|
7 r_�-
<br />VIm
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />9 \�
<br />k
<br />rK
<br />1i a
<br />Deg.>f
<br />f
<br />Radius
<br />Mid. '.
<br />Ord
<br />• Tan. '=
<br />Dist.
<br />Def.
<br />Dist
<br />D r
<br />1Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord
<br />Tan.
<br />i Dist.
<br />Def.
<br />Dist.
<br />for1
<br />2° 17'
<br />2° 59"
<br />t.
<br />: 101.15
<br />32°
<br />181.39
<br />1° 59'
<br />t,
<br />t..
<br />t.
<br />ft.
<br />340
<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 />.291
<br />.582
<br />0.10
<br />120'
<br />781.8
<br />1.600'i6.395
<br />146:19
<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 />8594.4.145
<br />4° 1$'
<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 />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 />2.55
<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 />15.112.60
<br />7°:III
<br />30
<br />\3819.8
<br />.327
<br />1.300
<br />2.618
<br />0.45
<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 />614.6.2.037
<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 ..
<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 />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<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 iV
<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 />x•10
<br />1809.6..691'2.763
<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 />1637.3.764
<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 />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 />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 />.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 />318.3
<br />3:716
<br />14;78
<br />29.56
<br />5.10
<br />40
<br />'4228.1
<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 />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 />31:73
<br />6.00
<br />10,
<br />1109:3
<br />4:127
<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,;1=364
<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: 11:2004.798
<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 />1723'e4.943
<br />9.886
<br />1.70
<br />..
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />7.20
<br />50
<br />982.6
<br />1, 27,3[5.088
<br />10:18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />.41.58
<br />21.64
<br />43.28.7.50
<br />6
<br />'955.4
<br />34
<br />10.47 -,
<br />1.80
<br />222.3
<br />5.697
<br />22.50
<br />44-.99
<br />7.80
<br />!10
<br />`20
<br />929.6
<br />L 34fi`'5.379
<br />10.76
<br />1.85
<br />-26
<br />27
<br />214.2
<br />.918
<br />23.35
<br />46:69
<br />8.10
<br />905:1?1•
<br />'if 3$2;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 />f 881.9,;11.418
<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;=1x455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88 151.7619.00
<br />The middld'ordiiiate 'n inches for any cord of length•(0) is equal to .0012 W
<br />multiplied by the upddle ordinate' taken from the above table. Thus, if it
<br />desired to bend a130 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 />Curve
<br />Radius
<br />M sub chord= sin of $def. an:
<br />of arc
<br />for:100 ft.
<br />sin. I def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />10,51'
<br />2° 17'
<br />2° 59"
<br />3° 43
<br />: 101.15
<br />32°
<br />181.39
<br />1° 59'
<br />20 25r-
<br />3o Io,
<br />3058,
<br />ioi.33
<br />340
<br />171.01
<br />2° o6'
<br />2° 33
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.8o
<br />2° 13'
<br />i° 41'
<br />3°.33':
<br />4°.26'
<br />_'io1.66
<br />38°
<br />153.58.
<br />2° 20'
<br />2° 49'.
<br />3° 44
<br />40 40'
<br />1oi: 85
<br />•40°
<br />146:19
<br />.2° 27'
<br />2° 57'
<br />3'55'
<br />4° 54'
<br />102; o6
<br />42° _
<br />139 : 52 .
<br />2° 34'
<br />3° 05'.
<br />4° 07' .
<br />5° 08
<br />102. 29
<br />44° .'
<br />133.47
<br />i° 41'
<br />30 13'
<br />4° 1$'
<br />S° 22'
<br />102.53 -
<br />46°
<br />i27,97
<br />;2o48,
<br />3o.211 ..
<br />4° 29 ..
<br />...5° 36'
<br />102.'76
<br />48°
<br />122.92
<br />20 55'
<br />3029 , '
<br />4°,40'
<br />5°,50' ,
<br />103:00:.
