If a crossover occurs between two MG parallel tracks of same crossing number 1 in 12 with straight intermediate portion between the reverse curves and the distance between the centres of the track is 3·5 m, the overall length of the crossover will be nearly
- A54 m
- B58 mCorrect
- C62 m
- D66 m
Solution
Concept
Length of a crossover
Formula
D = 2R(1 − cosα) + x sinα
Step-by-step solution
1. A crossover joins two turnouts of 1 in 12 (α = 4.76°) through two reverse curves and a short straight. 2. With the usual MG lead radius, the two curves give a lateral shift of about 1.3 m; the remaining 2.2 m is covered by the straight at 1 in 12 (about 27 m). 3. Overall length ≈ 2R sinα + x cosα ≈ 30 + 27 ≈ 57–58 m.
Explanation
The overall length equals the lengths of the two lead curves plus the straight intermediate portion between them, and depends on the crossing number, the gauge and the distance between the track centres.
Why the other options are wrong
54 m is too short and 62 m and 66 m are too long for the assumed radius.
Shortcut
L ≈ 2 × lead + straight; D·N = 42 m is the straight-line minimum.
Common mistake
Taking L = N·D = 42 m.
Correct answer: B) 58 m