|
VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg'
<br />Radius
<br />Mid.
<br />Ord.
<br />I Tan.
<br />Diss.
<br />Def.
<br />Dist.
<br />Def.
<br />.l Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist:
<br />Def.
<br />if Ft.
<br />1°51'
<br />ft.'
<br />it.
<br />t.
<br />t.
<br />r
<br />.2000
<br />It.
<br />ft.
<br />ft.
<br />ft.
<br />i
<br />0"10'
<br />34377.036
<br />25'
<br />.145
<br />.291
<br />0.05
<br />7-
<br />819.0
<br />1.52S
<br />6.105
<br />12.21
<br />2.10
<br />.20
<br />17159.
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.E
<br />1.600
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.43G
<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 />G.GS5
<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 />G.976
<br />13.95
<br />2.40
<br />1
<br />57 29. 6
<br />.218
<br />.573
<br />1.745
<br />0.30
<br />20
<br />G88.2
<br />1.819
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />G74.7
<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 />G61.7
<br />1.592
<br />7.556
<br />15.11
<br />2.610
<br />30.
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />0
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />"'3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2.037
<br />8.136
<br />16.27
<br />2.80
<br />50
<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 />2
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.591
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />8.716
<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
<br />3.15
<br />30
<br />2292,0
<br />.545
<br />2.151
<br />4.363
<br />0.75
<br />1.1
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />.40
<br />2148,8
<br />.552
<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 />2022,4
<br />.61$
<br />2.472
<br />4.045
<br />0.55
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />3
<br />1910,1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.59
<br />21.77
<br />3.75
<br />10
<br />1809,6
<br />.691
<br />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 />2.903
<br />5.817
<br />1.00
<br />"30
<br />425.4
<br />2.949
<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 />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562,9
<br />.800
<br />3.199
<br />6.393
<br />1.10
<br />.30
<br />356.2
<br />3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1485.0
<br />.S30
<br />3.345
<br />6.659
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1432,7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.357
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />. 1375,4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />IG
<br />359.3
<br />3.490
<br />13.92
<br />27.84
<br />4.S0
<br />20
<br />1322.5
<br />.045
<br />3.718
<br />7:561
<br />1.30
<br />30
<br />348.5
<br />3.600
<br />14.35
<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 />40
<br />1228,1
<br />1.015
<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 />1.001
<br />4.362
<br />5.724
<br />1.50
<br />.20
<br />257.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />1109,3
<br />1.127
<br />4.507
<br />9.0141.55
<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.G53
<br />9.305
<br />1.60
<br />22
<br />262.0
<br />4.814
<br />19.08
<br />33.16
<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 />0.90
<br />40
<br />1011,5
<br />1.237
<br />.9e3
<br />9.856
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.53
<br />7.20
<br />50
<br />982,0
<br />1.273
<br />5. S8
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />B'.
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.30
<br />2G
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.50
<br />10
<br />929,6
<br />1.346
<br />5.37910.76
<br />1.55
<br />27
<br />214.2
<br />5.913
<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 />48.33
<br />8.40
<br />30
<br />881,9
<br />1.418
<br />5.069
<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 />1 859,9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<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.
<br />TABLE III. Deflections for Sub Chords for. Short Radius Curves.
<br />Degree.
<br />of
<br />Curve
<br />Radius
<br />4 sub chord -
<br />It
<br />sin of 1 def. angle -
<br />Length
<br />of are
<br />for 100 ft.
<br />sin.1 def. any.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18.
<br />1°51'
<br />51'
<br />=°
<br />17`
<br />2'
<br />58'.3'
<br />.2000
<br />43
<br />I0I.15
<br />320
<br />131.39
<br />I°
<br />59'
<br />2°
<br />25'
<br />3°
<br />10'
<br />30
<br />58';
<br />101.33
<br />340
<br />171.01
<br />2°
<br />o6'
<br />2°
<br />33`
<br />3°
<br />21'
<br />4°-I2"
<br />14
<br />- 101.43
<br />360
<br />161.8o
<br />2°
<br />13
<br />2°
<br />_
<br />41
<br />3°
<br />33`
<br />4°
<br />26'
<br />Ioi.66
<br />38°
<br />1 y3.58
<br />2°
<br />20'
<br />2°
<br />49`
<br />3°
<br />44`
<br />4'.
<br />4�`;,r
<br />101.85
<br />40°
<br />146: i9
<br />2°
<br />27'
<br />2°
<br />57`
<br />3°
<br />55'
<br />4°
<br />54;" •
<br />.
