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VIII Ix
<br />IL - Radii, Ordinates and Deflections. Chord -100 ft. CURVE FORMULAS
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tau.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />1f Ft
<br />Des.
<br />Radios
<br />Mid
<br />Ord.
<br />Toa
<br />DIet.
<br />Def.
<br />Dim,
<br />Def'
<br />for
<br />1 Ft.
<br />51'
<br />2°
<br />17'
<br />2°
<br />58'
<br />3°
<br />43'
<br />101.15
<br />320
<br />181.39
<br />1°
<br />59'
<br />0"10'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7.
<br />810.0
<br />1,525
<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 />6.305
<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 />2.2:,
<br />40
<br />8594.4
<br />.145
<br />.582
<br />1.164
<br />0.20
<br />40
<br />747.0
<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 />.S73
<br />1.745
<br />0.30
<br />20
<br />6SS.2
<br />1.819
<br />7.269
<br />14.53
<br />2. E,11
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />t.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 />2.50
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2,618
<br />0.45
<br />0
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2-037
<br />8.136
<br />10.27
<br />2.80
<br />50
<br />3125.4.400
<br />54'
<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.S5
<br />3
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />503.4
<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 />3.60
<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 />409.7
<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 />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 />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />2,940
<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
<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 />1132.7
<br />.873
<br />3.490
<br />6.990
<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 />7.271
<br />1.25
<br />10
<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 />10
<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 />33.16
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.708
<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 />41.58'7.20
<br />50
<br />982.6
<br />1.273
<br />5.OS8
<br />10.18
<br />1.75
<br />25'
<br />231.0
<br />5.476
<br />21,64
<br />43.28
<br />7.50
<br />a
<br />055.4
<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 />029,6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />2t4.2f66
<br />.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 />206.7.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />.36025.04
<br />50.07
<br />8.70
<br />40
<br />.859.911.45615:814111.63
<br />2.00
<br />30
<br />193.2
<br />.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinato'n inches for any cord of length (0) is egqnal to 0012 C.
<br />multiplied bythe tllidd�e ordinate taken from the above tablo. Thus, if it
<br />desired to bend 30 ft, rail to fit 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36inehes.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />sin. } def. ang.
<br />M sub chordLength
<br />IL =sin of } def. angle
<br />.1833
<br />of arc
<br />for 100 ft.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193. IS
<br />I°
<br />51'
<br />2°
<br />17'
<br />2°
<br />58'
<br />3°
<br />43'
<br />101.15
<br />320
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25`
<br />3°
<br />10'
<br />3°
<br />58'
<br />701.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />2°
<br />33'
<br />3°
<br />21'
<br />40
<br />12'
<br />101.43
<br />36°
<br />t61. 8o
<br />2°
<br />13'
<br />2°
<br />41'
<br />3'
<br />33'
<br />4°
<br />26`
<br />ioi.66
<br />380
<br />153.58
<br />2°
<br />20'
<br />2°49
<br />55
<br />3°
<br />44'
<br />4°
<br />40'
<br />IOI.85
<br />40°
<br />146. i9
<br />2°
<br />27'
<br />2'
<br />57`
<br />3°
<br />55'
<br />4°
<br />54'
<br />lo2.o6
<br />42°
<br />139.52
<br />2°
<br />34'
<br />3'
<br />05'
<br />4°
<br />07'
<br />'5'08
<br />8
<br />102.29
<br />44°
<br />133.47
<br />20
<br />41'3'
<br />38
<br />13'
<br />4°
<br />i8'
<br />5°
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21`
<br />4°
<br />291
<br />5°
<br />36'
<br />102.76
<br />48°
<br />122.92
<br />2'
<br />55'
<br />3°
<br />29'
<br />4°
<br />40
<br />5°
<br />50'
<br />103.00
<br />50°
<br />118.31
<br />3°02'
<br />3°38'
<br />4°31'
<br />6°
<br />04'
<br />103.24
<br />52°
<br />I14 -o6
<br />3°
<br />09
<br />3°
<br />46'
<br />S.
<br />02
<br />6°
<br />17'
<br />103.54
<br />54°
<br />tto. t]
<br />30
<br />16'
<br />3'
<br />54'
<br />13'
<br />60311
<br />103.84
<br />56°
<br />io6.50
<br />3°
<br />22'
<br />4°
<br />02'
<br />.5°
<br />5°
<br />23'
<br />6°
<br />44'
<br />104.14
<br />58°
<br />103.14
<br />3°
<br />29'
<br />4'
<br />l0'
<br />5°
<br />34'
<br />6°
<br />57'
<br />104.43
<br />60°
<br />I00.00
<br />3°
<br />3$'
<br />4°
<br />IS'
<br />5°
<br />44'
<br />1 7'
<br />il' 1
<br />104.72
<br />T = .50 tan I I R = T cot. ' I Chord def, = chord'
<br />,r =tan 121 R
<br />Sin. a D R - 50
<br />Sin. a D' = 50 Sin. $ ll No. chords = I
<br />R; E= R ex. sec I I D
<br />Sin. .'D = 5° t'I I F T tan # 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 .01743 (def. for I' for I ft.
<br />see Table 11.), 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 too, Alt. 10A02 -200=.S. loo+.g=loo.5 hyp.
<br />Given Hyp. loo, Alt, 25.252 200=3.125. I00-3.125=g6,875=Base.
<br />Error in first example, .002; in last, .o4s.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by I t, and divide by 7.
<br />' LEVELING. The correction for curvature and refraction, 1n 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, id'. The combined car -
<br />1 rection is negative. .
<br />PROBABLE ERROR. If d1, d2; da, 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 - 7n(n-1)
<br />X0.6745
<br />SOLAR EPHEh1EEs. Attention 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$x6 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 and Polaris; stadia measurements;
<br />s
<br />magnetic declination; arithmetic constants, etc.
<br />TA13LF IV. -Minutes in Decimals of a Degree.
<br />1t
<br />.0167
<br />11'
<br />.1833
<br />2V
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />511
<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 />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7107
<br />63
<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
<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 />0333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9,500
<br />8
<br />.I333
<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 />T,�Ri.r; V. --Inches
<br />in Decimals of a Foot.
<br />1-16
<br />3-32
<br />Y
<br />3-16
<br />;;
<br />5-16
<br />V,
<br />;5
<br />%
<br />3'a
<br />-
<br />.0052 P
<br />.0078
<br />.0104
<br />.0156
<br />.0208
<br />.i&o
<br />.0313
<br />.0417
<br />.052E
<br />0625
<br />.0729
<br />I
<br />I
<br />.0833 I
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />: U00
<br />u833
<br />.6667
<br />.7,50{1
<br />.8353
<br />,9167
<br />
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