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i91II
<br />TABLE •- Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg'..-'
<br />Radius'-
<br />Mid.
<br />Ord. '
<br />Tan.
<br />Dist.
<br />Def.
<br />° Dist.
<br />Def.
<br />for
<br />I Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Orth'
<br />Tan.
<br />Dist.
<br />Def.
<br />`Dist.
<br />Det.
<br />for
<br />I Ft.
<br />51'
<br />t.
<br />t
<br />t.
<br />t.
<br />30
<br />.2000
<br />ft,
<br />ft.
<br />ft.
<br />IL
<br />i
<br />0"10,
<br />34377..038
<br />30
<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 />204'17189..'
<br />3°
<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•`11459..'
<br />33'
<br />:.109
<br />.436
<br />f..873
<br />0.15
<br />30
<br />764.6
<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.:182
<br />102.66
<br />"
<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 />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 />4Q
<br />' 3437.9
<br />..364
<br />1.454'
<br />"2.909'0.50
<br />0,2
<br />- 20
<br />614.6
<br />2.037.,
<br />8.138
<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 />a
<br />2864.9
<br />.436
<br />1.745
<br />;3.490
<br />0.60
<br />40.
<br />593.4
<br />2.1-10
<br />8.426
<br />.16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3.781
<br />0.65
<br />l0
<br />573.7
<br />2:183
<br />8.716
<br />17.43.3.00.
<br />18'
<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 />2.181
<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•.2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />° . 30
<br />499.1
<br />2.511'10.02
<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 .21.77
<br />3.75
<br />l0
<br />i 1809.,6
<br />.691.2.763
<br />5.526
<br />0.95 .`13
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />j 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 />30,;
<br />1637.3
<br />>:764
<br />3.054'
<br />8.108
<br />1.05
<br />14
<br />410.3
<br />3.058.12.18
<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 />lb
<br />383.1
<br />3.277
<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 />3.387'13.49-
<br />26.97
<br />4.65
<br />10'1375.4
<br />7:909
<br />3.635
<br />7.271-
<br />1.25
<br />i6'
<br />359.3
<br />3.496
<br />13,:92
<br />27.84
<br />4.80
<br />v.0 2:
<br />1322.5
<br />=.945
<br />3.718
<br />7.561
<br />1.30
<br />•' 30-
<br />348.5
<br />3.606'14.35
<br />'28.70'4.95
<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 />1.018:4.071
<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 />1185.8'1.055'4.217
<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 />34.73
<br />6.00
<br />10
<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 />,1109.3
<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;.38.16
<br />6.60
<br />::'30
<br />`.1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />'223,
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />40
<br />1011.5
<br />1.237:4.943
<br />9.886
<br />1.70.
<br />24'
<br />240.5
<br />5.255.20.79
<br />41.58
<br />-7.20
<br />" 50982:6
<br />-1.273:5.088
<br />10.18.
<br />1.75
<br />25
<br />231.0
<br />5.478',21.64
<br />43.28
<br />7.50
<br />8:-,
<br />955.4',1.309
<br />5.234
<br />10.47"
<br />1.80.
<br />26
<br />222.3
<br />5'.697
<br />22.50 ,44.99
<br />7.80
<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 />8.360
<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 />De f ee
<br />Curve
<br />Ra5diius
<br />50
<br />3i aubb chord. aia of def. angle
<br />Length
<br />'for 100 ft.
<br />sin. I def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.:
<br />25 Ft.
<br />30°
<br />193.18
<br />1°
<br />51'
<br />2°
<br />17..
<br />2°
<br />58't_
<br />30
<br />.2000
<br />IOI-45,
<br />32°-
<br />481.39
<br />- 10
<br />_
<br />59' -
<br />20
<br />i$'
<br />30
<br />Io'
<br />_
<br />3°.58'
<br />_43'
<br />101-33
<br />34°
<br />171.01
<br />20
<br />o6'
<br />2°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />360
<br />i61.8o
<br />2`
<br />13'
<br />20
<br />,-20
<br />41'-
<br />3'
<br />33'
<br />4'
<br />26'
<br />io1.66
<br />38°,,.
