|
VIII
<br />TABLE IL - Radii, Ordinates and Deflections, Chord =100 ft.'
<br />The mfddIe ordinate .n inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the lnfdd�e 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 />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />f.
<br />.D r
<br />l or
<br />Deg
<br />Radius
<br />Mid
<br />Ord.
<br />Tan.
<br />Dist,
<br />Def.
<br />,Dist.
<br />Def-_
<br />1 r t.
<br />193•.18
<br />t.
<br />- IL
<br />TE_
<br />tL
<br />101.15
<br />32°
<br />181.39
<br />it.
<br />r t.
<br />I t
<br />3° 58'
<br />0"10'
<br />34377.
<br />.036
<br />.145.291
<br />2° 33'
<br />0.05
<br />7.
<br />S19.0
<br />1.528
<br />6.105
<br />12.21
<br />?>10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.5S2
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.79
<br />2.2U
<br />ttio 30
<br />11459.
<br />.100
<br />.436
<br />.873
<br />0.15
<br />30
<br />761_5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />rift' 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 />21
<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.;.0
<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 />14.52
<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 />1.592
<br />7.558
<br />15.11
<br />2.60
<br />30
<br />3519.8
<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 />3137.9
<br />.304
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />6t4.6
<br />2.037.
<br />8.136
<br />16;.27
<br />2.80
<br />50
<br />3125.4.400
<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 />10•
<br />573.7
<br />2.183
<br />8.716
<br />17.43
<br />3.W
<br />20
<br />2155.7
<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 />it
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.00
<br />40
<br />2148.8
<br />.592
<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 />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 />j 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 />6.168
<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 />396.2.3.168
<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 />41432.7
<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 />1375.4.909
<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 />1.30
<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 />17
<br />335.3
<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 />319.4
<br />3.935
<br />15.64
<br />31,29
<br />5.40
<br />50
<br />11&5.8
<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 />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 />27-1.4.594.18.22
<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 />9.596
<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 />50
<br />982.6
<br />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />6.476-21.64
<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 />5.697
<br />22.50
<br />44.99
<br />7.S0
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918'23.35
<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
<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 1
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9:00
<br />The mfddIe ordinate .n inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the lnfdd�e 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 />Radius
<br />50
<br />A sub chord -sin of z def. angle
<br />.R
<br />Length
<br />of arc
<br />Curve
<br />sin. i def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />1 25 Ft:
<br />I for l00 ft.
<br />30°
<br />193•.18
<br />10 5t'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />101.15
<br />32°
<br />181.39
<br />I° 59'
<br />2° 25'
<br />3° 10'
<br />3° 58'
<br />101.33
<br />340
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3 ° 2t'
<br />° 12'
<br />4
<br />I0I.48
<br />36°-
<br />161.8o
<br />20 13'
<br />2° 41'
<br />3° 33'
<br />4° 26'
<br />lot.66
<br />380
<br />153.5$
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />101.8.5
<br />40°
<br />146. t9
<br />2° 27'
<br />2° 57'
<br />30 55'
<br />4° 54'.
<br />102.o6
<br />42°139.52
<br />35
<br />20 34'
<br />3° 05'
<br />40 07'
<br />5? 08
<br />102.29
<br />44°
<br />133.47
<br />2° 4t'
<br />3° 13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97
<br />2048
<br />3°.21'
<br />4° 29'
<br />5° 36'
<br />102.76
<br />48°
<br />122.92
<br />20 55'
<br />3° 29'
<br />4° 40'
<br />5° 5o'
<br />103.00
<br />50°
<br />1 t8.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.24
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46
<br />S° 02'
<br />6° 17'
<br />103•.54
<br />54°
<br />IIO.Ii
<br />3° 16'
<br />3° 54'
<br />50 13'
<br />6° 31'
<br />103.84
<br />56°
<br />106.•50
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14
<br />3° 29
<br />4° 10'
<br />S° 34
<br />6' Si'
<br />104.43
<br />6o°
<br />100.00
<br />3°35'
<br />4°18'
<br />5°44'
<br />7°11'
<br />104-72
<br />by .0 1745, and the product by the distance.
<br />GENERAL. DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide; by twice the
<br />lbase. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 10.10'=200=.5. 1oo+.5=io0.5 hyp.
<br />Given Hyp. loo, Alt. 25.252=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 r, 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 />1 The correction for curvature alone is closely, d'. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2, d3, etc. are the discrepancies of various
<br />t" 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= Ydl
<br />10.6745
<br />SOLAR EPHE&mRIS. 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 sun and Polaris; stadia measurements:
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE. IV. -Minutes in Decimals of a Degree.
<br />11
<br />.0167
<br />Ix
<br />1833
<br />CURVE FORMULAS `�'�
<br />.3500
<br />L
<br />T= ot�anl s Il
<br />5 §
<br />R= T cot. z 1
<br />chord'
<br />Chord def. =
<br />z o0
<br />T =
<br />1. Sin. D
<br />R = 50
<br />R .
<br />: .
<br />I; Sin. ; U = �o
<br />a
<br />Sin. 2 ll
<br />No. chords = I
<br />Z
<br />R
<br />E= R ex. sec 3 I
<br />D
<br />42
<br />Sin, 12 D= 5o tan I
<br />E= T tan t I
<br />Tan. def. = s chord def:
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />f The square of any distance, divided by twice the radius, will 'equal
<br />T
<br />the distance from tangent to curve, very nearly.
<br />'�--
<br />To find angle for a given distance and deflection.
<br />Z 3 0
<br />Rule 1. Multiply the given distance by .01745 (def. for I° for I ft.
<br />27 Gj
<br />see Table 11.), and divide given deflection by the product.
<br />14
<br />Rule 2. Multiply given deflection by 57.3, and divide the liroduct by
<br />_,e 6
<br />the given distance.
<br />�-
<br />To find deflection for a given angle and distance. Multiply the angle
<br />i
<br />. z
<br />by .0 1745, and the product by the distance.
<br />GENERAL. DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide; by twice the
<br />lbase. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 10.10'=200=.5. 1oo+.5=io0.5 hyp.
<br />Given Hyp. loo, Alt. 25.252=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 r, 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 />1 The correction for curvature alone is closely, d'. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2, d3, etc. are the discrepancies of various
<br />t" 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= Ydl
<br />10.6745
<br />SOLAR EPHE&mRIS. 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 sun and Polaris; stadia measurements:
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE. IV. -Minutes in Decimals of a Degree.
<br />11
<br />.0167
<br />1833
<br />21/
<br />.3500
<br />31./
<br />.516;7
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.0333
<br />l2
<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 />.7167
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />15
<br />.2333
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7:7,00
<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 />.9600
<br />39
<br />.6500
<br />49
<br />.167
<br />59
<br />.9833
<br />fl833
<br />10
<br />.16607
<br />20
<br />.33330
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TAHI,F. 1'. --Inches in Decimals of a Foot.
<br />1-16 3-32 is 3-18 1.3 5-16 ?'e i7 5'e 64 °s
<br />-0052 I .0078 .0104 I .0156 .0208 I .0260 .0313 .0417 .0521 I .062:, 0720
<br />1 3 4 4 :, 1; 7 S 9 30 11
<br />.3:333 A167 .5
<br />.0833 .1667 .2500 000 .5833 .6667 .75tH 8333 9167
<br />
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