The turning radius of a curve that a locomotive can handle easily is determined
by the amount of lateral travel allowed in each axle plus the amount of
extra gauge in the track at that turn.
Lateral travel is the amount an axle can move sideways in each direction relative to the frame. In some cases, differential travel between axles can be used. In other words (in the example below) if axles 1 and 4 can move left 1/8" and axles 2 and 3 can move right 1/8", you can say you have 1/4" of usable lateral travel.
Extra track gauge is just that. If your wheels are gauged at 7.25", but your rails are spaced at 7.35" in a curve, you have 0.1" of extra gauge.
To determine if you have enough lateral travel and/or extra gauge, use the equations below.
Note: All units must be the same (feet, inches, meters)
First, measure your turning radius (r), and then the distance (b) of each axle from the radius center (which can be the center of your frame). Note that all units of measure must be the same. If r is in feet then b must be in feet, etc. It may be easiest to convert all units to inches (or cm). You may only need to do the calculation on the axles farthest from the radius center..
Next do the calculations. If "d" exceeds the sum of your total lateral travel and your extra track gauge, you may have trouble in the turn. You can move the radius center if you need to reduce required travel in one axle, but have a surplus of travel in the opposite axle.
It is important to insure that all axles (including pilot and trailing) have enough travel with the extra gauge available.