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



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CHAPTER 2: WHAT ARE THE ATTRIBUTE-BASED CURVES THE AGENCIES ARE USING, AND HOW W ERE THEY DEVELOPED?

2.1 Standards are attribute-based and defined by a math ematical function ....... 22

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2.2 What attribute do the agencies use, and why? ......

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

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- 5 Field Code

Field Code

Field CodeDraft Joint Technical Support Document



## 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 math ematical function

As discussed in Section II.B of the NPRM, NHTSA and EPA are setting attributebased CAFE and CO 2 standards for MYs 2012-2016 passenger cars and lig ht 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 attribut e-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 advantage s of using attribute-based standards for light duty vehicles and given the goal of coordinating an d harmonizing CO 2 standards promulgated under the CAA and CAFE standards promulgated under EPCA, as expressed by President Obama in his announcement of the new National Progr am and by the agencies in the joint NOI, EPA is also proposing standards that are attri bute-based and expressed as mathematical functions.

Under an attribute-based standard approach, each ve hicle model has a fuel economy or CO 2 target, the stringency of which depends of the val ue of the attribute for the vehicle model. Thus, fuel economy and CO 2 targets are set for individual vehicles, and vary directly with the attribute, i.e. , becoming more stringent as the attribute decrease s and vice versa. For example, size-based ( i.e. , size-indexed) standards assign higher fuel econom y targets (lower CO 2 targets) to smaller vehicles and lower fuel econom y targets (higher CO 2 targets) to larger vehicles. The CAFE or fleet-wide average CO 2 level required of a particular manufacturer is determined by calculating the sales-weighted averag e of the model-specific fuel economy or CO 2 targets.
The form of the fuel economy or CO 2 standard can have a dramatic effect on the level of improvement required from various types of vehic les and the relative stringency of the standard for various manufacturers. These disparat e impacts derive from two facts concerning the current automotive market: 1) consum ers currently demand a wide variety of vehicle types and sizes, and 2) individual manufact urers focus their product offerings on different portions of this demand. Therefore, a co mparison of the advantages and disadvantages of attribute-based and flat (universa l) standards needs to consider both of these factors.

Methods to reduce the CO 2 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 utilit y, and 3) increasing the efficiency of theWhat are the Attribute-Based Curves the Agencies ar e Using, and How Were They Developed?

powertrain and accessories at maintaining constant performance and utility, and 4) reducing weight and aerodynamic drag while maintaining vehic le size and utility. a Stringent flat standards encourage all four of these methods. How ever, 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 capab ilities of the manufacturers of larger vehicles. Manufacturers of smaller vehicles will t end 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 t o 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 small er vehicles face lower costs than larger vehicles, consumers will be encouraged to purchase smaller vehicles.

Attribute-based standards are preferable to univers al 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 efficie nt technology each year, because the level of the compliance obligation of each manufacturer i s based on its own particular product mix.

Second, attribute-based standards minimize the ince ntive for manufacturers to respond to CAFE and CO 2 standards in ways that may be harmful to safety. c,2 Because each vehicle model has its own target (based on the attribute ch osen), attribute-based standards can, depending on the corresponding mathematical functio n ( i.e. , the shape of the attribute based standards), reduce or eliminate the incentive to bu ild smaller vehicles simply to meet a fleetwide average. Since smaller vehicles are subject t o 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 ru le, 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 vehic les, for instance, by changing their relative price s. EPA and NHTSA believe that existing technologies allow auto makers to meet the requirements of this the proposed rule s without changing the mix of vehicles sold (although the proposed rules would not prohibit su ch changes in mix)

.

b Widespread trading of credits could encourage fue l economy improvements or CO 2 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 wea lth between the two sets of manufacturers. However , most manufacturers have indicated that they would be unl ikely to trade credits with their direct competitor s.

c The 2002 NAS Report described at length and quanti fied the potential safety problem with average fuel economy standards that specify a single numeri cal requi rement for the entire industry. See NAS Report at 5,Draft Joint Technical Support Document

Third, attribute-based standards provide a more equ itable regulatory framework for different vehicle manufacturers. d,3 A universal industry-wide average standard impose s disproportionate compliance obligations on manufact urers 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 sha pe) 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 econo mic conditions and consumer choice. Manufacturers are required to invest in te chnologies that improve the fuel economy of their fleets, regardless of vehicle mix. Thus t he 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 efficie nt.
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 att ribute-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 dema nd toward larger vehicles. If manufacturers sell a greater number of larger vehic les than the agencies anticipate, fuel savings and CO 2 reductions would be lower than anticipated. In co ntrast, if fuel prices rise significantly, more fuel savings and CO 2 reductions than anticipated should be likely.

