|
611
<br />TABLE IL - Radii, Ordinates'and Deflection& Chord =100 ft.
<br />Deg: -
<br />Rad us
<br />i
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Doi
<br />1 Ft.
<br />Deg.
<br />Radius
<br />M'd..
<br />Ord.
<br />Tan
<br />Dist,
<br />Def.
<br />Dist.
<br />D�
<br />1 Ft.
<br />i° 17'
<br />2° 5813°
<br />" t.
<br />ft:
<br />ft.
<br />/
<br />1' 59
<br />ft,
<br />ft.
<br />ft.
<br />ft.
<br />34°
<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 />.29L
<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 />.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 />b0
<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
<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 />2.65
<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 />3819.8.327
<br />1.0000
<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 />50.-
<br />3125.4
<br />•400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8:281.16.56
<br />2.85
<br />V.:
<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 />3.7810.65
<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
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />8.
<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 />1.00
<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 />24.37.4.20
<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
<br />26.11
<br />4.50
<br />8
<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 />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50'1185.8
<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 />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 />39.87.8.90
<br />40
<br />1011:5
<br />1.2374.943
<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
<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 m1QQ1e OrCllnat0 In 1nChe9 IOr any cora or lengLn lVJ 19 a IIal zo Xu" v -
<br />multiplied by the middle ordinate taken from the above tab e. 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
<br />50
<br />sub chord _sin of } def. angle
<br />R
<br />��
<br />of arc
<br />for 100 ft' -
<br />t.30°
<br />sin. $ def, ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft,
<br />30 0
<br />193.18
<br />1° 51'
<br />i° 17'
<br />2° 5813°
<br />-3° 431._
<br />101.15
<br />32°
<br />181.39
<br />1' 59
<br />- 2° 25
<br />3° 10'
<br />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 />360
<br />16i.8o
<br />z° 13' -
<br />z° 41'
<br />3° 33` :.`
<br />4°.26' .
<br />__ io1.66
<br />380
<br />153.58.
<br />2° 20'
<br />2° 49' ,
<br />3°-44'
<br />4° 40' _
<br />101.85
<br />40°
<br />146.19
<br />2 o 27'_1 1
<br />20 57',
<br />3°55'
<br />4°54'
<br />102.05
<br />'_'102.29
<br />42°
<br />139.52
<br />2°34'
<br />3° 05'
<br />4°.07'
<br />5°08'
<br />35
<br />440 .
<br />133.47
<br />. 2° 41.
<br />3° 13' :
<br />4°. 18'.
<br />: 5° 2z'
<br />102.53
<br />.46 0
<br />127.97 '
<br />2° 48'
<br />3° 21'
<br />40 29'•--
<br />:'50 36'
<br />162.76
<br />48° 122.92,
<br />.56
<br />2'55'
<br />3°�9,..
<br />4°.40,
<br />51,
<br />103:00
<br />50°-
<br />118.31
<br />30 02'
<br />30 38'
<br />40 51' .
<br />6° 04'
<br />103:24
<br />520
<br />114.06,
<br />3° 09'
<br />30461
<br />59 02':
<br />60 lj' -
<br />103:54
<br />540
<br />110.11
<br />3° -16'
<br />30 54'
<br />5° 13' .
<br />60-31"
<br />103.84
<br />560
<br />zo6.50
<br />3° 22'
<br />40 02'
<br />5° 231 _•
<br />6° 44'.
<br />,. 104,14
<br />58° '
<br />103.14.
<br />3029'
<br />4° l0'
<br />5° 34'
<br />60,57
<br />104.43.
<br />600,
<br />100.00
<br />3° 35'
<br />4° 18'
<br />5° 44'
<br />7°- i•1'
<br />.,104.72 .
<br />CURVE FORMULAS
<br />T = R tan f I R= T cot' I oreChd df. =chord$
<br />i 50 tan 8 I, . R
<br />Sin. 8 D. - R = Sin: 60 _
<br />Sin. 8 = - D
<br />D No. chords = I
<br />1 E=R ex. sec; I' D
<br />5o tan i I
<br />Sin. J.D = r E = T tan } I Tan: def.= ;chord def;
<br />The square of any distance, divided by twice flue radius; will equal
<br />I "the, distance from tangent to curve, very nearly.
<br />To'find angle for a given distance and deflection.
<br />r, 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 find deflection for a given angle and distance. Multiply the angle
<br />by oz 74S, 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 .loo, Alt. 10.102+ 200 =.5. loo+.5 =1oo.5 hyp.
<br />Given Hyp. loo, Alt. 25.252+200=3.125, 100-3.125=96.875=Base.
<br />Error in first example, .o02; in last,..o45-
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by•zI, and divide by 7.
<br />LEVELING. The correction for curvature and -'refraction, in feet
<br />and•decimals of feet is equal to 0.574 de, where d is the distance in miles.
<br />The correction for curvature alone is closely, kill. 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 Y_ds=the sum of the square's of these diClOr-
<br />ences and n=the number of observations, then the probable error of the,
<br />mean=.� 0.6745,n n 1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemei5s foil
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 31,x58 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.
<br />TABLE IV. - Minutes
<br />'TABLE V. - Inches 1n Decimals of a Yoot.
<br />in Decimals of a Degree.
<br />1'
<br />.0167
<br />•11'
<br />1833
<br />21'
<br />3500'
<br />31'
<br />.5167
<br />41'
<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 />4
<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 />45.7500
<br />5
<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 />"47
<br />:7833
<br />"57
<br />-.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />..6167
<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 />Y°10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />1 40
<br />1 .6667 11
<br />50
<br />1 .833311
<br />60
<br />1.0000
<br />._1�
<br />'TABLE V. - Inches 1n Decimals of a Yoot.
<br />1-16 3-82
<br />3ti
<br />3-18
<br />Y
<br />518
<br />%
<br />% 9
<br />..0052• .0078
<br />.0104
<br />:0168
<br />.0208
<br />.0260
<br />.0313
<br />'.0417
<br />.0521 :0625 .049
<br />1 2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8
<br />9 10 11
<br />.0885- .1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />..5833
<br />.6667
<br />.7500• .8333 .9167
<br />._1�
<br />
|