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IIT TABLn IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg:'
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan..:
<br />Dist. ,
<br />Def..
<br />Diat:
<br />Def.
<br />IfFt.
<br />.'Deg.
<br />itsdms
<br />Mid
<br />.Ord.
<br />Tan
<br />Dist:_
<br />-Def.
<br />Dist.
<br />Def.
<br />r
<br />1
<br />- 2°t17'
<br />2° 58''
<br />.
<br />30 43'
<br />101.15
<br />t
<br />7
<br />1 59 ,
<br />it_ft
<br />3° 10r
<br />ft,
<br />fL
<br />i
<br />0"10
<br />34377.
<br />36
<br />.145
<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 />309
<br />.438
<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 •-•
<br />5729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />• 20'
<br />688.2
<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 />130
<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 />4:556
<br />36.11
<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 />" 40
<br />' 3437.9
<br />.364
<br />1.464.
<br />2.909
<br />0.50"
<br />20
<br />614.6
<br />2,037
<br />8.136
<br />16.27
<br />2.80
<br />50
<br />. 3125.4..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 />2864.9.436
<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 />44
<br />26.6
<br />.473
<br />1,891
<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 />18.30'3.15
<br />30
<br />2292.0
<br />.545
<br />2.181'
<br />4.363
<br />0.75
<br />11'
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<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 />2022:4
<br />:.618
<br />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 />a
<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 />21.77'3.75
<br />10.
<br />1809.6
<br />_691
<br />2.763,
<br />5:526
<br />0.95
<br />13'441.7
<br />2.839
<br />11.32.
<br />22.64
<br />3.90
<br />20
<br />.1719.1
<br />.727
<br />2.908
<br />5.817.1.00
<br />130
<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 />12118
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />:30
<br />396.2
<br />3.168
<br />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 />3.27.7
<br />13.05.
<br />26.11
<br />4.50
<br />1432.7
<br />.873
<br />3.490
<br />6:980
<br />1.20
<br />30
<br />370.8
<br />3.387,
<br />13.49
<br />26.97
<br />4.65
<br />10
<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 />3.606
<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 />1.018
<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 />W
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />6,00
<br />10
<br />1109.3
<br />1.127
<br />4:507
<br />9.014
<br />1.55
<br />21'
<br />274.4
<br />4.594
<br />18.22
<br />36'.44
<br />6.30
<br />'20,-1074.7.1.164
<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;.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 />50
<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
<br />22.50,
<br />44.99
<br />7.80
<br />10.
<br />929.6
<br />1.346
<br />6.379
<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
<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 IIL 'Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />sub chord
<br />R = sin of I def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. } def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193._18
<br />1°.51' _
<br />-°
<br />- 2°t17'
<br />2° 58''
<br />.
<br />30 43'
<br />101.15
<br />o-
<br />32
<br />-
<br />181.89
<br />1 59 ,
<br />2* 25'
<br />3° 10r
<br />3o 58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />20 333°
<br />21'
<br />4° 12'
<br />IOI.48
<br />36°
<br />i61. 8o
<br />2° 13'
<br />2° 41,
<br />3° 33'
<br />4° 26' .
<br />•:io1.66
<br />38°
<br />153.58
<br />2° 20'
<br />z° 49'
<br />3°.44'--
<br />•4° 40'.
<br />ioi.85
<br />40°
<br />_
<br />146. i9, '.
<br />2° 27'
<br />2° 57'
<br />3° 55' `
<br />4° 54'
<br />102.0--4z'
<br />5
<br />139.52.
<br />20 34'
<br />30 05'
<br />40 07'
<br />50 08'.
<br />i62.29
<br />44°
<br />133,47
<br />2° 41'
<br />3° 13'
<br />4° 18'-
<br />'5' 22'
<br />102.53
<br />460
<br />127.97
<br />20 48'30
<br />21'
<br />40 29'
<br />50 36'..
