Definition check: On Indian Railways, the “number” of a crossing is defined as which trigonometric function of the angle of crossing?

Introduction / Context:
Turnout design uses the concept of crossing number to express sharpness. A higher crossing number corresponds to a flatter angle, enabling higher diverging speeds and longer leads. Understanding the precise definition is essential for layout and yard design.

Given Data / Assumptions:

• Angle of crossing α measured in radians or degrees.
• Standard Indian practice equating number N with a trigonometric function of α.

Concept / Approach:
The crossing number N is defined by N = cot α. This links directly to the turnout splay and governs lead calculations and spacing requirements. As α decreases (flatter), cot α increases, giving a larger crossing number (e.g., 1 in 16 is flatter than 1 in 8.5).

Step-by-Step Solution:
1) Recognize that geometric definition relates run to offset across the crossing.2) Trigonometry shows run/offset corresponds to cot α for small angles.3) Hence the crossing ‘‘1 in N’’ reflects N = cot α.

Verification / Alternative check:
Design charts and tables invariably use N = cot α, ensuring consistency across turnout sizes and lead computations.

Why Other Options Are Wrong:

• Sine, cosine, tangent, secant do not match the standardized turnout numbering convention.

Common Pitfalls:

• Confusing tangent and cotangent: remember, a larger N means a smaller α, consistent with cotangent behavior.

Final Answer:
Cotangent of the angle of crossing.