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T <br /> FI LD BOOK 444 ; <br /> w <br /> IMPROVED TABLES <br /> AND .�� <br /> INFORMATION 8 <br /> T P 1.2 o <br /> Orc � <br /> CURVE FORMULAS <br /> Radius= (1) Degree of Curve=Iand•sia <br /> Tangent=T=Rtsnf(3) Length of Curve--=I--160,9(4) <br /> Middle ordinate—M=R(1—cos.Z) (5)=Rvers 2 (6) <br /> External=E=Ttana°—M? R+Coe.A2—R(8)=Rexwf(9) <br /> Long Chords-2 R sin.2 (10) p�entral Angle <br /> EXPLANATION AND USE OF TABLES <br /> Stations.—Given P. I.=Sta. 161{-60.35 to find Sta. of P. C. <br /> and P. T. p=-62° 10' D--8° 20'. From Table IV for 1° curve T- <br /> 3454.1 and=8jy=414.49 ft. From Table V correction=. or T <br /> 414.85 ft. P. C.=Sts. P.I.—T=157 -{-45.50. Also from (4) 1- <br /> 746.00 and P.T.—Sta.P.C.+I_-164-}-91.50. <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 /> offeet=7.27 '(54*50-100) 2.16, ft. Also square of any Mince <br /> divided by twice the radius a uals (approximately) the distance from <br /> tangent to curve. Thus(54.50==(2 x Cx2i6)=2.l)6 ft. <br /> Deflections!.—Deflection angle=% D for 100 ft., 1/D for 50 ft. <br /> etc: For a ft.�(n minutes) .3 x C x D°or=defl.for 14t.from Table <br /> III x C. For!Sts ' 158 of above curve--.3 x 54.5 x 8M=136.2' or <br /> 2° 16.2', or-n2.50 x 54.5-136.2'from Table III. For•Sts. 159 deflec- <br /> tion angle=20 16.21 +80 20' =2=6°26.21,etc. <br /> Externals.—May be found in similar manner to tangents. Thus <br /> E for curve above is 115.87. For from Table IV for 1°curve E-960.6 <br /> j for 8° 201=960.6+83 _115.27 and from Table V correction—.10 or <br /> E==�115.37 ft. Or aupppoossee A==412*and E is measured and!bund to be <br /> 42 ft. What is D? From Table IV 1230.9 and -42=1.5 or D- <br /> 50 30': <br /> t <br />