Permissible approximations in vertical curve computation
In the UK, civil engineering road design is carried out in a accordance with the Highways Agency’s Design Manual for Roads and Bridges.
In TD 9/93 the desirable maximum gradients for vertical curve design are:
Due to the shallowness of these gradients, the following VC approximations are permissible, thereby resulting in simplified computation .
(1) Distance T1D = T1BT2 = T1CT2 = (T1I IT2), without sensible error. This is very important and means that all distances may be regarded as horizontal in both the computation and setting out of vertical curves.
(2) The curve is of equal length each side of I. Thus T1C = CT2 = T1I = IT2 = L/2, without sensible error.
(3) The curve bisects BI at C, thus BC = CI = Y (the mid-offset).
(4) From similar triangles T1BI and T1T2J, if BI = 2Y, then T2J = 4Y. 4Y represents the vertical divergence of the two gradients over half the curve length (L/2) and therefore equals AL/200.
(5) The basic equation for a simple parabola is
Vertical curve approximations
where y is the vertical offset from gradient to curve, distance l from the start of the curve, and C is a constant. Thus, as the offsets are proportional to distance squared, the following equation is used to compute them:
where Y = the mid-offset = AL/800