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### Car Spoiler

A spoiler is an upside-down airfoil located in the back of a car whose objective is to provide a downward force on the moving vehicle. This downward force is in theory used to increase the stability and the maximum acceleration that the car can sustain. Imagine a car without a spoiler moving toward the left on a flat surface with an acceleration ax.

Drawing a free body diagram of the moving vehicle ( neglecting air friction for simplicity) and utilizing Newton’s second law on both the horizontal and vertical direction, one can find that the car maximum acceleration (ax) is equal to the static coefficient of friction between the tires and the road (μ) times the gravitational acceleration (g). Note that the car’s maximum acceleration does not depend on the mass of the car (m). Therefore, the only practical way to increase the vehicle  max acceleration would be to increase the friction between the tires and the road since the gravitational acceleration cannot be easily changed.

Drawing a free body diagram of a similar vehicle but this time including the aerodynamic force provided by the spoiler (Fs), one can deduced that the maximum acceleration of the car (ax) has increased compared to that of a car without a spoiler.

Two things are important to note:

1) The maximum acceleration that a car with a spoiler can have increases as the aerodynamic force provided by the spoiler increases

2) The maximum acceleration of a car with a spoiler depends on the mass of the car (as mass goes down, max acceleration goes up) while the maximum acceleration of a car without a spoiler does not depend on the mass of the vehicle.

So far, so good; however, there is a catch. Since the aerodynamic force of the spoiler (Fs) pushes down of the car on the back end, this force tends to rotate the car in such a way that the front wheels of the vehicle tend to be lifted up and the normal force on the front tires is reduced while the normal force on the back tires is increased. What does this means? For a front wheel drive vehicle, this means that the car’s maximum acceleration is actually diminished. For a back wheel drive vehicle, this means that the car’s maximum acceleration is in fact increased.

An increased maximum acceleration would also be true for a 4-wheel drive vehicle. Therefore, for a front wheel drive vehicle, a spoiler is more an accessory for looks. Nevertheless, for street legal vehicles, most of the time the max acceleration is limited by the engine’s capacity and not the friction on the road. For a formula 1 cars, a spoiler plays a very important role in stability and maximum acceleration.

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