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i <br /> 1 <br /> DIETZCE.N'S CURVE. <br /> AND <br /> REDUCTION TABLES' <br /> (byytlaht.1914,by Eugene Dletften Co..Now Yolk Ci1y <br /> - -� -- - + <br /> 7 <br /> CURVE FORMULAS ' 3 <br /> v ? T Radius=R=50(1)Degree of Curve=D and sin.n=#-n°(2) <br /> _ Z ry c J Tangent=T=RtanA(3)Length of Curve=L=100$(4) <br /> r) <br /> Middle ordinate=M=R(1—cos. =Rvers (6) <br /> - External=E=Ttan=-(7)=R+cos. Ft(8)=IZexsec (9) <br /> Long Chord=C=2 R sin.$(10)A_Central Angle <br /> - _ = 4 7 U_0 --__-_ __. ._ EXPLANATION AND USE OF TABLES <br /> 1 3 $ttt as.—Given P. I.=9ta. 161+60-35 to find Sta.. of P. C <br /> -_ said P. T. p--62° 10' D-°20'. From Table IV for 10 curve'T'= <br /> 8454.1 oad+$h-414.49 ft. From Table V correction=%36 or T- <br /> 414.85 It. P. C.—Sta. P.L--Ta157{•45.50. Also from (4) L— <br /> 2 v 746.00 land P.T.-&a.P.C.+L-184+91.50. <br /> - t)$sets. -Tangent offsets vary (appro�nmately) directly with <br /> S D *Ad YAth square of the distanoe. Thus tangent offset for Sta.. <br /> 158 on Wove ou"eis 2.16 ft,found as follows. From Table III tangent <br /> offset frq 100 ft.--7.27 ft. Distsnce=158—Sta.P. C.--54.50,hence <br /> - offset=7.27 (54.50+100)3@2.16 ft. Also square of any distance <br /> divided by twiey the radius equals(approximately)the distance from <br /> tangent.to curve. Thus (54 )3+(2x688.26)=2.16 ft. <br /> Dollecdous.Defleotion angle— D for 100 ft., 1/D for ft., <br /> j `1 mee�q,, Far o ft.—Cin minutde).3 x C x TI°or=�deR.for 1%.from Table <br /> III x C. For Sta. 159 of above ourre=.3 x 54.5 x 84-136,2' or <br /> -7 S°16.2,or-4.50 64.5-1362'from Table III. For Eta. 159 deDec- <br /> - tion mgle=-20 V+ 20'+2*== 4*26.2"etc. <br /> 3. #terpslitr-�llday be found 19similar manner to tamgente. Thus <br /> durve above is 91.37; For froth Table IV for P curve E-40.6 <br /> pp <br /> Ora 20'x900.6+$�§�.27 sad frora Table V correction—.10 or <br /> F 4127 ft. Of suppose A=.32PoodBiamewwedandfoxmdtobe <br /> 42 ft. WhAt is DY From Table IV EP=230.9 and+42=5.5 or D=a• <br /> 5°301. <br /> i <br /> A <br />