Two common methods of improving fuel efficiency of a vehicle are to reduce the drag coefficient and the frontal area of the vehicle. Consider a car with 1.85 m width and 1.75 m height, with a drag coefficient of 0.30. Determine the amount of fuel and money saved per year as a result of reducing the car height to 1.50 m while keeping its width the same. Assume the car is driven 25,000 km (15,000 miles) a year at an average speed of 100 km/h. Take the density and price of gasoline to be 0.74 kg/L and $1.04/L. Also assume the density of air to be 1.20 kg/m3, the heating value of gasoline to be 44,000 kJ/kg, and the overall efficiency of the car’s drive train to be 30%.

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Explanation:

The drag force is equal to:

Where is the drag coefficient and is the frontal area, respectively. The work loss due to drag forces is:

The reduction on amount of fuel is associated with the reduction in work loss:

Where and are the original and the reduced frontal areas, respectively.

The change is work loss in a year is:

The change in chemical energy from gasoline is:

The changes in gasoline consumption is:

Lastly, the money saved is:

answer:

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