Sizing a crossing from spread: If the spread between the point and the splice rails is 50 cm at a distance of 4.25 m from the theoretical point, what is the size of the crossing (expressed as 1 in N)?

Introduction / Context:
Crossing size on railways is often denoted as 1 in N, where N equals cotangent of the crossing angle. In field practice, N can be computed from the measured spread (divergence) over a known distance from the theoretical point.

Given Data / Assumptions:

• Spread between point and splice rails = 50 cm = 0.50 m.
• Distance from theoretical point = 4.25 m.
• Standard geometric relation for small angles: tanθ ≈ spread / distance.

Concept / Approach:
Crossing number N = 1 / tanθ = distance / spread (for the standard measurement line). Thus, knowing spread and distance directly yields N.

Step-by-Step Solution:
Compute tanθ = 0.50 / 4.25 = 0.11765 (approx.).Find N = 1 / tanθ = 4.25 / 0.50 = 8.5.Crossing size = 1 in 8.5.

Verification / Alternative check:
Typical standard sizes include 1 in 8.5, 1 in 12, 1 in 16, etc. The computed N matches a common standard, confirming plausibility.

Why Other Options Are Wrong:

• 1 in 6: Too sharp; N should be 8.5 from the measurement.
• 1 in 12 / 1 in 16: Too flat compared to calculated value.
• 1 in 10: Close but not equal to the computed 8.5, hence incorrect.

Common Pitfalls:
Mixing units (cm vs m); using chord length instead of the prescribed distance; rounding N to a different standard without checking the given data.

Final Answer:
1 in 8.5