model. Thus, fuel economy and CO2 targets are set for individual vehicles, and vary directly 

with the attribute, i.e., becoming more stringent as the attribute decreases and vice versa. For 

example, size-based (i.e., size-indexed) standards assign higher fuel economy targets (lower 

CO2 targets) to smaller vehicles and lower fuel economy targets (higher CO2 targets) to larger 

vehicles. The CAFE or fleet-wide average CO2 level required of a particular manufacturer is 

determined by calculating the sales-weighted average of the model-specific fuel economy or 

CO2 targets. 

The form of the fuel economy or CO2 standard can have a dramatic effect on the level 

of improvement required from various types of vehicles and the relative stringency of the 

standard for various manufacturers. These disparate impacts derive from two facts 

concerning the current automotive market: 1) consumers currently demand a wide variety of 

vehicle types and sizes, and 2) individual manufacturers focus their product offerings on 

different portions of this demand. Therefore, a comparison of the advantages and 

disadvantages of attribute-based and flat (universal) standards needs to consider both of these 

factors. 

Methods to reduce the CO2 emissions from and increase the fuel economy of 

individual vehicles can be generally grouped into four main categories: 1) reducing vehicle 

size, 2) reducing vehicle performance and/or utility, and 3) increasing the efficiency of the 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

powertrain and accessories at maintaining constant performance and utility, and 4) reducing 

weight and aerodynamic drag while maintaining vehicle size and utility.a Stringent flat 

standards encourage all four of these methods. However, the level of encouragement differs 

between manufacturers. Manufacturers of generally larger vehicles face a more difficult task 

in meeting a flat standard than those of generally smaller vehicles. Thus, the stringency of 

flat standards will tend to be limited by the capabilities of the manufacturers of larger 

vehicles. Manufacturers of smaller vehicles will tend to face lower compliance costs and may 

not even need to change their vehicles at all.b Thus, the overall level of control may be 

limited. The flat standard will encourage smaller, less powerful vehicles, as these vehicles 

face the least compliance costs. Sales will tend to be shifted to manufacturers of generally 

smaller vehicles as their overall compliance costs will be lower than those of manufacturers of 

average or larger vehicles. Finally, because smaller vehicles face lower costs than larger 

vehicles, consumers will be encouraged to purchase smaller vehicles. 

Attribute-based standards are preferable to universal industry-wide average standards 

for several reasons. First, if the shape is chosen properly, every manufacturer is more likely 

to be required to continue adding more fuel efficient technology each year, because the level 

of the compliance obligation of each manufacturer is based on its own particular product mix. 

Second, attribute-based standards minimize the incentive for manufacturers to respond 

to CAFE and CO2 standards in ways that may be harmful to safety.c,2 Because each vehicle 

model has its own target (based on the attribute chosen), attribute-based standards can, 

depending on the corresponding mathematical function (i.e., the shape of the attribute based 

standards), reduce or eliminate the incentive to build smaller vehicles simply to meet a fleetwide average. Since smaller vehicles are subject to more stringent fuel economy targets, a 

manufacturer’s increasing its proportion of smaller vehicles would not necessarily ease its 

compliance obligation. For the purposes of this rule, the agencies believe that setting 

attribute-based standards with careful attention to the slope of the target curves will not 

encourage wholesale changes in fleet mix to either smaller or larger vehicles. 

 

a

 Another method of increasing fleet fuel economy is to increase the number of high-fuel-economy 

vehicles and reduce sales of low-fuel-economy vehicles, for instance, by changing their relative prices. EPA and 

NHTSA believe that existing technologies allow automakers to meet the requirements of this the proposed rules

without changing the mix of vehicles sold (although the proposed rules would not prohibit such changes in mix). 

b

 Widespread trading of credits could encourage fuel economy improvements or CO2 emission 

reductions from manufacturers of smaller vehicles. This would allow the stringency of the standard to be 

increased, but would probably create a shift of wealth between the two sets of manufacturers. However, most 

manufacturers have indicated that they would be unlikely to trade credits with their direct competitors. 

c

 The 2002 NAS Report described at length and quantified the potential safety problem with average 

fuel economy standards that specify a single numerical requirement for the entire industrySee NAS Report at 5
Draft Joint Technical Support Document 

Third, attribute-based standards provide a more equitable regulatory framework for 

different vehicle manufacturers.d,3 A universal industry-wide average standard imposes 

disproportionate compliance obligations on manufacturers that need to change their product 

plans and no obligation on those manufacturers that have no need to change their plans. 

