The Principles Of Surveying by Clendinning J

Author:Clendinning,J.
Language: eng
Format: epub
Tags: NATURAL SCIENCES, Astronomy. Astrophysics. Space research.Geodesy, Astronomical instruments and techniques
Publisher: Blackie And Son Limited

I

2 sin

50

sin .VZ

, when 1 = 100.

This gives the exact relationship between R and Z), but in practice an approximate, but far more convenient, rule is generally used in all cases where extreme accuracy is not needed. This rule depends on the fact that the sine of a small angle is not very different from the radian measure of the angle itself. Let R± be the radius of a curve of degree D±. Then

and so

R

sn ---

sin

I 2 sin ^D l

Z), . . .

__i approximately. D ™ J

If D 1 == 1° and I = 100, R^ = 5729-6 = 5730 approximately, and hence

.

This rule may be used in all ordinary railway and road work so that, iSD — 3°, we take R as 5730/3 = 1910.

Again, when D is a small angle expressed in degrees,

R = Dr'

where r is the number of radians in one degree. Also, if ^ is another chord length on the same curve and D l the corresponding angle at the centre,

'' Dr

7. Tangent Lengths of a Circular Curve.

The first thing to be done in ranging out a circular curve is to find the intersection of the tangents, measure the angle of deflection, and calculate the distances of the beginning and end of the curve from the

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