Wheelbase

The wheelbase of a vehicle equals the distance between its front and rear wheels. At equilibrium, the total torque of the forces acting on a vehicle is zero. Therefore, the wheelbase is related to the force on each pair of tires by the following formula:

${\displaystyle F_{f}={d_{r} \over L}mg}$

${\displaystyle F_{r}={d_{f} \over L}mg}$

where ${\displaystyle F_{f}}$ is the force on the front tires, ${\displaystyle F_{r}}$ is the force on the rear tires, ${\displaystyle L}$ is the wheelbase, ${\displaystyle d_{r}}$ is the distance from the center of mass (CM) to the rear wheels, ${\displaystyle d_{f}}$ is the distance from the center of mass to the front wheels (${\displaystyle d_{f}}$ + ${\displaystyle d_{r}}$ = ${\displaystyle L}$), ${\displaystyle m}$ is the mass of the vehicle, and ${\displaystyle g}$ is the gravity constant. So, for example, when a truck is loaded, its center of gravity shifts rearward and the force on the rear tires increases. The vehicle will then ride lower. The amount the vehicle sinks will depend on counter acting forces, like the size of the tires, tire pressure, and the spring rate of the suspension. If the vehicle is accelerating or decelerating, extra torque is placed on the rear or front tire respectively. The equation relating the wheelbase, height above the ground of the CM, and the force on each pair of tires becomes:

${\displaystyle F_{f}={d_{r} \over L}mg-{h_{cm} \over L}ma}$

${\displaystyle F_{r}={d_{f} \over L}mg+{h_{cm} \over L}ma}$

where ${\displaystyle F_{f}}$ is the force on the front tires, ${\displaystyle F_{r}}$ is the force on the rear tires, ${\displaystyle d_{r}}$ is the distance from the CM to the rear wheels, ${\displaystyle d_{f}}$ is the distance from the CM to the front wheels, ${\displaystyle L}$ is the wheelbase, ${\displaystyle m}$ is the mass of the vehicle, ${\displaystyle g}$ is the acceleration of gravity (approx. 9.8 m/s²), ${\displaystyle h_{cm}}$ is the height of the CM above the ground, ${\displaystyle a}$ is the acceleration (or deceleration if the value is negative). So, as is common experience, when the vehicle accelerates, the rear usually sinks and the front rises depending on the suspension. Likewise, when braking the front noses down and the rear rises.:[2]

Because of the effect the wheelbase has on the weight distribution of the vehicle, wheelbase dimensions are crucial to the balance and steering. For example, a car with a much greater weight load on the rear tends to understeer due to the lack of the load (force) on the front tires and therefore the grip (friction) from them. 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 force (400 N). Likewise, a car may oversteer or even "spin out" if there is too much force 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 CM. Thus, in a car with a short wheelbase ("SWB"), the short lever arm from the CM 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.

In rail vehicles, the wheelbase follows a similar concept. However, since the wheels may be of different sizes (for example, on a steam locomotive), the measurement is taken between the points where the wheels contact the rail, and not between the centers of the wheels.

On vehicles where the wheelsets (axles) are mounted inside the vehicle frame (mostly in steam locomotives), the wheelbase is the distance between the front-most and rear-most wheelsets.

On vehicles where the wheelsets are mounted on bogies (American: trucks), three wheelbase measurements can be distinguished:

• the distance between the pivot points of the front-most and rear-most bogie;
• the distance between the front-most and rear-most wheelsets of the vehicle;
• the distance between the front-most and rear-most wheelsets of each bogie.

The wheelbase affects the rail vehicle's capability to negotiate curves. Short-wheelbased vehicles can negotiate sharper curves. On some larger wheelbase locomotives, inner wheels may lack flanges in order to pass curves.

The wheelbase also affects the load the vehicle poses to the track, track infrastructure and bridges. All other conditions being equal, a shorter wheelbase vehicle represents a more concentrated load to the track than a longer wheelbase vehicle. As railway lines are designed to take a pre-determined maximum load per unit of length (tonnes per meter, or pounds per foot), the rail vehicles' wheelbase is designed according to their intended gross weight. The higher the gross weight, the longer the wheelbase must be.