Gas Mileage

Gas mileage in an automobile is the distance travelled per gallon of gasoline, or equivalently, the distance per unit of energy or work, and this is the reciprocal of the force exerted by the engine on the car. 

This force can be represented by a sum of seven kinematic elements: 

F = ma + (P0 +Tw)/v + mg(mcosq + sinq) + (rAf + m/x0)v2/2 

The contributions are due to acceleration, auxilliary power usage such as radio, AC and headlights, transmission drag, rolling friction, hills, wind drag and stopping. The velocity terms cause the gas mileage to rise from zero, reach a maximum and decline to zero again. The components and total drag force are shown at left. 

Auxilliary power is roughly 2 kW. The transmission exerts a constant drag force for each gear, determined, from the difference in deceleration at zero engine power in and out of gear, to be about 250 N in high gear. Below 25 m/s, the transmission maintains nearly constant 1500 rpm when cruising, and this requires 6 kW power. A heavy foot significantly increases transmission drag and decreases gas mileage. 

The mass of the Buick Park Avenue is 1800 kg and the rolling coefficient of friction measured at low speeds on level ground in neutral is .010, leading to a constant drag force of 180 N. The total drag power as a function of speed is shown at left. 

The cross-sectional area is about 3 m2 ,the drag coefficient, f, is the typical modern value of .29 from the manual and the density of air is 1.23 kg/m3, varying inversely as the absolute temperature, being ten to twenty per cent higher in winter. Rain adds to this density less than one per cent except in the most torrential cases or as puddles or snow banks. The distance between stops is x0, which should exceed m/rAf = one mile on the interstate, and this precludes tailgaiting. The gas mileage variation with speed, shown at left, is the 50 MJ/gallon of gasoline is divided by 1608 meters per mile and the total drag force without acceleration or hills. The Park Avenue can easily exceed its rated 32 mpg at 55 mph. 
 The available acceleration is determined by subtracting the drag power from the 140 kW total power and dividing by the car's momentum, mv. The acceleration for low speeds is less than shown for three reasons: the engine is not at 1500 rpm but over 5000 rpm, the transmission has much greater drag in low gear, and the maximum acceleration is about g/2 since the force is only through the rear wheels.