Wheelbase

In automotives, the wheelbase is the distance between the center of the front wheel and the center of the rear wheel. It is equal to the distance of the rear tire from the CG(center of gravity) plus the distance from the front tire to the center of gravity. Due to torque, the wheelbase is related to the center of gravity of an automobile at rest and the weight on each tire by the following formula:

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$W_{f}={c \over L}mg$

$W_{r}={b \over L}mg$

Where $W_{f}$ is the weight on the front tire, $W_{r}$ is the weight on the rear tire, L is the wheelbase, c is the distance from the center of gravity to the rear wheel, b is the distance from the center of gravity to the front wheel, m is the mass of the car, and g is the gravity constant (approx. 9.8 m/s²). So, for example, when one loads the trunk with heavy goods, the center of gravity shifts rearward and the weight on the rear tire increases causing it to sink depending upon the stiffness of the suspension. If the automobile is accelerating or decelerating, extra torque is placed on the rear or front tire respectively, and the equation relating the wheelbase, height above the ground of the center of gravity, and the weight on each tire becomes:

$\mathrm {W_{f}={c \over L}mg-{h \over L}ma}$

$\mathrm {W_{r}={b \over L}mg+{h \over L}ma}$

Where W_f is the weight on the front tire, W_r is the weight on the rear tire, c is the distance from the CG to the rear wheel, b is the distance from the center of gravity to the front wheel, L is the wheelbase, m is the mass of the car, g is the acceleration of gravity (approx. 9.8 m/s<superscript>2</superscript>), h is the height of the car above the ground, a is the acceleration or deceleration if the value is negative. So, as is common experience, when the automobile accelerates, the rear usually sinks and the front rises depending on the suspension. Likewise, when braking the front noses down and the rear rises.

Because of the effect the wheelbase has on the weight transfer of the vehicle, wheelbase dimensions are crucial to the balance and steering of the automobile. For example, a car with a much greater weight load on the rear tends to understeer due to the lack of weight and therefore grip from the front tires. Likewise, a car may oversteer or even "spin out" if there is too much weight on the front tires and not enough on the rear tires. Also, when turning there is lateral torque placed upon the tires which imparts a turning force that depends upon the length of the tire distances from the center of gravity. Thus, in a car with a short wheelbase, the short lever arm from the center of gravity to the rear wheel will result in a greater lateral force on the rear tire which means greater acceleration and less time for the driver to adjust and prevent a spin out or worse.

See Also: torque, force, weight,static equilibrium, and center of gravity