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7. <br /> DIETZGEN'S RAILROAD CURVE <br /> d- <br /> - IV <br /> 7o' AND <br /> REDUCTION TABLES <br /> Copyright, 1914, by Eugene Dietsgen Co., New York City <br /> d jy _ P.4 T <br /> -A <br /> Y 1/O '04 .d <br /> -- .3f .0 fdu o ° <br /> 3 CURVE FORMULAS <br /> � n ao <br /> Radius=hr (1) De ree of Curve=D and sin. 2) <br /> ,�.n/a g <br /> 3 i 3i- v ce » o e <br /> _ _ _ Tangent=T=Rtan a(3) Length of Curve=I�l00D(4) <br /> v r�� <br /> (� •� / Middle ordinate=M=R(1-cos.a) (5)=Rvers s (6) <br /> External=F--Ttan4(7)=R-cos.a R(8)=Rexseo"(9) <br /> / �� <br /> Long Chord--C=2 R sin.2 (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 /> r rl 3 and P. T. p==62° 10' D-8° 20'. From Table IV for 1° curve T= <br /> and-83i=414.49 ft. From Table V correction--.36 or T= <br /> 414.85 ft. P. Q.-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 /> 3 y o 9 s2,of Offsets.-Tsn ent offsets va " <br /> g ry (apphro imately) directly with <br /> D and with square of the distance. TTus tangent offset for Sta. <br /> 3 3.s 7 r c,� / 158 on above curve is 2.16 ft.found as follows. From Table III tangent <br /> /�t _ _ offset for 100 ft=7.27 ft. Distance=�68--Stn. P. C.�4.50 hence <br /> ------ -- - ? - - — 3'p -- <br /> 9 3 3 08 P offset=7.27 (54.50-- 100) 2.16 ft. Also square of any distance <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 /> � Deflections.-Deflection angle=3j D for 100 ft., � D for 50 ft., <br /> - - - ° <br /> etc. For c ft.:(in minutes) .3 x C x D oi�-defl. for 1 t.-from Table <br /> 0-15,11 III x C. For Sta. 158 of above curve=.3 x 54.5 x 83j=t=i .2' or <br /> ` --- - ---- 2° 16.2', or--2.50 x 54.5=136.2'from Table III. For Sta.f189 deflec- <br /> tion angle---2 16.2' +8°20' -2==6°26.2',etc. <br /> dr• 3 _ _____.-- _- - Externals.-May be found in similar manner to tangents. Thus <br /> 6 • "-- E for curve above is 115.37. For from Table IV for 10 cgrie E--960.6 <br /> for 80 20'=-960.6-,8"� 115.27 and from Table V correction-.10 or <br /> E=115.37 ft. Or supppose 0=32°and E is measured and found to be <br /> 52 ft What is D? From Table IV E-=230.9 and -42=br.5 or D= <br /> 3 ' � <br />