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/ I <br /> -`3- /7- -- - °� _ - - DIETZGEN'S RAILROAD CURVE <br /> - AND <br /> REDUCTION TABLES <br /> COyyriaht,1914.by Eugene Mtn=Co.,New York Cdty <br /> r§ F <br /> ,6 7 <br /> FVEDBOx088 <br /> a <br /> CURVE FORMULAS <br /> Radius=R=B�5cU/T(1)Degree of Curve=D and sin.z=§P <br /> (2) <br /> - - - - ° <br /> Tangent=T=Rtan6%(3)Length of Curve=L=100,(4) <br /> - Middle ordinate=M=R(1-cos. ,)(5) =Rvers 3(6) <br /> - - External=E=Tian*-(7)=R+Cos.#-R(8)=Rexaec.#(9) <br /> ---- - Long Chord=C=2 R sin.s(10)A=Central Angle <br /> EXPLANATION AND USE OF TABLES <br /> Stations.-Given P. I.=Sta. 161+60.35 to find Sta. of P. C. <br /> and P. T. &==62° 10' D-8° 20'. From'Table'IV for 1° curve T= <br /> 3454.1 and+8h=.414.49 ft. From Table V correction-_36 or T= <br /> - - -- 414.85 ft. P. C.=Sta. P.I.-T=;=157+45.50. Also from (4) L. <br /> 746.00 and P.T.�Sta.P.C.+L=164+91.50. <br /> 8._ ,� 17.<Z _ Offsets.-Tangent offsets vary (approximately) directly with <br /> D and with square of the distance. Thus tangent offset for Sta. <br /> 158 on above curve is 2.16 ft.found as follows. From Table III tangent <br /> offset for 100 ft.=7.27 ft. Distance--158--Sta.P. C.=54.bq,hence <br /> --9_._6 8 /13� S,1S_ •4 offset--7.27 (54.50+100)2=2.16 ft. Also square of any distance <br /> divided by twice the radius equals(approxunately)the distance from <br /> - ;/6- ILr s 7 - •_�g__ 6�g_� �r.<, ,r,t - tangent to curve. Thus (54.50)2+(2x688.26)==2.16 ft. <br /> Defiections.-Deflection angle=34 D for 100 ft., �/�y D for 50 ft., <br /> 3 __ _ 6 4� _ etc. For c ft.=(in minutes).3 x C x D°or�iefl.for 1 ft.froom Table <br /> III x C. For Sts. 158 of above curve=.3 x 54.5 x 84=136.2' or <br /> M,0� 2e 16.21,or=2.50 x 54 05=136.2'f rom Table III. For Sta. 159 defieo- <br /> -- z x s,4-t-- tion angle==r 16.21+8 201+2==60 26.2,etc. <br /> ---- /•83 z`/. 98 /-.,-,7 25.71- _ 96'.S-1xx Externals.-May be found in similar manner to tangents. Thus <br /> E for curve above is 91.37. For from Table IV for 1'curve E=960.6 <br /> for 8e 21'=960.6+83x=91.27 and from Table V correction=•10 or <br /> E=91.37 fL Or suppose p==32e and E is measured and found to be <br /> 42 ft. What is D? From Table IV FA-i=.9 and+42=5.5 or D- <br /> 9 be 30'. <br /> Mo,•u <br /> S,e. P,� �► C, CV, o „wo C��9 <br /> /Y1 rkP . <br /> • <br /> v <br /> a <br />