This document contains examples of vehicle dynamics problems related to calculating resistive forces, power required to overcome those forces, vehicle balance and maximum speed, and braking and stopping distances. Problem 2.1 asks to calculate the power required to overcome aerodynamic drag for a sports car traveling at 100 mph. Problem 2.2 asks to calculate the final weight of a sedan if additional weight is added based on the power needed to reach 100 mph accounting for aerodynamic and rolling resistance. Problem 2.8 asks to calculate the maximum acceleration of a car given information about its engine torque, gear ratio, weight and other parameters.

1. Vehicle Dynamics
Example Problems

2. Example problems
• Calculate value of resistive forces
– Aerodynamic
– Rolling
– Gravity
• Power required to overcome resistive
forces

3. Problem 2.1
A new sports car has a drag coefficient of
0.29 and a frontal area of 20 ft2, and is
traveling at 100 mi/h. How much power is
required to overcome aerodynamic drag if
=0.002378 slugs/ft3?

4. Problem 2.2
A vehicle manufacturer is considering an engine for a new sedan (CD
= 0.25, Af = 17 ft2). The car will be tested at 100 mph maximum speed
on a concrete paved surface at sea level (ρ = 0.002378 slugs/ft3).
The car currently weights 2100 lb, but the designer selected an under-
powered engine because he did not account for aerodynamic and
rolling resistances. If 2 lb of additional vehicle weight is added for
each unit of horsepower needed to overcome the neglected
resistance, what will be the final weight of the car if it is to achieve its
100 mph speed?

5. Balance forces
• Calculate available tractive effort
– Maximum tractive effort
– Engine generated tractive effort
– Acceleration
• Calculate maximum speed
– Available engine power
– Resistive forces
– Maximum speed

6. Problem 2.8
A car is traveling on a paved road with CD = 0.35, Af = 21 ft2, W = 3000 lb,
ρ = 0.002378 slugs/ft3. Its engine is running at 3000 rpm and is
producing 250 ft-lb of torque. The car’s gear reduction ratio is 3.5 to 1,
driveline efficiency is 90%, driveline slippage is 3.5%, and the road-wheel
radius is 15 inches. What will the car’s maximum acceleration be under
these conditions on a level road? (assume the available tractive effort is
the engine-generated tractive effort)

7. Problem 2.10
• A 2500-lb car has a maximum speed of
150 miles/hour with 14 inch radius wheels,
a gear reduction of 3 to 1, and a driveline
efficiency of 90%. It is known that at the
car’s top speed the engine is producing
200 ft-lb of torque. If the car’s frontal area
is 25 ft2, what is its drag coefficient?

8. Braking and stopping
• Braking
– Braking force
– Brake force ratio
• Theoretical stopping distance
• Practical stopping distance
• Driver perception/reaction

9. Problem 2.20
• A driver is traveling at 110 miles/hour
down a 3% grade on good, wet pavement.
An accident investigation team noted that
braking skid marks started 590 ft before a
parked car was hit at an estimated 55
mi/h. Ignoring air resistance, and using
theoretical stopping distance, what was
the braking efficiency of the car?

10. Problem 2.23
• A car is traveling at 75 mi/h down a 3% grade on
poor, wet pavement. The car’s braking
efficiency is 90%. The brakes were applied 300
ft before impacting a object. The car had an
antilock braking system, but the system failed
200 ft after the brakes had been applied (wheels
locked). What speed was the car traveling at
just before it impacted the object? (Assume
theoretical stopping distance, ignore air
resistance, and let frl=0.015.)