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# Wheelbase

In both road and rail vehicles, the wheelbase is the distance between the center of the front and rear wheels.

In automobiles, the wheelbase is the distance between the center of the front wheel and the center of the rear wheel. At equilibrium, the total torque of the forces acting on the car is zero, and thus the wheelbase is related to the weight on each tire by the following formulas:

$W_f = {c \over L}mg$
$W_r = {b \over L}mg$

where Wf is the weight on the front tire, Wr is the weight on the rear tire, L is the wheelbase, c is the distance from the center of gravity (CG) 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 CG, 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 Wf is the weight on the front tire, Wr is the weight on the rear tire, c is the distance from the CG to the rear wheel, b is the distance from the CG 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/s2), h is the height of the CG 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. This is why it is crucial, when towing a single-axle caravan, to distribute the caravan's weight so that down-thrust on the tow-hook is about 100 pounds. 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 CG. Thus, in a car with a short wheelbase, the short lever arm from the CG 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.

Wheelbases provide the basis for one of the most common vehicle size class systems.