Highway Engineering

Alternative method for computing Ms

If the radius of horizontal curvature is large, then it can be assumed that SD

approximates to a straight line. Therefore, again assuming that the sight distance

length SD lies within the curve length, the relationship between R, Ms and SD

can be illustrated graphically as shown in Fig. 6.13.

Using the right-angle rule for triangle A in Fig. 6.13:

R^2 =x^2 +(R-Ms)^2

Therefore:

x^2 =R^2 - (R-Ms)^2 (6.20)

Now, again using the right-angle rule, this time for triangle B in Fig. 6.13:

(SD/2)^2 =x^2 +Ms^2

Therefore:

x^2 =(SD/2)^2 - Ms^2 (6.21)

Combining Equations 6.20 and 6.21:

(SD/2)^2 - Ms^2 =R^2 - (R-Ms)^2

Therefore:

(SD/2)^2 - Ms^2 =R^2 - (R^2 +Ms^2 - 2 ¥R¥Ms)

Cancelling out the R^2 and Ms^2 terms:

(SD/2)^2 = 2 ¥R¥Ms

Therefore:

Ms =SD^2 /8R (6.22)

172 Highway Engineering

SD/2

R

Ms

R-Ms

x

A

B

Figure 6.13

Horizontal curve/SD

relationship

(assuming SD to be

measured along

straight).