Bicycle and motorcycle geometry

File:Head angle rake and trail.svg

Bike wheelbase, head angle, fork offset, and trail

Bicycle and motorcycle geometry is the collection of key measurements (lengths and angles) that define a particular bike configuration. Primary among these are wheelbase, steering axis angle, fork offset, and trail. These parameters have a major influence on how a bike handles.

Wheelbase

Wheelbase is the horizontal distance between the centers (or the ground contact points) of the front and rear wheels. Wheelbase is a function of rear frame length, steering axis angle, and fork offset. It is similar to the term wheelbase used for automobiles and trains.

Wheelbase has a major influence on the longitudinal stability of a bike, along with the height of the center of gravity. Short bikes are much more likely to perform wheelies and stoppies.

Steering axis angle

The steering axis angle, also called caster angle, is the angle that the steering axis makes with the horizontal or vertical, depending on convention. The steering axis is the axis about which the steering mechanism (fork, handlebars, front wheel, etc.) pivots.

In bicycles, the steering axis angle is called the head angle and is measured clock-wise from the horizontal when viewed from the right side. A 90° head angle would be vertical. For example, Lemond offers:

• a 2007 Filmore, designed for the track, with a head angle that varies from 72.5° to 74° depending on frame size
• a 2006 Tete de Course, designed for road racing, with a head angle that varies from 71.25° to 74°, depending on frame size.

In motorcycles, the steering axis angle is called the rake and is measured counter-clock-wise from the vertical when viewed from the right side. A 0° rake would be vertical. For example, Moto Guzzi offers:

• a 2007 Breva V 1100 with a rake of 25°30’ (25 degrees and 30 minutes)
• a 2007 Nevada Classic 750 with a rake of 27.5° (27.5 degrees)

Fork offset

The fork offset is the perpendicular distance from the steering axis to the center of the front wheel.

In bicycles, fork offset is also called fork rake. Virtually all road racing bicycle forks have an offset of 43-45mm due to the almost-standard frame geometry and 700c wheels, so racing forks are widely interchangeable.

In motorcycles with telescopic fork tubes, fork offset can be implemented by either an offset in the triple tree, adding a rake angle (usually measured in degrees from 0) to the fork tubes as they mount into the triple tree, or a combination of the two. Other, less-common motorcycle forks, such as trailing link or leading link forks, can implement offset by the length of link arms.

Trail

Trail is the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. The measurement is considered positive if the front wheel ground contact point is behind (towards the rear of the bike) of the steering axis intersection with the ground.

Trail is often cited as an important determinant of bicycle handling characteristics [1], and is sometimes listed in bicycle manufacturers' geometry data, although Wilson and Papodopoulos argue that mechanical trail may be a more important and informative variable.

Trail is a function of head angle, fork offset or rake, and wheel size. Their relationship can be described by this formula.:

$Trail={\frac {(R_{w}\cos(A_{h})-O_{f})}{\sin(A_{h})}}$

where $R_{w}$ wheel radius, $A_{h}$ is the head angle measured clock-wise from the horizontal and $O_{f}$ is the fork offset or rake. Trail can be increased by increasing the wheel size, decreasing or slackening the head angle, or decreasing the fork rake or offset. Trail decreases as head angle increases (becomes steeper), as fork offset increases, or as wheel diameter decreases.

Motorcyclists tend to speak of trail in relation to rake angle. The larger the rake angle the larger the trail. Note that, on a bicycle, as rake angle increases, head angle decreases.

Trail can vary as the bike leans or steers. In the case of traditional geometry, trail decreases (and wheelbase increases if measuring distance between ground contact points and not hubs) as the bike leans and steers in the direction of the lean.

At least one motorcycle, the MotoCzysz C1, has a fork with adjustable trail, from 89mm to 101mm.

Mechanical trail

Mechanical trail is the perpendicular distance between the steering axis and the point of contact between the front wheel and the ground. It may also be referred to as normal trail.

Although the scientific understanding of bicycle steering remains incomplete , mechanical trail is certainly one of the most important variables in determining the handling characteristics of a bicycle. A higher mechanical trail is known to make a bicycle easier to ride "no hands" and thus more subjectively stable, but skilled and alert riders may have more path control if the mechanical trail is lower.

Legal requirements

The state of North Dakota (USA) actually has minimum and maximum requirements on rake and trail for "manufacture, sale, and safe operation of a motorcycle upon public highways."

"4. All motorcycles, except three-wheel motorcycles, must meet the following specifications in relationship to front wheel geometry:

MAXIMUM: Rake: 45 degrees - Trail: 14 inches [35.56 centimeters] positive

MINIMUM: Rake: 20 degrees - Trail: 2 inches [5.08 centimeters] positive

Manufacturer's specifications must include the specific rake and trail for each motorcycle or class of motorcycles and the terms "rake" and "trail" must be defined by the director by rules adopted pursuant to chapter 28-32."

Other aspects

For other aspects of geometry, such as ergonomics or intended use, see the Bicycle frame article. For motorcycles the other main geometric parameters are seat height and relative foot peg and handlebar placement.

See also

• Bicycle and motorcycle dynamics
• Bicycle fork
• Motorcycle fork

External links

• A useful trail calculator on the Kogswell website
• Motorcycle Steering Geometry