|
7M
<br />TABLE II. = Radii, Ordinates"and Deflections. Chord'-- 100 ft.
<br />Deg,��
<br />Radius
<br />50
<br />Mid
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def,
<br />Dist.
<br />Dor'
<br />I Ft
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def. ,
<br />Dist.
<br />Dar
<br />I Ft
<br />2° 17'
<br />t.
<br />ft.
<br />ft.
<br />ft.
<br />-/-
<br />__.
<br />.ft:'.'
<br />"ft.-
<br />- ft.
<br />ft.
<br />i
<br />0'10'
<br />34377.
<br />.036.145
<br />3°21'
<br />.291
<br />0.05'.
<br />7"
<br />819,0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />,073
<br />,291'
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6".395
<br />12.79
<br />2,20
<br />30-
<br />11459. ,
<br />.109
<br />.436
<br />.873
<br />0.15
<br />.30.
<br />764.5
<br />1.637
<br />6,540
<br />13.08
<br />2.25
<br />:.40'
<br />8594.4
<br />:145
<br />.582
<br />1.164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2,30
<br />50.
<br />6875.5-
<br />.182
<br />.727
<br />1.454
<br />0.25'
<br />"8 •
<br />716.8
<br />1.746'
<br />6.976
<br />13.95
<br />2.40
<br />1 -',--,r
<br />. 5729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20:
<br />688.2
<br />1.819'
<br />7:266"14'.53
<br />i io.11
<br />2.50
<br />10
<br />4911.2
<br />,255
<br />1.018
<br />2.036
<br />0.35
<br />-30
<br />674.7
<br />1.855
<br />7.411
<br />14',82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164'
<br />2.-327
<br />0.40
<br />40
<br />661.7
<br />1.892-
<br />"7.556
<br />15'.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1,309
<br />2.618
<br />0.45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2:70
<br />1.40;
<br />3437.9,•.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />16.27.2.80
<br />50-
<br />'
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30-
<br />603.8
<br />2:074
<br />8.281
<br />16.56
<br />2,85
<br />a
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />493.4
<br />2,110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />'2644.6
<br />.473
<br />1.891
<br />3.781.0.65.
<br />10
<br />573.7
<br />2.183
<br />84716
<br />17:43
<br />3.00
<br />20
<br />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2,292
<br />9:150
<br />18:30.3.15
<br />30
<br />2292.0
<br />.645
<br />2.181
<br />4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />9,585
<br />1916.
<br />3,30
<br />40-
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2,511
<br />10.02
<br />20.04
<br />3.45
<br />50"
<br />"
<br />2022.4
<br />.618.2.472
<br />4.945
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45.
<br />20.91
<br />3,60
<br />8
<br />.1910.1
<br />,.655
<br />2.618
<br />5:235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10,89.
<br />21.77
<br />3.75
<br />10.
<br />1809.6
<br />.691-2.763
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />.727.
<br />2.908
<br />5.817
<br />1.00,
<br />30
<br />425.4
<br />2.9.49
<br />11.75,
<br />23.51
<br />4.05
<br />30-
<br />1637.3
<br />..764
<br />3.054
<br />6:108
<br />1.05
<br />14
<br />410.3
<br />3.05$
<br />12,•18
<br />24.37
<br />4.20
<br />40""1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.168.12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4:50
<br />i.
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387.13.49
<br />'26.97
<br />4:65
<br />30
<br />1375.4
<br />.909'3.635
<br />7!271
<br />1,25
<br />16
<br />359.3
<br />3.496
<br />13.92-
<br />27.84
<br />4.80
<br />20,
<br />1322:5
<br />.945
<br />3.718
<br />7.561
<br />1,30
<br />30
<br />348.5
<br />3:60614:35'
<br />28.70
<br />4.95
<br />30
<br />1273,6
<br />.982
<br />3.926
<br />7.852
<br />1.35
<br />17.
