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V WO' <br /> b oa - DIETZGEN'S RAILROAD CURVE <br /> , li AND <br /> - REDUCTION TABLES. <br /> w a <br /> Coyyright,1914,by Eugene Dietzgen Co.,New York Citg <br /> S i P.G T P. <br /> cD <br /> a <br /> —1 I <br /> 4r, YA QoR oc PT <br /> d <br /> Je <br /> i <br /> j �1 ,c1 <br /> CURVE FORMULAS (2 <br /> '7 .� jWius=R=i�S(1)Degree of Curve=D and sin.!)=6—n° ) <br /> Tangent=T=Rtan 2( 3)Length of Curve=L=100D(4) <br /> I � <br /> Middle ordinate=M=R(1—cos. a)(5) =Rvers 2(6) <br /> External=E=Ttanq' (7)=Acos.+—R(8)=Rexsec#(9) <br /> Long Chord=C=2 R sin.s (10)A=Central Angle <br /> EXPLANATION AND USE OF TABLES <br /> Cl r�-`c Stations.--Given P. L---Sta. 161 f 60. . oP. C. <br /> 35 to find 5taf <br /> _- and P. T. o==62° 10' D---8°20'. From Table IV for 10 curve T= <br /> 8454.1 and+8%=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 /> _ S 3 748.00 and P.T.=.Sta.P.C.+1r--164+91.50. <br /> y ' <br /> Offsets.—Tangent offsets vary ry (a roximately) direct] with <br /> j 3 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 /> } — .� :• ,' M , Z offset for 100 ft.=7.27 ft. Distance=158—Sts.P. C.=.54.50,hence <br /> offset-7.27 (54.50+100)2=2.16 ft. Also square of any distance i <br /> divided by twice the radius equals(approximately)the distance from <br /> tangent to curve. Thus (54.50)2+(2 x 688.26)=2.16 ft. <br /> e„ Deflections.—Deflection angle---Y2 D for 100 ft., V4 D for 50 ft., <br /> etc. For c ft:(in minutes).3 x C x D°or==iefl.for 1 ft,from Table <br /> III x C. For Sta. 158 of above curve=.3 x 54.5 x 8�-136.2' or <br /> 2° 16.2,or=2.50 x 54.5=136.2'from Table III. For Sta. 159 deflec- <br /> tion angle.=2°16.2'+8°20'+2=;W 26.2',etc. <br /> 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 8° 20' 60.6+8%==91.27 and from Table. V oorrection=10 or <br /> E--91.37 ft. Or suppose p==32°and E is measured and found to be <br /> 42 ft. What is D7 From Table IV E=230.9and+42�m&5 or D= <br /> BO <br />