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TAIAX II. - Radii, Ordinakes•and Deflections. Chord =100 ft.
<br />---
<br />Deg.'
<br />Radius
<br />olid.
<br />Ord.
<br />Tan. '
<br />Dist.
<br />Def. -
<br />Dist.
<br />Def.
<br />Lfort.:
<br />Deg.
<br />Radius
<br />Mid.
<br />O,d.
<br />T.S.
<br />Dist:
<br />'Def. -
<br />Dist.
<br />Def.
<br />fcr
<br />1 Ft.
<br />--
<br />ft.
<br />ft..
<br />IE
<br />[Lf
<br />101.15
<br />32°
<br />t. ft,
<br />- ft.
<br />ft,
<br />ft.
<br />r
<br />0°10'
<br />34377-'
<br />.030
<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 />.5S2
<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 />.109
<br />.436
<br />.873
<br />0.15-
<br />30
<br />764.5
<br />1.037
<br />6:540
<br />13.08
<br />2.25
<br />40'
<br />8594.4
<br />.145
<br />.582
<br />1.104
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.035
<br />13.37
<br />2.30
<br />50'
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />716.5
<br />1.746
<br />6:976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.573
<br />1.745
<br />0.30
<br />20
<br />68S.2
<br />1.819
<br />7.2GG
<br />14.53
<br />2.50
<br />10
<br />4911.2.255
<br />3° 54
<br />1.018'
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.41L
<br />1.4.82
<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 />1.592
<br />7.556
<br />15.11.2.60
<br />4° 18'
<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 />20
<br />614.6
<br />2.037
<br />8:1.36
<br />16.27
<br />2.80
<br />50',3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55-
<br />30
<br />G03.8
<br />2.074
<br />8.25116.56
<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 />1.891'
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />8.716.17.43
<br />3.00
<br />-'20
<br />2455.7
<br />.509
<br />2.030
<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 />11
<br />521.2
<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 />0.60
<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 />$
<br />1910.1
<br />.655
<br />2.615
<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 />2.908
<br />5.817
<br />1.00 '
<br />30
<br />42.5.4
<br />2,049
<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;15
<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 />25.24'4.35
<br />50
<br />1495.0.
<br />:.830
<br />3.343
<br />6.689
<br />1.15
<br />15.
<br />383.1
<br />3.277
<br />13.05
<br />26,11
<br />4.50
<br />!
<br />1432:7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />'30
<br />370.8
<br />3: =5
<br />13.-40
<br />26.97
<br />4.65
<br />10
<br />1375'.4
<br />.909
<br />3.633
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />1'3.92
<br />27:84
<br />4.50
<br />20
<br />1322.5
<br />.945
<br />3:718
<br />7.501
<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 />3.920
<br />7:852
<br />1.35,
<br />11
<br />338.3
<br />3.716
<br />14..78
<br />29.56
<br />5.10
<br />40
<br />_1228.•11.018
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.04
<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 />},155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1140.3
<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
<br />18.22-
<br />36.44
<br />6.30
<br />`20
<br />1074.7
<br />1.164
<br />4.653
<br />-9.305
<br />L.GO
<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 />9.88G
<br />1.70
<br />•24
<br />240.5
<br />5.255
<br />20.79
<br />41.55
<br />7.20
<br />50
<br />982.6
<br />1.273,
<br />5.058
<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 />905.4
<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-rS0
<br />10"
<br />929.6
<br />1.346
<br />5.379
<br />10-.7G.
<br />1.85
<br />27"
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />S.10
<br />20
<br />. '905.1
<br />1.3S2
<br />5.524
<br />11-05
<br />.1.90
<br />28
<br />206.7
<br />G.139
<br />24.19
<br />48.3S
<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 />6.3GO
<br />25.04
<br />50.07
<br />5.70
<br />40
<br />.'859.9
<br />1.455
<br />5.514
<br />11.63
<br />2.00. 1
<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 />multi111ied by the middle ordinate token. 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 .Q012X900X2.163 or 2.36 inches.
<br />TABLC III. Deflections for Sub Chords for Short Radius -Curves.
<br />Degrofee
<br />"l7adins.
<br />. .50.
<br />'�Bubchord
<br />Tt = Bin of def. angle
<br />Loingth
<br />Curve
<br />sin. Fdef. ano
<br />, t2.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft..
<br />for 100 ft.
<br />30°
<br />193•18
<br />1° 51,
<br />17'
<br />2 58,
<br />3° 43'..
<br />101.15
<br />32°
<br />281.39
<br />I° 59'
<br />° 25`
<br />3° lo'
<br />3158,
<br />101.33
<br />34°-
<br />171. 01'
<br />2° 06'
<br />^° It
<br />3° 21'
<br />° 12'
<br />101.48 -
<br />360
<br />16T.86
<br />.2° 13:`.
<br />2°'41`,
<br />3° 33'4'
<br />?6'
<br />io1.66
<br />38°
<br />153.58
<br />2,20,-
<br />2° 49
<br />3° 44'
<br />4° 40'
<br />101 , 85
<br />40°
<br />146,.19
<br />2027'
<br />2° 57
<br />3°55'
<br />4'54'
<br />102.o6
<br />42,
<br />134.52
<br />-.34
<br />3.05P
<br />4° 071.
