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r = 7 DIETZGEN'S RAILROAD CURVE 1 AND REDUCTION TABLES / (;W4tht,1914,by Eugene Dietsgen Co.,Now York City Za? PCIlk T P C S C' 4 CURVE FORMULAS Radius=R= Lm �(1) Degree of Curve=D and sin.D=s (� Tangent=T=RtanA (3)Length of Curve=L=100 (4) Middle ordinate=M=R(1—cos. (5) =Rvers (6) External=E=TtanA-(7)=R+cos.Q R(8)=Rexsee#(9) Long Chord=C=2 R sin.y(10)A=Central Angle EXPLANATION AND USE OF TABLES Stations.—Given P. I.=Sta. 161+60.35 to find Sta. of P. C. and P. T. p==620 10' D-8e 20'. From Table IV for 1° curve T= 3454.1 and+SA-414.49 ft. From Table V correction—,36 or T= 414.85 ft. P. C.=Sts. P.L—T-157+45.50. Also from (4) L= 746.00 and P.T.—Sta.P.C.+Lm164+91.50. Offsets.—Tangent offsets vary (a roximately) directly with D and with square of the distance. Thus tangent offset for Sta. 158 on above curve i92.16 ft.found as follows. From Table III tangent offset for 100 ft.7.27 ft. Distance-158-Sta.P. C.-54.50,hence offset---7.27 (54.50+100)2==2.16 ft. Also square of any distance divided by twice the radius equals(approximately)the distance from tangent to curve. Thus (54.50)2+(2 x 688.26)=2.16 ft. Deflections.—Deflection angle-34 D for 100 ft., 34 D for 50 ft., etc. For c ft:(in minutes).3 x C x D°or=-deft.for 1 ft.from Table III x C. For Sta. 158 of above curve.3 x 54.5 x 8X=136.2' or 2° 16.2', or-2.50 x 54.5=136.2'from Table III. For Sts. 159 deflec- tion angle=2°16.2'+8*20'+2-6e 26.2',etc. Externals.—May be found in similar manner to tangents. Thus ` E for curve above is 91.37. For from Table IV for 1e curve E=960.6 j for 8° 20'=980.6+83s==91.27 and from Table V correction=.10 or E---91.37 ft. Or suppose p==32°and E is measured and found to be 42 ft. What is D7 From Table IV E=230.9 and+4q--5.5 or D_- =5°3050301. '.