Question

Homework

The history of performance automobile design and production has been characterized by trying to get more speed for less power. High power engines are heavy, require more cooling, and consume fuel at a high rate. It is therefore advantageous for a race car to have an aerodynamic body to reduce drag. This assignment will walk you through how to estimate the top speed of a car given that we know the power rating of the engine and a few key design characteristics. For this assignment, we assume that the top speed of our race car is limited only by the power produced, and air resistance.

1. Say the car is traveling along at it’s top speed along a flat road. Draw a free body diagram of the car, and write out Newton’s second law for the horizontal direction. For now, call the forward force Fe and the drag force FD.

2. If the car travels at top speed, vm, what is the the power supplied to the car by the drag force? Hint: imagine that the car travels a known distance. How much work does the drag force do over this distance? How long does it take to cover the distance?

3. Let the horsepower supplied by the engine be denoted by Pe. and also assume that all of the necessary factors to calculate the drag force are known, i.e., the effective cross sectional area, the density of air, and the drag coefficient. What is vm in terms of these parameters?

Answer 1