|
VIII -
<br />TABLE IL -- Radii; Ordinates and Deflections. Chord =100 ft.
<br />beg.
<br />•
<br />$adios
<br />Mid.
<br />Ord.
<br />Tan.
<br />Diaz.
<br />Def.
<br />Dist.
<br />lief.
<br />for
<br />I Ft.1
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist
<br />for
<br />o
<br />fit.
<br />2° I-1'2°
<br />it. ,.
<br />ft,
<br />ft.
<br />ft.
<br />!
<br />1° 59'
<br />ft,
<br />ft.
<br />it.
<br />tt.
<br />34°
<br />0°10'
<br />34377.
<br />036
<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 />11600
<br />6.395
<br />12.70
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.436
<br />.873
<br />0;15
<br />30
<br />704.5
<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 />2.80
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />715'8
<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 />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 />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 />7.55G
<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 />7.844
<br />15.69
<br />2,70
<br />C 40
<br />3437.9
<br />.3G1
<br />1.454
<br />2.909
<br />0.50.
<br />20
<br />61.4.6
<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.S
<br />2.074
<br />8.281
<br />1 6. 50
<br />2.85
<br />2864.9
<br />.436
<br />1.745
<br />3.400
<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 />1.831
<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 />24.55.7
<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 />2.181
<br />4.3(3
<br />0,75
<br />11
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />214,3:8
<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 />3
<br />1910.1
<br />.65:5
<br />2.613
<br />5.235
<br />0.90 "
<br />30
<br />459.3
<br />2.736
<br />10.89
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.911
<br />13
<br />44 1. 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 />2.949
<br />11.75
<br />23.51
<br />4.o5
<br />30
<br />1637.3
<br />'.764
<br />3.054'
<br />6.145
<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 />6.395
<br />1.10
<br />30
<br />39G.2
<br />3.163
<br />12.62
<br />25.24
<br />4.35
<br />-50
<br />1495.0
<br />.93G
<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 />0
<br />1432.7
<br />.873
<br />0
<br />3.49,
<br />6.950
<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
<br />3.63.5'
<br />7.271
<br />1.25
<br />to
<br />359.3
<br />3.496
<br />13.92
<br />27:84
<br />4.80
<br />20,
<br />1322.5
<br />.945'3.718`
<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 />3.92(;
<br />7.852
<br />1.35
<br />11
<br />338.3
<br />3.710
<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 />319.61
<br />3.935
<br />15.64.
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />5.433
<br />1.-45
<br />19
<br />302.9,4.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146,8
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />1109:3
<br />1.1'27
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />36.44
<br />0.30
<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 />1.9.94
<br />39.87
<br />0.90
<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 />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 />43.23
<br />7.50
<br />0
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1,80
<br />U.
<br />222,3
<br />5.697
<br />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 />21412
<br />5.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5.524'11.05
<br />1.90
<br />28
<br />206,7
<br />6.139
<br />24.19
<br />48.38
<br />8.40
<br />80
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.3610
<br />2.5.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814'11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />i,1.7G
<br />9.00
<br />The middle ordinate in inches far any cord of length (C) is egnal to 0012 C'
<br />multiplied by the middle ordijinto 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 />50
<br />A sub chord- sin of 1 def, angle
<br />1t
<br />Length
<br />of are
<br />for 100 ft.
<br />sin. i def. ang.
<br />72,5 Ft.
<br />15 Ft.
<br />20 Ft. _
<br />25 Ft.
<br />30'0
<br />193.18
<br />i° 51`
<br />2° I-1'2°
<br />58`-
<br />-30-43'
<br />-10I.15
<br />320
<br />181.39
<br />1° 59'
<br />2° 251
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161 , 80
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />4° 26'
<br />loi . 66
<br />380
<br />153 -'58
<br />2° 20'
<br />2° 49'
<br />3° 44
<br />4° 40'
<br />101.85
<br />40°
<br />146.19
<br />2° 27'
<br />2°57'
<br />3° 55'
<br />4° 54'
<br />Io2, o6
<br />420
<br />139.52
<br />20 34'
<br />3° 051
<br />.4° 07'
<br />5°.08
<br />102.29
<br />44
<br />133.47
<br />2041'
<br />3° 13e
<br />4 18'
<br />5° 22'
<br />102.53
<br />46°
<br />.127.97
<br />2° 48'
<br />3° 21'
<br />40 29'
<br />5° 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 55'
<br />3° 29'
<br />4 4c'
<br />5° 5o'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />3,3 S',
<br />4 51'
<br />6° 04'-
<br />103.24
<br />52°
<br />114•.-06
<br />3° 09`
<br />3 46'
<br />5° 02'
<br />6° 17' .
