Simple Circular Curve Formulas |
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c \;=\; 2 \cdot r \cdot sin \dfrac{ \theta }{ 2 } E \;=\; r \cdot sec \dfrac{ \theta }{ 2 } - r l \;=\; \dfrac{ \pi \cdot r \cdot \theta }{ 180 } M \;=\; r - r \cdot cos \dfrac{ \theta }{ 2 } T \;=\; r \cdot tan \dfrac{ \theta }{ 2 } |
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| 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.
