Question

A car weighing 3200 lb and equipped with a 175 HP engine is travelling along a 3% grade, assume standard conditions and the following vehicle specific parameters: rolling coefficient = 0.023, drag coefficient = 0.4, and frontal area = 22 ft^2.

What is the road load due to only rolling resistance?

What is the road load due to only road grade?

What is the maximum speed the vehicle is capable of on the grade?

Answer 1

given weight mg = 3200 lb car

engine Hp = 175 HP

grade = 0.03 = dh/dx

hence

tan(theta) = 0.03

theta = 1.718358 deg

coefficient of rolling friciton, uk = 0.023

drag coefficient, Cd = 0.4

frontal area, A = 22 ft^2

a. load due to rolling reissitance = uk*mg*cos(theta) = 73.5669023 lb

b. road load due to road grade = mg*sin(theta) = 95.95682904573 lb

c. maximum speed = v

then

Drag force = D

rolling load = R

gravity load = W

D + W = R + P/v ( where P is power, hence P/v is thrust force)

1 hp = 550 lbf

hence

Cd*0.5*rho*v^2*A + 95.95682904573 = 73.5669023 + 550/v

rho = 0.0765 lb/ft^3 density of air

hence

0.3366v^3 + 22.38992674573v - 550 = 0

solving

v = 9.914 ft/s = 6.759545 mph