Minimum Radius

(of rigid wheelbase vehicle)

The minimum radius curve around which a rigid wheel base vehicle will operate without wheels binding may be found by calculating the values of a chord (effectively the rigid wheelbase of a vehicle) of a circle from the formula below:-

where:- R = radius of the curve C = length of the chord (rigid wheelbase, or W) h = distance chord to circumference (#)
[#] h= 1) clearance between rail and wheel flange, plus 2) extra gauge allowance for curves, plus 3) lateral play in middle axle

Minimum Radius Calculator
Enter the values below to calculate minimum radius.
[ALL values must be in the same measurement units.
ALL in feet, or ALL in inches, or ALL in mm, metres etc.
Radius will be in same units.]

Handy conversion factors
1 in = 25.4mm 1 ft = 0.3048m 1 yd = 0.9144m	1mm = 0.03937 ins 1m = 3.28084 ft 1m = 1.09361 yds

For example, a NSWGR C30 class 4-6-4 tank engine has a rigid wheelbase of 10ft 9ins. For a 5"g model to 1.125"/ft scale, the wheelbase is 12.094" (or 307.2mm). From the AALS wheel standards, the flange-rail clearance is 2.6mm (narrow gauge, or 2.2mm for fine scale), and we assume the side play in the centre axle is 0.1mm. Assume zero gauge widening on curves, this gives a theoretical minimum radius of approx 4.37 metres (NG) or 5.13m (FS). For a NSWGR Z19 class 0-6-0, the wheelbase is 12.656" (321.5mm), and using the same rail clearances and side play gives 4.78m (NG) or 5.62m (FS). Note that this ignores other issues such as leading or trailing truck side movement on curves, clearances to other items such as cylinders, frames etc., which is often the limiting factor.

These calculations are for guidance only and should not be the sole basis for any design. Usage of this calculator is at your own risk.

Further geometrical formulas for circles and other shapes can be found at the Internet Math Forum.

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