<br />102.76
<br />48°
<br />122.92
<br />..2° 55'
<br />3° �9'
<br />4° 40'
<br />5° 50'
<br />103,00
<br />500..
<br />118 -31,
<br />3°02'
<br />3° 38'
<br />4° 51'
<br />60.641
<br />103.24
<br />520
<br />114.06
<br />3009' _
<br />, 30 46"'5°
<br />02'
<br />60 17'
<br />103-54
<br />540
<br />i 10.11
<br />30 16'--,
<br />3°54'
<br />5° 13'
<br />6°• 31'
<br />io3.84
<br />56°
<br />io6.5o
<br />3° 22'
<br />4° O2'
<br />5° 23'
<br />60 44'-
<br />104.14
<br />58°
<br />103.14
<br />3°29'
<br />4°l0'
<br />5°34'
<br />6°57'
<br />104.43
<br />60°
<br />Ioo.00
<br />3° 35'
<br />4° 18'
<br />50 44'
<br />7° II'
<br />104.72
<br />zpb.J N %vim
<br />.CURVE FORMULAS
<br />T= R tan I R= T cot. z Chord chord°
<br />50 tan I ord def. = R
<br />T . Sin. J; D R - 50
<br />Sin. D . 50 Sin., J D' No. chords - I
<br />R • E _ ,R ex: sec a I'
<br />Sin. D = 56 tan J -1.E,':= T tan I I Tan. def. _ ; 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 angle for a given distance and deflection.
<br />Rule 1. Multiply the given distance by .01745 (def. for I° for i ft.
<br />see ;Table II.), and divide given deflection by the product.
<br />Rule 2. `Multiply given deflection by 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 -61745, and the product by the distance.
<br />GENERAL DATA
<br />'RIGHT ANGLE,TRIANGLES. 'Square, the, altitude, divide by twice the
<br />base. Add quotient to base 'for, hypotenuse.
<br />Given Base loo, Alt: 10.102_200=.5..100-{-.5=100.5 hyp.
<br />Given Hyp. loo, Alt.'25.252=200=3.I25, 100-3.125:=96.875=:Base.
<br />Error in first example, .002; m 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 d2, where d is the. 'distance, in miles.
<br />The,correction for, curvature alone is closely; Jd2. The combined cor-
<br />rection is negative..
<br />' PROBABLE ERROR'. If d�, de, da, etc. are the discrepancies of various
<br />results from, the mean;•and if 7_da=the sum of the squares of these diflcr-
<br />ences and, n=the number bf observations; then the probable error of the.
<br />mean- 4- 0.6745
<br />SOLAR EPHEMERIS. 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 314x5J 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 f ormulas; Natural andLogarithmic Functions;
<br />and Logarithms of 'Numbers.
<br />TABLE IV: - Minutes
<br />TABLE V. - Inches in Decimals of a Foot.
<br />in Decimals of h Degree.
<br />1'
<br />.0167.
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167.
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />a
<br />.0333
<br />12
<br />.2000
<br />22'
<br />,3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3f
<br />.0500
<br />,
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />:7167
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<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 />8
<br />.1333
<br />.18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />119
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1 .160711
<br />20
<br />1 .3333 1130
<br />.5000
<br />11 40
<br />1 .6667
<br />50
<br />.8333
<br />60
<br />1,0000
<br />TABLE V. - Inches in Decimals of a Foot.
<br />j
<br />.1-16 3-3234
<br />3-16
<br />4
<br />5-16
<br />35
<br />Y4 t
<br />1.07S-
<br />.0052 ••0078
<br />.0104
<br />.,0156
<br />.0208
<br />.0260
<br />'.0313
<br />.0417 .0521
<br />.0625
<br />1 2
<br />3
<br />4
<br />b6
<br />7
<br />8 9 1
<br />10 1 11
<br />.0833 .1667-
<br />.2500
<br />..3333.
<br />.4167
<br />.5000
<br />.5833.
<br />.6667 .7500
<br />1 -8333 1.9167
<br />
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