|
7III '
<br />TABLn IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Dom"
<br />Radius iius
<br />Mid
<br />Ord.
<br />Tan. •
<br />Diet.
<br />Def..
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord'
<br />.
<br />Tan
<br />Dist,
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />51.'
<br />t.
<br />17'. -
<br />ft.
<br />ft.
<br />7
<br />43'
<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°
<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 />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 />.445
<br />.582
<br />:1.164'0:20
<br />f9
<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 />0.25
<br />8716.8
<br />3'
<br />1.746
<br />6.976.13.95
<br />07'
<br />2.40
<br />I -
<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 />1.104
<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 />20'
<br />614.6
<br />2:037•
<br />8.136
<br />16.27
<br />2.80
<br />=' b0"
<br />3125.4
<br />,400
<br />1.600
<br />.3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281.16.56
<br />3°
<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 />1
<br />3.780.65
<br />104.43
<br />10
<br />573:7
<br />2.183
<br />8.716
<br />17.43
<br />3.00
<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.
<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 "'478.3
<br />2.620
<br />10.45,
<br />20.91.3.60
<br />0 -
<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 />21.77'3.75
<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:'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 />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 .26.11
<br />4.50
<br />A.
<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 />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 />-.982.3.926
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />401
<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--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 />0.305
<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 />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 />0
<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 />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 />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 />The middle ordinate in inches for any cord of length (C) isequal 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 />Degree
<br />of
<br />Curve
<br />Radius iius
<br />� subb,,clwrd='sin 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 />,.300
<br />193.18
<br />1°
<br />51.'
<br />2°
<br />17'. -
<br />2°
<br />58''
<br />3°
<br />43'
<br />IOI, 15
<br />32°
<br />181.39
<br />10
<br />59'
<br />2°
<br />25'
<br />3°
<br />10'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />2°
<br />06'
<br />2°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />360
<br />161.86
<br />20
<br />13'
<br />2°
<br />41' :
<br />3°
<br />33' °
<br />4°26'
<br />5-
<br />ioi.66
<br />38°-
<br />-153.58
<br />.2°20'
<br />.4167
<br />2°
<br />49'
<br />3°
<br />44'
<br />•4°40'
<br />.9167
<br />101.85
<br />40°
<br />f9
<br />2°"27'
<br />26
<br />2°
<br />57'
<br />3°
<br />55
<br />4°
<br />54'
<br />102.06
<br />._42°
<br />.146.
<br />139.52
<br />2°
<br />34'
<br />3'
<br />05'
<br />4°
<br />07'
<br />S°
<br />08'.
<br />102.29
<br />44°133.47
<br />8
<br />2°
<br />41'
<br />3°
<br />13'
<br />4°
<br />18'
<br />5°
<br />22'
<br />102.53 '
<br />460
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21`
<br />4°
<br />29':
<br />50
<br />36`
<br />102.76
<br />48°
<br />122.92
<br />z°
<br />55'
<br />3°29'
<br />20
<br />.4°
<br />40'
<br />S°50'
<br />11 40
<br />103.00
<br />50°'
<br />118.31.
<br />3°
<br />02'
<br />30
<br />38.
<br />4°
<br />511
<br />6°
<br />04'.103.24
<br />52°
<br />114.06
<br />3°
<br />09'
<br />3"461
<br />50
<br />02'
<br />6°.17'
<br />103.54
<br />'540
<br />II0.11.
<br />3`•16'
<br />3°54,
<br />5°
<br />13'
<br />60311
<br />103.84
<br />56`
<br />I06.5o
<br />3°
<br />22'
<br />4°
<br />02'
<br />S°
<br />23'
<br />60
<br />44'
<br />104.14
<br />580,
<br />I03'.14
<br />3°
<br />29'.
<br />4°
<br />10'
<br />5034
<br />1
<br />60
<br />57'
<br />104.43
<br />60°
<br />100. o0
<br />3.35
<br />4°
<br />i8'
<br />S°
<br />44'
<br />7°
<br />I1'
<br />104.72
<br />1
<br />CURVE FORMULAS
<br />T _ o tan J I _ R = T cRtanIot. J.,I Chord def, =chord$
<br />T 50 R
<br />Sin. } D R ._
<br />J D = 5° ;Sin. D1.. chords = I ;
<br />o tan J I E= R ex: sec. i I.
<br />Sin: D -: T E = T tail I I Tan. def. _ J, 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 I.' Multiply the given distance by -OIA5 (def. for I° for I ft.
<br />see Table II.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 573, 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 100, Alt. 10.102,+200=:z.5. 100-x-.5=100.5 hyp.
<br />Given Hyp. ioo,Alt. 25.zg2=z°o=3.125. io0-3.125=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 0.574d9,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�, de; da, etc. are the discrepancies of various
<br />results from the mean; and if 7-da.=the sum of the squares of these differ-
<br />ences and n=the number of observations; then the probable error of the,
<br />mean- ±_ 0.6745 �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 31.fx5 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 and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - Minutes
<br />in Decimals of a Degree.
<br />V
<br />'.0167.
<br />11'
<br />.1833'
<br />21'
<br />.3500
<br />31' •
<br />" .5167
<br />41'
<br />. 6833
<br />.51'
<br />.9500
<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 />14
<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 />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 />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />1.4667
<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 1130
<br />1 .5000
<br />11 40
<br />1 .666711
<br />50
<br />1 .83331,
<br />60
<br />11.0000
<br />TABLE V. -'inches in Decimals of a Foot.
<br />f
<br />1-16
<br />M2
<br />3-16
<br />5-161
<br />%
<br />f4 �
<br />.0052
<br />•.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />'.0313
<br />.0417 .0521
<br />.0 25 .0T19
<br />1
<br />2
<br />3
<br />C
<br />5
<br />6.
<br />7
<br />8- 9
<br />10 11
<br />.0833
<br />.,.1667_
<br />.2500
<br />.3333__.4167
<br />.5000
<br />.5833
<br />.6667 .7500
<br />.8333 .9167
<br />
|