|
V(74/
<br />7MI- .- t i - _ _
<br />TABLE IL -Radii, Ordinates. and Deflections. Chord =100 ft.
<br />Deg: °
<br />Radius
<br />Mid •
<br />'Ord."
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />Ifor
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />• , Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />DeL
<br />1 Ft.
<br />2°:17-
<br />t,
<br />t
<br />t.
<br />ft.
<br />1
<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 />0.05
<br />'7'
<br />819.0
<br />1•.528
<br />6.105
<br />.
<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
<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 />8:540
<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 />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 />4.745
<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 />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 />8:281.16.56
<br />2.85
<br />a
<br />2864.9':.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 />1
<br />3.780.65
<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 />2.035
<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 />2.1811
<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 />E.. :.1910.1
<br />1.655
<br />2.618
<br />5.235
<br />0.90
<br />.30.459.3
<br />2.730
<br />10.89'
<br />21.77.3.75
<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
<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 />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 />4.50
<br />6' .::,'1432.7
<br />.873
<br />3:490
<br />6.980
<br />1.20
<br />X30.
<br />370.8
<br />3:387
<br />,261.11
<br />13.49,
<br />26.97
<br />4:65
<br />10
<br />:1375.4
<br />:.009,3.635
<br />7.271
<br />1.25
<br />16•
<br />359.3
<br />3.496'13:92'
<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 />.9823.926
<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 />1228:1,1.018
<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 />8:30
<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 />9.596
<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 />60.
<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 />'929.8
<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 />1:346
<br />6.379
<br />10.78
<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 />1.082
<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 />51.76
<br />9.00
<br />The middle ordinate in inches foi 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 III. ; Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />SU
<br />34 sub'chord
<br />R =sin of } def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. } def, ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />10 5il
<br />2°:17-
<br />2o581
<br />3° 43�
<br />IOI.15
<br />32°
<br />181.39
<br />1° 59'
<br />2' 25'
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34°171.OI
<br />4
<br />2° o6'
<br />2° 331.
<br />3° 21'
<br />40 12'
<br />I0I.48
<br />360
<br />161.80
<br />2° 131"
<br />2° 41'.
<br />3° 33'.
<br />. 4° i6'
<br />ioi.66
<br />38°
<br />153.58.
<br />20 20'
<br />20 49f
<br />- 3° 44�
<br />4°"40'
<br />101..85.
<br />40°
<br />146.19
<br />.2? 27"
<br />2'.57'.
<br />30 55'•
<br />4'-54' ,
<br />102.o6
<br />42°'-
<br />139.52
<br />2°34'
<br />3°05'
<br />4°07'
<br />S°08'
<br />1'02:29
<br />44°
<br />133.47.
<br />20.41'
<br />3°.131.
<br />40 18'
<br />•5°22'
<br />.--102.53
<br />.460
<br />j27.97
<br />2° 48':
<br />3° 21'
<br />40 29'
<br />5036
<br />102.76 "
<br />480
<br />122.92.
<br />20 55''
<br />30'29'
<br />4° 40'
<br />50501
<br />103;00
<br />5o°
<br />118.31
<br />- 3° 02'
<br />3' 381.
<br />4° 51'
<br />6004 1
<br />103'.24
<br />520
<br />114. o6
<br />30 09'
<br />3° 46'
<br />5° 02'
<br />6' 17'
<br />103:54
<br />54.
<br />110-'11
<br />3° 16'
<br />3° 54�
<br />5° 13''
<br />6- 31'
<br />103.84 .
<br />560.
<br />106.50
<br />3° 22'
<br />4°•02'
<br />50 23'
<br />6° 44'
<br />104.14
<br />58°'103:14
<br />.8167
<br />3029
<br />4010'
<br />5° 34' '
<br />6° 57'
<br />104.43
<br />60°
<br />100.00
<br />3035,
<br />4° 18'
<br />_ 5° 441
<br />70Ill.
<br />1 104.72
<br />CURVE FORMULAS
<br />0
<br />T= R tan J I R= T cot. ' I chord9
<br />-50 tan 2 I - 2 Chord def. _
<br />T" .Sin..J DR 50 R
<br />=
<br />Sin. D. = 50 Sin. D' No, chords = I
<br />R E ='R ex. sec z I
<br />Sin.' D - So tan T a I E T tan J 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 .01945 (def. for I° for 1' 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 Igiven angle and distance. Multiply the angle
<br />by .bi745, 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. 10.102,_200=.5. 1oo-1-.5=1oo•5 hyp•
<br />Given 'Hyp. Ioo, Alt. 25.252 . 200=3.125. 100-3.125 =96.875 =Base.
<br />Eiror'iri 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 flivide by 7: ' .- .
<br />LEVELING:. The -correction' for curvature and refraction, in feet
<br />and decimals of feetis-equalto 0.674d2, where d is the. distance in miles.
<br />The .correction for curvature alone is closely,.Jd2: The combined cor-
<br />rection: is.negative.
<br />-PROBABLE ERROR. If d;, de; da, etc. are the discrepancies of various
<br />results from the mean ;.and if 7-da=the sum of the squares of these difiicr-
<br />ences and n=the number of observations, then the probable error of the,
<br />mean t 0.6745 n (n-1)
<br />SOLAR EPHEMERIS. Attention is'called to the Solar Ephemen"s.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 oil the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas, Natural andI ogarithmic Functions;
<br />and Logarithms of 'Numbers:
<br />TABLE IV. - Miniites
<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 />12.
<br />.0333
<br />12
<br />.2000
<br />22 '
<br />.3667
<br />32
<br />.5333
<br />42.7000
<br />4
<br />52
<br />.8667
<br />3
<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
<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
<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 />710
<br />.1667
<br />20
<br />:3333 1130
<br />1 .5000
<br />40
<br />.6667
<br />50
<br />.93331,
<br />60
<br />1.0000
<br />-TABLE
<br />V. - Inches in Decimals of a Foot.
<br />1-16
<br />3-32H
<br />3-16
<br />Y 5-16
<br />%
<br />H
<br />.0052
<br />..0078
<br />.0104
<br />.0156
<br />.0208 .0260
<br />.0313
<br />.0417 .0521
<br />.0 25. .0729
<br />1
<br />2
<br />3
<br />4
<br />5 6
<br />7
<br />8 9.
<br />10 11
<br />.0883
<br />.1667
<br />.2500
<br />.3333.
<br />.4167 .5000
<br />.5833
<br />.6667 .7500
<br />.8333 .9167
<br />
|