Attribute-based standards (that have the proper shape) spread the regulatory cost burden for 

fuel economy more broadly across all of the vehicle manufacturers within the industry. 

And fourth, attribute-based standards respect economic conditions and consumer 

choice. Manufacturers are required to invest in technologies that improve the fuel economy 

of their fleets, regardless of vehicle mix. Thus the consumer is likely to enjoy the same wide 

range of vehicles to choose from in 2016 as they do now. The difference will be, of course, 

that most of the vehicles will be more fuel efficient. 

The agencies recognize that, because manufacturers’ compliance obligations under 

attribute-based standards are based in part on the mix of vehicles that they produce, the fuel 

savings and emissions reductions produced under attribute-based standards can vary 

depending on market conditions. For example, fuel prices lower than those anticipated at the 

time of rulemaking will tend to shift consumer demand toward larger vehicles. If 

manufacturers sell a greater number of larger vehicles than the agencies anticipate, fuel 

savings and CO2 reductions would be lower than anticipated. In contrast, if fuel prices rise 

significantly, more fuel savings and CO2 reductions than anticipated should be likely. 

One potential way to mitigate the variability of results under attribute-based standards 

due to market conditions is through the use of explicit backstops, standards below which 

manufacturers may not drop. For purposes of the CAFE program, EISA requires a backstop 

for domestically-manufactured passenger cars—a universal minimum, non-attribute-based 

standard of either “27.5 mpg or 92 percent of the average fuel economy projected by the 

Secretary of Transportation for the combined domestic and non-domestic passenger 

automobile fleets manufactured for sale in the United States by all manufacturers in the model 

year...”4

, whichever is greater. In the MY 2011 final rule, the first rule setting standards since 

EISA added the backstop provision to EPCA, NHTSA considered whether the statute 

permitted the agency to set backstop standards for the other regulated fleets of imported 

passenger cars and light trucks. Although commenters expressed support both for and against 

a more permissive reading of EISA, NHTSA concluded in that rulemaking that its authority 

was likely limited to setting only the backstop standard that Congress expressly provided, i.e., 

the one for domestic passenger cars. A backstop, however, is permissible under the CAA (as 

are universal standards generally). 

For purposes of the CAFE and CO2 standards proposed in this NPRM, NHTSA and 

EPA recognize that the risk, even if small, does exist that low fuel prices in MYs 2012-2016 

might lead indirectly to less than currently anticipated fuel savings and emissions reductions. 

The NPRM seeks comment on whether backstop standards, or any other method within the 

agencies’ statutory authority, should and can be implemented for the import and light truck 

 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

fleets in order to achieve the fuel savings that attribute-based standards might not absolutely 

guarantee. 

2.2 What attribute do the agencies use, and why? 

Consistent with the MY 2011 CAFE standards, EPA and NHTSA are proposing to use 

footprint as the attribute for the MY 2012-2016 CAFE standards and CO2 emissions 

standards. There are several policy reasons why the agencies believe that footprint is the most 

appropriate attribute on which to base the standards, as discussed below. 

It is important that the CAFE and CO2 standards be set in a way that does not 

encourage manufacturers to respond by selling vehicles that are in any way less safe. 

Although NHTSA’s research also indicates that reductions in vehicle mass tend to 

compromise vehicle safety, footprint-based standards provide an incentive to use new and 

advanced lightweight materials and structures that could be otherwise discouraged by weightbased standards, because manufacturers can use them to improve a vehicle’s fuel economy 

without their use necessarily resulting in a change in the vehicle’s target level of fuel 

economy or CO2 emissions and without a substantial impact on the safety (in terms of 

crashworthiness) of that vehicle. 

