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TABLE X CURVE FORMULAE FOR SIMPLE CURVES COMPILED BY J. CALVIN LOCKE, C.E. (1) c = 1/2Ra (2) C = ,%/a2+b2 (3) c = 1/2R (R - V (R b) (R - b) = 2R(R - V R2 - b2) (4) c = 2'N/ m (2R - m) (5) c = 2R sin 4 I (6) c = 2T cos 3,i,I (7) e = R exsee % I (8) a= R tan Y2 I tan y i (9) e= T tan V I (10) b = a (2R --a 2 _ 4 (11) b = J�ei 2R X 2R / - c2 4R2 (12)b=Rsin 1 (13)b=scot %I 062 +b2 et d2C2+4m2 (14) R = 2a = 2a (15) R = 2m - 8m (16) d = •,/R (2R - V (2R+c) (2R - c) = 1/R(2R - d 4R2 - c2) (17) .d =1/2Rm (18) d = 2R sin % I (19) In = 2R _ C1 (20)m = R=r R+ l` 2 !\R 2 R� R2 4 (21)m = R vera %I (22) m = R sin yI tan XI (23) m =>�c tan Y41 C2 (24) s = - (25) a = R- 1/(R�-b)• (R -b) = R-1%R2'"bz 2R (26) a = 2R (8in2 % I)2 (27) a = R vers I (28) a = R sin I tan lie I (29.) a= b tan Y2 I (30) a T sin I (31) T= R tan Y2 I (32) I = R. X57.295780 (33) R = 1 X57.295780 c (34) L = IR.X0.01745329 (35) L = 3 (36) Area Seg. = LR-- 2 Sm I = LR 2 Rb 2 _ C. TABLE XI. --CALCULATION OF EARTHWORK HEIGHT Width 1 9 3 4 8 6 7 8 9 10 11 12 19 14 15 1 .02 .04 .08 .07 .09 .11 .13 .15 .17 .18 .20 .22 .24 .26 .28 a .04 .07 .11 .15 .18 .22 .26 .30 .33 .37 .41 .44 .48 .52 .56 3 .06 .I1 .17 .22 .28 .33 .39 .44 .50 .56 .61 .67 .72 .78 S3 4 ..07 .15 .22 .30 .37 .44 .52 .59 .67 .74 .81 .89 .96 1.04 1.11 6 ,09 :19 .28 .37 .46 .56 .65 .74 .83 .93 1.02 1.11 1.20 1.30 1.39 6 .11 .22 .33 .44 .56 .67 .78 .89 1.00 1.11 1.22 1.33 1.44 1.55 1.67 7 .13 .26 .39 .52 .65 .78 .91 1.04 1.16 1.30 1.42 1.55 1.68 1.81 1.94 8 .15 .30 .44 .59 .74 .891.04 1.19 1.33 1.48 1.63 1.78 1.92 2.08 2.22 9 .17 .33 .50 .67 .83 1.00 1.17 1.33 1.50 1.67 1.83 2.00 2. 17 2.33 2.50 10, .18 .37 .56 .74 .93 1.11 1-301.48 1.67 1.85 2.04 2.22 2.41 2.59 2.78 11 .20 •.41 .61 .82 1.02 1.22 1.43 1.63 1.83 2.04 2.24 2.44 2.65 2.85 3.06 14 .22 .44 .67 .89 1. ll 1.33 1.56 1. 78 2.00 2. 22 2.44 2.67 2.89 3.11 3.33 18 .24 .48 .72 .96 1.20 1.44 1.68 1.92 2.16 2.41 2.65 2. 89 3.13 3.37 3.61 14 .26 .52 .781.04 1.30 1.55 1.81 2.08 2.33 2.59 2.85 3.11 3.37 3.63 .3.89 18 .28 .56 .83 1.11 1.39 1.67 1.94 2.22 2.50 2.78 3.06 3.33 3.61 3.89 4.17 16 .30 .59 .89 1.18 1.48 1.78 2.07 2.37 2.67 2.96 3.26 3.56 3.85 4.15 4.44 17 .31 , .83 .94 1.26 1.57 1.89 2.20 2.52 2.83 3.15 3.46 3.78 4.09 4.41 4.72 18 .33 :67 1.00 1.33 1.67 2.00 2.33 2.67 3.00 3.33 3.67 4.00 4.33 4.67 5.00 19 .35 .70 1.06 1.41 1.76 2.11 2.46 2.82 3. 17 3.52 3.87 4.22 4.57 4.92 5.28 80 .37 .74 1.11 1.48 1.85 2.22 2.59 2.96 3.33 3.70 4.07 4.44 4.81 5.18 5.56, 91 .39 .78 1:17 1.55 1.94 2.33 2.72 3.113. 