345 
1911-12.] The Railway Transition Curve. 
P{x, y ), Pft', y') two points on the curve, AN = x, NP = y, AR = g, RP = rj, 
YR' = u, KP =v. 
Then, by projection, 
£ = x cos a + y sin a, 
y = x sin a - y cos a, 
also 
v = H-y\ 
The curve is set out by the co-ordinates g and y from the tangents AU and 
BU/ and by the co-ordinates u and v from the tangent UVTJ', the two arcs 
meeting near the point Z. 
Where the ordinates are greatest, and where consequently there is most 
chance of error in setting out — viz., near the point Z, there is a safeguard in 
the fact that for correct junction of the two arcs in the field the offsets 
from the two tangents must determine the same points. 
Owing to the symmetry about the axis SC the portion of curve YB is 
set out in the same manner as the portion AY. The offsets from the three 
tangents are all small, and so may be set out with ease and accuracy. 
The equation of the curve referred to the origin A and the axis AB is 
and hence 
H « 7i«l/ 
sm— , 
dy _ 
dx 
TT 7r irX 
= h l cos l ’ 
or tana = H-. 
J_J 
This gives L when H is known, and conversely ; and hence we locate the 
points A, B, C, Y, U, U', W. 
The radius of curvature at the vertex is H tan 2 w, which from practical 
considerations must not be less than some given value. 
A systematic method for obtaining the values of £, y, u, v, is indicated 
by the following calculation scheme. 
