Simple Circular Curve
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.
Simple Circular Curve formulas |
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\(\large{ c = 2 \; r \; sin \; \frac{ \theta }{ 2 } }\) \(\large{ E = r \; sec \; \frac{ \theta }{ 2 } \;-\; r }\) \(\large{ l = \frac{ \pi \; r \; \theta }{ 180 } }\) \(\large{ M = r \;-\; r \; cos \; \frac{ \theta }{ 2 } }\) \(\large{ T = r \; tan \; \frac{ \theta }{ 2 } }\) |
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| Symbol | English | Metric |
| \(\large{ \theta }\) = angle | \(\large{deg}\) | \(\large{rad}\) |
| \(\large{ BT }\) = back tangent | \(\large{deg}\) | \(\large{rad}\) |
| \(\large{ c }\) = chord length | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ E }\) = external distance | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ FT }\) = forward tangent | \(\large{deg}\) | \(\large{rad}\) |
| \(\large{ l }\) = length of curve | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ M }\) = middle ordinate | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ PC }\) = point on curve | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ PI }\) = point of intersection | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ PT }\) = point on tangent | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ r }\) = radius of curve | \(\large{ft}\) | \(\large{m}\) |
| \(\large{ T }\) = subtangent | \(\large{deg}\) | \(\large{rad}\) |
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