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Long Chord 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

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

Middle Ordinate (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

External Distance (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

Curve sight distance (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

Horizontal Curve - Degree of curve

Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The ... more

Horizontal Curve - Allowable radius

The allowable radius for a horizontal curve can then be determined by knowing the intended design velocity, the coefficient of friction, and the allowed ... more

Horizontal curve - Sight obstraction distance (S<L)

Horizontal curve – Sight Distance Properties (S<L)

Horizontal Curves are one of the two important transition elements in geometric ... more

Horizontal curve - Sight obstraction distance (S>L)

Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve ... more

Sag curve length when S<L (Vertical curves for highway design)

When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long ... more

Sag curve length when S>L (Vertical curves for highway design)

When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long ... more

Accident modification factor

The safety of a horizontal curve is affected by the length of the curve, the curve radius, whether spiral transition curves are used, and the ... 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

Crest curve length when S>L (Vertical curves for highway design)

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

Crest curve length when S<L (Vertical curves for highway design)

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

Desired radius of a curve

The equation for the desired radius of a curve, takes into account the factors of speed and superelevation (e). This equation can be algebraically ... 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

Minimum railway curve radius (by the track gauge and the cant)

The minimum railway curve radius, the shortest allowable design radius for railway tracks under a particular set of conditions.
Track gauge is a ... more

Vertical Curve - Offset

Offsets are vertical distances from the initial tangent to the curve, play a significant role in vertical curve design.

Vertical Curves are the ... more

Vertical Curve - Parabolic formula

Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical ... more

Hypotrochoid (parametric equation Y- coordinate)

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is ... more

Minimum railway curve radius

The minimum railway curve radius, the shortest allowable design radius for railway tracks under a particular set of conditions. It has an important bearing ... more

Tractrix (General formula-cartesian coordinates)

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

Tractrix

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

X-Coordinate of the involute of a circle

An involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its ... more

Y-Coordinate of the involute of a circle

An involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its ... more

Cissoid of Diocles (Cartesian coordinates)

The Cissoid of Diocles is a cubic plane curve member of the conchoid of de Sluze family of curves and in form it resembles a tractrix.( Tractix is the ... more

Conic section (polar system and one focus on the pole and the other somewhere on the 0° ray )

conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. A conic ... more

Cycloid ( parametric equation Y-coordinate)

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more

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