|
11
<br />VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deq:"
<br />Radius .
<br />'Mid.
<br />Ord
<br />Tan.
<br />Dist.
<br />Det.
<br />Dist.
<br />for
<br />1 Ft.
<br />Deg
<br />Radins
<br />Mid
<br />Ord,
<br />Tan
<br />Dist,
<br />Def.
<br />Dist
<br />Dom•
<br />1 Ft.
<br />2° 17'
<br />2° 58'.
<br />3° 43'
<br />I01.15
<br />3z
<br />...151..39-....
<br />1 59
<br />10
<br />t,
<br />t.
<br />t.
<br />t.
<br />34°
<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 />" 26
<br />17189.
<br />.073
<br />.291
<br />':582
<br />0.10•
<br />20'
<br />781.81.600
<br />-
<br />460. ,..
<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 />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 />T. 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 />638.2
<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 />i. 40
<br />. 3437:9.
<br />.364
<br />4.454.
<br />2.909
<br />0.50:
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />16.27
<br />2.80
<br />.,s50._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 />t10
<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 />1.072
<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 />'.618
<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 />2.472
<br />4.945
<br />0.85'.12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />1910.1...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 />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 />S-10.
<br />-10...1719.1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />.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 />.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 />.168
<br />12.62
<br />26.24
<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 />.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 />'18
<br />359.3
<br />.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 />.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 />.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 />.374
<br />17.37
<br />34.73
<br />6.00
<br />10-
<br />1109.3,1.127
<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 />1074:7
<br />1.164
<br />4.653
<br />.9.305
<br />1.60
<br />22
<br />262.0
<br />.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 .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 />e
<br />955.4,1.309
<br />5.234
<br />10.47
<br />1.80
<br />28
<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 />b.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />b.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />5.40
<br />30
<br />881.9
<br />1.418
<br />b.689
<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 />b.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 />Degree
<br />of
<br />Curve
<br />Radius
<br />SU _
<br />e sub chord � sin of I def. angle
<br />Length
<br />of are
<br />for 100 ft :
<br />sin. z`def. ang.
<br />12.5', Ft.
<br />15 Ft.
<br />20 Ft.
<br />25,Ft.
<br />300
<br />193.18
<br />I° 51'
<br />2° 17'
<br />2° 58'.
<br />3° 43'
<br />I01.15
<br />3z
<br />...151..39-....
<br />1 59
<br />10
<br />2 25
<br />3 Io
<br />3 58
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />rf�l
<br />30 21'
<br />4° 12'
<br />101.48
<br />360
<br />161:80
<br />.2° 13'
<br />-2° 411..
<br />_3° 331-
<br />.. 4o 26'
<br />ioi.66 .
<br />38'
<br />153.•.58
<br />IIG 9, The middle ordinate in inches for any cord of length (0) is equal to .0012 C'
<br />tt (tmultiplied by the middle ordinate taken from the above table. Thus, if it
<br />(�7desired 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 />t�. TABLE III. 'Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />SU _
<br />e sub chord � sin of I def. angle
<br />Length
<br />of are
<br />for 100 ft :
<br />sin. z`def. ang.
<br />12.5', Ft.
<br />15 Ft.
<br />20 Ft.
<br />25,Ft.
<br />300
<br />193.18
<br />I° 51'
<br />2° 17'
<br />2° 58'.
<br />3° 43'
<br />I01.15
<br />3z
<br />...151..39-....
<br />1 59
<br />10
<br />2 25
<br />3 Io
<br />3 58
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />30 21'
<br />4° 12'
<br />101.48
<br />360
<br />161:80
<br />.2° 13'
<br />-2° 411..
<br />_3° 331-
<br />.. 4o 26'
<br />ioi.66 .
<br />38'
<br />153.•.58
<br />2° 20'
<br />2° 49'
<br />44'
<br />4° 40'
<br />IoI.85
<br />-
<br />460. ,..
<br />_
<br />-146.19,
<br />-2°,�7,,..
<br />2°.57'
<br />.3°
<br />30 5J'
<br />40 54,
<br />.102.06
<br />42o
<br />139 • 52.