50 3.89 4.28 4.67 5.06 5.44 5.83 22. 41 : S t 1.22 1.63 2.04 2.44 2.85 8.26 3.67 4, 07 4.48 4.89 5.30 5.70 6.11 SS .43 :95 1.28 1.70 2.13 2.56 2.98 3.41 3.83 4.26 4.68 5. 11 5.54 5.96 6.39 -94 .44 .89 1.33 1.78 2.22 2.67 3.11 3.56 4.00 4.44 4.89 5.33 5.78 6.22 6.67 98 .46 .921-39 1.85 2.31 2.78 3.24 3.70 4.17 4.63 5.09 5.56 6.02 6.48 6.94 26 .48 .961.44 1.92 2.41 2.89 3.37 3.85 4.33 4.82 5.30 5.78 6.26 6.74 7.24 97 .50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 28 .52 1.04 1.55 2.07 2.59 3. I 13.63 4.15 4.67 5.18 5.70 6.22 6.74 7.26 7.78 29 .54 1.07 1.612. 15 2.68 3.22 3.76 4.30 4.83 5.37 5.91 6.44 6.98 7.52 8.06 80 .56 1.11 1.67 2.22 2.78 3.33 3.89 4.44 5.00 5.55 6.11 6.67 7.22 7.78 8.33 81 .57 1.15 1.72 2.30 2.87 3.44 4.02 4.59 5. 17 5.74 6'.32 6.89 7.46 8.04 8.61 92 .59 1.18 1.78 2.37 2.96 3.56 4.15 4.74 5.33 5.92 6.52 7.11 7.70 8.30 8.89 a9 .61 1.22 1.83 2.44 3.05 3.67 4.28 4.89 5.50 6. 116. 72 7.33 7.94 8.55 9.17 34 .63 1.26 1.89 2.52 3.15 3.78 4.40 5.04 5.67 6.29 6.93 7.56 8. 18 8.81 9.44 95 .65 1.30 1.94 2, 59 3.24 3.89 4.53 5.18 5.83 6.48 7.13 7.78 8.42 9.08 9.72 88 .67 1.33 2.00 2.67 3.33 4.00 4.66 5.33 6.00 6.67 7.33 8.00 8.67 9.33 10.00 87 .68 1.37 2.06 2.74 3.42 4: 11 4.79 5.48 6. 17 6.85 7.54 8.22 8.91 9.59 10.28 a8 .70 1.41 2.11 2.82 3.52 4.22 4.92 5.63 6.33 7.03 7.74 8.44 9.15 9.85 10.56 a9 .72 1.44 2.17 2.89 3.61 4.33 5.05 5.78 6.50 7.22 7.95 8.67 9.39 10. 11 10.83 40 .74 1.48 2.22 2.96 3.70 4.44 5.18 5.92 6.67 7.41 8.15 8.89 9.63 10.37. 11.11 Table gives cu. yds. in 1 ft. of a triangle of'given width and height. Corrections for tenths of width are one tenth the values found under each height considering the widths from 1 to 9 as tenths and similarly the corrections for tenths of height are one tenth the figures opposite width considering the heights from 1 to 9 as tenths. Thus if w=16.2 and h-5.3, cu. yds. -1.4S+.018+.089 =1.587 cu. yds. or practically 160 cu. yda. per 100 ft. If'w exceeds 40 ft., use one-half and multiply result by 2, if both w and h are large use one-half of each and multiply result by 4. Any cross-section may be divided into triangles by the following rule. To the triangle of the+ sum of the outside cuts (or fills) =b, and M the roadbed =w, add the triangles formed by taking the distance out to each break in turn ( =w'e) by the difference between the cuts (or fills) on each side of it ( -h's) always sub- ubtracting tractingthe outer from the inner.