A passenger car has a weight of 4520 lb and a wheelbase of 10.5 ft. The ratio of the distance between the center of gravity of the vehicle and front axle to the wheelbase is 0.45. The cornering stiffness of each of the front tires is 8750 lb/rad and that of the rear tires is 8600lb/rad.

Question

A passenger car has a weight of 4520 lb and a wheelbase of 10.5 ft. The ratio of the distance between the center of gravity of the vehicle and front axle to the wheelbase is 0.45. The cornering stiffness of each of the front tires is 8750 lb/rad and that of the rear tires is 8600lb/rad.

i) Determine if the vehicle is oversteered or understeer.

ii) Based on the answer to question. i) find the characteristics speed or the critical speed of the vehicle.

Answer 1

To determine if the vehicle is oversteered or understeered, we need to calculate the understeer gradient. The understeer gradient is a measure of how the vehicle responds to steering inputs. A positive understeer gradient indicates understeer, while a negative understeer gradient indicates oversteer.

The understeer gradient can be calculated using the following formula:

UG = (CF - CR) * WB / W

Where:
UG = Understeer gradient
CF = Cornering stiffness of the front tires
CR = Cornering stiffness of the rear tires
WB = Wheelbase
W = Weight of the vehicle

i) Calculate the understeer gradient:
UG = (8750 - 8600) * 10.5 / 4520

To determine if the vehicle is oversteered or understeer, we need to check the sign of the understeer gradient. If the value is positive, the vehicle is understeered, and if the value is negative, the vehicle is oversteered.

ii) To find the characteristic speed or critical speed of the vehicle, we need to use the following formula:

Vcritical = sqrt((w * WB * UG) / (2 * F))

Where:
Vcritical = Critical speed
w = Weight distribution on the front axle (ratio of distance between the center of gravity and front axle to the wheelbase)
WB = Wheelbase
UG = Understeer gradient
F = Total lateral force on the tires (CF + CR)

First, calculate the weight distribution on the front axle:
w = WB * 0.45 / WB

Next, calculate the total lateral force on the tires:
F = CF + CR

Finally, calculate the critical speed:
Vcritical = sqrt((w * WB * UG) / (2 * F))

By following the above steps and substituting the given values into the formulas, you can determine if the vehicle is oversteered or understeer and find the characteristic speed or critical speed of the vehicle.