<br />103.54
<br />54°
<br />110.11
<br />3°16'
<br />3°54
<br />5°13'
<br />6°31'
<br />103.84
<br />560
<br />106.5o
<br />3° 22`
<br />4 02'
<br />S° 23''
<br />6° 44'
<br />104.,14
<br />58
<br />10,3.14
<br />3° 29'
<br />40 lo' ,
<br />5° 34'
<br />60 57'
<br />104.43
<br />600
<br />100.00
<br />3°35
<br />4° 18'
<br />5°44`
<br />7° 11'
<br />104.72
<br />- hX -
<br />CURVE FORMIA-AS
<br />T= R tan $ I R= T cot. 1 1 chord2
<br />T go tan j I a Chord def. = R
<br />Sin. j D R = 50
<br />50 Sin, 12 D 1
<br />Sin. I D =' No, chords = --
<br />R F= R ex. sec I D
<br />_o tan
<br />5; I
<br />Sin. Ll - l $ = 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 angle for a given distance and deflection.
<br />Rule 1. Multiply the given distance by .01745 (def. for 0 for i ft.
<br />see Table II.), and divide given deflection by the product.
<br />Ru1e.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 .o1745, 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 Ioo,Alt. io.lo22oo=.5. 1oo+.S-100:5 hyp.
<br />Given Hyp, loo, Alt. 25.252 --.200.=3,125. 100-3,125=96.875=Base.
<br />Error in first example, .cot; in fast, .045.
<br />To find Tons of Rail in one mile of track:. multiply weight per yard
<br />by I r, and divide by 7..
<br />LEVELING. The Correction -for Curvature and refraction, in feet
<br />and decimals of feet is equal to 0,574d2, where d is the distarice in miles.
<br />The correction for curvature alone is closely, jd2 The combined cor-
<br />reetion is negative.
<br />PROBABLE ERROR. If d, d3, da; etc. are the discrepancies of various
<br />results from the mean, and if Eda=the sum of the squares of these differ-
<br />ences and n -the number of observations, tben the probable error of the
<br />mean- 4.6745 Ed'
<br />1 11 (n-1)
<br />SOLAR FPREDIERIS. 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 31x68 in., with about 90 pages of data very
<br />useful to t'_:e 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 and Logarithmic Functions;
<br />and Logarithms -of Numbers.
<br />. TABLE 1V. - lklinutes
<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 />.6833
<br />51'
<br />.8500
<br />2.0333
<br />12
<br />-2000
<br />22
<br />.3G67
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />8
<br />.0500
<br />13
<br />.21G7
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.5833
<br />4
<br />.OG67
<br />14
<br />:2333
<br />24
<br />,4000
<br />34
<br />.5607
<br />.44
<br />.1333
<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 />6.1000
<br />LO
<br />2667
<br />26
<br />,4333
<br />30
<br />,G000
<br />46
<br />.7667
<br />56
<br />.0333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4300
<br />31
<br />.6167
<br />47
<br />.7833
<br />57.
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4UU7
<br />38
<br />.0333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19 .
<br />8167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9533
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />:6667
<br />50
<br />.8333
<br />GO
<br />1.0000
<br />A
<br />TAul n V. =
<br />Inches in Decimals of a Foot.
<br />-
<br />1-16
<br />3-32
<br />3
<br />3-1,6_T
<br />Y
<br />5-1.6
<br />yl
<br />.0052
<br />.0078
<br />.0lOt
<br />.0156
<br />.0368
<br />.0260•
<br />.0313
<br />.0417
<br />.052 1
<br />.0625
<br />. 0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6�
<br />7
<br />S
<br />9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />:6667
<br />.7500
<br />.8333
<br />.9167
<br />A
<br />
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