Further, although the agencies recognize that weight is better correlated with fuel 

economy and CO2 emissions than is footprint, the agencies continue to believe that there is 

less risk of “gaming” (artificial manipulation of the attribute(s) to achieve a more favorable 

target) by increasing footprint under footprint-based standards than by increasing vehicle 

mass under weight-based standards—it is relatively easy for a manufacturer to add enough 

weight to a vehicle to decrease its applicable fuel economy target a significant amount, as 

compared to increasing vehicle footprint. The agencies also agree with concerns raised in 

2008 by some commenters to NHTSA’s MY 2011 CAFE rulemaking that there would be 

greater potential for gaming under multi-attribute standards, such as standards under which 

targets would also depend on attributes such as weight, torque, power, towing capability, 

and/or off-road capability. Standards that incorporate such attributes in conjunction with 

footprint would not only be significantly more complex, but by providing degrees of freedom 

with respect to more easily-adjusted attributes, they would make it less certain that the future 

fleet would actually achieve the average fuel economy improvement and CO2 reduction 

levels projected by the agencies. 

However, although NHTSA and EPA believe initially that footprint is the most 

appropriate attribute upon which to base the proposed standards (and the MY 2011 CAFE 

standards use footprint as the exclusive attribute), recognizing strong public interest in this 

issue, the NPRM seeks comment on whether the agencies should consider setting standards 

for the final rule based on another attribute or a combination of attributes. If commenters 

suggest that the agencies should consider another attribute or a combination of attributes, the 

agencies specifically request that the commenters address the concerns raised in the 

paragraphs above regarding the use of other attributes, and explain how standards should be 

developed using the other attribute(s) in a way that contributes more to fuel savings and CO2 

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2.3 What mathematical function do the agencies use, and why? 

The MY 2011 CAFE standards are defined by a continuous, constrained logistic 

function, which takes the form of an S-curve, and is defined according to the following 

formula: 

( )

( )

1

1 1 1

1

FOOTPRINT c d

FOOTPRINT c d

TARGET

e

a b a e

−

−

=

 

+ −     +

Here, TARGET is the fuel economy target (in mpg) applicable to vehicles of a given 

footprint (FOOTPRINT, in square feet), b and a are the function’s lower and upper 

asymptotes (also in mpg), e is approximately equal to 2.718,ec is the footprint (in square feet) 

at which the inverse of the fuel economy target falls halfway between the inverses of the 

lower and upper asymptotes, and d is a parameter (in square feet) that determines how 

gradually the fuel economy target transitions from the upper toward the lower asymptote as 

the footprint increases. Figure 2-1shows an example of a logistic target function, where b = 

20 mpg, a= 30 mpg, c = 40 square feet, and d = 5 square feet. 

 

e

e is the irrational number for which the slope of the function y = numberxis equal to 1 when x is equal 

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What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Footprint (Square Feet)

Target (Miles per Gallon)

LIMIT

UPPER

LIMIT

LOWER

Figure 2-1 Sample Logistic Curve 

After fitting this mathematical form (separately) to the passenger car and light truck 

fleets and determining the maximum feasible stringency of the standards (i.e., the vertical 

positions of the curves), NHTSA arrived at the curves shown in Figure 2-2 to define the MY 

2011 standards. 

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20

25

30

35

40

45

35 40 45 50 55 60 65 70

Footprint (sf)

Target (mpg)

Passenger Cars

Light Trucks

Figure 2-2 MY 2011 CAFE Standards for Passenger Cars and Light Trucks 

In finalizing the MY 2011 standards, NHTSA noted that the agency is not required to 

use a constrained logistic function and indicated that the agency may consider defining future 

CAFE standards in terms of a different mathematical function. NHTSA and EPA have done 

so jointly in preparation for the proposed CAFE standards and CO2 emissions standards. 

