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19 <br />} <br />i <br />1. <br />r <br />I <br />DIETZOEN'S RAILROAD CURVE <br />AND <br />REDUCTION TABLES <br />Copyright, 1914, 6y Eugene,Dietzgen Co., New York City _ <br />.. M"o 17 <br />CURVE FORM13LAS <br />Radius-_-R� D�2(1) Degree of Curve=D and sin. D� (2) <br />Tangent=T=Rtan A (3) Length of. Curve=L=100D (4) <br />Middle. ordinate=M-R(1-cos. A°z) (5)=Avers a (6) <br />External=E=Tian 4 -(7) �R _ cos. a -R (8)=Rexsee 2 (9) <br />Long Chord= -C=2 R sin. a (10) p --Central Angle f <br />EXPLANATION AND USE OF TABLES <br />Stations: -Given P. L=Sta. 161}60.35 to find Sta. of P. C. <br />and P. T. A=62' 10' D=8° 20'. From Table IV for I° curve T= <br />3454.1 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) 1-- <br />74:6.00 <br />=746.00 and P. T.-Sta. P. C.+L=164+9L50. <br />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.=54.50 hence <br />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 x 688.26)-2.16 ft. <br />Deflections. -Deflection angle= Y2 D for 100 ft.,/ D for 50 ft., <br />etc. For c ft.=(in minutes) .3 x C x D° or --deft. for 1 it. from Table <br />III x C. For Sta. 158 of above curve -.3 x 54.5 x 8Aj 136.2' or <br />2' 16.2', or --2.50 x 54.5=136.2' from Table III. For Sta. 159 deflee- <br />tion angle=20 16.2' +8' 20' -: 2_6° 26.2', etc. <br />Externals May be found in similar manner to tangents. Thus <br />E for curve above is 115.37, For from Table IV for I' curve E=960.6 <br />for 8' 20'=960.6=8�4=115.27 and from Table V correction -.10 or <br />E=115.37 ft. Or suppose A=32° and E is measured and found to be <br />42 it. What is D? From Table IV E=230.9 and _42=5.5 or D-- <br />5' <br />-5' 30'. <br />9- <br />