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:-

Circle chord equation
where:-
R =
C =
h =
radius of the curve
length of the chord (= rigid wheelbase, or W)
distance of chord to circumference (made up of 3 parts):
   
h1 =
h2 =
h3 =
clearance between rail and wheel flange, plus
extra gauge allowance for curves, plus
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 given in the same units.]

Rigid wheelbase W: units
Rail/wheel clearance h1: units
Extra gauge on curves h2: units
Lateral play in axle h3: units
Minimum Radius (R)= 0 units
Note: Simple formulas using +-*/() may be entered
if desired, not just straight plain numbers.
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

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 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 123/32" ([W=(12+3/32)*25.4] or 307.2mm). From the AALS wheel standards, the flange-rail 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 0-6-0 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.