577 6.6 7.3 CURVE FORMULAE D = Degree of Curve 1° = 1-Degree of Curve 2° = 2-Degree of Curve P.C. = Point of Curve P.T. = Point of Tangent P.I. = Point of Intersection I = Intersection of Angle, Angle between Two Tangents L = Length of Curve, from P.C. to P.T. T = Tangent Distance E = External Distance R = Radius L.C. = Length of Chord M = Length of Middle Ordinate c = Length of Sub-Chord d = Angle of Sub-Chord R = L.C. / (2 sin 1/2 I) T = R tan 1/2 I = L.C. / (2 cos 1/2 I) L.C. / 2 = R sin I/2, D 1° = R = 5730, D 2° = 5730/2, D = 5730/R M = R(1 - cos 1/2 I), = R - R cos I/2 (E + R) / R = sec I/2, (R - M) / R = cos I/2 c = 2 R sin 1/2 d, d = c/(2R) L.C. = 2 R sin 1/2 I, E = R(sec 1/2 I - 1), = R sec I/2 - R Minutes in Decimals of a Degree 1' .0167 2 .0333 3 .0500 4 .0667 5 .0833 6 .1000 7 .1167 8 .1333 9 .1500 10 .1667 11' .1833 12 .2000 13 .2167 14 .2333 15 .2500 16 .2667 17 .2833 18 .3000 19 .3167 20 .3333 21' .3500 22 .3667 23 .3833 24 .4000 25 .4167 26 .4333 27 .4500 28 .4667 29 .4833 30 .5000 31' .5167 32 .5333 33 .5500 34 .5667 35 .5833 36 .6000 37 .6167 38 .6333 39 .6500 40 .6667 41' .6833 42 .7000 43 .7167 44 .7333 45 .7500 46 .7667 47 .7833 48 .8000 49 .8167 50 .8333 51' .8500 52 .8667 53 .8833 54 .9000 55 .9167 56 .9333 57 .9500 58 .9667 59 .9833 60 1.0000 Inches in Decimals of a Foot 1/16 .0052 3/32 .0078 1/8 .0104 3/16 .0156 1/4 .0208 5/16 .0260 3/8 .0313 1/2 .0417 5/8 .0521 3/4 .0625 7/8 .0729 1 .0833 2 .1667 3 .2500 4 .3333 5 .4167 6 .5000 7 .5833 8 .6667 9 .7500 10 .8333 11 .9167