# Bicycle and motorcycle geometry

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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,[ clarification needed ] along with the height of the center of mass of the combined bike and rider. Short bikes are much more suitable for performing wheelies and stoppies.

## Steering axis angle

The steering axis angle is called caster angle when measured from vertical axis or head angle when measured from horizontal axis. The steering axis is the axis about which the steering mechanism (fork, handlebars, front wheel, etc.) pivots. The steering axis angle usually matches the angle of the head tube.

### Bicycle head angle

In bicycles, the steering axis angle is measured from the horizontal and called the head angle; a 90° head angle would be vertical. For example, Lemond [1] 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.

Due to front fork suspension, modern mountain bikes—as opposed to road bikes—tend to have slacker head tube angles, generally around 70°, although they can be as low as 62° (depending on frame geometry setting). [2]

At least one manufacturer, Cane Creek, offers an after-market threadless headset that enables changing the head angle. [3]

### Motorcycle rake angle

In motorcycles, the steering axis angle is measured from the vertical and called the caster angle, rake angle, or just rake; [4] a 0° rake is therefore vertical. For example, Moto Guzzi [5] offers:

• a 2007 Breva V 1100 with a rake of 25°30' (25.5 degrees)
• a 2007 Nevada Classic 750 with a rake of 27.5°

## 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. Road racing bicycle forks have an offset of 40–50 mm (1.6–2.0 in). [6]

The offset may be implemented by curving the forks, adding a perpendicular tab at their lower ends, offsetting the fork blade sockets of the fork crown ahead of the steerer, or by mounting the forks into the crown at an angle to the steer tube. The development of forks with curves is attributed to George Singer. [7]

In motorcycles with telescopic fork tubes, fork offset can be implemented by either an offset in the triple tree, adding a triple tree rake [8] (usually measured in degrees from 0) to the fork tubes as they mount into the triple tree, or a combination of the two. [9] Other, less-common motorcycle forks, such as trailing link or leading link forks, can implement offset by the length of link arms.

## Fork length

The length of a fork is measured parallel to the steer tube from the lower fork crown bearing to the axle center. [10]

## Trail

Trail is the horizontal distance from where the front wheel touches the ground to where the steering axis intersects the ground. The measurement is considered positive if the front wheel ground contact point is behind (towards the rear of the bike) the steering axis intersection with the ground. Most bikes have positive trail, though a few, such as the two-mass-skate bicycle and the Python Lowracer, have negative trail. [11]

Trail is often cited as an important determinant of bicycle handling characteristics, [12] [13] and is sometimes listed in bicycle manufacturers' geometry data. Wilson and Papodopoulos [ citation needed ] argue that mechanical trail may be a more important and informative variable, [14] although both expressions describe very nearly the same thing.

Trail is a function of steering axis angle, fork offset, and wheel size. Their relationship can be described by this formula: [15]

${\displaystyle {\text{Trail}}_{\text{bicycle}}={\frac {R_{w}\cos(A_{h})-O_{f}}{\sin(A_{h})}}}$ and ${\displaystyle {\text{Trail}}_{\text{motorcycle}}={\frac {R_{w}\sin(A_{r})-O_{f}}{\cos(A_{r})}}}$

where ${\displaystyle R_{w}}$ is wheel radius, ${\displaystyle A_{h}}$ is the bicycle head angle measured from the horizontal, ${\displaystyle A_{r}}$ is the motorcycle rake angle measured from the vertical, and ${\displaystyle O_{f}}$ is the fork offset. Trail can be increased by increasing the wheel size, decreasing or slackening the head angle, or decreasing the fork 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. [16] Trail can also vary as the suspension activates, in response to braking for example. As telescopic forks compress due to load transfer during braking, the trail and the wheelbase both decrease. [17] [ self-published source? ] At least one motorcycle, the MotoCzysz C1, has a fork with adjustable trail, from 89 to 101 mm [3.50 to 3.98 inches]. [18]

## Mechanical trail

Mechanical trail is the perpendicular distance between the steering axis and the point of contact between the front wheel and the ground. [19] It may also be referred to as normal trail. [20] In each case, its value is equal to the numerator in the expression for trail.

${\displaystyle {\text{MechanicalTrail}}_{\text{bicycle}}=R_{w}\cos(A_{h})-O_{f}}$, and
${\displaystyle {\text{MechanicalTrail}}_{\text{motorcycle}}=R_{w}\sin(A_{r})-O_{f}}$

Although the scientific understanding of bicycle steering remains incomplete, [14] mechanical trail is certainly one of the most important variables in determining the handling characteristics of a bicycle. A trail of zero may give some advantages: [21]

• the influence of the position of the center of pressure of wind forces coming from the side is eliminated
• the wheel flop effect (see below) is eliminated

Skilled and alert riders may have more path control if the mechanical trail is lower while a higher trail is known to make a bicycle easier to ride "no hands" and thus more subjectively stable.

