This tool calculates the required sleeper spacings for curved railway tracks. On curves, the outer rail must travel a greater distance than the inner rail, necessitating a slight difference in sleeper spacing to maintain correct perpendicular alignment.
Calculates the constant sleeper spacings for the inner and outer rails on a curve with a fixed radius.
Calculates the variable sleeper spacings along a transition curve, where the radius changes from a starting to an ending value.
The calculation is based on the constant angle ($\theta$) subtended by the required sleeper spacing ($S$) on the track's centerline radius ($R$).
Inner and outer rail radii:
$$R_{inner} = R - G/2$$ $$R_{outer} = R + G/2$$Angle of turn:
$$\theta = S / R$$Sleeper spacings for inner and outer rails:
$$S_{inner} = R_{inner} \times \theta = (R - G/2) \times (S/R)$$ $$S_{outer} = R_{outer} \times \theta = (R + G/2) \times (S/R)$$Where $G$ is the track gauge (1435mm).
The radius $R(l)$ at a given distance $l$ along the transition curve is determined by a linear relationship of its curvature (the inverse of the radius).
The formula for curvature ($\kappa = 1/R$) is:
$$\frac{1}{R(l)} = \frac{1}{R_{start}} + \left(\frac{1}{R_{end}} - \frac{1}{R_{start}}\right) \times \frac{l}{L}$$Where: