Simple Circular Curve

Simple circular curve is a curve that does not cross itself.

 

Simple Circular Curve formula

\(\large{ c = 2 \; r \; sin \; \frac{ \theta }{ 2 }  }\)
\(\large{ E = r \; sec \; \frac{ \theta }{ 2 } \;-\; r  }\)
\(\large{ l = \frac{ \pi \; r \; \theta }{ 180 }  }\)
\(\large{ M = r \;-\; r \; cos \; \frac{ \theta }{ 2 }   }\)
\(\large{ T = r \; tan \; \frac{ \theta }{ 2 }  }\)

Where:

\(\large{ \theta }\) = angle

\(\large{ BT }\) = back tangent

\(\large{ c }\) = chord length

\(\large{ E }\)  = external distance

\(\large{ FT }\) = forward tangent

\(\large{ l }\)  = length of curve

\(\large{ M }\)  = middle ordinate

\(\large{ \pi }\) = Pi

\(\large{ PC }\) = point on curve

\(\large{ PI }\) = point of intersection

\(\large{ PT }\)  = point on tangent

\(\large{ r }\)  = radius of curve

\(\large{ T }\) = subtangent