One potential way to mitigate the variability of re sults under attribute-based standards due to market conditions is through the use of expl icit backstops, standards below which manufacturers may not drop. For purposes of the CA FE program, EISA requires a backstop for domestically-manufactured passenger cars—a univ ersal minimum, non-attribute-based standard of either “27.5 mpg or 92 percent of the a verage fuel economy projected by the Secretary of Transportation for the combined domest ic and non-domestic passenger automobile fleets manufactured for sale in the Unit ed 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 co nsidered whether the statute permitted the agency to set backstop standards for the other regulated fleets of imported passenger cars and light trucks. Although commente rs 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 sta ndard that Congress expressly provided, i.e.
, the one for domestic passenger cars. A backstop, h owever, is permissible under the CAA (as are universal standards generally).

For purposes of the CAFE and CO 2 standards proposed in this NPRM, NHTSA and EPA recognize that the risk, even if small, does ex ist that low fuel prices in MYs 2012-2016 might lead indirectly to less than currently antici pated fuel savings and emissions reductions. The NPRM seeks comment on whether backstop standard s, or any other method within the agencies’ statutory authority, should and can be im plemented for the import and light truckWhat are the Attribute-Based Curves the Agencies ar e Using, and How Were They Developed?

fleets in order to achieve the fuel savings that at tribute-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 CAF E standards and CO2 emissions standards. There are several policy reasons why th e agencies believe that footprint is the most appropriate attribute on which to base the standard s, 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 vehic les that are in any way less safe. Although NHTSA’s research also indicates that reduc tions in vehicle mass tend to compromise vehicle safety, footprint-based standard s 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 weigh t is better correlated with fuel economy and CO2 emissions than is footprint, the ag encies continue to believe that there is less risk of “gaming” (artificial manipulation of t he attribute(s) to achieve a more favorable target) by increasing footprint under footprint-bas ed 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 agen cies also agree with concerns raised in 2008 by some commenters to NHTSA’s MY 2011 CAFE rul emaking 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 wei ght, torque, power, towing capability, and/or off-road capability. Standards that incorpo rate such attributes in conjunction with footprint would not only be significantly more comp lex, but by providing degrees of freedom with respect to more easily-adjusted attributes, th ey would make it less certain that the future fleet would actually achieve the average fuel econo my improvement and CO2 reduction levels projected by the agencies.

However, although NHTSA and EPA believe initially t hat footprint is the most appropriate attribute upon which to base the propos ed 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 agenci es 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 a ttribute or a combination of attributes, the agencies specifically request that the commenters a ddress the concerns raised in the paragraphs above regarding the use of other attribu tes, and explain how standards should be developed using the other attribute(s) in a way tha t contributes more to fuel savings and CO2 reductions than the footprint

- based standards, without compromising safety and wh ileDraft Joint Technical Support Document



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

The MY 2011 CAFE standards are defined by a continu ous, constrained logistic function, which takes the form of an S-curve, and i s 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, e c is the footprint (in square feet) at which the inverse of the fuel economy target fal ls halfway between the inverses of the lower and upper asymptotes, and d is a parameter (in square feet) that determines ho w gradually the fuel economy target transitions from the upper toward the lower asymptote as the footprint increases. Figure 2-1shows an exampl e 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 = number x is equal to 1 when x is equal Field CodeWhat are the Attribute-Based Curves the Agencies ar e 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) t o the passenger car and light truck fleets and determining the maximum feasible stringe ncy of the standards ( i.e. , the vertical positions of the curves), NHTSA arrived at the curv es shown in Figure 2-2 to define the MY 2011 standards. Field CodeDraft Joint Technical Support Document

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 Ca rs and Light Trucks

In finalizing the MY 2011 standards, NHTSA noted th at the agency is not required to use a constrained logistic function and indicated t hat 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 sta ndards and CO 2 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 slop ed 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 foo t inflection point, and many passenger car models have footprints at which the curve is relati vely 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 mathema tical function that has some slope at most footprints where vehicles are produced is a dvantageous in terms of fairly balancingWhat are the Attribute-Based Curves the Agencies ar e Using, and How Were They Developed?

to new standards by downsizing vehicles in ways tha t compromise vehicle safety. For example, a flat standard has the drawbacks of a uni versal standard: it may be very difficult for a full-line manufacturer to meet, while requiring v ery 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 v ehicles subject to the same standard.

