Simple Circular Curve Formulas |
||
|
\( c \;=\; 2 \cdot r \cdot sin \left(\dfrac{ \theta }{ 2 } \right)\) \( E \;=\; r \cdot sec \left( \dfrac{ \theta }{ 2 } \right) - r \) \( l \;=\; \dfrac{ \pi \cdot r \cdot \theta }{ 180 } \) \( M \;=\; r - r \cdot cos \left( \dfrac{ \theta }{ 2 } \right) \) \( T \;=\; r \cdot tan \left( \dfrac{ \theta }{ 2 } \right) \) |
||
| Symbol | English | Metric |
| \( \theta \) = angle | \(deg\) | \(rad\) |
| \( BT \) = back tangent | \(deg\) | \(rad\) |
| \( c \) = chord length | \(ft\) | \(m\) |
| \( E \) = external distance | \(ft\) | \(m\) |
| \( FT \) = forward tangent | \(deg\) | \(rad\) |
| \( l \) = length of curve | \(ft\) | \(m\) |
| \( M \) = middle ordinate | \(ft\) | \(m\) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( PC \) = point on curve | \(ft\) | \(m\) |
| \( PI \) = point of intersection | \(ft\) | \(m\) |
| \( PT \) = point on tangent | \(ft\) | \(m\) |
| \( r \) = radius of curve | \(ft\) | \(m\) |
| \( T \) = subtangent | \(deg\) | \(rad\) |
A simple circular curve is a curve that is part of a circle. A circle is defined as the set of all points in a plane that are a given distance (radius) from a given point (center). A circular curve, then, is a segment of this circle. Simple circular curve is a curve that does not cross itself.
