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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:





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 given in the same units.] 


Example 1.
(All dimensions in mm but with mixed English/Metric dimension inputs. All example inputs shown in [green] using millimetres.)
A NSWGR C30 class 464 tank engine has a rigid wheelbase of 10ft 9ins. For a 5"g model to 1.125"/ft scale, the wheelbase is 12^{3}/32" ([W=(12+3/32)*25.4] or 307.2mm). From the AALS wheel standards, the flangerail clearance is 2.6mm [h1=2.6] (or 2.2mm for fine scale), and we assume the side play in the centre axle is 0.1mm [h3=0.1]. Assume zero gauge widening on curves [h2=0], this gives a theoretical minimum radius of approx 4369mm (4.37 metres) or 5.13m (FS).
Example 2.
(All dimensions in metres. All example inputs shown in [green] using metres.)
For a 5"g NSWGR Z19 class 060 shunter, the wheelbase is 12.656" (321.5mm [W=0.3215]), and using the same wheel/rail clearances and side play and 1mm gauge widening [h1=0.0026, h2=0.001, h3=0.0001] gives 3.49m (or 3.92m FS).
Note that the above ignores other issues such as rail/wheel profiles, and leading or trailing truck side movement on curves, clearances to other items such as cylinders, frames etc., which is often the limiting factor.
Disclaimer 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.
[Updated: 17 Apr 2013] 407 
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