<br />_ 153.-58-
<br />_2020'
<br />35
<br />49' -
<br />, -3 °
<br />44'--
<br />. 4°
<br />40: _
<br />.. 101.85
<br />400
<br />146. i9
<br />20
<br />27', -
<br />. 210.57'-,-
<br />36
<br />30
<br />55'
<br />40
<br />54' :
<br />102.66
<br />"
<br />42°
<br />.139.52
<br />20
<br />34''
<br />3°
<br />05'
<br />'
<br />4°
<br />07'
<br />5`
<br />08' _
<br />102.29
<br />44°
<br />131-47
<br />2°
<br />41'
<br />3°
<br />13' ;
<br />4°
<br />18', .
<br />- 50
<br />22'
<br />102.53
<br />..469:"
<br />. 127.97
<br />2°
<br />48' '
<br />3°
<br />21'
<br />40
<br />29'
<br />5'36'
<br />.6500
<br />102.76
<br />480
<br />122.92
<br />2°55'.
<br />10
<br />3°29'
<br />20.
<br />4°40'
<br />'
<br />5°50'
<br />40
<br />103:00
<br />500
<br />118:31
<br />3'
<br />02' .
<br />30
<br />38,,•
<br />.4°
<br />5i,..
<br />60
<br />04'
<br />103.24
<br />52'
<br />114.06
<br />3°
<br />09'
<br />3°
<br />46
<br />5.°
<br />0,2
<br />6°'17'
<br />103.54
<br />540.
<br />110. I1
<br />3°
<br />16'
<br />" 3054.
<br />5°
<br />13`
<br />60
<br />31•'-
<br />103.84
<br />56.0
<br />106.5o
<br />3°22'
<br />40
<br />02'
<br />5°
<br />23'
<br />6°
<br />44'
<br />104.14..
<br />58°
<br />103: 14
<br />3°
<br />29'
<br />• 4°.1o'
<br />5°
<br />34'
<br />6°
<br />57'
<br />104.43
<br />60'
<br />ioo.00
<br />30
<br />35'
<br />4°
<br />18'
<br />5044
<br />1'
<br />7'_if'
<br />104.72
<br />-"CURVE FORMULAS
<br />T o tan Rtan� I
<br />Sin.�D R= T cot. s I Chord def. = chord9
<br />T'= 60 R
<br />.. R, _
<br />Sin. J D = 50 Sin. # D No. chords =�
<br />R- E =Rex. sec z I
<br />_
<br />Sin.: D - 5o tan $ I E = T tan I Tan. def. _ chord def.
<br />` T:.
<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 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 />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />the given distance.
<br />To finddeflection for a given angle and distance. Multiply the angle
<br />by -.oi745, 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.1oz^200=-5.. i6o+.s=100.5- hyp•
<br />=
<br />Given; Hyp. ioo, Alt: 25.25$200=3.125- ioo-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: multiplyweight per yard
<br />by x ; and divide by 7.
<br />LEVELING. The correction for curvature .and refraction, in feet
<br />and decimalsof feet is equal to 0.574d2, where d is the distance in miles.
<br />The :correction for, curvature alone is -closely, Ida. The combined cor-
<br />rection is negative.
<br />-'PROBABLE ERROR. If d;, de, de, etc:'are* the discrepancies of various
<br />results from the mean, and if Xda=the sum of the squares of these difior-
<br />ences and n=the number of observations; then the probable error' of the.
<br />mean f 0.6745 n n-11(
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeras fort
<br />the current year,. published by Keuffel& Esser Co., and furnished free: of
<br />charge upon request, which- is 3Jx5} 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... r.
<br />TAB_LE`IV. - Minutes
<br />TABLE- - Inches in Decimals of a Foot.
<br />in Decimals of a Degree.
<br />Y
<br />0167
<br />11'
<br />.1833
<br />21'3560
<br />r
<br />31'
<br />.5167
<br />4Y
<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 />a
<br />..0500
<br />13
<br />..2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />,&
<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 />8,'
<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 />91111500,
<br />' 19
<br />3167`
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />x1667
<br />20.
<br />:':3333-
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />11.0000
<br />-•-
<br />TABLE- - Inches in Decimals of a Foot.
<br />1-16 3-32
<br />je 3-18
<br />516
<br />S35
<br />r
<br />OOb2 z. 0078
<br />..0104...0156• .0208
<br />.0260
<br />.0313
<br />.0417 .0521
<br />.0625 0729
<br />1 2
<br />3 4 5
<br />6
<br />7
<br />8 9
<br />1 10 11
<br />.0883 .1667
<br />,.2500 .3333.. .4167
<br />.5000
<br />.5M33
<br />.6667. ..7500...8333
<br />.9167•
<br />
|