Rail Track Tolerance

What track gauge (it is of crucial importance to the matter!)?

For Stephenson's gauge, a nominal 4ft 8¹/₂in between running edges, the tolerances stated in "British Railway Track Bullhead Supplement" 1991 (published by the Permanent Way Institution) are as follows:

Where London Transport Stock only operates:

• Straight track 4ft 8³/₈in.
• Unchecked curves 4ft 8¹/₂in.
• Checked curves 4ft 8⁵/₈in with 2in check flangeway
• Switches and crossings 4ft 8¹/₂in with 1³/₄in flangeway.

Anecdotally, London Transport pulled the gauge down to 4ft 8¹/₄in on the departure side of stations so as to stop the power bogies thrashing about under hard acceleration.

Where surface stock also operates:

• Straight track 4ft 8³/₈in.
• Unchecked curves 4ft 8¹/₂in.
• 10 to 7 chains radius 4ft 8⁵/₈in with 2in check flangeway.
• 7 to 5¹/₂ chains radius 4ft 8⁷/₈in with 2¹/₄in check flangeway.
• Under 5¹/₂ chains radius 4ft 9¹/₈in with 2¹/₂in check flangeway.
• Switches & Crossings 7 chains radius and over 4ft 8¹/₂in with 1³/₄in flangeway.
• Switches & crossings under 7 chains radius 4ft 8³/₄in with 2in flangeway.

Where Stephenson gauge track is curved, the equilibrium cant is given by the equation:

H = 0.06(V²/R)

where H is the cant in inches, V is the line speed in mph, and R is the radius in chains. However, it is common to put on ²/₃ of the equilibrium cant so as to reduce the mutual wear at the wheel/rail interface.

Twist across the track should usually be less than 1 in 300, and is immediately actionable if more than 1 in 150. The difference in rail head height for adjoining fished rails should not exceed ¹/₈in at 50mph.

The above covers UK practice up to about 1956 and is adopted by many of the heritage lines across the country. The UK's current National Rail standards are similar, though metricated, and do not cover London Transport lines, non-Stephenson gauge lines, light rail, nor anything in Northern Ireland, where CIE standards predominate. However, the local track gauge and standards might be different from those above.

In a yard situation, the track is better laid flat rather than worry about cant, as speeds are usually low, and rail wear and passenger comfort is hardly an issue.

For more guidance on first principles, obtain a copy of Kempe's Engineers' Yearbook, a more modern edition, and check out the chapter on track construction. Though based on UK practice, the principles are applicable to rail systems across the globe. India also has many publications on the same topic, most of which tackle the broader gauge found in some places in some detail.

Track center to center distance is 6mtrs and another 7mtrs

Irrelevant.