. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . 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. 35, if oh representsthe reaction, oc will represent theweight G, and ao will represent therequired cen
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . 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. 35, if oh representsthe reaction, oc will represent theweight G, and ao will represent therequired centripetal force. Fromsimilar triangles we may writesn : sm :: ao : oc. Call g = 72 = 5730--D, which is suffi-ciently accurate for this purpose (see§ 48). Call V = 5280F -3600, in which V is the velocity in milesper hour. m7i 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 4f inches. Callingsn=e, measured in feet, we have ^D. Fig. 35. ao . .Gv^ 1 e=sm~ = ~=r — oc gR G ^X5730 6 = .0000572 y^D (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 §72. ALINEMENT. 83 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 justifiable. For exanTple, theabove formula contains the approximation that J? = the extreme case of a 10° curve the error involved would beabout 1%. A change of about 4 of 1% in the velocity, or sayfrom 40 to miles per hour,
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