As a potential alternative to the constrained logis tic function, NHTSA had, in proposing MY 2011 standards, presented information regarding a constrained linear function (or piecewise linear function). As shown in the 20 08 NPRM, a constrained linear function has the potential to avoid creating a localized reg ion (in terms of vehicle footprint) over which the slope of the function is relatively steep. Alt hough 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 c onstrained linear function for purposes of the proposed standards, NHTSA and EPA t entatively conclude that for both passenger cars and light trucks, it remains meaning fully sloped over a wide footprint range, thereby providing a well-distributed disincentive t o downsize vehicles in ways that could compromise highway safety. Also, the function prop osed is not so steeply sloped that it would provide a strong incentive to increase vehicl e size in order to obtain a lower CAFE requirement and higher CO 2 limit, thereby compromising energy and environment al benefits. Therefore, the CAFE and CO 2 emissions standards proposed in the NPRM are defin ed by constrained linear or piecewise linear functions.

The NHTSA constrained linear function is defined ac cording 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 slope d 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 i f extended to a footprint of 0 square feet. The MIN and MAX

functions take the minimum and maximum, respective ly 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. Field CodeDraft Joint Technical Support Document

0.000 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 accord ing 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 ar e Using, and How Were They Developed?

d = is the intercept or zero-offset for the line (i n 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 slope d 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) orFuel 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 Attri bute Based Curve
For purposes of the proposed standards, NHTSA, work ing with EPA, developed the basic curve shapes for both agencies’ respective st andards, using statistical fitting methods similar to those applied by NHTSA in fitting the cu rves 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 TSD f were applied, by taking the following

f The agencies excluded diesel engines and strong h ybrid vehicle technologies from this exercise (and only this exercise) because the agencies expect tha t manufacturers would not need to rely heavily on t hese technologies in order to comply with the proposed s ta ndards. NHTSA and EPA did include diesel engines a nd Field CodeDraft Joint Technical Support Document

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 gi ven manufacturer’s fleet. These steps helped to increase technological parity among vehic le models, thereby providing a better basis (than the baseline fleet) for estimating the statis tical relationship between vehicle size and fuel economy. In other words, this process normalized t he fleet such that differences in technology had a minimal contribution to the variat ion (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 a chievable at small footprints, and that it does not unduly burden manufacturers focusing on sm all 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 moto r vehicle safety standards can necessitate the addition of structural elements that add mass a nd thereby reduce fuel economy and increase emissions. On the other side of the funct ion, 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 do wnsizing as a compliance strategy apply weakly—if at all—to the very largest vehicles. Lim iting the function’s value for the largest vehicles leads to a function with an inherent absol ute minimum level of performance, while remaining consistent with safety considerations.

Before fitting the sloped portion of the constraine d 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 a gencies 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, H yundai 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 ac hieve 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. F or 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 ab ove 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 th e Rolls Royce Phantom. The agencies are therefore proposing to “cut off” the linear por tion of the passenger car function at 56 square feet. Finally, the agencies noted that alth ough public information is limited regarding the sales volumes of the many different configurati ons (cab designs and bed sizes) of pickupWhat are the Attribute-Based Curves the Agencies ar e 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 li ght truck function at 66 square feet. These “cut-off” values of footprint serve as the constrai nts to the functions shown above. The lower and upper levels are determined from where the slop ed line meets these cut-off points.

In the NPRM, EPA and NHTSA invite comment on this a pproach to fitting the curves. The agencies note that final decisions on this issu e 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 parame ters c and d were determined for cars and trucks separately. Values for c and d were initially set such that the average (equivale ntly, sum) of the absolute values of the differences was minimized between the “maximum technology” fleet fuel consumption (within the foot prints 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. , CO 2 ) space rather than fuel economy space because the manufacturer targets are in terms of th e harmonic average fuel economy (or average CO 2 ), and so it is more important that the curve fit t he fuel consumption ( i.e. , CO 2 ) data well than that it fit the fuel economy data we ll. NHTSA also explained in the MY 2011 final rule that it chose to use MAD in this Step in stead 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 m ore 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 Fi gure 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 fun ction was 14 percent. For trucks, the corresponding MAD was 10 percent. Field Code

Field CodeDraft Joint Technical Support Document

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060

35 40 45 50 55 60 65 70 75 80 Footprint (sf)Fuel Consumption (gpm)

Figure 2-5 “Maximum Technology” Passenger Fleet wi th Fitted Constrained Linear FunctionWhat are the Attribute-Based Curves the Agencies ar e Using, and How Were They Developed?

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060

35 40 45 50 55 60 65 70 75 80 Footprint (sf)Fuel Consumption (gpm)

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

The agencies used these functional forms as a start ing point to develop mathematical functions defining actual proposed standards. As d iscussed in Sections II.B of the NPRM preamble, the agencies transposed these functions v ertically ( i.e. , on a gpm basis, uniformly downward) to produce the maximum feasible passenger car and light truck CAFE standards, and corresponding CO 2 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 quanti fied the potential safety problem with average fuel economy standards that specify a single numerical r equirement 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).