|
:VIII - _ ]EX
<br />TABrx IL' -'Radii, Ordinates and Deflections. Chord =100 ft. CURVEFORMULAS
<br />Deg:
<br />Rsdiue
<br />Mid.
<br />Ord. •
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist.
<br />Der.
<br />1 r
<br />Deg.'
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist:
<br />•Def.
<br />Dist.
<br />Dor.
<br />1 r
<br />2':i7'
<br />t. ,
<br />t..
<br />ft.
<br />ft.
<br />/
<br />1° 59'
<br />ft,
<br />ft.
<br />ft,
<br />ft:,
<br />i
<br />0"30'
<br />34377x'1.036.145
<br />20 33�
<br />30 21'
<br />.291
<br />0.05
<br />71
<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 />781,8.1.600
<br />40°
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.-
<br />.109
<br />.436
<br />.873
<br />0.15`
<br />30
<br />764,5'1.637
<br />5o 08'
<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 />`.182
<br />.727,
<br />3.454
<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 />1.411
<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 />1309
<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 />Z
<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 />" 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 />499.1
<br />2.511
<br />10.02
<br />20,04
<br />3.45
<br />t 50
<br />2022.4
<br />.618
<br />2.472
<br />.4.945
<br />0.85
<br />12 ':478,3
<br />2.620
<br />10:45:
<br />20,91
<br />3.60
<br />Q' '.
<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•,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
<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 />L'• •"
<br />1432"' 7,
<br />,873
<br />3:490
<br />6:980
<br />1.20
<br />30
<br />370.8
<br />3.387.13.49:
<br />26.97
<br />4.65
<br />lo:
<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 />.1:80.30
<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 -.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 />6
<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 />38'.16
<br />6.60
<br />30:
<br />1042.1
<br />1.200
<br />4,798
<br />9.59 6
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />6.90
<br />40•:1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />.39.87.
<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
<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 />6.583.25.88
<br />51.76
<br />9.00
<br />The 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 />M sub chord =six of }def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin, $ def. ang,12.5
<br />Ft:.
<br />15 Ft.
<br />20 Ft. '
<br />25 F.t.
<br />..30°
<br />193.18
<br />1° 51'
<br />2':i7'
<br />2° 58'
<br />3° 431
<br />IOI.-15
<br />32'
<br />181.39
<br />1° 59'
<br />20 25 '
<br />°l0'
<br />3°58'
<br />3
<br />101.33
<br />34°
<br />171,01
<br />2° o6'
<br />20 33�
<br />30 21'
<br />4° 12'
<br />I0I.48
<br />360
<br />_J61.8d_
<br />20 13'
<br />-2°'41'.
<br />3' 33'
<br />4' 26'
<br />ioi.66
<br />38`
<br />,.153.58
<br />2°.20'
<br />20 49'•
<br />:. 3° 44'
<br />4° 40'.
<br />101.85
<br />40°
<br />146.19
<br />2° 27'"
<br />20 57' '
<br />30 55'
<br />4° 54'
<br />zo2. o6
<br />42'
<br />139.52
<br />20.34'
<br />3° 05'
<br />4° 07'
<br />5o 08'
<br />102.29
<br />440
<br />133.47
<br />2° 4,i'.
<br />3' 13
<br />40 18'
<br />5° 22'
<br />102.53:
<br />-460
<br />127.97 '
<br />2° 48'.
<br />. ._302I,
<br />4' 29'
<br />5° 36'
<br />102-76
<br />48°
<br />122'..92
<br />20 55'
<br />3° z9'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° oa'
<br />3° 3g'
<br />- 4° 51'
<br />6° 04'"
<br />Io3.24
<br />52°'
<br />114.06
<br />3° 09'
<br />3° 46'
<br />50 o2'
<br />6° 17'
<br />103.54
<br />540II0.II
<br />-
<br />3° 16
<br />3° 54'
<br />5° 13'
<br />31
<br />103.84.
<br />56°:
<br />ro6.5o30
<br />22
<br />q° 02.
<br />5° 23'
<br />6°44'
<br />IO¢.I¢
<br />58°'
<br />103.14.
<br />3029 1
<br />4° 10'
<br />5° 341
<br />6° 57'
<br />104.43
<br />6o°.
<br />ioo.00
<br />°35'
<br />3035 1
<br />°18'
<br />4018 ,
<br />5° 44'
<br />7° II,
<br />104.72
<br />T R tan o tan � I. •. R = T cot, .z I Chord def. = chord$
<br />60 R
<br />T
<br />Sin. J,1) R V
<br />l D
<br />Sin. D: = So Sin. ' No. chords
<br />R'. E ='R ex. sec s I. `
<br />Sin.,10 °= 5o tan• a I E = T' tan I Tan. def. _ ? chord def,
<br />T`
<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 -1.'. Multiply the given distance by .01745 (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 .61W, 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 ioo, Alt. io.io2=200=.5-.1oo-E.5=1oo•5 hyp•
<br />Given Hyp. loo, Alt..25.23a=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 ,i i, and divide by 7.-
<br />.
<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, •8d2. The combined cor-
<br />rection is negative,," ..
<br />PROBABLE ERROR: If,dt, da, da, etc. are the discrepancies of various
<br />results from the mean; and if Ida=the sum of the squares"of these dif1cr-
<br />ences and n=the. number of observations; then the probable error of the,
<br />mean= + 0.6745 oda
<br />n (n-1)
<br />SOLAR EPHEMERIS. 'Attention is called to the Solar Ephemeils .for
<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 1V: = Minutes
<br />in Decimals of a•Degree.
<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
<br />.3667
<br />32
<br />.5333'
<br />42
<br />.7000
<br />52
<br />.8867
<br />80500
<br />4
<br />.
<br />13
<br />.2167
<br />23
<br />.3833
<br />33'
<br />.5500
<br />43 -
<br />:7167
<br />53
<br />.8833
<br />L
<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 />.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 />58.9667
<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 />1 .1667
<br />20
<br />.3333'
<br />30
<br />:5000
<br />11 40
<br />1 .6667 11
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE
<br />V. - Inches.in' Decimals of a Foot.
<br />,
<br />1-16
<br />3 32
<br />3=16
<br />5-16
<br />,.0052
<br />,0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />'.0313
<br />:0417 .(521
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />,0833
<br />.1667.
<br />.2500
<br />:3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667 .7500
<br />.8333
<br />.9167
<br />
|