<br />5° 08'
<br />102:29
<br />44°
<br />133-47
<br />2° 41'
<br />3°'13'
<br />4° 48'
<br />5°22'
<br />102.53
<br />46°
<br />127.97
<br />2°'481
<br />3°21'
<br />4°a9'
<br />S°36'
<br />IO2:76
<br />4S°.
<br />122.92
<br />20 551
<br />3* 29'
<br />4° 40'1
<br />50'
<br />103. GO
<br />50° _
<br />115.31
<br />3° 02'
<br />3, 38°
<br />4° 51'
<br />G° o4'
<br />103.24
<br />28
<br />114:06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />. G°.1;'
<br />103.54
<br />54o
<br />110.11:
<br />3°-16'
<br />3° 54
<br />5° 13
<br />G°31'
<br />103,84
<br />56°
<br />fo6.50
<br />3° 22'4°
<br />02'
<br />5° 23,
<br />6° 44"
<br />104.14
<br />58°
<br />103.14
<br />3° 29'
<br />4° 10'
<br />5° 34`
<br />6° 57'
<br />104.43
<br />600
<br />100.00 1
<br />3° 35" 1
<br />4° 18'
<br />S° 44'
<br />7° 11'
<br />1 104.72
<br />TX
<br />CURVE FORM ELAS
<br />T = .It tan zd R T cot. z I Chord def. = chord2
<br />,I _ 5o tan f I R
<br />Sin.I D R_= 50f -
<br />} I
<br />Sin. I D = 50 Sin. 2 D No. chords- =
<br />12E= R ex. sec 1 I v
<br />50 tan
<br />Sin. ly:i3;. I E = T tiara li l 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 />Ruled. Multiply the given distance by .01745 (def. for l° for 1 ft.
<br />see Table H.), and divide given deflection by the product.
<br />Rule 2. Multiply given, deflection by 57.3, and divide the pr6duct by
<br />the given distance.
<br />To find deflection for a given angie.and-distance. Multiply the angle
<br />by .0174; 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 />Liven Base loo, Alt: J0.l02=200=:5. loo+.', ioo.5 hyp.
<br />Given Hyp. 1oo,Ait.25.252-'200=3.125.100=3:125=96.875=Base.
<br />F-rrer 1n first example,::002;, in last, .045•.
<br />To find Tons. of -Rail in one mile of trach: multiply weight per yard
<br />by 11 and divide by 7. -
<br />-LEVELING. The correction ,for curvature and refraction, in feet
<br />and decimals of feet is equal to 0; 574da, where d=is the distance in miles.
<br />The correction for curvature alone is -closely, idP. The combined cor-
<br />rection is negative.. '
<br />P1013ASL8ERROR. If d„d2,d,,,etc. are the discrepancies of various. .
<br />results from the, mean, and if FdI=the sum of the squares'of these differ-
<br />ences and n=the number of observfations, then the -probable error of the
<br />mean=
<br />SOLAR EP116.1ERIS. Attention.is,calied 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 Jyx5A in,, with about 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solar attacllments; 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; trigon ometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />Teur.v 117 _ Rdinii+a° in TV,; -1, -of of n. rlaaraa- '
<br />I'
<br />.0167
<br />11'•
<br />.1833
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6533
<br />51'
<br />3500
<br />2
<br />0333
<br />12
<br />.2000
<br />!21'
<br />922
<br />.3667
<br />32
<br />.5333
<br />42.7000
<br />020S
<br />52
<br />8667
<br />3
<br />.0500
<br />13
<br />.2167
<br />I 23
<br />.3833
<br />33
<br />.5500
<br />43
<br />,7167
<br />.53
<br />.8833.
<br />4.0G67
<br />10
<br />14
<br />0833
<br />24
<br />.2 500,
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5 `
<br />0533
<br />15
<br />.2333
<br />.^500
<br />�25
<br />.4000
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.91G7
<br />6
<br />.1000
<br />i6 -
<br />.2667
<br />2G
<br />4333
<br />36
<br />.6000
<br />40
<br />.7667
<br />56
<br />9333 '
<br />.
<br />7'
<br />.1107
<br />17
<br />..2S33
<br />37
<br />_500
<br />37.
<br />-.6167
<br />47
<br />.7533
<br />57.
<br />.9500
<br />8
<br />:1333
<br />18
<br />:3000
<br />28
<br />.4667
<br />•38
<br />.0333
<br />48
<br />.3000
<br />58
<br />.9607
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />'39
<br />,G500
<br />49
<br />.^107
<br />59
<br />.9533
<br />10
<br />.1667 11
<br />20
<br />.3333
<br />'30
<br />1 .5000
<br />49
<br />1 .6667
<br />1150
<br />1 .5333
<br />I I GO
<br />•1,0000
<br />TADLE V. -
<br />inches in Decima12 of a I1oot.
<br />1-16
<br />"-32
<br />3-1G
<br />5-1G
<br />r
<br />/a
<br />.00.;2
<br />.0075
<br />.0104
<br />.0186
<br />020S
<br />-0260
<br />-.0313_
<br />.0417
<br />.0521
<br />.0625
<br />.0729_
<br />1
<br />2
<br />3.
<br />4
<br />5
<br />G
<br />7
<br />8
<br />9
<br />10
<br />it
<br />0833
<br />.1667
<br />.2 500,
<br />.3333
<br />.4167
<br />.5000
<br />.5533
<br />.6667
<br />.',wo
<br />'.8333
<br />.9167
<br />
|