|
VIIIr ,-
<br />TABLE IL - Radii, Ordinates'and: Deflections. Chord' =100 ft.
<br />me mfaaie orainate }n incnes for any cord of length (0) is equal to .0012 0'
<br />multiplied by the Bliddla 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 III. ' Deflections'for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radias
<br />Mid
<br />Ord '
<br />Tan.
<br />Dist.
<br />-Def.
<br />Dist."'"
<br />for.-
<br />1 Ft.
<br />Deg.`
<br />Radius
<br />, Mid.
<br />Ord.
<br />. Tan.
<br />Dist.
<br />. Def.
<br />Dist.
<br />Dof-
<br />0740'
<br />34377.
<br />t.17.+
<br />036
<br />L145
<br />291
<br />0.05
<br />17'
<br />819.0
<br />=17
<br />1:528
<br />- it.
<br />'6.,105
<br />t.
<br />12.21
<br />2.10
<br />r 20
<br />17189.
<br />''.073
<br />.291
<br />` 1582
<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 />1.637:
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />. 8594.4
<br />'.145.582
<br />139;52
<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 />0:20
<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 />638.2
<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 />674.7'1.855
<br />54'01
<br />'7.411
<br />14.82
<br />2.55
<br />20
<br />'_-30
<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 />3029'
<br />'3819.8
<br />•.327
<br />1:300
<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 />8:136
<br />16.27
<br />2.80
<br />.'50
<br />3125.4
<br />.400
<br />1.600
<br />3.2000.55
<br />30
<br />603.8
<br />2.074:'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
<br />-20
<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
<br />17.43
<br />3.00
<br />'2455.7
<br />-.509
<br />2.036'
<br />'4':072
<br />0.70
<br />30
<br />516.4
<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''
<br />2148.8
<br />..582
<br />2.x27
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02._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 />2.620:10.45
<br />.
<br />20.91
<br />3.60
<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 ..13:
<br />:.
<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 />425.4
<br />2:949-11:75
<br />23.51
<br />4.05
<br />5.30
<br />I. 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 />,
<br />12.62'25.24
<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
<br />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 />: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 />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 />1.60
<br />12
<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 ,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 />214.2
<br />P.918
<br />23.35 '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 />.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 />me mfaaie orainate }n incnes for any cord of length (0) is equal to .0012 0'
<br />multiplied by the Bliddla 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 III. ' Deflections'for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />sin. f def. ang.
<br />sub chord - sin of 's def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft.
<br />25Ft.c
<br />30°
<br />193.18
<br />I° 51'
<br />z° 17'
<br />2° 58'
<br />3° 43'
<br />fol -15
<br />.,32°. ..
<br />181.39 ....1°-59,..,.
<br />•1.3667
<br />_. ZP25,...,
<br />3°.10,
<br />3--58
<br />161._33
<br />161:33
<br />340
<br />171.01
<br />2°'o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />16'I:8o
<br />2° 13'.
<br />2°'41''
<br />'3° 33�
<br />: 4 ° 26'
<br />io> .66
<br />38°
<br />153.58
<br />2°20'
<br />2° ,
<br />49
<br />° .
<br />3 44
<br />° ,..:
<br />4 40
<br />io1.85
<br />.. o.-
<br />40 .,
<br />.146.:i9
<br />..-
<br />- o z7 '.
<br />z
<br />.----
<br />2 - o 57 .
<br />o r-•-
<br />:3 .55`
<br />-4'-S4-
<br />_
<br />, .
<br />to -x406'
<br />42° ...
<br />139;52
<br />2034
<br />•3°.05"..:
<br />4° 07,
<br />' 5e.o8
<br />.162.29 ,
<br />;44°
<br />133.47
<br />2°,41
<br />3°..13'..
<br />4° 18..,
<br />.5°'.22-'-..
<br />162:53
<br />460
<br />127.97
<br />2°.48' ,_
<br />3° 21'.
<br />4P �9'
<br />50,36'
<br />-102.. 76
<br />48''
<br />122:92
<br />2°.55'
<br />3° 29'-,
<br />4o.40 1�
<br />5° 50'
<br />103.- 00
<br />.so'
<br />118:31
<br />3° 02'.
<br />3° 38 :.
<br />':4°• 51' .
<br />60 04(.
<br />; 103.24. :
<br />52° ..
<br />• i 14:06
<br />'
<br />3° 09, ..
<br />, .3° 46',
<br />-.
