|
VIII
<br />Te13i,E 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 />De '
<br />1for
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def•
<br />for
<br />1 r t.
<br />2° 58'
<br />30 43'
<br />I0I.15
<br />3 °..:.
<br />2
<br />181'
<br />39
<br />__°59'
<br />I
<br />° 5,...
<br />2 �2
<br />t,
<br />t.
<br />t
<br />t.
<br />171.01
<br />0"10'
<br />34377:
<br />.036
<br />.145
<br />- .291
<br />0.05
<br />7'
<br />819.0.1:528
<br />•2° 41'
<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 />6.395
<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 />.185
<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 />201
<br />688.2
<br />1:8197:266
<br />IIo. it
<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 />1.300
<br />12.618
<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.S0
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />055
<br />30
<br />603.8
<br />2.074
<br />8.281'16.56
<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 />2455.7.509
<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 />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 />8
<br />1010.1
<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 />2.7G3
<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 />2.949-11'.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 />1562.0
<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 />.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 />...009
<br />3.635
<br />7.271
<br />1.25
<br />16 -
<br />359.3
<br />.496
<br />13.92
<br />27.84'4.80
<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-'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 />.1.127
<br />4.507
<br />.9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22 .36.44
<br />6.30
<br />20
<br />1074'.7
<br />1:164
<br />4.653
<br />9.3Q5
<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 />`9.856
<br />1.70'.-.24
<br />240.5
<br />5.255
<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 />6' -.
<br />955.4
<br />1.309
<br />5.234
<br />10.47=
<br />1.80
<br />26
<br />222.3
<br />6.697
<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 />.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 />.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 />199.7.6.360
<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 />51.78
<br />9.00
<br />'1•ne mrdc119 ordinate1-n inches for any cord of length (0) is equal to .0012 0'
<br />multiplied by the truddle ordinate taken from . the above table.. Thus; if it
<br />desired to bond 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches.
<br />TAin rg III. Deflections�for Sub Chords for Short Radius Curves.
<br />Degree
<br />Of
<br />Curve
<br />Radius
<br />50
<br />sin, It def. ang.
<br />sub chord
<br />i R = sin of 8 def. angle
<br />Length,
<br />a arc
<br />for 100 ft.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. ,
<br />25 Ft.
<br />30°
<br />193.18
<br />I° 51'
<br />2° 17'
<br />2° 58'
<br />30 43'
<br />I0I.15
<br />3 °..:.
<br />2
<br />181'
<br />39
<br />__°59'
<br />I
<br />° 5,...
<br />2 �2
<br />_.3°. ,:
<br />IO
<br />..3°58,:..__
<br />101:33'
<br />340
<br />171.01
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />116i ..8o ;::
<br />- 2° 13'..
<br />•2° 41'
<br />3° 33'
<br />4° 26'.,
<br />ioi .66
<br />380
<br />'153.58
<br />2° 20'
<br />20 49'
<br />3° 44'
<br />4° 40
<br />-ioi.85
<br />o
<br />40.
<br />-146.19"
<br />- o- i---•
<br />2,27 -
<br />o
<br />2 '51
<br />o r
<br />3 55
<br />o-
<br />4.54'
<br />102.06
<br />420
<br />139:52
<br />2° .34,
<br />3°.05'
<br />4° 07'
<br />S' 08
<br />";102.29 •_
<br />.44°
<br />133.47-
<br />.: 2° 41,
<br />3° 13.
<br />4° 18'
<br />5° 22'_ .
<br />102.53
<br />.46° .-
<br />.. 127.97 -
<br />' -2° 48' _
<br />3°.21'
<br />4°.'29'. _
<br />5° 36'
<br />102.. 76
<br />,4.
<br />122: 2-
<br />9
<br />20 •
<br />55
<br />0 2 "
<br />3 9
<br />4:40'
<br />o
<br />5 50
<br />I03.00
<br />50°
<br />118.31.
<br />'3' 02'
<br />3° 3$' .
<br />4 51.
<br />6° 04,
<br />103.24
<br />-520 .,+
<br />114.06
<br />30 091 .
<br />3° 46'
<br />5° oz'
<br />6° 17' .
<br />103.54
<br />54°
<br />IIo. it
<br />3° 16'
<br />3° 54'
<br />50 13'.
<br />.6° 31'-
<br />103.84
<br />56° .f
<br />io6.50
<br />3° 22'
<br />4° 02'
<br />S° 231
<br />6° 44',
<br />104.14
<br />580 j
<br />103.14
<br />3o 29�
<br />40 lo'
<br />. 5034 �
<br />60 57�
<br />104.43
<br />60
<br />100.00
<br />3 35
<br />4 18-
<br />5 44
<br />7 II
<br />104.72
<br />IX
<br />CURVE FORMULAS
<br />T = 1t tanI R = T cot. ; I chord'
<br />T _ 5o tan- Z" I Chord def. R
<br />50
<br />Sin. z D R
<br />Sin. 12 D 5o = Sin. z_D No. chords = I
<br />R E= R ex. -sec 2 I D
<br />3
<br />Sin. s D= 5o t T z I E= T tan } I Tan. def. = z 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 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 .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 ioo, Alt. 16.102=zoo=.5. Ioo+.5=ioo.5 hyp• .
<br />Given, Hyp. -loo, Alt. 25.252=200=3.125. Ioo-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 />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, 3d2: The combined cor-
<br />rection is negative. .
<br />PROBABLE ERROR: If dl, 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= Id
<br />-0.6745
<br />SOLAR EPHEMERIS. 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; 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 suis and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc..•
<br />• TARr V. IV. -Minutes in Decimals of a Degree.!
<br />1t
<br />'.0167
<br />111-
<br />.1833'
<br />21'
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />511
<br />.8500
<br />2
<br />.0625
<br />.0729
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0333
<br />,12
<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 />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.0833
<br />16
<br />.2667
<br />26
<br />-.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1000
<br />17
<br />.2833
<br />' 27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57:
<br />.9500
<br />8
<br />.1167
<br />18
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />'.9833
<br />9
<br />.1333
<br />19
<br />.3000
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />10
<br />.1500
<br />1 .1667 11
<br />20
<br />.3167
<br />1 .3333 11
<br />30
<br />1 .5000
<br />40
<br />1 .6667
<br />50
<br />.8333
<br />60
<br />L0000
<br />TABLE V.
<br />-Inches In Uecimals ot a 1'001.
<br />1-16I 3-32
<br />.0052 .0078
<br />)e
<br />.0104
<br />3-I6
<br />.0156
<br />%
<br />.0203
<br />5-16
<br />.0260
<br />.0313
<br />.0417
<br />I
<br />.0521
<br />.0625
<br />.0729
<br />I? 2 I
<br />3 I
<br />4 I
<br />5 I
<br />6 I
<br />7
<br />-8
<br />9
<br />10
<br />11
<br />.0833 .1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
|