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F iELD <br />BOOK. 58l � <br />CURVE AND REDUCTION TABLES <br />Published by Eugeae Diatsgan Co. <br />CIIRVE FORMULAS <br />1. Radius __ 50 <br />R sin D/2 <br />2. Degree of Curve: D= 1'00 L� Also, sin D/2= 50 <br />R <br />3. Tangent T=Rtan%I. Also, T=Tfor 1°curve}C. <br />D <br />4. Length of Curve: L=100 D <br />5. Long Chord L. C.=2R sin % I. <br />6. Middle Ordinate: M=R{1—cos j I) <br />7. External E=gos % I—R' Also, E=T tan % I. <br />ERPLANATION AND USE OF TABLES <br />Given P.I. Sta. 83}40.7, I =45° 20' and D =6°30' find: <br />Stations—P. C.=P.I.—T. T=T for 1°Curve+ C. From Tables V and VI <br />D <br />2398 8 <br />T= 6.6 }.197=363.32=3}68.32. Sta. P. C.=83}40.7—(3}68.32)=79}72.38. <br />P. T.=P. C.}L, and L=100 I =1004'5_33=697.38 Therefore, P. T. =(78}72.38) <br />D 6.5 <br />} (6}97.38) =86}69.76. <br />OHaeta—Tangent offsets ry (approximately) directly with D nd 'th the <br />square of the distance. From Table III Tangent O&set f\or 100 feet =5.669 feet. Distance <br />=80—Sts. P. C.=27.82. Hence odset=5.66X\210 /r=.432 ft. Also, s <br />quare of any <br />distance, divided by twice the radius equals (approximately) the distance from tangent <br />to ourve. Thus (27.62) =(2 X881.B5) =.432 ft. <br />Deflections—Deflection angle =y D for 100 ft., y, D for 50 ft., etc For "X" ft.• <br />Deflection Angle (in minutes) =.3 XX XD. For Sta. 80 of above curve Deflection Angle <br />=.3 X27.62 X6.5 =53.86'. Also Deflection Angle =df1. for 1. ft. from Table III XX =1.9.5 <br />X27.62=53.86'. For ata. 181 Deflection Angle=53.86'}6°20=4°8.86'. <br />Erteraala—From Table V for 1° curve, with central angle of 45° 20',.E =479.6. <br />Therefore, for 6° 30' curve, E =469.6} Correction from Table VI - <br />-7.378}.039 =7.417. <br />7 <br />