Rail diamond geometry: if G is the gauge (mm) and α is the crossing angle, what is the distance along the through rail between the nose of the acute crossing and the nose of the obtuse crossing?

Introduction / Context:
Diamond crossings combine an acute and an obtuse crossing. Designers frequently need the longitudinal spacing between the two noses measured along the non-diamond (through) rail for setting component positions and check rails.

Given Data / Assumptions:

• G is the gauge distance between gauge faces.
• α is the diamond crossing angle between gauge faces.
• Simple right-triangle trigonometry applies to plan geometry.

Concept / Approach:

Consider the plan geometry triangle formed by the gauge distance as the side opposite the angle α, and the required spacing along the rail as the adjacent side. The relation between opposite and adjacent through tangent/cotangent gives the spacing.

Step-by-Step Solution:

Verification / Alternative check:

Check limiting behavior: as α decreases (sharper diamond), tan α decreases and L increases, which matches intuition that noses are farther apart.

Why Other Options Are Wrong:

G tan α or G sin α would reduce spacing with sharper angle incorrectly; G cos α does not reflect the opposite/adjacent relationship; G/tan α is algebraically the same as G cot α but not listed verbatim in most formula sheets—select the canonical expression.

Common Pitfalls:

Mixing α with its complement; confusing gauge G with track center spacing.

Final Answer:

G cot α