Most of the current formulae for spiral length use either unbalance, Eu or actual super-elevation, Ea to calculate spiral length, L as applied to light rail, commuter rail, and rapid transit. In reality, a train suffers both Eu and Ea run-off simultaneously. Super-elevation unbalance run-off produces the effect of radial acceleration and actual super-elevation run-off produces the effect of rotation. As a result due to this spiral length design should be based on both Ea and Eu. The current formulae underestimate spiral length which affects comfortable jerk rate, roll criteria, and twist rate. These formulae do not shed any light on how to proportion actual and unbalance superelevation to realize desired results. Consequently from these formulae, desirable values of Ea and Eu cannot be calculated, so it is necessary to re-evaluate the current formulae. It is mathematically established that combined effects of Ea and Eu run-off set a limit of 45mm/sec. A new formula for spiral length comes out to be: L = 0.006(Ea+Eu)V. But this formula does not reflect the effect of proportion of Ea and Eu. This gives the same length whatever be the proportion of Ea and Eu. To overcome this deficiency a second formula is derived as:
The article analyzed the effect of proportion of Ea and Eu on spiral length. The formulae developed in the paper satisfy both cant gradient and rotation criteria that are currently used. If these formulae are used, these criteria do not require checking. The analysis reveals the basis of cant gradient that is to be used for spiral length design. As extensions of these new formulae are developed for minimum spiral length, minimum length of circular curve, rate of twist, maximum safe speed etc. For Heavy haul operation issues of over-loading and off-loading on the twisted track is also discussed to review cant gradient for spiral length design.
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