. Railroad construction. Theory and practice . l on curves. When a massis moved in a circular path it requires a centripetal force to keepit moving in that path. By the principles of mechanics weknow that this force equals Gv^-^gR, in w^hich G is the weight,r the velocity in feet per second, g the acceleration of gravity infeet per second in a second, and R the radius of the two rails of a curved track were laid on a level (trans-versely), this centripetal force could only be furnished by thepressure of the Wheel-flanges against the rails. As this is veryobjectionable, the outer r
. Railroad construction. Theory and practice . l on curves. When a massis moved in a circular path it requires a centripetal force to keepit moving in that path. By the principles of mechanics weknow that this force equals Gv^-^gR, in w^hich G is the weight,r the velocity in feet per second, g the acceleration of gravity infeet per second in a second, and R the radius of the two rails of a curved track were laid on a level (trans-versely), this centripetal force could only be furnished by thepressure of the Wheel-flanges against the rails. As this is veryobjectionable, the outer rail is elevated so that the reaction ofthe rails against the wheels shallcontain a horizontal componentequal to the required centripetalforce. In Fig. 30, if ob representsthe reaction, oc will represent theweight G, and ao will represent therequired centripetal force. Fromsimilar triangles we may writesn : sm :: ao : oc. Call g = i? =5730-1), which is suffi-ciently accurate for this purpose (see§ 19). Call r=o2S0r-3600, in which T. Fig. 30. IS the velocity in milesper hour, mn is the distance between rail centers, which, foran 80-lb. rail and standard gauge, is feet sm is slightlyless than this. As an average value we may call it , whichis its exact value when the superelevation is 4J inches. Callingsn^e, we have Gv^l ^22) e=sm—= ^ ^oc gR G e = .0000b72VD. (30) It should be noticed that, according to this formula, the re-quired superelevation varies as the square of the velocity, whichmeans that a change of velocity of only 10% would call for achange of superelevation of 21%. Since the velocities of trainsover any road are extremely variable, it is impossible to adopt 44 RAILROAD COJSTSTRUCTIOX. §42. any superelevation which will fit all velocities even approx-imately. The above fact also shows why any over-iefinementin the calculations is useless and why the above approximations,which are really small, are amply justifiabl
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