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S <br /> r: DIETZGEN'S RAILROAD CURVE <br /> AN <br /> REDUCTION TABLES' j <br /> ,I 1914 <br /> Co t, ,b <br /> _�e5 �k��✓ - � �yr�h Y Eugene_Die4 sgen Co..Now York 60 <br /> P. <br /> PC T j <br /> f <br /> 9 <br /> j 3 ' —AO%US=�� ���CURVE FORMULAS <br /> Z' ` Radius=R— 50 ao(2) <br /> —s-fa b (1) egree of Curie=D and sin.a a=0 <br /> 7�Y L t I Tangent—T=Rtan'�' (3)Length of Curve=L=100,(4) <br /> Middle ordinate=M=R(1—cos. (5) =Rvers (6) <br /> I ; External=E=Ttan--(7)=R+cos.g-•R(8)—Rexsee4(9) • <br /> Long Chord=C=2 R sin.4,L(10)&=Central Angle <br /> J EXPLANATION AND USE OF TABLES_ u <br /> Statiods.—Given P. I.=Sta. 161+60.35 to find Sta. of P. C. <br /> and P.T. n==62° 10' D=am'20'. From Table IV for 1° curve T= <br /> '3454.1 and+8%=414.49 ft. From Table V oorrection=.36 or T= <br /> / // f 414.85 it. P. C.�Sta. P.L—T 157+45.50. Also from (4) L= <br /> 3 746.00 and P.T. <br /> s 4,X =Sta.P.C.+ 164+91.50. <br /> a7 Offsets.Tangent offsets vary (approaimately) d read with <br /> D and with square of the distance. Thus tangent offset for Sta. <br /> !, E 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.X54.50,hence <br /> t offset=7.27 (54.50+100)2=2.16 ft. Also square of any distance <br /> divided by twice the radius equals(apprwdmately)the distance from <br /> tangent to curve. Thus (54.50)2+(2 x 688.26)=2.16 ft. <br /> Deflections,—Deflection angle=% D for lop ft., Y4 D for 50 ft., <br /> etc.. For c ft.—(in minutes).3 x C x D°o{�=defl,for 1 ft.from Table <br /> III x C. For Sta. 158 of above curve=.3 x 54.5 x 8H--136.2' or <br /> -S Z ; 21 16.21,or-2.50 x 54.5=136.2'from Table M. For Sta. 159 deflec- <br /> �/� rl tion angle=2°16.2'+8°20'+2==6°26.21,etc. <br /> Externals.—May.be found in similar manner to tangents. Thus <br /> r. O E for curve:above is 91.37. For.frog Table IV for 1o*curve'E-960.6 <br /> I for 8° 20'=-960.6+83§ 1.27 and from Table V correction=.10 or <br /> 5 ,Po I E-91.37 ft. Or suppose p=32°and E is measured and found to be <br /> 42 ft. What is D? From Table IV E=230.9 and+42=5.5 or D= <br /> /�rS <br /> r <br />