iPOGO - 10 Chord Spiral Curve Calculator
Example with formulas:
Given Ls=200.0, Total Delta=2°51', Dc=0.75° chord definition
1) radius of simple curve
Rc = 50 / sin(Dc/2) = 7639.49181 feet
2) total spiral delta
SD = (LS*Dc) / 200 = 0.75°
3) length along original tangent to offset at end of spiral
X = Ls - (Ls^3 / 40 * Rc^2) = 199.996573 feet
4) perpendicular offset from original tangent to end of spiral
Y = Ls^2 / (6 * Rc) = 0.872658 feet
5) throw distance from original curve to end of spiral
O = Y - (Rc * (1 - cos(SD))) = 0.21816 feet
6) distance from OFFSET T.C. to T.S.
Xo = X - (Rc * Sin(SD)) = 99.998715 feet
7) tangent length of original curve
Tc = Rc * Tan(TotalDelta/2) = 190.04054 feet
8) tangent length from original PI to TS
Ts = Xo + Tc + (O * Tan(TotalDelta/2)) = 290.0447 feet
9) tangent length from original TC to TS
TcTs = Xo + (O * Tan(TotalDelta/2)) = 100.0041 feet
10) spiral chord length
Sc = (X^2 + Y^2)^0.5 = 199.998477 feet
11) rate of change in radius
a = 100 * (Dc / Ls) = 0.375° per 100 feet
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