|
r�-,
<br />_'YII -
<br />TABiM IL -'Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.Radius
<br />Radius
<br />50
<br />Mid .
<br />Ord.-
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def'
<br />for
<br />I Ft.
<br />Deg.
<br />Radius
<br />Mid •
<br />Ord.
<br />Tan
<br />.Dist.
<br />Def. •
<br />Dist.'
<br />Def.
<br />for
<br />1 Ft.
<br />51'
<br />t.
<br />t..
<br />t.
<br />t-
<br />7
<br />43' - _
<br />it.
<br />ft.
<br />ft,
<br />ft..
<br />42
<br />0"40'
<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 />6.395'12.79
<br />20
<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 />6:540.13.08
<br />491-
<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 />-.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 />S
<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 />1.164
<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 />270
<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 />.436.1.745
<br />23'
<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 />`4.072
<br />0.65
<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 />104.72
<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 />21.77:3.75
<br />10;'.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 />.764.3.054
<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
<br />26.11
<br />4.50
<br />6 =
<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 />16.64
<br />31.29,5.40
<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 />8,30
<br />.20
<br />1074.7
<br />1.164
<br />4:653
<br />9:305
<br />1.60
<br />22262.0
<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 />8
<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 />51.78
<br />9.00
<br />'.rhe middle ordinate in 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 IIL Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />sub chord _ern of }def. angle
<br />R'
<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 />30°
<br />193.18
<br />I°
<br />51'
<br />2°=17'
<br />.8500
<br />_2°-58'
<br />.0333
<br />3°
<br />43' - _
<br />101.-15
<br />32°
<br />i81
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />V
<br />.0500
<br />13
<br />101.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />z°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />360
<br />161.8o- '
<br />2°
<br />13'
<br />20
<br />41'
<br />3°
<br />33'
<br />4°
<br />26'_
<br />_ io1.66
<br />3$0-
<br />153.58..
<br />z°
<br />20'
<br />z°
<br />491-
<br />30
<br />44'
<br />4°
<br />40'
<br />101.85
<br />40°
<br />146.19
<br />2°
<br />27'
<br />2°
<br />57'.
<br />30
<br />55
<br />40
<br />54'
<br />-102.06
<br />-42 0
<br />.139•'52.
<br />2'
<br />34'
<br />30
<br />05' '
<br />4°
<br />07'
<br />5°
<br />o8'
<br />_102.29
<br />44°
<br />133.47
<br />2°
<br />41'
<br />3'
<br />13'
<br />4°
<br />18'
<br />5°
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21'
<br />4°
<br />29'.
<br />5°
<br />36,
<br />202.76
<br />48°
<br />122.92
<br />2°
<br />55'
<br />3°
<br />29.
<br />4°
<br />401
<br />5°
<br />So'
<br />Io3.00
<br />50°
<br />118.31
<br />3°
<br />02'
<br />3°
<br />38'
<br />4'
<br />SI'
<br />6°
<br />04'
<br />103.24
<br />52°
<br />114.06
<br />3°09'
<br />3°46'
<br />4
<br />5°O2'
<br />' 6°17'
<br />103.54
<br />54°
<br />110.11,
<br />3°
<br />16'
<br />3°
<br />.
<br />5°
<br />13'
<br />60
<br />31'
<br />103.84
<br />560
<br />106.50
<br />3°
<br />22'
<br />4°
<br />02
<br />5°
<br />23'
<br />6°
<br />44'
<br />104.14 .
<br />580
<br />103.14
<br />3.29°
<br />'
<br />4°
<br />10'
<br />50
<br />34'
<br />60
<br />57'
<br />164.43
<br />6o°
<br />ioo.00
<br />3
<br />35'
<br />4°
<br />18'
<br />S°.44'
<br />7°
<br />12'
<br />104.72
<br />M
<br />CURVE FORMULAS
<br />T= R tan f 1 R= T cot. ; Chord chord'
<br />_ 50 tan ,�. I ord def. = 60 R
<br />}: D
<br />T Sin.
<br />. =
<br />Sin. Ij = 50 R Sin. J D, No. chords = I
<br />R E= R ex. sec # I'
<br />5o tan I
<br />.Sin. }' D = T E = T. tan I 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 -01745 (def, for I° for I ft.
<br />see invendistance Table II.), and divide given deflection by the product.
<br />Rule 2.'' Multiplygiven deflection by 57.3,,and divide the product by
<br />th •" .
<br />e •' '
<br />To find 'deflection "for a given- angle arid* distance. Multiply the angle
<br />by -01745i 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 basefor'hypo tenuse.
<br />Given, Base Ioo, Alt. 10.10s-' 200=.5. 100-1-.5=110.5 hyp• '
<br />Given Hyp: loo, Alt. 25.252,=2oo=3.125, 106-3-125.-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 -11, and divide by 7.
<br />LEVELING. The, correction for curvature .and refraction, in feet
<br />and decimals of feetis equal.to 0.574 da, where. d: is the.distance in miles.
<br />The "correction for. curvature alone is closely, fid'. . The combined cor-
<br />rection is.negative. '
<br />PROBABLE ERROR. If d;, da, de, etc. are the discrepancies of various
<br />results from the meari;_and If Yde=the sum of the squares of these dlfl0r-
<br />elices.and n=the number of observations,. then the probable error Of the,
<br />mean= + 0.6746 n n-1)
<br />SOLAR EPHEMERIS. Attention: is called to the Solar Ephemeris for'
<br />the'current year, publishedby Keuffel:$ Esser Co., and furnished free of
<br />charge upon request, which is 3}x5} in., with about 90 pages of data very
<br />useful to the: Surveyor; such as the adjustments of .transits, levels and
<br />so
<br />lar.attachments; directions and tables for determining the meridian
<br />I and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric F
<br />conversions; trigonometric formulas; Natural and Logarithmic unctions;
<br />and Lozitrithms of Numbers. -
<br />. TABLE IV. - Minutes
<br />in Decimals of a De ee.
<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 />22.3667
<br />.0208
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />V
<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 />„ 5.0833
<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 />.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 />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />_N
<br />'I'ABLE V. - Inches In L)ecimaJs of a root. --
<br />-
<br />i
<br />1-16
<br />342
<br />1 "-16
<br />b-16
<br />'1
<br />Y4
<br />0052
<br />.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />••0417
<br />X521
<br />.0 25
<br />.0729
<br />1
<br />23
<br />4
<br />5
<br />6
<br />7
<br />8
<br />9
<br />10
<br />11 .
<br />.0833
<br />.1667
<br />.2500
<br />.333,3
<br />.4167
<br />.5000
<br />.5833
<br />.8667
<br />.7500
<br />.8333
<br />.9167
<br />_N
<br />
|