Question
NEED HELP
You are in the process of converting your Corvette into an electric vehicle. Your objective is to be able to drive up to Park City to go skiing. Make the following assumptions: the mass of the car, including motor, batteries, driver, etc, is estimated to be 750 kg the maximum grade is 8% (ie. 8 m. increase in elevation for every 100 m. driven) the transmission is 60% efficient the drag coefficient is .29, the density of air is 1.1 kg/m 3 and the frontal area is 2.265 m 2 F = Cd A rho/2 U2 Cd = coefficient of drag A = Frontal area of vehicle rho= density of air U= Relative air velocity Note: the force due to the headwind is calculated as all other losses are neglected What horsepower rating would be required for the motor if you want to make that drive without ever dropping below 95 mph? Your mother looked over your shoulder and saw the speed you were aiming for and got real upset. To make her happy, recalculate at the speed limit of 65 mph. Another design approach would be to eliminate the transmission and direct couple a motor to each wheel. If you do this, what size should each of the four motors be (for the 65 mph case)?
Explanation / Answer
a)
95 mph = 42.47 m/s
F_drag = 0.29*2.265*1.1/2*42.47^2 = 651.6 N
F_gravity = mg*sin theta = 720*9.81*0.08 = 565 N
Total force = 651.6 + 565 = 1216.6 N
Power = F*v = 1216.6*42.47 = 51671.4 Watts = 69.29 hp
Actual power = 69.29 / efficiency = 69.29 / 0.6 = 115.48 hp
b)
65 mph = 29 m/s
F_drag = 0.29*2.265*1.1/2*29^2 = 303.8 N
F_gravity = mg*sin theta = 720*9.81*0.08 = 565 N
Total force = 303.8 + 565 = 868.8 N
Power = F*v = 868.8*29 = 25196 Watts = 33.79 hp
Actual power = 33.79 / efficiency = 33.79 / 0.6 = 56.3 hp
c)
Motor size = 33.79 / 4 = 8.45 hp