<br />338.3
<br />3,716
<br />14.78
<br />29.56
<br />5,10
<br />10
<br />1228.1
<br />1.018
<br />4,071'
<br />8.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />'.50
<br />1185.8
<br />1.055
<br />4.217
<br />8:433
<br />1.45
<br />,19.
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />3473
<br />0.00
<br />10
<br />1109.3
<br />.1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />36,44
<br />6.30
<br />20
<br />1074,7
<br />1,164
<br />4.653
<br />9.305
<br />1,60
<br />22.
<br />262.0
<br />4,814'
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />"1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />',40
<br />1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />:24
<br />240.5
<br />5.255
<br />20.79.
<br />41.58
<br />7,20
<br />56
<br />'982,6
<br />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5:476
<br />21.64
<br />43,28
<br />7.50
<br />6: -
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697:22.50,
<br />44,99
<br />7,80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5.524
<br />11.05
<br />1.90
<br />28;
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29.
<br />199.7
<br />6.360
<br />25.04
<br />50'.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00 1
<br />30' 119MI
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 10 degree, curve, its middle ordinate'should
<br />be .0012X900X2.183 or 2.36 inches. 1
<br />TABLE III. - Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />3� sub chord
<br />R =sin of $def. angle
<br />Length
<br />of arc
<br />r 100 .
<br />fo ft
<br />sin. s def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°193,18
<br />.5167
<br />1°51'
<br />2° 17'
<br />2° 58'`
<br />3°43'
<br />Io1.15
<br />320
<br />181.39•
<br />1' 59'
<br />2° 25'
<br />301I0' ...3,
<br />58, .._
<br />.Ioi:33
<br />34°
<br />171.01
<br />2°o6'
<br />2°331
<br />3°21'
<br />4° 12'
<br />101,48
<br />360
<br />161,80
<br />2° 13'
<br />�° 41 '
<br />° '
<br />3 33
<br />4 ° 26'
<br />101.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44,
<br />4° 40'io1.85
<br />24
<br />400
<br />146.19
<br />20 21'
<br />2° 57'
<br />3° 55, . ..
<br />4° 54,
<br />16i. o6
<br />420
<br />139.52
<br />20341
<br />3°05'.
<br />4° 07'
<br />50 o8'
<br />'i02.29
<br />44°
<br />133.47.;
<br />20 4.i,
<br />3° ?31.
<br />4° 18'::
<br />. 5°.22'
<br />402.53
<br />46°
<br />127 •.97. ".
<br />2° 48'
<br />3° 2I'
<br />4° 29'
<br />5-36'-
<br />102,- 76
<br />48°"
<br />122.92
<br />2° 55'
<br />3° 291
<br />4° 40'
<br />S° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° Q2'
<br />3° 38'.:
<br />4° 51c
<br />6° 04'
<br />_ f03.24
<br />52°
<br />114,o6
<br />3° 09'
<br />3°.46'
<br />S° oz'.
<br />6°;i7'
<br />103,54
<br />540
<br />i io.11
<br />3° 16'
<br />3° 54�
<br />�° 13'
<br />` 6° 31'
<br />103.84
<br />560,
<br />1o6.5o
<br />3° 2z'
<br />40 02'
<br />5° 23'
<br />6°44'
<br />104:14
<br />5go
<br />103.14
<br />30 29'
<br />4a lo' :
<br />50 34
<br />60 57'
<br />100.00
<br />..
<br />60
<br />30
<br />3 35
<br />4 18
<br />104,43
<br />5 44�
<br />7 41
<br />104,72
<br />CURVE FORMULAS .
<br />T= R tan j I R= T cot. 2 I I chord$
<br />T ,_..5o tan } I • Chord def. = R_ .
<br />R = b0
<br />50 Sin: J D . I,
<br />Sin. } D = - No. chords = -
<br />R E=R ex. secII D
<br />Sin. 'D- = 50 tan I E = T tan I I Tan. def. = a chord def. `
<br />The, square of any distance, divided by twice the radius, '•will equal
<br />the: distance from tangent to curve, very nearly.
