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Radius of the turn of an upright bike (for small steering angles)

In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any ... more

Leaning ( for bikes and motorcycles)

Bikes must lean during a turn to balance the relevant forces: gravitational, inertial, frictional, and ground support. The angle of lean can be ... more

Trail (for motorcycles)

Trail, or caster, is the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. The ... more

Lean angle due to a tire thickness of a bicycle

The finite width of the tires alters the actual lean angle of the rear frame from the ideal lean angle described above. The actual lean angle between the ... more

Steering ratio

The steering ratio is the relationship between how far you turn a steering wheel and how far the actual wheels turn as a result. A higher steering ratio ... more

Weight transfer ( or load transfer)

In the automobile industry, weight transfer customarily refers to the change in load borne by different wheels during acceleration and the change in ... more

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 ... more

Vertical Forces at the wheels for a bicycle (rear wheel)

Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... more

Vertical Forces at the wheels for a bicycle (front wheel)

Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... more

Trail ( for bicycles)

A factor that influences how easy or difficult a bike will be to ride is trail, the distance that the front wheel ground contact point trails behind the ... more

Stuart Number

The Stuart number (N), also known as magnetic interaction parameter, is a dimensionless number of fluids, i.e. gases or liquids.

It is defined as ... more

Law of cotangents (in term of tangents)

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more

Spirograph (rotation angle of the inner circle)

Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
A ... more

Bend allowance

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Bend Deduction - right angles

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Archimedean spiral

The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed ... more

Tangent Length (Horizontal curves for highway design)

Horizontal alignment in road design consists of straight sections of road, known as tangents, connected by circular horizontal curves. Circular curves are ... more

Spirograph (Y-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Spirograph (X-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Arbitrary Cherenkov emission angle

Cherenkov radiation, also known as Vavilov–Cherenkov radiation,[a] is electromagnetic radiation emitted when a charged particle (such as an electron) ... more

Maximum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Minimum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Velocity in Frictionless Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Tangent of the difference of two angles (Bhāskara formula)