|
X37.9
<br />TAsi m IL - Radii, Ordinates and Deflections. Choid =100 ft.
<br />-D,.,
<br />-°�
<br />Mid. -
<br />Ord.
<br />Tan. +
<br />Dist.
<br />• Def.
<br />Dist.
<br />Def.
<br />for -
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid..
<br />prd.
<br />Tan. _
<br />Dist,
<br />-Def.
<br />Dist.
<br />Det,
<br />for
<br />1 Ft.
<br />z°_ 171.
<br />t.
<br />t
<br />t.
<br />ft
<br />/
<br />1' 59'
<br />ft,
<br />ft.
<br />ft.
<br />ft.
<br />I
<br />0"10°
<br />34377:•'
<br />.036
<br />:145.
<br />' .291
<br />-
<br />0.05
<br />7"
<br />819.0
<br />1.528
<br />6.105.12.21
<br />3' 33'
<br />2.10
<br />20.
<br />17189::
<br />153.58.
<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 />-.073
<br />.109
<br />.436
<br />- :873
<br />0.15
<br />30
<br />764.5'1.637
<br />50 08'.
<br />6.540
<br />13.08
<br />2.25
<br />=•40.
<br />8594:4
<br />..145
<br />.582
<br />11.164
<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 />0.25
<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 />1'4.82
<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 />2.909
<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 />8 - '•
<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 />,..473.1.891
<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 />11'1
<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•':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 />b0..
<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 />T
<br />1432.7
<br />`.873
<br />3.490'
<br />6.9801.20
<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
<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 />8
<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•=1074:7,1.164
<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•;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 />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 />i905.1
<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 />1881.9
<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 (a) 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 Curpes.
<br />Degree
<br />of
<br />Curve
<br />' Radius
<br />50
<br />/ sub chord
<br />R =ern of } def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. j def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. ,
<br />25 Ft.
<br />.34°.193.18
<br />.5167
<br />I° 51'
<br />z°_ 171.
<br />:. z° 58'.
<br />3. 43'
<br />101.15
<br />32°
<br />181,39
<br />1' 59'
<br />2° �5'
<br />3° 10'
<br />3° 58'
<br />101,33
<br />34°
<br />171.0I
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101,48
<br />36°
<br />161: 8o
<br />-20 13'--'
<br />2° 41'-
<br />3' 33'
<br />4° 26'
<br />•.101.66
<br />38°..
<br />153.58.
<br />..2° 20',.,,
<br />_ 2° 49'...
<br />. 30 44.
<br />40 40' :,
<br />1ol .85
<br />40°
<br />'146•;19:
<br />-20 27'
<br />2° 57'
<br />3° 55':.
<br />4° 54'
<br />102.06-
<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 />'20 41.'
<br />3' �3'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°:
<br />127.97.
<br />2° 48'
<br />-3° 21'
<br />40 29'
<br />50.36'
<br />102.76
<br />48*
<br />122.'92 122.'92
<br />2°"55'
<br />3° 29
<br />4° 40'
<br />5° 50'
<br />103:00
<br />50°
<br />118'•31
<br />3°,O2'
<br />3 ° Sg',
<br />° '
<br />451
<br />6° 04'
<br />103.24.
<br />52'
<br />14.06
<br />3°.09'
<br />3o.46'-
<br />5° 02'
<br />6° 17'
<br />103-54
<br />54°
<br />410-H I
<br />30 16' .
<br />- 3° 54' _
<br />50 13'
<br />6031 1
<br />103.84
<br />..56°
<br />lo6.50
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6044.1
<br />104.14
<br />58`
<br />io3'. 14.
<br />3' 29'
<br />4° lo'
<br />5° 34
<br />6° 57' 104.43
<br />20
<br />6o°
<br />100.00'
<br />3°35'
<br />_ 40.18'
<br />5044'
<br />7°11'
<br />104.72
<br />CURVE FORMULAS
<br />T= R tan � 1. R= T cot. a rds
<br />I _ 50 tan I _ Chord def. = R
<br />Sin. } D R = - 50
<br />Sin. i D = 5° Sin., D No. chords = I
<br />R E= R ex. sec I I
<br />$in. j Ij '_ 50 tan I E = T tan t I Tan. def. _ ; 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 .o1745 (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 •01745V 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. 10.162-* 200 =.5., loo+.5 =1oo.5 hyp.
<br />Given' Hyp' ioo,A1t.25.252=200=3.125. 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 IT, and divide bY.7."
<br />LEVELING. 'The' -correction. for. curvature and refraction, in feet
<br />and decinialg of feet is equal to 0.674d2, where d is the distance in miles.
<br />The 'correction for curvature alone is closely, §d2. The combined -cor-
<br />rection-is'negative.
<br />PROBABLE ERROR. If dk, d2, da; etc. are the discrepancies of various
<br />results from the mean, and if 7_d2=the sum of the squares of these difior-
<br />ences-arid. n=the number of observations, then the probable error of the.
<br />mean F1d2
<br />± 0.6745 n (n-1)
<br />,&SOL -EPHEMERIS. Attention is called to the Solar Ephemeris Ephemeris. or.
<br />the current year,. published by Keuffel.& Esser Co., and furnished free of
<br />charge upon request,. which is 31x58 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 />,1'
<br />0167
<br />'ll'
<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 />8'
<br />.0833
<br />13,
<br />.2167
<br />23
<br />-.3833
<br />33
<br />.5500
<br />43
<br />.7167'
<br />53
<br />.8833
<br />.4.0667
<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 />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />65
<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 />67 '
<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 />.1500
<br />19
<br />,3167'
<br />29
<br />'.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59.9833
<br />10
<br />:1667
<br />20
<br />:3333
<br />30'
<br />•.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />A
<br />-TABLE V. - Inches in D&imals-of a Foot. --
<br />1-10
<br />3-32
<br />3-16
<br />YA
<br />5-16 Vs
<br />H
<br />I4 4
<br />0052.
<br />0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260 .0313
<br />.0417 .0521
<br />.0 25 0729
<br />1
<br />2
<br />3
<br />4
<br />b
<br />6 7
<br />8 9
<br />10 11
<br />.0833
<br />.1867_
<br />.2500,
<br />..3333
<br />.41flT
<br />.5000 .6833
<br />.8667 _.7500
<br />1 .8333 .9167
<br />A
<br />
|