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90 t. e; .; e)", 7C <br /> i <br /> ' NDIE.TZGEN'S RAILROAD CURVE <br /> AND <br /> FIELD E30OKa. 1 . <br /> REDUCTION JABLES <br /> ' GbRYnsht.1914.by Eugene Dietzgen Co..New York City <br /> ` PCM70 <br /> 41 <br /> CURVE.FORMULAS <br /> Radius=R=since(1)Degree of Curve=D and sin.D=R(2) <br /> _,. <br /> Tangent=T=Rtan a (3)Length of Curve=L=101 n-(4) <br /> Middle ordinate=M=R(1—cos. A,)(5) =Rvers s(6) <br /> External=E=Ttan4-(7)=R=cos. —R(8)=Rexsec (9) <br /> 0r3'S j073 RrP, l04 q Long Chord=C=2 R sip.a(10)A=Central Angle , <br /> EXPLANATION AND USE OF TABLES <br /> p9 8X 22 F4 f L. '2Z$ 3 F L. Stations.—Given P, L—Sta. 161+60.35 to find Sta. of P. C. <br /> and P. T. p=620 10' D=8° 20'. From Table IV for 10 curve T= <br /> y 84 4.1 and+8%=414.49 ft. From Table V oorreetion=.36 or T- <br /> 414.85 ft. P. C.=Sta. P.I.—T=157+45.50. Also from (4) IF. <br /> 0 9 `7 746.00 and P.T.—Sta.P.C.+L=164+91.50. <br /> �7.ae Offsets.—Tangent offsets vary (approximately) directly with <br /> j <br /> 4-- D and with square of the distance. Thus tangent offset for. Sta. <br /> -s 158 on above curve is 2.16 ft.found as follows. from Table III tangent° <br /> offs9t for 100 ft=7.27 ft. Distance-158—Sta.P. C.--544.60 hence <br /> .,' offot.=7.27 (54.50+100)2=2.16 ft. Also squ y Af distance <br /> divided by twice the radius equals(a *.I <br /> �j the=ce from <br /> tangent to curve. Thus (54.50)2+(2x688.26)-2.16 ft. <br /> Deflections.—Deflection angle=Y2 D for 100 ft., I/- <br /> D for 50 ft., <br /> 3 # p ett. For a ft.=(in minutes).3 x C x D*or�iefl.for 1 ft.from Table <br /> ;e ti a III x C. For Sta. 158 of above curve=.3 x 54.5 x 834=136.2' or <br /> - 2° 16.2',orA4.50 x 54.5=136.2'from Table III. For Sta. 159 defiec- <br /> tigg angle-2°16.21+80 20'+2==O°26.2',etc. <br /> i 3 Stternals.—May be found iu#aman <br /> lar ner to tangents. Thus <br /> 7; � T for curve above is 91.37. For from Table IV for 1'curve E=960.6 <br /> for 80 20'=960.6+8%=91.27 and from Table V correction=.10 or <br /> f 2 !' /'Y P� 10:r` E "''� X91.37 ft. Or suppose A==32*and E is measured and found-to be <br /> Ofoo 42 ft. What is D7 From Table IV Es230.9 and+42=5.5 or D= <br /> f , <br /> 1 <br />