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Horizontal Curves
Basic Properties Of
Horizontal Curves
Location Of Tangent
Points
Setting Out
Offsets From The Tangent
Offsets From The Chord
Deflection Angles
Deflection Distances
Quartering
Coordinates
Transitions Curves
Setting Out - Offsets From The Tangent
When the tangent points have been located, the curve may be set out by means of offsets from the tangents. Consider the circular arc illustrated below with centre O and one of the tangent points, T. It is necessary to calculate the length of the offset BA(c) at distance TB(g) along the tangent. Let radius of arc be R.
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Applying Pythagoras Theorem to triangle OAC, we have: OA2 = OC2 + AC2 = (TO - TC)2 + AC2 or OA2 = (TO - BA)2 + TB2 |
Substituting for x, y, and R in this equation:
R2 = (R - x)2 + y2
or
(R - x)2 = (R2 - y2)
\ x = 
(R2 - y2)
Hence, values of x may be calculated for regular intervals of y. This method is useful when the angle through which the road deflects is small such that offsets are short. The curve may be adequately defined by setting out offsets from both tangents.