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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 - Deflection Angles
The use of deflection angles (the angle deflected by a chord) is considerable more rigourous than either of the two previous methods. The method also follows the centreline of the curve, unlike the previous two which require access to the chord and centreline.
The method is based on the following geometry:
It will be remembered that the angle subtended at the circumference by a chord is one half of the angle subtended at the centre (in this case f and q). The first angle through which the chord being used for pegging is deflected is therefore half the angle subtended by that chord at the centre. The next angle through which the next chord is deflected is the equal to twice this value, that is the same as the angle subtended at the centre. A typical application of the method is as follows:
Set the instrument up at the tangent point, sight along the tangent and turn off the first deflection angle f ( =
).fix one end of tape at A, measure off 'c' metres, and swing tape until it aligns with the line of sight. Put in peg B.
Turn theodolite a further q°. Fix one end of tape at B, measure off 'c' metres, and swing tape until that point on the tape crosses the line of sight. Put in peg C.
Repeat step (iii) until you peg the curve. If the line of sight becomes obstructed, then simply set up on any peg on the curve, sight back along the chord to the previous peg and continue to establish the deflection angles.
Precautions to take
Calculate the angle q to seconds, or errors will be considerable if many pegs must be placed.
The final reading, to the other tangent point, should equal
I.