<br />To find arrgle'for a given distance and deflection.
<br />a Rule I.,: Multiply, the .given distance by .01745 (def. for =i° for -I ft.
<br />see Table II.),�and divide' given deflection by.the-product.
<br />4 • = Rule 2. Multiply given deflection by 57 3.
<br />thegiven distance. and divide the product by
<br />, .
<br />To find deflection for .a given angle and distance: Multiply the angle
<br />by .0i745,'and the product by the distance.
<br />GENERAL' DATA
<br />RIGHT ANGLE TRIANGLES. -Square the, altitude, divide liy'twice the
<br />base. Add quotient to base'for hypotenuse.
<br />Given Base loo, Alt. 10.102=200=.5. 100-.5=I0o.5 hyp,
<br />Given Hyp. loo, A1t.25.252-200=3.125.;i0o-3.I25=96.875=Base.
<br />Error in first example, .00a;'in last, .045•
<br />To find Tons" of Rail in one mile of track: multiply weight per yard
<br />by:i-I, and divide by 7..
<br />• LEVELING. The correction for 'curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574 de, where d is the distance in miles.
<br />The correction for curvature"alone is closely, ids. The combined cor-
<br />rection'is Iiegative:
<br />PRosasLE ERROR. If. d�, da, d8, etc. are the discrepancies of ,various
<br />results from'the mean, and if "7_de=the sum of the squares of these diffor-
<br />ences"and n=the number of observations, then the probable error of the,
<br />mean=+ 0.6746' nn 1)
<br />SOLAR EPHEMERIS. Attention is called to the, Solar: Ephemefis, for
<br />the current year; published by Keuffel & Esser .Co.; and furnished free of
<br />charge upon request, which is 3;x51 in., with about 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transit's; levels and
<br />1) solar attachments; directions and tables for determining the meridian
<br />and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />i
<br />TABLE IV. - Minutes
<br />in Decimals of'a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />A_Sb3
<br />51'
<br />.8506
<br />2=`
<br />.0333
<br />12
<br />.2000
<br />22
<br />3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />8
<br />.0500
<br />.13
<br />-,2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43,
<br />.7167
<br />53
<br />.8833
<br />A
<br />0667
<br />'14 ....2333"
<br />24
<br />4000
<br />34
<br />.5667
<br />•44.
<br />.7333
<br />54
<br />.9000'
<br />6
<br />.0833
<br />15 '
<br />:2500.
<br />25
<br />.4167
<br />35
<br />5833
<br />45
<br />.7500
<br />65'
<br />.9167
<br />6 :
<br />.1000
<br />16
<br />.2667
<br />26''
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7.:
<br />.1167
<br />17'
<br />.2833:
<br />27'
<br />.4500
<br />.37
<br />.6167_
<br />47
<br />.7833
<br />57
<br />.9500
<br />S.
<br />.1333
<br />1S
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9 67
<br />9 "'
<br />1.1500
<br />19
<br />.3167_
<br />29
<br />.4833
<br />39
<br />.6500
<br />49'
<br />,8167
<br />59
<br />.9 3
<br />10':
<br />'.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />,6667
<br />50
<br />.833311
<br />60
<br />1.0000
<br />-TABLE V. -Inches in Decimals of ti: Foot.-
<br />1-16
<br />3-32
<br />04
<br />5-16
<br />3-16 08
<br />0452
<br />00 8
<br />10
<br />:0156 .02 .02 0
<br />313
<br />.0417 21.
<br />.0 25
<br />.0729
<br />1
<br />2
<br />3
<br />4 5 6
<br />7
<br />8 9
<br />10
<br />11
<br />_•0833_
<br />,.1667
<br />.2500-,-.333,3
<br />..4187. .5000
<br />.5833
<br />1 .6667 .7509
<br />.8333
<br />.9167
<br />
|