In revisiting this question jointly, EPA and NHTSA found that the final MY 2011 

CAFE standard for passenger cars, though less steep than the MY 2011 standard NHTSA 

proposed in 2008, continues to concentrate the sloped portion of the curve (from a compliance 

perspective, the area in which upsizing results in a slightly lower applicable target) within a 

relatively narrow footprint range (approximately 47-55 square feet). In practical terms, this 

results in a portion of the fleet that has a large change in emissions and fuel consumption with 

just a minor change in footprint. This potentially increases the incentive for gaming by 

upsizing slightly to meet less stringent standards. Further, most passenger car models have 

footprints smaller than the curve’s 51.4 square foot inflection point, and many passenger car 

models have footprints at which the curve is relatively flat (see figure above). The resulting 

fit to the data was forced by choice of asymptotes defining the constrained logistic function. 

The agencies discuss below an alternative function that seeks to prevent this from occurring. 

For both passenger cars and light trucks, a mathematical function that has some slope 

at most footprints where vehicles are produced is advantageous in terms of fairly balancing 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

to new standards by downsizing vehicles in ways that compromise vehicle safety. For 

example, a flat standard has the drawbacks of a universal standard: it may be very difficult for 

a full-line manufacturer to meet, while requiring very little of a manufacturer concentrating on 

small vehicles, and a flat standard may provide an incentive to manufacturers to downsize 

certain vehicles, in order to “balance out” other vehicles subject to the same standard. 

As a potential alternative to the constrained logistic function, NHTSA had, in 

proposing MY 2011 standards, presented information regarding a constrained linear function 

(or piecewise linear function). As shown in the 2008 NPRM, a constrained linear function 

has the potential to avoid creating a localized region (in terms of vehicle footprint) over which 

the slope of the function is relatively steep. Although NHTSA did not receive public 

comments on this option, the agency indicated that it still believed a linear function 

constrained by upper (on a gpm basis) and possibly lower limits could merit reconsideration 

in future CAFE rulemakings. 

Having re-examined a piecewise linear function or constrained linear function for 

purposes of the proposed standards, NHTSA and EPA tentatively conclude that for both 

passenger cars and light trucks, it remains meaningfully sloped over a wide footprint range, 

thereby providing a well-distributed disincentive to downsize vehicles in ways that could 

compromise highway safety. Also, the function proposed is not so steeply sloped that it 

would provide a strong incentive to increase vehicle size in order to obtain a lower CAFE 

requirement and higher CO2 limit, thereby compromising energy and environmental benefits. 

Therefore, the CAFE and CO2 emissions standards proposed in the NPRM are defined by 

constrained linear or piecewise linear functions. 

The NHTSA constrained linear function is defined according to the following formula: 

1

1 1

, ,

TARGET

MIN MAX c FOOTPRINT d

a b

=

      × +      

Here, TARGET is the fuel economy target (in mpg) applicable to vehicles of a given 

footprint (FOOTPRINT, in square feet), b and a are the function’s lower and upper 

asymptotes (also in mpg), respectively, c is the slope (in gpm per square foot) of the sloped 

portion of the function, and d is the intercept (in gpm) of the sloped portion of the function 

(that is, the value the sloped portion would take if extended to a footprint of 0 square feet. 

The MIN and MAX functions take the minimum and maximum, respectively of the included 

values; for example, MIN(1,2) = 1, MAX(1,2) = 2, and MIN[MAX(1,2),3)]=2. Figure 2-3 

shows an example of a linear target function, where a = 0.0241 gpm (41.6 mpg), b = 0.032 

gpm (31.2 mpg), c = 0.000531 gpm per square foot, and d = 0.002292 gpm (436 mpg). 

Because the function is linear on a gpm basis, not an mpg basis, it is plotted on this basis. 

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0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

35 40 45 50 55 60 65 70

Footprint (sf)

Fuel Consumption (gpm)

1/LIMIT UPPER

1/LIMIT LOWER

INTERCEPT

SLOPE

Figure 2-3 Sample Linear Function 

The EPA piecewise linear function is defined according to the following 

formula: 

Target = a, if x ≤ l 

Target = cx + d, if l < x ≤ h 

Target = b, if x > h 

This equation takes the simplified form (consistent with NHTSA’s function): 

Target = MIN [ MAX ( c * x + d , a) , b] 

Where, 

Target = the CO2 target value for a given footprint (in g/mi) 

a = the minimum target value (in g/mi CO2) 

b = the maximum target value (in g/mi CO2) 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

d = is the intercept or zero-offset for the line (in g/mi CO2) 

x = footprint of the vehicle model (in square feet, rounded to the nearest tenth) 

l & h are the lower and higher footprint limits or constraints or the boundary (“kinks”) 

between the flat regions and the intermediate sloped line (in sq ft) 

Figure 2-4 shows the basic curve. 

