Consider a truck with the following specifications:

Mass: 2300 kg Wheelbase: 2.5 m Centre of mass location: 1.0 m behind the front axle Centre of mass height: 0.7 m above the ground Drive axle ratio: 3.5:1 Tire rolling radius: 0.35 m

a) If the redline (maximum permissible engine speed) is 4500 rpm, and the maximum vehicle speed in first gear is 40 km/h, what must the first gear ratio be?

b) If the truck is rear wheel drive, what is the maximum acceleration it can achieve on a flat surface with coefficient of friction of ???? = 0.8, before wheelspin occurs? Assume the truck is moving slowly enough to ignore wind and rolling resistance. How much torque must the engine produce in order to spin the wheels in first gear on this surface?

c) If the engine can produce a maximum of 380 Nm of torque, what is the maximum grade it can climb? Is it limited by the engine torque, or the tire grip? Assume ???? = 0.8.

d) If the truck is travelling at 85 km/h, and the engine is running at 3000 rpm, while in fourth gear, what must the fourth gear ratio be?

Assume that tire slip is 2%.

e) If the working speed range of the engine is the same in all gears, estimate the ratios of second and third gear.