Mechanical Trail Calculator

The mechanical trail is a small geometric value that helps keep the steering straight. As the contact point of the wheel is behind the intersection between the steering axis and the ground, the wheel will be pulled back like the castor wheels on a shopping cart, which automatically returns the steering to center position. This calculator computes the mechanical trail from the tire radius, the caster angle, and fork offset, while also showing the mechanical trail (normal trail) and the ground contact trail. It also supports reverse calculation: if one of the values Radius, Caster Angle or Trail is missing, it can be computed.

What is the mechanical steering angle?

Imagine two points on the road. The first is the steering axis, a straight line around which the wheel rotates and whose extension cuts the ground at a point. The second point is the center of the tire's contact area. The distance between these two points is the caster angle. If the steering axis lies ahead of the contact area, then the caster angle is positive, and the wheel follows the axis backwards. This is why the steering remains stable and goes straight ahead.

There are two different methods of measuring this distance that are often confused with each other. The mechanical trail, also called normal trail, is measured at a direction perpendicular to the steering axis. The ground contact trail is measured horizontally along the road surface. Both values describe the same geometric relationship, but differ only in the cosine of the caster angle, which means they are not identical. Confusing these two values is a common mistake in this context.

The formula for mechanical steering angle:

The mechanical steering angle is determined by the wheel radius (measured perpendicularly), the trail of the steering axis and the offset at which the axle deviates from the steering axis forward.

Here t_m is the mechanical trail, R is the wheel radius, φ is the fork rake angle and d is the offset of the fork or triple clamp. The ground trail is calculated by dividing that same value by the cosine of the fork rake angle.

When the steering axis passes through the center of the wheel, the offset is zero and the mechanical trail can be simplified to R multiplied by the sine of the caster angle. As the offset in cars is small, this form is used for basic car trail.

Example calculation:

Let's take a motorcycle front wheel with a radius of 300mm, a fork angle of 25 degrees and a fork offset of 30 mm. As the sine of 25 degrees is approximately 0.4226, the mechanical trail works out to be:

When the angle of attack is 25 degrees, the ground contact point will be divided by the cosine which is approximately 0.9063.

For street motorcycles both values are reasonable and stable. The ground contact point is larger since the division by a cosine smaller than 1 always leads to a larger result.

This is how this calculation tool works:

Enter the tire diameter and trail angle. Select your preferred units. If you know the fork offset, enter that as well. The result will show mainly mechanical trail, but also ground contact trail. To calculate a different unknown quantity, simply leave the corresponding field blank. If you input desired trail and trail angle, the radius is calculated. If you input trail and radius, the trail angle is calculated. There is no mode selection required, as leaving fields blank tells the calculator which value to solve for.

If you only know the tire size like "205/55R16" then open the Tire Size Helper to convert it into a radius. By opening the Steering Feel layer and adding in some cornering force, you can calculate and see the self-aligning torque due to ground contact. If you open up the Ground Contact and Trail Diagrams, you can see how each value changes as the angle is changed.

Mechanical follow-through and ground contact.

It is important to make this point because many online calculators only show one value and often the representation of these values is not consistent. Ground clearance is the distance measured along the ground from the tire contact patch to where the steering axis intersects with the ground, while mechanical trail is the perpendicular distance, measured at right angles to the steering axis the wheel rotates around, from the tire contact patch to the point where the steering axis intersects the ground, thus representing the actual lever arm that generates the self-aligning torque. In general, ground clearance is what you will find quoted in suspension or motorcycle spec sheets, whereas mechanical trail is often used when analyzing vehicle dynamics. This calculator shows both values so you don't have to guess which value a particular specification entry represents.

Why Trail Is Important

Track spread is a significant factor in determining the handling characteristics of a vehicle. A larger track spread increases stability and self-centering force, but results in heavier steering behavior and slower response when entering curves. Smaller track spread provides lighter steering feel, but can lead to instability at high speeds. Motorcycle and bicycle designers combine trail with offset to achieve optimal track spread for each vehicle. Automobile suspension engineers also adjust track spread using the caster angle.

The table below shows these relationships in three different ways, and assigns them to the possible missing values.

Track deviation and aerodynamic effect

The wheel perceived toe-out is not only made up of geometric factors. Tires deform when cornering, and the point of application of the resulting lateral force is slightly behind the center of pressure on the contact patch. This additional distance is the aerodynamic toe-out which adds to the mechanical toe-out to give the total effective toe-out. When a cornering force acts on the effective toe-out, it creates a torque that tries to return the wheel back to the straight-ahead position - this is called the self-aligning torque. Within the steering adjustment range these values can be calculated.

Warnings and Restrictions

Use trail measured relative to the vertical, not the angle measured relative to the horizontal. The bike head tube angle uses a reversed notation with the horizontal as reference so that a 72 degree head tube angle is equivalent to 18 degrees of trail. The calculator also shows the angle relative to the horizontal for comparison purposes. Make sure your units for radius and offset match or let the calculator convert them. Keep in mind that mechanical trail is just one geometric part of steering feel, and load, tire structure, and aerodynamic effects will affect actual behavior.