|
Iq
<br />VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg. `
<br />m ul' Ie db
<br />tip y the cuddle ordmate taken from the above tab1
<br />Radius
<br />. Mid.
<br />Ord
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Dor `
<br />1 Ft.
<br />" .Deg..
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan .
<br />Dist.
<br />Def.
<br />Dist.
<br />Dor
<br />I Ft.
<br />2° 17' -
<br />2° 58'
<br />30 43'
<br />IOI. 15
<br />320
<br />181.39
<br />1° 59'
<br />t.
<br />ft.
<br />f t. -
<br />t.
<br />34°
<br />o'i0''34377.
<br />2006 ,
<br />.036
<br />.145
<br />:231
<br />0.05
<br />36°
<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*11459..
<br />4° 54'
<br />',.109.
<br />.430.
<br />:873
<br />0.15
<br />_
<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 />50.
<br />6875.5
<br />.188
<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 />.2181
<br />.873
<br />1.745
<br />0.30`
<br />1 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 />1.164
<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 />1.309
<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 />2.969
<br />0.50
<br />20
<br />614.6
<br />2.037-
<br />8.136
<br />16.27
<br />2.50
<br />50
<br />3125.4
<br />_.400
<br />1.600
<br />3.200
<br />0.55
<br />:30
<br />603.8
<br />21074
<br />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 />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 />.5092.036
<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 />2.327
<br />4.654.0.80
<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 />4.945.0.85
<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 />3.00
<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 />1037.3
<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 />4.2Q
<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 />.1.195,0
<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 />! '
<br />1132.7
<br />..873
<br />3.490
<br />6:950
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.40
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.2711.25
<br />16
<br />359.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20.`.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 />b0
<br />1185'.8
<br />1.055
<br />4`.217
<br />8.433
<br />1.45
<br />19
<br />302.9
<br />4.155=16.51"
<br />33.01
<br />5.70
<br />S
<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 />WQ
<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 />140.
<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 />955:4
<br />1:309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697.22.50'
<br />44.99
<br />7.50
<br />10
<br />'929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />_
<br />27
<br />1214.2
<br />5.918"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 />1206.7
<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
<br />middle ordinate
<br />1•
<br />in inches for any cord of length (C) is equal to .0012 C'
<br />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 III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />' of
<br />Curve
<br />Radius
<br />59
<br />Ma sub:chord
<br />R = sin of $def. angle
<br />Length
<br />of arc
<br />for. 100 ft.
<br />sin, i def. ang.
<br />12.5 -Ft.
<br />1 15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1° 51'
<br />2° 17' -
<br />2° 58'
<br />30 43'
<br />IOI. 15
<br />320
<br />181.39
<br />1° 59'
<br />2° 25'-
<br />3° 10'
<br />3° 58'
<br />iol .33 "
<br />34°
<br />171.01
<br />2006 ,
<br />20 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.80
<br />2° 13!2°
<br />41�
<br />3°.33
<br />4° 26'
<br />foI.66
<br />3$0
<br />X40°;
<br />153.58
<br />2° 20'
<br />20 49'
<br />3° 44'
<br />4°40',
<br />lol .85
<br />.
<br />146.19
<br />2° 27'
<br />2° 57:
<br />30:55'
<br />4° 54'
<br />102.06
<br />420
<br />:139.'52
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />S° o8
<br />102.29 .
<br />.44'
<br />133.47
<br />2° 41'3°
<br />13'-
<br />4° 18' _
<br />5° 22'
<br />IW .'53
<br />46*...--
<br />127.97
<br />2° 48'
<br />3°. 21'
<br />4°-29, .
<br />_ So 36'
<br />-102.76
<br />48°
<br />i22. 92
<br />2° 5.5'
<br />3°_29'
<br />4o 46'
<br />50 50'
<br />•103:00_.
