|
7M
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />`per''
<br />us
<br />Mid.
<br />Ord.
<br />Tan.
<br />Diat..
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan '
<br />Di
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft•
<br />s0 12� _
<br />t.
<br />ft.
<br />rt-
<br />__
<br />32
<br />/
<br />-
<br />i 59
<br />ft,,
<br />ft.
<br />ft,
<br />ft.
<br />i
<br />0°.10'
<br />34377.
<br />.036
<br />.145
<br />' ,291
<br />0.05
<br />7'819.0
<br />t6i ..80;
<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' 781.8
<br />1o1.85
<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 />16875.5
<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..873
<br />o6
<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 />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 />40
<br />'3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50'
<br />20614.6
<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 />2074.
<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':2644.6
<br />1*20
<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 />30 .00
<br />2455.7
<br />.509
<br />2:036
<br />4.072
<br />0.70
<br />3
<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 />4.363
<br />0.75
<br />it
<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
<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 .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 />4.05
<br />i30,
<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 />6.398
<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 />3.277
<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 />3.387.13.49
<br />26.97
<br />4.65
<br />10-
<br />1375:4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />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 />501185.8
<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 />6
<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 />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 />4.594,18:22
<br />36.44
<br />6.30
<br />'20
<br />1074.7
<br />1.164
<br />4.653
<br />9.905
<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 />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 />5.379
<br />10.76
<br />L.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 />881.0
<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 />5.81411'.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. 1
<br />TABLE III. 'Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />' Radius
<br />50
<br />M sub chord
<br />R =sin of i def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin, i def, ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. '
<br />25 Ft.
<br />300
<br />193.18
<br />1° 5i
<br />s0 12� _
<br />__?0 58�
<br />_ 30 43'
<br />10.1.15
<br />__
<br />32
<br />- 181.39
<br />-
<br />i 59
<br />2 25
<br />-.
<br />3 10
<br />--
<br />3 58
<br />101.33
<br />34°
<br />171.01
<br />2° o6'
<br />2° 33'3°
<br />21'
<br />4° 12'
<br />10I.48
<br />360
<br />t6i ..80;
<br />2° 13�
<br />20 41' .
<br />, -0 331
<br />40 26'
<br />101.66
<br />380
<br />¢46-
<br />153.58
<br />2° 20'.
<br />. z,° 49' _
<br />-5
<br />3' 441
<br />40 40'_;
<br />1o1.85
<br />o
<br />46.19
<br />2'_2 7'
<br />2o 7i
<br />30 55'
<br />4o.54r
<br />102.06
<br />5
<br />139.52
<br />or.
<br />°.0
<br />3 -,'
<br />1
<br />5o.08"-42
<br />IO2.29
<br />44 '
<br />133.47
<br />2041
<br />3013'
<br />4°18'
<br />5°22`
<br />102.53
<br />46°
<br />127.97
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />5° 36'
<br />102.76
<br />48°122.92,
<br />56
<br />2°55'
<br />3°29''
<br />4°40'
<br />S°5o'
<br />103.00
<br />50°
<br />'
<br />118.31
<br />3°02'
<br />3°38'
<br />4°51'6°04'
<br />.7833
<br />103.24
<br />114.
<br />520
<br />o6
<br />: 30 091
<br />30 461
<br />50 021
<br />60 �7�103.54
<br />54
<br />.4667
<br />38
<br />110.11
<br />3 16
<br />3 54
<br />5: 13'6
<br />31
<br />103.84
<br />56°
<br />106.50
<br />3° 22'
<br />40 02'
<br />5° 23'
<br />60 44'
<br />'104.14
<br />580
<br />103. 14
<br />30 29'
<br />40 10•'
<br />50 34'
<br />60 57'
<br />104.43
<br />60°
<br />106.00
<br />3° 35'
<br />4° 18'
<br />5044 ,
<br />°44'
<br />7° 111
<br />104.72
<br />1�
<br />CURVE FORMULAS -
<br />T= R tan j I R= T cot. '2 I chord$
<br />,I, _ 5o tan j I Chord def. R
<br />_ _ Sin. I D 50
<br />R = a
<br />Sin. I D= 50 Sin. 2 D No: chords= I
<br />R E =Rex. see I D
<br />Sin. } D = 50 tT # I 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 .o1745 (def. for 1° 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 .01745, 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 =10
<br />-200=.5. Ioo+.5o.5 hyp,
<br />-Given Hyp. loo, Alt. 25.252=200=3.125, 100-3.125=96.875=Base.
<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 II, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is -equal to 0.574 da, where d is the distance in miles.
<br />The correction for curvature alone is closely', Ids. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d„ da, da, etc. are the discrepancies of various
<br />results from the mean, and if Id2=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the,
<br />2
<br />mean= ± 0.6745 n n-1)
<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 3x5} 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 1V. -,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 />.6833
<br />51'
<br />.8500
<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 />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 />554�
<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 />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<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
<br />30
<br />.5000
<br />40
<br />.66671,
<br />50
<br />.8333
<br />60
<br />1.0000
<br />ME
<br />TABLE V. -
<br />Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />3-16
<br />5-16
<br />%
<br />%
<br />Y
<br />.'•.0052
<br />-.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417 .0521
<br />.0625 ,0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10 11
<br />0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.8667 .7500
<br />.8333 .9167.
<br />ME
<br />
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