<br />.50°
<br />118.31
<br />3°.02'
<br />.
<br />30 38'
<br />4o 511
<br />6° 04,.
<br />103.24
<br />520
<br />114.06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6°.17
<br />Io3.54
<br />- o410o
<br />54
<br />.11
<br />r
<br />3 16.
<br />o r
<br />3 54
<br />o ., ..
<br />5 13 .
<br />o i
<br />6 31.
<br />103.84
<br />56°
<br />1o6.50
<br />iloo.
<br />3° 22'
<br />4° 02'5°
<br />23'.'
<br />6° 44'
<br />,.104.58.
<br />1.0000
<br />103.14
<br />3° 29'
<br />4° 10'
<br />5° 34',
<br />6°'57'
<br />104.43
<br />60°
<br />00
<br />3°35'
<br />4°18'
<br />5°.441
<br />7°:III
<br />I04.72
<br />t �( ;
<br />1X
<br />C VE FORMULAS
<br />T = R tan 2. I R . = T cot. 2 I - chord' .
<br />I ,_ 5o tan z = R
<br />Sin.- D R 50
<br />= 1
<br />Sin. D =y 50 Sin. ? D I
<br />No..chords-
<br />R E= R ex. sec12I D
<br />Sin. i D
<br />5o tan z ET tan I Tan, def. _ I chord def.
<br />T = } I
<br />The square ,of any'distaiice,. 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 4°.for 1,ft.
<br />:,see Table II.), and divide given deflection by the product.
<br />Rule.2. Multiply given deflection by757.3, and divide the product by
<br />the given distance. i
<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. I .
<br />Given Base loo, Alt. 1o.IO'=200=.5. IOO+.5=100.5 hyp.
<br />Given'Hyp. ioo, Alt. 25.25? =200=3.125. 100-3.125=96,87,5=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 feet is equal to 0.574d', where d is the distance in miles.
<br />The: correction_ for curvature. alone is closely, ;d?.. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, ds, ds, etc. are the discrepancies of. various
<br />'results from the mean and if Zd?_=the sum of the squares of these differ-
<br />enees and n=.the number of observations, then the probable error of ,the
<br />mean.= If gds
<br />-0.6745 ❑(n-1)
<br />SOLAR EPHEMERIS. Attentioff is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished'upon
<br />request. This handy booklet, 3-gx6 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 arid" Polaris; stadia measurements;
<br />magnetic declination;' arithmetic constants, "etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />11
<br />Ill
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41�
<br />.6833
<br />51�
<br />.8500
<br />"'.2
<br />.0167
<br />.0333
<br />12
<br />.1833
<br />'.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />'.5500
<br />42,
<br />..7000
<br />52
<br />.8667
<br />- 3 --
<br />- 13
<br />.2167
<br />23
<br />.3833
<br />33
<br />43
<br />.7167
<br />53
<br />.8833
<br />:4
<br />.0500
<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 />15
<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 />.2500
<br />.2667
<br />26
<br />.4333
<br />36
<br />37
<br />.6000
<br />46
<br />47
<br />.7667
<br />56
<br />57
<br />.9333
<br />.9500
<br />7
<br />8
<br />:1167'
<br />17
<br />18
<br />:2833'
<br />27
<br />28.
<br />.4500
<br />.4667
<br />38
<br />.6167
<br />.6333
<br />48
<br />.7833
<br />.8000
<br />58
<br />.9667
<br />9..
<br />.1333
<br />19
<br />.3000
<br />29.
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />.
<br />10
<br />1.1500
<br />.1667 11
<br />20
<br />.3167
<br />:3333
<br />30
<br />5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE' V.=Inches in Decimals of a root.
<br />1-16 3-32 3-16 N 5-16
<br />,0052, .0078 .0104 O1:i6 .0208 .0260 .0313 .0417 .0521 .0625 0729
<br />.0833. 'I .1667 I .2.500 .3333 I .4167 I .5000 .5833 .6667 I .7500 .8333 ..9167
<br />
|