Question

Many sports cars are convertibles. The air flow over such a car is significantly different depending on whether the convertible top is up or down. The engine of the 1000-kg car delivers 135 kW to the wheels, the car frontal area is 1.9 m² and rolling resistance is 2.5% of the car weight. The drag coefficient when the top is down is 0.43 and 0.31 when it is up. For 20 ºC air at one atmosphere, determine:

a. the maximum speed with the top up (in m/s)

b. the maximum speed with the top down (in m/s)

Answer 1

Rolling resistance = 0.025 x (weight of car) = 0.025 x 1000 x 9.81 = 245.25 N

Power = Force x velocity

Force = Resistance by drag + Rolling resistance = ( Coefficient of drag x 0.5 x Density of air x Area x V² ) + 245.25

Power = ( ( Coefficient of drag x 0.5 x Density of air x Area x V² ) + 245.25 ) x V

135000 = ( ( Coefficient of drag x 0.5 x Density of air x Area x V³) + 245.25V )

If Top up then coefficient of drag = 0.31

So 135000 = (0.31 x 0.5 x1.2 x 1.9 x V³ ) + 245.25V

Solving above equation we get

V=69.37 m/s

If Top down then coefficient of drag = 0.43

So 135000 = (0.43 x 0.5 x1.2 x 1.9 x V³ ) + 245.25V

Solving above equation we get

V = 62.49 m/s