<br />50°:
<br />.119! 31
<br />3° 02'
<br />.3° 38'
<br />4° 51'
<br />6° 04'
<br />Io3. 24
<br />Se ..
<br />1.141.06
<br />3° 09',
<br />; .3°-.46'
<br />S° oz'
<br />6° 17'
<br />103.54
<br />54°•'.
<br />IIo. II
<br />3° 16' .
<br />3° 54'
<br />. 5°•13.
<br />6° 31
<br />103.84
<br />56°
<br />1o6.50 _,
<br />3° 22'
<br />-4° 02' ,
<br />5° 23' :
<br />6° 44'
<br />104.14
<br />580.
<br />103. �4 '
<br />- 30 �9;
<br />4o 10'
<br />S°.34, .
<br />6° 57'
<br />104.43•
<br />6o°.
<br />,100.00
<br />30-35'
<br />4° 18'
<br />50 44'
<br />7° 11'
<br />104.72
<br />f
<br />� IX
<br />CURVE FORMULAS
<br />T= R tan 32 I R= T cot. -1 1 chord= ,
<br />I - So tan 2 I Chord def.
<br />Sin. 2 DR. = 50
<br />3
<br />Sin. 2 D = 50 Sin. , D No. chords =I
<br />`R, E= R ex. sec 2 I D
<br />Sin.` 2 D' Sot T 2 I E= T tan I I Tan. def. = 2 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 .01745 (def. for I° for 1 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 :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 loo, Alt. 10.102_200=.5. IOO+.5=Ioo.S hyp. -
<br />Given Hyp. loo, Alt. 25.252-Zoo=3.I25. loo-3.125=86.875=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 0.574d2, where d is the distance in miles.
<br />The correction - for curvature alone is closely, .2:,d2. The combined -cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, 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= FY_ d2
<br />-0.6745 n(n71)
<br />SOLAR EPHEMERIS. Attention is called -toy 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 />j latitude from observations on the sun and, Polaris;'stadia measurements;
<br />j magnetic declination; arithmetic constants; etc.
<br />`: TABLE IV. -Minutes in Decimals of a Degree.
<br />11
<br />11f
<br />.1833
<br />21
<br />3500
<br />31f
<br />.5167.
<br />411
<br />".6833
<br />511
<br />.8500
<br />2
<br />.0167
<br />12
<br />.2000
<br />22
<br />.3667
<br />325333
<br />42
<br />.7000
<br />52
<br />:8667
<br />3
<br />.0333
<br />-.0500.
<br />13
<br />.2167
<br />23
<br />.3833
<br />33 '':5500
<br />"43'
<br />.7167
<br />.-53,,
<br />.8833-
<br />4
<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 />25
<br />.4167
<br />35
<br />.5833
<br />45_
<br />.7500
<br />55
<br />'
<br />.9167
<br />6
<br />.0833
<br />16
<br />.2500
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />'56
<br />.9333
<br />7
<br />.1000
<br />17
<br />27
<br />.4500
<br />37
<br />s.6167-
<br />47_..7833
<br />57
<br />'.9500
<br />8
<br />.1167
<br />18
<br />.2533
<br />.3000
<br />28
<br />.4667
<br />38
<br />..6333
<br />48
<br />.8000
<br />.,58
<br />.6667
<br />9
<br />.1333
<br />',19
<br />29
<br />.4833
<br />39'
<br />.6500
<br />59
<br />'60
<br />.9833
<br />10.
<br />.1500'
<br />.1667
<br />20
<br />.3167
<br />.3333
<br />30
<br />1, .5000
<br />40
<br />•.6667
<br />.49.8167
<br />50
<br />.8333.
<br />1V0000
<br />TABLE V. -Inches in Decimals of a Foot.
<br />1-163-32 Y 3-16 % 5-16 % Y
<br />.0052 .0078 I .01304 .0156 .02508 I .02660 .0313 I .04817 L .05021 I .06025 I .0119
<br />.0833 I .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167
<br />
|