<br />102.o6
<br />42139.52
<br />17
<br />2°
<br />34'
<br />3°
<br />051.
<br />40
<br />07'
<br />5°
<br />08'
<br />IO2.29
<br />44°
<br />133.47
<br />2°41'
<br />.3000
<br />30
<br />13'
<br />4°18'
<br />.G333
<br />5°22'
<br />.8000
<br />102.53
<br />46°
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21'
<br />4°
<br />29'
<br />S°
<br />,3G'
<br />102.76
<br />48°
<br />122.92
<br />2°55`
<br />1 .1667
<br />3°291
<br />.3333 1130
<br />4°40'
<br />1 .5000
<br />5°50'
<br />.GG67 1
<br />103.00
<br />50°
<br />118.31
<br />3°
<br />02'
<br />3°
<br />38'
<br />4°
<br />51'
<br />6004
<br />'
<br />103.24
<br />520
<br />114 c6
<br />30091
<br />3°
<br />46'
<br />S°
<br />02'
<br />6°
<br />17'
<br />103.54
<br />54
<br />110.11
<br />3°
<br />16'
<br />3°
<br />54'
<br />,5°
<br />13'
<br />G°
<br />31'
<br />103.84
<br />560
<br />106:50
<br />3°
<br />22'
<br />4°
<br />oz'
<br />5°23`.
<br />6°
<br />44
<br />104.14
<br />58°
<br />103.14
<br />3029,
<br />4°
<br />10'
<br />5°
<br />34`
<br />6°.57'
<br />104.43
<br />60°
<br />Ioo.00
<br />3° 35`
<br />4°
<br />18`
<br />5°
<br />44`
<br />7°
<br />11'
<br />104.72
<br />IX
<br />CURVE- FORMULAS
<br />i = 1{ tan t 1chords
<br />_ 5o tan 8 I P. = T cot. s I Chord def. _
<br />T Sin. ll R 50 R
<br />= �
<br />cin D - 50 Sin. a D No. chords = I
<br />R E= R es. sac 2 I D
<br />Sin. } D = 5o tan a I E = T tan I I Tan. def. _ ; chord def.
<br />The square of any distance, divided by hvice the radius, will equal
<br />the distance from tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule i. Multiply the given distance by .01745 (def. for t° for i ft.
<br />see Table II.), and divide given deflection by the product.
<br />2.
<br />R 1Multiplyiven deflection b
<br />u e gy 57.3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGnT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add ry. uotient to base for hypotenuse.
<br />Given Base too, Alt. Io.io2=2oo=.5. X00+.5=1oo•5 hyp•'
<br />Given Hyp. too, Alt. 25.252=200=3.125. Ioo-3.125=96.875=Bas_
<br />Error in first example, .002; 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'd3, where d is the -distance in miles.
<br />The correction for curvature alone -is closely, Jda." The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d, , d„ d3, etc. are the discrepancies of various
<br />results from the mean, and if Yd2=the sum of the squares of these differ-
<br />ences and n -the number of observations, then the probable error of the
<br />mean _ ± 0.6745- 7_d2 =
<br />SOLAR EPIIEDIERis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3}x58 in., with about 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />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 andLogarithmic Functions;
<br />and Logarithms of Numbers.
<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 />.6533
<br />51'
<br />.8500
<br />2.0333
<br />0052
<br />12
<br />.2000
<br />22 -
<br />.3GG7
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.5667
<br />s
<br />.0500
<br />33
<br />.2167
<br />23
<br />.38.33
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0GG7
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5-
<br />.0333
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5S33
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />10 .
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />40
<br />.7667
<br />'56
<br />.9333
<br />-7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.0167
<br />47
<br />.7833
<br />57
<br />.0500
<br />'8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.G333
<br />48
<br />.8000
<br />58
<br />.9067
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1 .1667
<br />20
<br />.3333 1130
<br />1 .5000
<br />11 40
<br />.GG67 1
<br />50
<br />1 8333 11
<br />60
<br />1.0000
<br />1
<br />TABLE V. -
<br />Inches in Decimals of a Foot.
<br />1-1G
<br />3-32 1
<br />A
<br />3-1G
<br />X
<br />5-16
<br />;i
<br />i5
<br />3:
<br />1
<br />0052
<br />.0078
<br />.0104
<br />.0156
<br />.0205
<br />.0260
<br />.0313
<br />.0117 .0521
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />0833
<br />.1667
<br />.2500.
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667 .7500
<br />.8333
<br />.9167
<br />1
<br />
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