|
t
<br />R
<br />T
<br />r I _
<br />TABLE X '
<br />CURVE FORMULAE FOR SIMPLE CURVES
<br />COMPILED BY3, CALVIN LOCSE, C.E., -
<br />{1) a 1/2Ra (2)
<br />-\/2R"(k--'\/ (R+b) (R .b) = 2R(Ii-..'✓Ra-b2)
<br />(4) c = 2'\/ m {2R - m)
<br />(6) c = 2T'cota-I
<br />(7) a ._= R exsee ,K Is; ,
<br />(8) a =. R tan I tan y, 1 . (0), e •= T tan YA J,
<br />J �2 c2. C2- e°
<br />(11) b'=nJ,o-f 2R � 2R
<br />(12) b: = R -sin I (13) b a cot Y2I
<br />tie+b2. c$ .'dl : c2+�2. .
<br />72a 2a (15j'R2m F 8m ';
<br />(16) d =1/R (2R-1/ (2R -}-c) ,(297 c) = 1✓R{2R-1% 4R2- 0)
<br />(17)fl= d
<br />1/2Rm ' (18) d = 2R sin Y4 I (19) rn = 2R
<br />J ! 2
<br />(20)m = R=,- e�rje� (R+ 2 �a R 2 R_�R2- 4
<br />(21) m = R vV Y21 (22) `In = R sin Y2I tan Y41 (23) m = %c tan Y4I
<br />(24) a = ,2R (25) a=R-N/(R+b) (R -b) ='R -1/R2 -b2
<br />(26) a = 2R (sins M I)2 (27) a = R vera I (28) a = R sin I tan JIJ I
<br />(29) a = ti tan % 1 (30) a = T sin I . (31) T = R tanji
<br />(32) 1 - R X57.295780 (33) R = I X57.295780
<br />(34) L = I�X0.01745329. (35) L = -3 c
<br />(36) Area Seg. = LR- Ri Sin I - LR - Rb
<br />2 2
<br />" TABLE XI. --CALCULATION OF EARTHWORK
<br />HEIGHT
<br />Width,•
<br />---
<br />1
<br />2
<br />8
<br />d.
<br />. 8
<br />a
<br />7
<br />a
<br />9
<br />Is
<br />11
<br />12
<br />18
<br />i4
<br />10
<br />1
<br />:02
<br />.04
<br />.06
<br />'.07
<br />.09
<br />.11
<br />.13
<br />.15
<br />.17
<br />AS
<br />.20
<br />.22
<br />.24
<br />26
<br />.29
<br />8
<br />.04`.07
<br />.11
<br />•.15
<br />.18
<br />.22
<br />.26
<br />.30
<br />.33
<br />,37
<br />.41
<br />.44
<br />AS
<br />.52
<br />.W
<br />9
<br />.06
<br />.11
<br />.17
<br />.22
<br />.28
<br />.33
<br />.39
<br />:44
<br />.50
<br />.56
<br />.61
<br />.67
<br />.72
<br />.78
<br />.83
<br />4
<br />.07
<br />.15
<br />.22
<br />.30
<br />.37
<br />.44
<br />.52
<br />:59
<br />.67
<br />.74
<br />-81
<br />.89
<br />.96
<br />1.04
<br />1.11
<br />8
<br />.09
<br />:19
<br />.28
<br />.37
<br />.46
<br />.56
<br />.65
<br />.74
<br />.83
<br />.93
<br />1-021.11
<br />1.20
<br />1.30
<br />1.39
<br />6
<br />I1
<br />..22
<br />.33
<br />.44
<br />'.56
<br />.67
<br />.78
<br />.89
<br />1.00
<br />L 11
<br />L- 22
<br />1_13
<br />1.44
<br />1.55
<br />1.67.
