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 = 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 = 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 = 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)
Engine-generated tractive effort
Fe = 250(3.5)(0.90)/(15/12) = 630 lbs
Velocity
V = 2π(15/12)(3000 rpm/60)( )/3.5 = ft/sec = 73.9 mph
Resistance
Ra = ( /2)(0.35)(21)(108.27)2 = lb
frl = 0.01( /147) =
Rrl = (3000) = 52.1 lb
Final Equation
γm = ε2 = (3.5)2 =
m = 3000 lb / 32.2 ft/sec2 = slugs
630 – – 52.1 = (93.17)a
a = 4.77 ft/sec2

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 Theoretical stopping distance
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.)