These assumptions are very important. It is obvious that reducing vehicle size will reduce fuel consumption. Also, the reduction of vehicle acceleration capability allows the use of a smaller, lower-power engine that operates closer to its best efficiency. These are not options that will be considered.

As shown in Table 2.3^[1], in the past 20 or so years, the net result of improvements in engines and fuels has been increased vehicle mass and greater acceleration capability while fuel economy has remained constant (EPA, 2008). Presumably this tradeoff between mass, acceleration, and fuel consumption was driven by customer demand. Mass increases are directly related to increased size, the shift from passenger cars to trucks, the addition of safety equipment such as airbags, and the increased accessory content. Note that although the CAFE standards for light-duty passenger cars have been for 27.5 mpg since 1990, the fleet average remains much lower through 2008 due to lower CAFE standards for light-duty pickup trucks, sport utility vehicles (SUVs), and passenger vans.

TRACTIVE FORCE AND TRACTIVE ENERGY

The mechanical work produced by the power plant is used to propel the vehicle and to power the accessories. As discussed by Sovran and Blaser (2006), the concepts of tractive force and tractive energy are useful for understanding the role of vehicle mass, rolling resistance, and aerodynamic drag. These concepts also help evaluate the effectiveness of regenerative braking in reducing the power plant energy that is required. The analysis focuses on test schedules and neglects the effects of wind and hill climbing. The instantaneous tractive force (F_TR) required to propel a vehicle is

(2.1)

where R is the rolling resistance, D is the aerodynamic drag with C_D representing the aerodynamic drag coefficient, M is the vehicle mass, V is the velocity, dV/dt is the rate of change of velocity (i.e., acceleration or deceleration), A is the frontal area, r_o is the tire rolling resistance coefficient, g is the gravitational constant, I_w is the polar moment of inertia of the four tire/wheel/axle rotating assemblies, r_w is its effective rolling radius, and ρ is the density of air. This form of the tractive force is calculated at the wheels of the vehicle and therefore does not consider the components within the vehicle system such as the power train (i.e., rotational inertia of engine components and internal friction).

The tractive energy required to travel an incremental distance dS is F_TRVdt, and its integral over all portions of a driving schedule in which F_TR > 0 (i.e., constant-speed driving and accelerations) is the total tractive-energy requirement, E_TR. For each of the EPA driving schedules, Sovran and Blaser (2006) calculated tractive energy for a large number of vehicles covering a broad range of parameter sets (r₀, C_D, A, M) representing the spectrum of current vehicles. They then fitted the data with a linear equation of the following form:

(2.2)

where S is the total distance traveled in a driving schedule, and α, β, and γ are specific but different constants for the UDDS and HWFET schedules. Sovran and Blaser (2006) also identified that a combination of five UDDS and three HWFET schedules very closely reproduces the EPA combined fuel consumption of 55 percent UDDS plus 45 percent HWFET, and provided its values of α, β, and γ.

The same approach was used for those portions of a driving schedule in which F_TR < 0 (i.e., decelerations), where the power plant is not required to provide energy for propulsion. In this case the rolling resistance and aerodynamic drag retard vehicle motion, but their effect is not sufficient to follow the driving cycle deceleration, and so some form of wheel braking is required. When a vehicle reaches the end of a schedule and becomes stationary, all the kinetic energy of its mass that was acquired when F_TR > 0 has to have been removed. Consequently the decrease in kinetic energy produced by wheel braking is

(2.3)

The coefficients α′ and β′ are also specific to the test schedule and are given in the reference. Two observations are of interest: (1) γ is the same for both motoring and braking as it relates to the kinetic energy of the vehicle; (2) since the energy used in rolling resistance is r₀M g S, the sum of α and α′ is equal to g.

Sovran and Blaser (2006) considered 2,500 vehicles from the EPA database for 2004 and found that their equations fitted the tractive energy for both the UDDS and HWFET schedules with an r = 0.999, and the braking energy with an