An automobile has been designed to maintain a constant speed of 55 mph on a +5%
ID: 1828734 • Letter: A
Question
An automobile has been designed to maintain a constant speed of 55 mph on a +5% grade. The weight of the vehicle when fully loaded is 6000 lbs. What is the total resistance in still air of this vehicle? What would be the resistance on a level road? What horsepower must be delivered to the wheels on the grade? If the efficiency is 80%, what must be the rated horsepower of the motor? Use:
R = 0.01T + 0.0001Tv + 0.0028CAv2
where
R = resistance (lb)
T = weight (lb)
v = velocity (mph)
C = air resistance parameter = 0.040
A = maximum cross section = 100 ft2.
Discuss your results.
Explanation / Answer
From the given formula,
v = 55mph = 80.67fps
Total resistance in still air = 0.01*6000 + 0.0001*6000*80.67 + 0 = 108.402 lbf
Resistance on a level road= 93 + 0.0028*0.04*100*55*55 = 181.29 lbf
Horse power to be delivered to wheels = 181.29*80.67 = 14.6243 * 10^(3) foot-pound/sec
= 26.59 HP
Power to be delivered by motor = 26.59/0.8 = 33.23 HP
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