<br />2° 34�.
<br />3° 05'.
<br />4° 07
<br />5° 08
<br />102.29
<br />'441'
<br />:133.47
<br />2° 411.
<br />30 13,.
<br />-4° 18'
<br />5° 22'
<br />102:53
<br />.;
<br />46° _
<br />.' _
<br />::• I2j.97.
<br />i0-48'.
<br />3°21'. -
<br />4° 29'
<br />50 36'
<br />102..76
<br />4go .,
<br />-L 1221.92
<br />2° 55' ,
<br />3° 29'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />=50.°
<br />, it&:31. _ ,
<br />..30.02.'
<br />3° 38`
<br />,4° 5i'
<br />6° 04`
<br />103.24
<br />sz'
<br />11y. 06::
<br />:.'3° oq'
<br />30 46'
<br />5o O2'.
<br />6° 17'
<br />103.54...
<br />54.0
<br />110'11 -. i
<br />30 i6'
<br />,: 30.541
<br />5° 13'
<br />6°.3�'
<br />103.84
<br />#5tr°
<br />Io6:5o
<br />-.
<br />k-3° 2z'
<br />4° 02...
<br />50 23'
<br />6° 44` `.
<br />Io4: rd' -
<br />580.
<br />103.14 .
<br />-` 3'129'. .'.--
<br />do 16'
<br />50.34'
<br />60.57
<br />.10443
<br />{0°
<br />;ioo.00-.
<br />':3°35'
<br />4018,.
<br />..5°,44
<br />7° 11'
<br />104.72
<br />IX
<br />CURVE FORMULAS
<br />T= 1l tan i I R= T cot. Z I chord' .
<br />,I, _ '50 -tan 2 I 50 . Chord def. = R
<br />Sin. Z D R =
<br />Sin. 2 D 5o Sin. 2 D No. chords = I
<br />D
<br />R E= R ex. sec
<br />Sin. 2 D = 5o tan 2 l . E = T tan } I Tan. def. = 2 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 1 ° 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 :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 loo, Alt. 10.102-200=.5: 100-}-.5=foo.5 hyp.
<br />Given Hyp. ioo, Alt. 2S.252-,. 200=3.125. 100-3.125=96.875=Base.
<br />Error in first example, .602; in last, .045-
<br />'To
<br />045.'To find Tons of Rail in one mile of track: multiply weight per yard
<br />by I I' and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in 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, 102. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, d2, d3, 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= Ed2
<br />-0.6745AJ n(n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />ihe`current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 38x6 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 />magnetic declination; arithmetic constants, etc.
<br />• TARr.F TV. -Minutes in Decimals of a Degree.
<br />1/
<br />:0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />31
<br />.5167
<br />411
<br />.6833
<br />511
<br />.8500
<br />•2
<br />12
<br />.2000
<br />22
<br />.3667
<br />32,
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0333
<br />13
<br />.2167
<br />23
<br />.3833
<br />33'
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0500
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0667
<br />15
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6 -
<br />.0833
<br />16
<br />.2500
<br />.2667
<br />26
<br />-4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />C. 7,:
<br />.1000
<br />17.
<br />27
<br />.4500
<br />137
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1167'
<br />18
<br />.2833
<br />28
<br />.4667
<br />139
<br />.6333
<br />48
<br />00
<br />067
<br />58
<br />.9667
<br />9
<br />.1333
<br />19
<br />.3000
<br />29
<br />.4833
<br />.6500
<br />49
<br />.838
<br />59
<br />.9833
<br />10
<br />.1500
<br />1 .1667
<br />20
<br />.3167
<br />1 .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 hoot.
<br />1-16 3-32 Yg 3-16 % 5-16
<br />0052 1 .0078 .0104 .0156 .0208 .0260 .0313 .0417 .0521 .0625 .0729
<br />10 Il
<br />.0133 I .1667 .I 2500- .3333.1 .4167 I .5000 I .5833 .6667 .7500 .8333 .9167
<br />V
<br />_1\
<br />
|