30 35 40 45 50 55 60 65 70 Footprint (sq feet)

CO2 (gram/mile) or 

Fuel Consumption (gallons/mile)

lower limit = l Intercept = d

upper 

limit = h

slope = c

min = a

max = b

Figure 2-4 The Shape of the Piecewise Linear Attribute Based Curve 

For purposes of the proposed standards, NHTSA, working with EPA, developed the 

basic curve shapes for both agencies’ respective standards, using statistical fitting methods 

similar to those applied by NHTSA in fitting the curves defining the MY 2011 standards. The 

first step begins with the market inputs discussed above, but because the baseline fleet is 

technologically heterogeneous, NHTSA used the CAFE model to develop a fleet to which 

nearly all the technologies listed in Ch. 3 of the TSDf were applied, by taking the following 

 

f

 The agencies excluded diesel engines and strong hybrid vehicle technologies from this exercise (and 

only this exercise) because the agencies expect that manufacturers would not need to rely heavily on these 

hliidlih hd ddNHTSA d EPA did ilddil id 

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steps: (1) treating all manufacturers as unwilling to pay civil penalties rather than applying 

technology, (2) applying any technology at any time, irrespective of scheduled vehicle 

redesigns or freshening, and (3) ignoring “phase-in caps” that constrain the overall amount of 

technology that can be applied by the model to a given manufacturer’s fleet. These steps 

helped to increase technological parity among vehicle models, thereby providing a better basis 

(than the baseline fleet) for estimating the statistical relationship between vehicle size and fuel 

economy. In other words, this process normalized the fleet such that differences in 

technology had a minimal contribution to the variation (scatter) in the data. This process also 

served to slightly flatten the slope of the line (a goal sought after as described above). 

In fitting the curves, EPA and NHTSA also continued to apply constraints to limit the 

function’s value for both the smallest and largest vehicles. Without a limit at the smallest 

footprints, the function—whether logistic or linear—can reach values that would be unfairly 

burdensome for a manufacturer that elects to focus on the market for small vehicles; 

depending on the underlying data, an unconstrained form could apply to the smallest vehicles 

targets that are simply unachievable. Limiting the function’s value for the smallest vehicles 

ensures that the function remains technologically achievable at small footprints, and that it 

does not unduly burden manufacturers focusing on small vehicles. Obviously, passenger 

compartments can only become so small; this means, among other things, that a vehicle’s 

frontal area—a key determinant of aerodynamic drag—can only become so small. Also, as 

vehicle size decreases, complying with federal motor vehicle safety standards can necessitate 

the addition of structural elements that add mass and thereby reduce fuel economy and 

increase emissions. On the other side of the function, without a limit at the largest footprints, 

the function may provide no floor on required fuel economy. Also, the safety considerations 

that support the provision of a disincentive for downsizing as a compliance strategy apply 

weakly—if at all—to the very largest vehicles. Limiting the function’s value for the largest 

vehicles leads to a function with an inherent absolute minimum level of performance, while 

remaining consistent with safety considerations. 

Before fitting the sloped portion of the constrained linear form, NHTSA and EPA 

selected footprints above and below which to apply constraints (i.e., minimum and maximum 

values) on the function. For passenger cars, the agencies noted that several manufacturers 

offer small and, in some cases, sporty coupes below 41 square feet, examples including the 

BMW Z4 and Mini, Saturn Sky, Honda Fit and S2000, Hyundai Tiburon, Mazda MX-5 

Miata, Suzuki SX4, Toyota Yaris, and Volkswagen New Beetle. Because such vehicles 

represent a small portion (less than 10 percent) of the passenger car market, yet often have 

characteristics that could make it infeasible to achieve the very challenging targets that could 

apply in the absence of a constraint, the agencies are proposing to “cut off” the linear portion 

of the passenger car function at 41 square feet. For consistency, the agencies are proposing to 

do the same for the light truck function, although no light trucks are currently offered below 

