thrshold radius for restraining rail

this paper deals with the threshold radius that warrants the use of single restraining rail for transit and railroads. different railways use different threshold radius from 91m to 365m to provide restraining rail. these threshold figures are probably experience driven choices. the need for restraining rail may be related to a so-called derailment alarm coefficient of 1.2 sustained over 2m length (according to uic leaflet 518 a safe maximum value of y/q ratio of 0.8 over the length of 2m is recommended) but it needs a wheel/rail interaction software to estimate derailment coefficient. the author is not aware if it has been done for this purpose. a quick and simple assessment method is developed here. a restraining rail reduces the angle of attack (aoa) to reduce the likelihood of wheel climb derailment and to reduce wear provided it is installed close enough to the inner (lower) rail to prevent flange contact with the outer (higher) running rail. angle of attack depends on wheel base, curve radius and free play. the threshold radius is formulated by considering these three parameters. an assumption made to derive the equation is that twice the aoa on tangent track due to free play is a critical aoa on circular curves to warrant a restraining rail. the assumption is validated by comparing the threshold radius obtained by the formula with real world examples. it is also shown that curvature resistance of the threshold radius is too high to warrant a restraining rail. if the radius of the curve is less than threshold radius then the restraining rail needs to be extended into the spiral up to a point where the radius matches with the threshold radius. a formula substantially based on current practice is given to determine the extension of single restraining rail into the spiral subject to a minimum requirement.