<br />7
<br />.13
<br />.25
<br />.39
<br />.52
<br />'.65
<br />.78
<br />.911.04
<br />1.16
<br />1.31)
<br />1.42
<br />1.55
<br />1.08
<br />181
<br />3.94
<br />8
<br />.15'.30
<br />.44
<br />.59
<br />.74
<br />.89
<br />1.04
<br />1.19
<br />1.33
<br />1.48
<br />1.63
<br />1.78
<br />1.92
<br />2.08
<br />2.22
<br />9
<br />17
<br />.33
<br />.50
<br />.67
<br />.83
<br />I. 00
<br />I . t7
<br />1.-33
<br />1.50
<br />167
<br />1.83
<br />2.00
<br />2.17
<br />2.33
<br />2.50
<br />10
<br />IS
<br />.37-
<br />-56
<br />.74
<br />.93111
<br />1-301.48
<br />1.07
<br />t.852.042,222.41
<br />2-59
<br />2178
<br />11
<br />.20
<br />.41
<br />.61
<br />.82
<br />1.02
<br />1.22
<br />1.43
<br />1.63
<br />1. 83,
<br />2.04
<br />2.24
<br />2.44
<br />2.65
<br />2.85,
<br />3.06
<br />19
<br />22
<br />.44
<br />-:67
<br />.89
<br />1.1'1
<br />I.33
<br />1.56
<br />1:78
<br />2.00
<br />2.22
<br />2, 44
<br />2.67
<br />2, 89
<br />3.11 ,
<br />8-33
<br />1s
<br />.24
<br />.48
<br />.72
<br />.96
<br />1,.20
<br />1.44
<br />1.68
<br />1.92
<br />2.16
<br />2.41
<br />2.65
<br />2; 89
<br />3.13
<br />3.37
<br />3.61
<br />14
<br />i.20'
<br />. 52
<br />.18
<br />1.04
<br />1.30
<br />1.55
<br />1.81
<br />2.08
<br />2.33
<br />2,00
<br />2-,85
<br />3. I1
<br />3.37
<br />3.63
<br />18
<br />28'
<br />:56
<br />'.83
<br />1.1I
<br />1.39
<br />1.67
<br />1.94
<br />2.22
<br />2.50
<br />2,78
<br />3.08
<br />3.33
<br />3, 61
<br />' 3.89
<br />_3.89
<br />4.17
<br />16
<br />:30
<br />.59
<br />.89
<br />1.18
<br />1.48
<br />1.78
<br />2.07
<br />2-37
<br />2.97.2,
<br />96
<br />3.26
<br />3.66
<br />3.85
<br />.4.15
<br />4.44
<br />17
<br />.31'
<br />. 63
<br />.94
<br />1.26
<br />1.57
<br />1.89
<br />2.20
<br />2.52
<br />2. 83
<br />3.15
<br />3.46
<br />3.78
<br />4.09
<br />4.41
<br />4.72
<br />18
<br />.33
<br />.67
<br />1.00
<br />1.33
<br />1.67
<br />2.00
<br />2.33
<br />2.67
<br />3.00
<br />3.33
<br />3.67
<br />4.00
<br />4.33
<br />4.67
<br />5.00
<br />19
<br />.35
<br />.701-06
<br />1.41
<br />1-702.11
<br />2,46
<br />2.82
<br />3.17
<br />3.52
<br />3.87
<br />4.22
<br />4.57
<br />4.92
<br />5.28
<br />.20 "
<br />.37
<br />.74
<br />1:11
<br />148
<br />1','85
<br />2.22
<br />2.59
<br />2.98
<br />3.33
<br />3.70
<br />4.07
<br />4.44
<br />4.81
<br />,5.18
<br />5:56
<br />21
<br />.39
<br />,78'1.171,551.942,332.723.113.503.894.284.675.06
<br />5.44
<br />5.83
<br />22 •
<br />41
<br />: 81
<br />1.22
<br />1,032
<br />, .04
<br />2,44
<br />2.85
<br />3.26
<br />3,87 87
<br />4.07
<br />4.48
<br />4.89
<br />5.30
<br />5.70
<br />6.11
<br />28
<br />.48
<br />.85
<br />1.28
<br />1.70
<br />2.13
<br />2.56
<br />2.98
<br />3.41
<br />3.53
<br />4.26
<br />4.68
<br />5. 11
<br />5.54
<br />5.96
<br />6.39
<br />s4
<br />.44
<br />.89
<br />1.33
<br />1.78
<br />2.22
<br />2.67
<br />3,113.
