Horizontal Alignment and Superelevation Questions and Answers

Answer: B

The shift is \(L^2/24R\).

When a transition curve is inserted, the circular curve has to be moved inward by the shift

\[ S = \frac{L^2}{24R} \]

where L is the length of the transition curve and R the radius of the circular curve. (The stem calls L the long chord.) \(L^2/6R\) is the offset at the end of the transition curve, four times the shift, and \(L^2/2R\) is the offset of a simple curve, so they are the usual traps.

Answer: B

Psychological widening is \(V/9.5\sqrt{R}\).

On curves, drivers tend to keep a greater clearance from the vehicle alongside, so IRC adds a psychological widening in metres:

\[ W_{ps} = \frac{V}{9.5\sqrt{R}} \]

with V in km/h and R in metres. The total extra width is this plus the mechanical widening \(nl^{2}/2R\), which allows for the rear wheels tracking inside the front wheels; that formula, with n lanes and wheelbase l, is the trap option. \(V/2R\) and \(nl^{2}/R\) are not standard forms.

Answer: C

The IRC minimum length for plain terrain is \(2.7\ V^{2}/R\).

IRC gives the minimum length of a transition curve from the empirical formula:

\[ L_s = \frac{2.7\,V^{2}}{R} \]

for plain and rolling terrain (and \(V^{2}/R\) for mountainous terrain), with V in km/h and R in metres; the design length is the larger of this and the lengths from the rate of change of centrifugal acceleration and the rate of introducing superelevation. \(0.0215\ V^{3}/CR\) is the centrifugal acceleration criterion, not the plain-terrain minimum, and the other two options are not IRC formulae.