<br />5° 02'
<br />`
<br />6- 17'
<br />-103,54
<br />54'01
<br />110. ra
<br />3° 16'
<br />3° 54'�.
<br />5° i3',:
<br />. .6° 31'
<br />163.84. .
<br />-.56
<br />io6. 5o
<br />3° 22'
<br />4° 02'
<br />S° 23' .
<br />' 6° 44'.164-14-
<br />58a
<br />103:14,
<br />3029'
<br />4' Io
<br />5034
<br />6'57
<br />104.434
<br />6o.,
<br />100.00.3
<br />35
<br />4 -18'
<br />S 44
<br />7 -Ii,
<br />164-72
<br />fO
<br />X,o/lt. IX
<br />CURVE, -FORMULAS
<br />T R tan z 1 R= T cot. z I chord'
<br />1 I ` 50 -tan Z: -I _ : Chord -def. = R
<br />Sin. -z D R =--
<br />1 50
<br />Sin. z D 5o Sin. z -D No.'chords = I
<br />R' E- R ex. "sec ;-1. D'
<br />i _ 50 tan - z I Tan. def. _ ;chord def.
<br />Sin: 1 D _. 1 E T tan I I
<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 disfancc and deflection.
<br />'Rule i. Multiply the given distance by .01745 (def: -for f° for f 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;t a angle
<br />•by,.01-745, and the product by the distance.
<br />-GENERAL DATA- '
<br />''RIGHT ANGLE:TRIANGLES: Square the altitude, divide' hy'.twice the
<br />'-,base. -Add- quotient to -base for hypotenuse.` . -
<br />Given Base-ioo, Alt. 10.10'=zoo=.5.100+.g=100.5 hyp. '
<br />Given Hyp. 100; Alt."25.z5'=Zoo=3.ii5.'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 i i; and divide by 7.' _.
<br />" --LEVELING. The correction for curvature, :and refraction; :in feet
<br />and'decimals of feet is. equal to 0.574d', `where d is the distance in miles.
<br />The correction for curvature, 'alone,;is closely, 3d',; .The_comUined cor-
<br />rection`is negative. "_
<br />PROBABLE ERROR. If df,dzr d3, etc. are'the. discrepancies of -various
<br />,
<br />results from -the mean; and if Ed'=the sum -of the, squares of -these differ-
<br />ences-and'n=the number'of observations, then the. probable:error of the
<br />mean Ed' ..
<br />'-0:6745 n(n 1)
<br />SOLAR-•EPHFmtRIs. Attention is called .to .the Solar Ephemeris for
<br />the"current year, published by Keuffel & Esser -Co., and furnished upon
<br />'request. This handy booklet, 38x6 in:, has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; directions and tables'for determining the meridian.and the
<br />latitude from observations on the sun: and- Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants;.etc.
<br />TASLE'IV.-Minutes in Decimals of a Degree.
<br />It
<br />'.0167
<br />'111
<br />.1833
<br />21!,
<br />.3500
<br />31
<br />:5167
<br />411
<br />.6833
<br />"51f
<br />.8500
<br />- 2
<br />.0333
<br />12
<br />.2000
<br />22
<br />•1.3667
<br />"- 32 -
<br />.5333-
<br />42
<br />.7000
<br />52
<br />.8667
<br />;3
<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 />.0833
<br />14
<br />.2333-
<br />24
<br />.4000
<br />-34
<br />.5667
<br />44
<br />:7333
<br />54
<br />.9000
<br />5 '
<br />..0667
<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 />,•,
<br />8.
<br />.1333
<br />,
<br />'18
<br />,
<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 />.4533
<br />39
<br />'.6500
<br />49
<br />.8167
<br />59
<br />'.9833
<br />d0 -
<br />-:1667
<br />_
<br />20 •
<br />.3333
<br />30 '
<br />'.5000
<br />-'40 -
<br />'.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />2 - -.--- - TABLE V. -Inches
<br />in Decimals of a P oot.
<br />-
<br />1-16
<br />3-32
<br />)s
<br />3-16
<br />%
<br />5-16
<br />%
<br />�
<br />%
<br />?i
<br />..0052
<br />-.0078
<br />.0104
<br />.0156.
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />1
<br />2
<br />I 3
<br />4
<br />;�
<br />( 6
<br />I 7
<br />I S
<br />I 9
<br />10
<br />I 11
<br />.0833
<br />. ] firi7
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
|