From Engineering Surveying, Sixth Edition


Although equations are available which solve compound curves (Figure 10.14) and reverse curves (Figure 10.15), they are difficult to remember so it is best to treat the problem as two simple curves with a common tangent point t.

Figure 10.14: Compound curve

Figure 10.15: Reverse curve

In the case of the compound curve, the total tangent lengths T 1 I and T 2 I are found as follows:

R 1 tan ? 1/2 = T 1 t 1 = t 1 t


R 2 tan ? 2/2 = T 2 t 2 = t 2 t, as t 1 t 2 = t 1 t + t 2 t

then triangle t 1 It 2 may be solved for lengths t 1 I and t 2 I which, if added to the known lengths T 1 t 1 and T 2 t 2 respectively, give the total tangent lengths.

In setting out this curve, the first curve R 1 is set out in the usual way to point t. The theodolite is moved to t and backsighted to T 1, with the horizontal circle reading (180 - ? 1/2). Set the instrument to read zero and it will then be pointing to t 2. Thus the instrument is now oriented and reading zero, prior to setting out curve R 2.


Copyright W. Schofield and M. Breach 2007 under license agreement with Books24x7

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