## Wheel flop

Wheel flop refers to steering behavior in which a bicycle or motorcycle tends to turn more than expected due to the front wheel "flopping" over when the handlebars are rotated. Wheel flop is caused by the lowering of the front end of a bicycle or motorcycle as the handlebars are rotated away from the "straight ahead" position. This lowering phenomenon occurs according to the following equation:

${\displaystyle f=b\sin \theta \cos \theta }$

where:

${\displaystyle f}$ = "wheel flop factor," the distance that the center of the front wheel axle is lowered when the handlebars are rotated from the straight ahead position to a position 90 degrees away from straight ahead
${\displaystyle b}$ = trail
${\displaystyle \theta }$ = head angle

Because wheel flop involves the lowering of the front end of a bicycle or motorcycle, the force due to gravity will tend to cause handlebar rotation to continue with increasing rotational velocity and without additional rider input on the handlebars. Once the handlebars are turned, the rider needs to apply torque to the handlebars to bring them back to the straight ahead position and bring the front end of the bicycle or motorcycle back up to the original height. [22] The rotational inertia of the front wheel will lessen the severity of the wheel flop effect because it results in opposing torque being required to initiate or accelerate changing the direction of the front wheel.

According to the equation listed above, increasing the trail and/or decreasing the head angle will increase the wheel flop factor on a bicycle or motorcycle, which will increase the torque required to bring the handlebars back to the straight ahead position and increase the vehicle's tendency to veer suddenly off the line of a curve. Also, increasing the weight borne by the front wheel of the vehicle, either by increasing the mass of the vehicle, rider and cargo or by changing the weight ratio to shift the center of mass forward, will increase the severity of the wheel flop effect. Increasing the rotational inertia of the front wheel by increasing the speed of the vehicle and the rotational speed of the wheel will tend to counter the wheel flop effect.

A certain amount of wheel flop is generally considered to be desirable. Bicycle Quarterly magazine states, "A bike with too little wheel flop will be sluggish in its reactions to handlebar inputs. A bike with too much wheel flop will tend to veer off its line at low and moderate speeds." [23]

## Modifications

Forks may be modified or replaced, thereby altering the geometry of the bike.

### Changing fork length

Increasing the length of the fork, for example by switching from rigid to suspension, raises the front of a bicycle and thus decreases its head angle. [10] Lengthening the fork would have the opposite effect on the rake of a motorcycle, since rake is measured in the opposite direction.

A rule of thumb is a 10 mm change in fork length gives a half-degree change in the steering axis angle.

### Changing fork offset

Increasing the offset of a fork reduces the trail, and if performed on an existing fork by bending without lengthening the blades, shortens the fork. [24]

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." [25]

"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.

## Related Research Articles

A mountain bike (MTB) or mountain bicycle is a bicycle designed for off-road cycling. Mountain bikes share some similarities with other bicycles, but incorporate features designed to enhance durability and performance in rough terrain, which makes them heavier, more complex and less efficient on smooth surfaces. These typically include a suspension fork, large knobby tires, more durable wheels, more powerful brakes, straight, extra wide handlebars to improve balance and comfort over rough terrain, and wide-ratio gearing optimised for topography and application. Rear suspension is ubiquitous in heavier-duty bikes and now common even in lighter bikes. Dropper posts can be installed to allow the rider to quickly adjust the seat height.

A recumbent bicycle is a bicycle that places the rider in a laid-back reclining position. Most recumbent riders choose this type of design for ergonomic reasons: the rider's weight is distributed comfortably over a larger area, supported by back and buttocks. On a traditional upright bicycle, the body weight rests entirely on a small portion of the sitting bones, the feet, and the hands.

A tricycle, sometimes abbreviated to trike, is a human-powered three-wheeled vehicle.

A bicycle frame is the main component of a bicycle, onto which wheels and other components are fitted. The modern and most common frame design for an upright bicycle is based on the safety bicycle, and consists of two triangles: a main triangle and a paired rear triangle. This is known as the diamond frame. Frames are required to be strong, stiff and light, which they do by combining different materials and shapes.

A touring bicycle is a bicycle designed or modified to handle bicycle touring. To make the bikes sufficiently robust, comfortable and capable of carrying heavy loads, special features may include a long wheelbase, frame materials that favor flexibility over rigidity, heavy duty wheels, and multiple mounting points.

