AREA 10 Chord Spiral

Notation

For curve points, the first initial represents the alignment on the side toward station zero, the second that away from station zero.
 
T.C.  The point of change in alignment from tangent to circular curve.
C.T. The point of change from circular curve to tangent.
C.C. The point of change in degree of circular curve; the point of compound curve, the point of reverse curve.
T.S. The point of change from tangent to spiral.
S.C. The point of change from spiral to circular curve.
C.S. The point of change from circular curve to spiral.
S.T. The point of change from spiral to tangent.
S.S. The point of change from one spiral to another.

The symbols T.C. and C.T., T.S. and S.T., and S.C. and C.S. become transposed when the direction of stationing is changed.
 
a The angle between the tangent at the T.S. and the chord from the T.S. to any point on the spiral.
A The angle between the tangent at the T.S. And the chord from the T.S. and the S.C.
b The angle at any point on the spiral, between the tangent at that point and the chord from the T.S.
B The angle at the S.C. between the chord from the T.S. and the tangent at the S.C.
c The chord from the T.C. to any point of the spiral.
C The chord from the T.S. to the S.C.
d The degree of curve at any point on the spiral.
D The degree of central circular curve.
I The angle between the initial and final tangents; the total central angle of circular curve and spirals.
k The increase in degree of curve per station on the spiral.
l The length of the spiral in feet from the T.S. to any given point.
L The length of the spiral in feet from the T.S. to the S.C.
o The ordinate of the offset T.C.; the distance between the tangent and a parallel tangent to the offset curve.
r The radius of the osculation circle at any given point of the spiral.
R The radius of the central circular curve.
s The length of the spiral in stations from the T.S. to any given point.
S The length of the spiral in stations from the T.S. to the S.C.
u The distance of the tangent from the T.S. to the intersection with a tangent through any given point of the spiral.
U The distance of the tangent from the T.S. to the intersection with a tangent through the S.C.; the longer spiral tangent.
v The distance on the tangent through any given point from that point to the intersection with the tangent through the T.S.
V The distance on the tangent through the S.C. from the S.C. to the intersection with the tangent through the T.S.; the shorter spiral tangent.
x The abscissa or tangent distance of any given point, referred to the T.S.
X The abscissa or tangent distance of the S.C., referred to the T.S.
y The ordinate or tangent offset of any point on the spiral.
Y The ordinate or tangent offset of the S.C.
Z The abscissa or tangent distance of the offset, T.C. referred to the T.S.
The central angle of the spiral from the T.S. to any given point.
The central angle of the whole spiral.
Ts  The tangent distance of the spiraled curve; distance from T.S. to P.I. (point of intersection of tangents).
Es The external distance of the offset curve.
 

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