<br />86
<br />4.00
<br />4...44
<br />4.89
<br />5:33
<br />5.78
<br />6.22
<br />6.67
<br />98
<br />.46
<br />.92
<br />1.39
<br />1.85
<br />2.31
<br />2.78
<br />3.24
<br />3.70
<br />4.17
<br />4.63
<br />5.09
<br />5.56
<br />6.02
<br />6.48
<br />,
<br />6.94
<br />S8
<br />.48
<br />.98
<br />1.44
<br />1.022.412.893.373.854.334.825.305:796.26
<br />6.74
<br />7.24
<br />27
<br />'.501.001.502.002.503.003.504.004.505.005.506.006.50
<br />7.00
<br />7.50
<br />28
<br />.521.04'1.552.072.593.113.634.154.67
<br />5.185.706.226-74
<br />7.26
<br />7.78
<br />20
<br />.54
<br />1.07
<br />1.61
<br />2.15
<br />2.68
<br />3.22
<br />3.76
<br />4.30
<br />4.83
<br />5.37
<br />5 91
<br />6.44
<br />6.98
<br />7.52
<br />8.06
<br />80
<br />.56
<br />1.11
<br />1.67
<br />2.22
<br />2.78
<br />3.33
<br />3.89
<br />4.44
<br />5.00
<br />5.55
<br />6. 11
<br />6.07
<br />7.22
<br />7.78
<br />8.33
<br />St ,
<br />.57
<br />1.15
<br />1.72
<br />2.30
<br />2.87
<br />3.44
<br />4.02
<br />4.59
<br />5.17
<br />5.74
<br />6.32
<br />6.89
<br />7.46
<br />8.04
<br />8.61
<br />88
<br />.59
<br />1. 18
<br />1.78
<br />2.37
<br />2.96
<br />3.56
<br />4.15
<br />4.74
<br />5.33
<br />5.92
<br />6.52
<br />7,11
<br />7,70
<br />•8.30
<br />8-89
<br />88
<br />.61
<br />1.22
<br />1.83
<br />2.44
<br />3:05
<br />3.67
<br />4.28
<br />4.89
<br />5.50
<br />0. 11
<br />6.72
<br />7.33
<br />7.04
<br />8.55
<br />9.17
<br />sa
<br />63
<br />1.26
<br />1.89
<br />2.52
<br />3, 15
<br />3.78
<br />4.40
<br />5.04
<br />5.67
<br />0.29
<br />6.03
<br />7.56
<br />8.18
<br />8.81
<br />9.44
<br />36 '
<br />85
<br />1: 30
<br />1.94
<br />2.59
<br />3.24
<br />3.89
<br />4.53
<br />5.18
<br />5.88
<br />6.48
<br />T, 13
<br />7.78
<br />8.42
<br />9, D8
<br />9.72
<br />66
<br />- 6711"33
<br />2.00
<br />2.67
<br />3.33
<br />4' '004,111
<br />5-33
<br />6.00
<br />11.67
<br />7.33
<br />8.00
<br />8.67
<br />9.33
<br />10,00
<br />By
<br />.08
<br />1.37
<br />2.06
<br />2.74
<br />8.42
<br />4. 11
<br />4.70
<br />5.48
<br />6.17
<br />8: 85
<br />7.54
<br />8.22
<br />8.91
<br />9.59
<br />10.28
<br />86' .
<br />. 70
<br />1,412.
<br />11
<br />2.82
<br />3.52
<br />4,22
<br />4,92
<br />5.63
<br />6.33
<br />7.03
<br />7.74
<br />8, 44
<br />9. 15
<br />9.85
<br />10.56
<br />s9
<br />721.442,172.893.614.333.055.786.507.227.958.679.3910.11
<br />10.83
<br />40
<br />.74
<br />1.48
<br />2.22
<br />2.96
<br />3.70
<br />4.44
<br />5,18
<br />5.92
<br />6.67
<br />7.41
<br />8.15
<br />8.89
<br />9.63
<br />10.37
<br />1,1.11
<br />Table gives cu. -yds. in I it. of a triangle of'given width and height. Corrections fo
<br />tenths of width are one tenth the values found under each height considering the width)
<br />from 1 to 9 as tenths and similarly the corrections for tenths of height are one tenth thl
<br />figures opposite width considering the heights from 1 to 9 as tenths. Thus if w=16.2 ant
<br />h-5.3, cu. yds.=1.48+.DIS+.089=1.587 cu, yds. or practically 160 cu. yds: per 100 ft
<br />If 'w exceeds 40 ft., use one-half and multiply result by 2, if both w and b are large un
<br />one-half of each and multiply result by 4. Any cross-section may be divided into triangle
<br />by the following rule. To the triangle of the sum of the outaide cute (or fills) =h, and ',,
<br />the roadbed =w, add the tries formed by taking the distance out to each break in turn
<br />( =w's) by the difference between the eute (or fills) on each Bide of it (=h's) always sub
<br />tracting the outer from the inner.
<br />
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