[Illustration]
Stretch a string, say 20 feet long, or longer if the curve is not a
sharp one, across the curve corresponding to the line from A to C in
the diagram. Then measure from B, the center of the line A C, and at
right angles with it, to the rail at D.
Multiply the distance A to B, or one-half the length of the string in
inches, by itself; measure the distance D to B in inches, and multiply
it by itself. Add these two products and divide the sum by twice the
distance from B to D, measured exactly in inches and fractional parts
of inches. This will give the radius of the curve in inches.
It may be more convenient to use a straight edge instead of a string.
Care must be taken to have the ends of the string or straight edge
touch the same part of the rail as is taken in measuring the distance
from the center. If the string touches the bottom of the rail flange
at each end, and the center measurement is made to the rail head, the
result will not be correct.
In practice it will be found best to make trials on different parts of
the curve to allow for irregularities. It is best not to measure across
from one end of the curved track to the other even when the curve is
so located that this is possible, since if any portion of the straight
track at either end of the curve is included the result will be
incorrect. This rule does not apply to curves of over one-half circle
if the line is drawn connecting the two ends of the curve. It is a good
plan to make the measurement on the inside of the outer rail of the
curve, as this is often more convenient. In this case one-half of the
width of gauge should be deducted from the radius when calculated, as
the radius of the curve should be measured to the center of the track.
EXAMPLE--Let A C be a 20-foot string; half the distance, or A B, is
then 10 feet, or 120 inches. Suppose B D is found on measurement to
be 3 inches. Then 120 multiplied by 120 is 14,400, and 3 multiplied
by 3 is 9; 14,400 added to 9 is 14,409, which, divided by twice 3,
or 6, equals 2,401½ inches, or 200 feet 1½ inches, which is the
radius of the curve.
A B² plus B D²
The formula is thus stated: -------------- == R.
2 B D
Or applied to the above example,
120² plus 3²
------------ == 2,401½ in. == 200 feet 1½ inches.
2 times 3