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CURVE AND REDUCTION TABLES <br /> Published by Eugene Dietagen Co. <br /> C. �l r <br /> I <br /> 1 <br /> 1 <br /> 1 <br /> 1 <br /> CURVE FORMULAS <br /> 1. Radius R= 50 <br /> sin D/2 <br /> 2. Degree of Curve: D=100 L• Also,sin D/2=5 <br /> 3. Tangent T=R tan%I. Also,T=T for 1°curve+C. <br /> D <br /> 4. Length of Curve: L=100 D <br /> 5. Long Chord L. C.=2R sin %I. <br /> 6. Middle Ordinate: M=R (1—cos %I) <br /> 7. External E=cos 2 I—R. Also, E=T tan Y4 I. <br /> E]CBLANATION AND USE OF TABLES <br /> ,8,/A•f 'YZ /o,3/ C Z. 30 N- Cor S$, Given P.I.Sts.93+40.7,1-45*20'and D=6'30'find: <br /> Al., 3 ,65 Stations-P.C.=P.I.-T. T=T for 1'Curve <br /> ��� D C. From Tables V and VI <br /> {vly T=89 <br /> Tr' Al.9 ,3 .3 9l 58-}-.197=368.32=3+68.32. Sts. P. C.=83-}40.7-(3+68.32)=79+72.38. <br /> . � <br /> P.T.-P.C.+L,and L=100 =10046.53'897.38 Therefore,P.T.=(79+72.38) <br /> 7/6* JF F-7 +(6+97.38)=86+69.78. <br /> Offsets--Tangrnt offsets vary (approximately) directly with D and with the <br /> square of the distance.From Table III Tangent Offset for 100 feet=5.869 feet.Distapee <br /> '61M. / 70 Sr 3/. 73 FoPP,aND 27.82 r <br /> A c G I Tx:�$ . _ =80-Ste.P.C.=27.62.Hence offset=5.66 X( 100> =.432 ft.Al.,square of any <br /> Al. •41 C> . '• ! 8 distance,divided by twice the radius equals((approximately)the distance from tangent <br /> to curve.Thus(27.62)2+(2 X881.95)=.432 ft. <br /> TP Deflections-Deflection angle=%D for 100 ft.,Y,D for 50 ft.,etc.For"X"ft., <br /> Deflection Angle(in minutes)=.3 XX XD.For Sta.80 of above curve Deflection Angle <br /> =.3 X27.62 X6.5=53.86'.Also Deflection Angle=dfl.for 1 ft.from Table III XX=1.95 <br /> v.S 9 b'• 9 7 X 27.62=53.86. For Sts.181 Deflection Angle-53.86'+6'20'=4°8.86'. <br /> 3l0 ernals-From Table V for 1'curve,with central angle of 45'20',E=479.6.l i 3'9 3 ,33, 3 8 r�, s 6sak. lft <br /> Therefore,for 6'301 curve,E=40 56+Correction from Table VI=7.378+.039=7.417. <br /> ,C33/y i SSS 39. �,�- .��.•7� <br /> �s� <br /> 4.3 <br />