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A primary input to any study of automobile fuel economy is the tractive energy required by vehicles to negotiate prescribed driving schedules. This energy depends on both the particular characteristics of a vehicle and the detailed velocity profile of the particular schedule. Two schedules of special interest are the EPA Urban and Highway used in government fuel-economy regulation. In making comprehensive studies of the influence of various vehicle parameters on fuel economy, an ability to readily and accurately predict the tractive and braking energy requirements of vehicles can be very valuable. The author published such a capability in 1981. (Numbers in brackets denote References at the end of the paper.) Since that time he has used it for addressing several different fuel-economy related issues (2,3,4). Over these same years the physical basis for the near linearity of solutions of the equations for tractive and braking energy has become clearer.

Driving schedules prescribed for fuel-economy regulation are composed of two generic modes: (1) accelerations and constant-speed travel, requiring a positive tractive force at a vehicle's driving wheels; (2) decelerations, requiring a negative or braking force at those wheels. In the first mode, a total tractive energy, ETR, is required to overcome a vehicle's tire rolling resistance, aerodynamic drag, and the inertia of its mass. In the second mode, all the kinetic energy that a vehicle's mass acquired in the first mode has to be removed. The inherent rolling resistance and aerodynamic drag remove some of it. The remainder, EBR, has to be removed by a wheel-braking force. In vehicles with conventional braking the wheel-braking force is frictional, and so all of EBR is dissipated. However, if this force is not inherently frictional some of EBR can be captured, stored, and subsequently used to provide part of the ETR required for propulsion.

Hybrid vehicles combine a powerplant with an energy-storage device, the presence of which permits several fuel-reducing capabilities. Among these is regenerative braking. Its impact on vehicle fuel consumption can be determined by vehicle testing and/or computer simulation. In this paper, equations are developed that complement these results by offering a means for readily quantifying the potential impacts of regenerative braking on a vehicle's tractive-fuel consumption. Driving schedules can be decomposed into three generic modes - powered driving, braking, and idling. Without regenerative braking, the tractive-fuel consumed for powered driving is determined by the tractive energy required to propel a vehicle along a driving schedule, and the efficiency with which this energy can be delivered by the powertrain. The addition of regenerative braking reduces the portion of tractive energy that must be directly supplied by the powerplant.

The fuel economy of an automobile is a highly complex function of the detailed characteristics of the vehicle and its subsystems (particularly the engine, transmission and drivetrain), as well as being dependent on the manner in which the vehicle is driven. For existing vehicles, automotive manufacturers utilize laboratory test procedures to evaluate fuel economy. However, during new-vehicle design, and to assess the fuel economy potential of new technologies, computer programs that simulate the operation of the vehicle system over prescribed driving schedules are used. Of particular interest are the integrated fuel consumptions on the EPA Urban and Highway driving schedules since these are subject to Federal regulation. Since neither detailed subsystem test data nor simulation programs are typically used by those outside the automotive industry, the physics of fuel economy is not always well understood.

Underbody diffusers are used on racing cars to generate large downforce that will permit them to achieve reduced lap times through aerodynamically-enhanced traction. Both the configuration of these cars and their underbody flows are complex, so the design of optimum underbody geometries is a formidable task. The objective of the present study is to generate data and understanding that will facilitate design through knowledge of the relevant physics and the application of a numerical analysis that provides generalised design guidance. The approach taken is one that is traditional in the study of complex problems: to identify a less-complex but still relevant sub-problem that has the key elements and flow physics of the main one, and study it to generate a first phase of cause-and-effect relationships. In addition to having immediate utility, it can serve as the foundation upon which future research activity can be built.