CURVE AND REDUCTION TABLES Published by Eugene Dietzgen Co. P.C. T PI L C PT 1/2 I 1/2 I CURVE FORMULAS 1. Radius : R=50/sin D/2 2. Degree of Curve: D=100*I/L. Also, sin D/2=50/R 3. Tangent : T=R tan 1/2 I. Also, T=T for 1°curve/D + C. 4. Length of Curve: L=100*I/D 5. Long Chord : L. C.=2R sin 1/2 I. 6. Middle Ordinate: M=R (1-cos 1/2 I) 7. External : E=R/(cos 1/2 I) - R. Also, E=T tan 1/4 I. EXPLANATION AND USE OF TABLES Given P.I. Sta. 83+40.7, I=45° 20' and D=6°30' find: Stations-P.C.=P.I.-T. T=T for 1° Curve/D + C. From Tables V and VI T=2392.8/6.5+.197=368.32=3+68.32. Sta. P. C.=83+40.7-(3+68.32)=79+72.38. P.T.=P.C.+L, and L=100*I/D=100*45.33/6.5=697.38 Therefore, P.T.=(79+72.38)+(6+97.38)=86+69.76. Offsets-Tangent offsets vary (approximately) directly with D and with the square of the distance. From Table III Tangent Offset for 100 feet=5.669 feet. Distance =80-Sta. P. C.=27.62. Hence offset=5.66*((27.62)/100)^2=.432 ft. Also, square of any distance, divided by twice the radius equals (approximately) the distance from tangent to curve. Thus (27.62)^2/(2*881.95)=.432 ft. Deflections-Deflection angle=1/2 D for 100 ft., 1/4 D for 50 ft., etc. For "X" ft., Deflection Angle (in minutes)=.3*X*X*D. For Sta. 80 of above curve Deflection Angle =.3*27.62*6.5=53.86'. Also Deflection Angle=dfi. for 1 ft. from Table III *X*=1.95 *27.62=53.86'. For Sta. 181 Deflection Angle=53.86'+(6°30')/2=4° 8.86'. Externals-From Table V for 1° curve, with central angle of 45° 20', E=479.6. Therefore, for 6° 30'curve, E=479.6/6.5 + Correction from Table VI =7.378+.039=7.417. 1