A racing bicycle, also known as a road bike is a bicycle designed for competitive road cycling, a sport governed by and according to the rules of the Union Cycliste Internationale (UCI).

A bicycle fork is the part of a bicycle that holds the front wheel.

The caster angle or castor angle is the angular displacement of the steering axis from the vertical axis of a steered wheel in a car, motorcycle, bicycle, other vehicle or a vessel, as seen from the side of the vehicle. The steering axis in a car with dual ball joint suspension is an imaginary line that runs through the center of the upper ball joint to the center of the lower ball joint, or through the center of the kingpin for vehicles having a kingpin.

Countersteering is used by single-track vehicle operators, such as cyclists and motorcyclists, to initiate a turn toward a given direction by momentarily steering counter to the desired direction. To negotiate a turn successfully, the combined center of mass of the rider and the single-track vehicle must first be leaned in the direction of the turn, and steering briefly in the opposite direction causes that lean. The rider's action of countersteering is sometimes referred to as "giving a steering command".

The head tube is the part of a cycle's tubular frame within which the front fork steerer tube is mounted. On a motorcycle, the "head tube" is normally called the steering head. On bicycles the manufacturer's brand located on the head tube is known as a head badge.

Wheel alignment sometimes referred to as breaking, or tracking is part of standard automobile maintenance that consists of adjusting the angles of wheels to the car manufacturer specifications. The purpose of these adjustments is to reduce tire wear and to ensure that vehicle travel is straight and true. Alignment angles can also be altered beyond the maker's specifications to obtain a specific handling characteristic. Motorsport and off-road applications may call for angles to be adjusted well beyond normal, for a variety of reasons.

Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today.

A motorcycle's suspension serves a dual purpose: contributing to the vehicle's handling and braking, and providing safety and comfort by keeping the vehicle's passengers comfortably isolated from road noise, bumps and vibrations.

A downhill bike is a full suspension bicycle designed for downhill cycling on particularly steep, technical trails. Unlike a typical mountain bike, durability and stability are the most important design features, compared to lighter, more versatile cross-country bikes. Downhill bikes are primarily intended for high-speed descent, and downhill riders will usually push, or shuttle via chairlifts or motorized vehicles, to the trailhead. Downhill bikes share similarities with freeride bikes due to their large strong frames and increased travel.

A motorcycle fork connects a motorcycle's front wheel and axle to its frame, typically via a yoke, also known as a triple clamp, which consists of an upper yoke joined to a lower yoke via a steering stem, a shaft that runs through the steering head, creating the steering axis. Most forks incorporate the front suspension and front brake, and allow the front wheel to rotate about the steering axis so that the bike may be steered. Most handlebars attach to the top clamp in various ways, while clip-on handlebars clamp to the fork tubes, either just above or just below the upper triple clamp.

The Kawasaki Ninja ZX-9R is a motorcycle in the Ninja sport bike series from Japanese manufacturer Kawasaki, produced from 1994 until 2003. There were five model incarnations across two basic designs.

A steering damper, or steering stabiliser is a damping device designed to inhibit an undesirable, uncontrolled movement or oscillation of a vehicle steering mechanism, a phenomenon known in motorcycling as wobble.

In vehicle acrobatics, a wheelie, or wheelstand, is a vehicle maneuver in which the front wheel or wheels come off the ground due to sufficient torque being applied to the rear wheel or wheels, or rider motion relative to the vehicle. Wheelies are usually associated with bicycles and motorcycles, but can be done with other vehicles such as cars, especially in drag racing and tractor pulling.

## References

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2. Paul Aston (28 September 2015). "First Ride: Nicolai Mojo GeoMetron". PinkBike. Retrieved 26 February 2017. GeoMetron Details: 62–63.5° head angle, dependent upon shock and fork length.
3. Matt Pacocha (23 December 2011). "Cane Creek AngleSet review". BikeRadar. Retrieved 14 April 2013.
4. Rider Contributor (30 June 2009). "Suspension and Understanding Motorcycle Rake and Trail". Rider Magazine. Retrieved 14 December 2013. Rake is the angle, in degrees, that the steering head of the frame...is tilted back from the vertical{{cite web}}: |author= has generic name (help)
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19. Tony Foale (2006). Motorcycle Handling and Chassis Design: The Art and Science. p. 3-1. ISBN   9788493328634 . Retrieved 18 October 2013. the distance between the ground contact patch and the steering axis as measured at right angles to that axis. The SAE refer to [this] as 'Mechanical Trail'
20. Vittore Cossalter (2006). Motorcycle Dynamics. p. 32. ISBN   9781430308614 . Retrieved 18 October 2013. normal trail is the perpendicular distance between the front contact point and the steering head axis
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