Bump Force Calculator

When driving over speed humps or other road irregularities a sudden force is transmitted through the wheels to the suspension. This force is called impact force and represents all of the energy that must be absorbed by the springs and shock absorbers in order to provide a comfortable ride and ensure good tire contact with the road.

This calculator uses four values which are related by a single equation, so you can leave any one field blank to calculate it.

What is impact force?

When a wheel hits an obstacle, the impact force is a vertical force transmitted from the road through the tire and suspension to the vehicle body. The suspension absorbs this force to ensure that the chassis and occupants are not subjected to severe jolts on every impact.

This effect is achieved through two mechanisms. The spring stores energy when compressed, and creates a force that resists the compression proportionally. The damper, also known as shock absorber, damps the motion depending on the speed of the wheel and converts this energy into heat. The sum of these two effects results in the total suspension force.

where k is the spring constant, x is the compression distance, c is the damping coefficient and v is the vertical velocity of the wheel. The spring takes note of how much it has been compressed while the damper notes how fast the wheel was moving.

Here's how to use this calculator.

If you enter the spring constant, suspension deflection, damping coefficient and vertical speed of the wheel, then the total braking force will be shown as the main result at the top of the page. In a side panel, the total forces are broken down into spring force and damper force, with the contribution from the damper also being indicated.

Since these five quantities are related by a single equation, any one of them can be calculated if the other four are known. To determine the deflection required to produce a given force, enter the force and three other values and leave the field for deflection blank; the calculator will then fill in the result. The drop-down menus next to each field allow you to switch between metric and imperial units, with conversions done automatically.

Understanding the formula for takeoff thrust:

Let's take a car with a spring constant of 25,000 Newtons per meter as an example. When the suspension hits a bump, it compresses by 5 centimeters, which is equal to 0.05 meters. The damping coefficient of the shock absorber is 1,500 Newton-seconds per meter, and the wheel is moving upwards at a speed of 2 meters per second.

First, we calculate the spring force by multiplying the spring constant with the compression distance.

Next we calculate the damper force by multiplying the damping coefficient with the velocity.

If we add these two values together, the total starting thrust is as follows:

The damper produces a force of 3000 N and opposes the spring's force of 1250 N, which is almost two-and-a-half times as much. This follows from physical laws. As the damping force depends on speed, at high speeds the wheels will move up quickly when hitting an irregularity. This also explains why a small adjustment to the damper can have such a big effect on ride comfort.

Why are two values distinguished?

The split between spring and damper forces is the most useful feature of this calculation tool. The spring force depends only on the deflection of the suspension and does not change regardless of how fast the wheel is moving. The damper force increases with speed, so it normally plays a more important role in rough impacts and has the greatest effect on how hard an impact feels.

The force split below shows the two contributions side by side while the speed plot shows that the spring contribution remains stable while the damper contribution increases. When you consider both together, you can see the typical compromise in suspension tuning: a stiff damper reduces vibrations but transmits more forces to the chassis when moving fast; a soft damper provides a more comfortable ride but leads to larger body motions.

The meaning of each result:

In addition to the total value, the calculation tool also displays the following values:

Applications in vehicle technology:

Suspension engineers rely on spring rate data for various tasks. To achieve the desired ride feel, they will tune the size of springs and dampers, and input peak loads into structural analysis to ensure that the chassis can withstand those stresses. This data also helps them optimize the balance between comfort and handling or figure out how different wheels and tires affect the way a car feels.

Racing teams constantly adjust these settings, with each choice a compromise. Softer spring rates reduce the spring forces but cause more body roll in corners. Stiffer shocks can control the wheels better, but transmit more jolts to the chassis when driving over bumps. Much of suspension tuning is deciding which compromises are acceptable.

Tips for accurate results:

The spring constant is usually stated on the spring element or in manufacturer's specifications. The damping ratio is a bit harder to determine; check a shock absorber test datasheet or consult product documentation. The vertical velocity depends on vehicle speed and the shape of the bump, and under typical driving conditions in city traffic it ranges from 1 to 3 meters per second, but can be much higher on racetracks. Roughly speaking, the vertical velocity is approximately the product of the vehicle speed and the sine of the approach angle of the bump.