|
VIII`
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 f t.
<br />Deg.
<br />-
<br />Radius
<br />"Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />:t -
<br />Def.
<br />1 Ft.
<br />Deg.'
<br />-
<br />Radius
<br />Mid.`
<br />Ord.
<br />--t....
<br />Tan.
<br />Dist.
<br />'-Def.
<br />Dist:
<br />Dor
<br />] r t.
<br />2°.17� .
<br />?°.58 ..
<br />t.
<br />.-.101.15
<br />32°
<br />181.39
<br />._.I° 59,
<br />t
<br />. 3' 10,
<br />t.
<br />t
<br />34°
<br />0"to'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7°.
<br />819.0
<br />1.528
<br />41'.
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073.291
<br />2° 20'
<br />'582
<br />0.10
<br />20'
<br />781.8
<br />1:600
<br />,6.105
<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 />1637
<br />6.540
<br />13.08
<br />2.25
<br />_'40'
<br />8594.4
<br />.145
<br />.582
<br />1c1164
<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 />0:25
<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 />688.2'1.819
<br />103.54
<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 />4297.3.291
<br />4° lo' .'
<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 />1.300
<br />.2:618
<br />0.45`
<br />_
<br />9
<br />637.3.1:965
<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 />3:200
<br />0.55"
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />2_1
<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
<br />17.43
<br />3.00
<br />20
<br />2155.7
<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 />499.4
<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 />3
<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
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />"5.817
<br />1.0030
<br />425.4
<br />2.949
<br />11.75
<br />23:51.4.05
<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 />24.37.4.20
<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 />1495.0.836
<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 />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 />:935
<br />15.64 .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 />1:155
<br />16.51 '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 />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 />4943
<br />9_.886
<br />1.70 '
<br />24 ..
<br />240.5
<br />5.255.20.79
<br />41.58,7.20
<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 />96
<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 />.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 />206.7.139
<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 }}'n 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 III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />A sub chord
<br />R = sin of $ def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. z def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft..
<br />25 Ft.
<br />30°
<br />193: i8
<br />I° 51'
<br />2°.17� .
<br />?°.58 ..
<br />3°.43'._
<br />.-.101.15
<br />32°
<br />181.39
<br />._.I° 59,
<br />2°.�5,
<br />. 3' 10,
<br />30 58,
<br />101.33
<br />34°
<br />171.01
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161-: 8o
<br />2° 13'2°
<br />41'.
<br />3° 33 '
<br />4° 26' ...
<br />ioi.66
<br />38o
<br />153.58
<br />2° 20'
<br />2° 4913°
<br />441
<br />4°_49'
<br />fo1.85
<br />40°
<br />146.19
<br />2° 27'
<br />2° 57,.
<br />30 55'
<br />4° 54'
<br />102.o6
<br />42°
<br />139.52
<br />2° 34'.
<br />3° 05'
<br />4° 07'
<br />50 08
<br />102.29
<br />'44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />.5° 22'
<br />102.53. .
<br />46°
<br />127-97
<br />2°48'
<br />3°21'
<br />4o 29?
<br />5o 36,
<br />102.76
<br />48° ,
<br />122.92
<br />2o,55'
<br />3° 29'
<br />4°40r
<br />5° 5W
<br />103.00
<br />50°
<br />118.31
<br />3o O2'.'
<br />30 38'
<br />40 51'
<br />6o 041
<br />103.24
<br />,52°,
<br />114.06
<br />.3o 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />.54o
<br />i10:1'1
<br />3°•16'.
<br />3° 541
<br />5°1.3,
<br />60 31'-
<br />103.84
<br />56°
<br />106.50
<br />3°,22'
<br />4° O2'
<br />5° 23
<br />6° 44
<br />104.14
<br />58°
<br />103.1.4
<br />, 3° 29'
<br />4° lo' .'
<br />5034"
<br />60.57'
<br />104.43
<br />ol�
<br />100.00
<br />30 35'
<br />4° 18'•
<br />5° 44'
<br />7° 11'
<br />104.72
<br />Ix
<br />``CURVE FORMULASA
<br />T= R tan m 1 R =. T cot. z
<br />I 59 tan Ii, I . Chord"def. = R
<br />Sm:zD - R= 50
<br />Sin. z D = 10 . Sin. I D No. chords ID
<br />E R ex. sec Z I
<br />i So tan 2
<br />Sin. Z D = T E Tian' I I . Tan. def. _ chord def.
<br />The square`of any Aistance, 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 .01945 (def. for I° for I ft.
<br />7see Table IL), and divide given deflection by the product.
<br />Rule'2. Multiply given deflection by`57.3, and divide the product by
<br />lthe given., distance..
<br />To find deflection for a given angle and distance.- Multiply the angle
<br />`by `.oIW1' and the product byahe 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.1o2,,-200=.5.'106+.5 = ioo.5 hyp
<br />Given Hyp. ioo, Alt. 25.252=200=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 Ii, and divide by 7..
<br />LEVELING. The correction Jor 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, 8d?: The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, d2, d3; etc. are the discrepancies of various
<br />results from the mean, and if Ede=the sum.of the squares of these differ-
<br />ences and n=.the number of observations, then the probable error of the
<br />mean 1;d2 '
<br />-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 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 />TABLE IV. -Minutes in Decimals of a.Degree.
<br />1/
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />..5167
<br />41'
<br />.6833
<br />511
<br />.8500
<br />2
<br />.0167
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42.
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0333
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />:5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4'
<br />.0500
<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 />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6.'
<br />.0833
<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 />737
<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 />9'
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />':8167,
<br />59
<br />.9833
<br />"10
<br />.1500
<br />'.1667 11
<br />20
<br />.3333
<br />30
<br />-.5000
<br />40
<br />.6667
<br />50'
<br />.8333
<br />60
<br />11.0000
<br />t; ` -
<br />TABLE V.
<br />-Inches in Decimals of a Foot.
<br />1-I6
<br />3-32
<br />3-16
<br />5-16
<br />%
<br />Y
<br />.0052
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />1
<br />0729
<br />1
<br />1..0078 I
<br />2
<br />3
<br />4
<br />I
<br />:i
<br />6
<br />7
<br />I
<br />8
<br />9
<br />10
<br />I
<br />11
<br />.0833
<br />.1667
<br />..2500 .
<br />- .3333 :.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
|