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Astroid (Perimeter)

An astroid is a particular mathematical curve: a hypocycloid with four cusps. The astroid is a real locus of a plane algebraic curve of genus zero. The ... more

Astroid (Area)

An astroid is a particular mathematical curve: a hypocycloid with four cusps. The astroid is a real locus of a plane algebraic curve of genus zero. The ... more

Elliptic curve (equation)

In mathematics, an elliptic curve (EC) is a smooth, projective algebraic curve of genus one, on which there is a specified point.Any elliptic curve can be ... 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

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

Darcy friction factor - Blasius correlation with correction for curved or helically coiled tubes

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Runoff curve number

Surface runoff is the water flow that occurs when the soil is infiltrated to full capacity and excess water from rain. The runoff curve number (also called ... more

Tortuosity - alternative method

Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property. ... more

Hypocycloid ( parametric equation X- coordinate)

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

Hypocycloid ( parametric equation Y- coordinate)

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

Limaçon of Pascal

A limaçon is a bicircular rational plane algebraic curve of degree 4. Limaçon of Pascal, is defined as a roulette formed when a circle rolls around the ... 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

Standard logistic sigmoid function (k=1, x0=0, L=1)

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes ... 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

Eccentricity of an ellipse

Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more

General Logistic Sigmoid Function

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes ... 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

Hyperboloid of one sheet equation

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of one sheet can be obtained by ... more

Hyperboloid of two sheets equation

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of two sheets can be obtained by ... 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

Vertical Curve - Stopping Sight Distance

Sight distance is dependent on the type of curve used and the design speed. For crest curves, sight distance is limited by the curve itself, as the curve ... more

Catenary curve

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The ... more

Curve 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

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

Tortuosity

Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property. ... more

Darcy friction factor - Blasius correlation with correction for curved or helically coiled tubes (Variable Rc)

In fluid dynamics, the Darcy friction factor ormulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... 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

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

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