41 square feet. The agencies further noted that above 56 square feet, the only passenger car 

model present in the MY 2008 fleet were four luxury vehicles with extremely low sales 

volumes—the Bentley Arnage and three versions of the Rolls Royce Phantom. The agencies 

are therefore proposing to “cut off” the linear portion of the passenger car function at 56 

square feet. Finally, the agencies noted that although public information is limited regarding 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

Toyota Tundra), appear to fall above 66 square feet in footprint. The agencies are therefore 

proposing to “cut off” the linear portion of the light truck function at 66 square feet. These 

“cut-off” values of footprint serve as the constraints to the functions shown above. The lower 

and upper levels are determined from where the sloped line meets these cut-off points. 

In the NPRM, EPA and NHTSA invite comment on this approach to fitting the curves. 

The agencies note that final decisions on this issue will play an important role in determining 

the form and stringency of the final standards, the incentives those standards will provide 

(e.g., with respect to downsizing small vehicles), and the relative compliance burden faced by 

each manufacturer. 

Having developed a set of baseline data to which to fit the mathematical fuel 

consumption function, the initial values for parameters c and d were determined for cars and 

trucks separately. Values for c and d were initially set such that the average (equivalently, 

sum) of the absolute values of the differences was minimized between the “maximum 

technology” fleet fuel consumption (within the footprints between the upper and lower limits) 

and the straight line function defined above at the same corresponding vehicle footprints. 

That is, c and d were determined by minimizing the average absolute residual, commonly 

known as the MAD (Mean Absolute Deviation) approach, of the corresponding straight line. 

The curve was fit in fuel consumption (i.e., CO2) space rather than fuel economy space 

because the manufacturer targets are in terms of the harmonic average fuel economy (or 

average CO2), and so it is more important that the curve fit the fuel consumption (i.e., CO2) 

data well than that it fit the fuel economy data well. NHTSA also explained in the MY 2011 

final rule that it chose to use MAD in this Step instead of minimizing the sum of the square 

errors (“least squares,” another common approach in curve fitting) in order to lessen the 

influence of outliers. NHTSA believes that it is more appropriate to use unweighted data in 

fitting the curve rather than weighting the data by sales because of large variations in model 

sales. 

Finally, the agencies calculated the values of the upper and lower limits based on the 

corresponding footprint constraints discussed above (41 and 56 square feet for passenger cars, 

and 41 and 66 square feet for light trucks). 

The result of this methodology is shown below in Figure 2-5 and Figure 2-6 for 

passenger cars and light trucks, respectively. The fitted curves are shown with the underlying 

“maximum technology” passenger car and light truck fleets. For passenger cars, the mean 

absolute deviation of the sloped portion of the function was 14 percent. For trucks, the 

corresponding MAD was 10 percent. 

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Figure 2-5 “Maximum Technology” Passenger Fleet with Fitted Constrained Linear Function 
What are the Attribute-Based Curves the Agencies are Using, and How Were They Developed? 

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Footprint (sf)

Fuel Consumption (gpm)

Figure 2-6 “Maximum Technology” Light Truck with Fitted Constrained Linear Function 

The agencies used these functional forms as a starting point to develop mathematical 

functions defining actual proposed standards. As discussed in Sections II.B of the NPRM 

preamble, the agencies transposed these functions vertically (i.e., on a gpm basis, uniformly 

downward) to produce the maximum feasible passenger car and light truck CAFE standards, 

and corresponding CO2 emissions standards. 
Draft Joint Technical Support Document 

References 

1

 49 U.S.C. § 32902(a)(3)(A). 

2

 The 2002 NAS Report described at length and quantified the potential safety problem with average fuel

economy standards that specify a single numerical requirement for the entire industry. See NAS Report at 5, 

finding 12. 

3

Id. at 4-5, finding 10. 

4

 49 U.S.C. § 32902(b)(4).