|
f VIII
<br />TABLE IV- Radii, Ordinates and Deflections. Chord =100 ft. :,...,`_ CURVE FORMULAS
<br />Deg.--
<br />Radius
<br />Mid
<br />Ord
<br />Tsn.
<br />Dist.
<br />• Def...
<br />Diet'
<br />e. for :
<br />1Ft.
<br />-'. Deg.,
<br />Radios
<br />Mid
<br />Ord:
<br />Tan
<br />Dist.
<br />Def.
<br />Dist
<br />Def
<br />] Ft
<br />193.18
<br />1051'
<br />20 17
<br />20 58';
<br />30 43'
<br />101.15
<br />320-`
<br />181:39'
<br />t.
<br />t,
<br />t.
<br />3.58'
<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 />20
<br />17189.'.-.073
<br />'lof .66
<br />.291
<br />- .582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.39512.79
<br />40
<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 />A45.582
<br />.3..05'--'
<br />30 �3,-.
<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;`6875,.5
<br />102.76
<br />.18E
<br />.727
<br />1.454
<br />0.25
<br />" S
<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 />11.745
<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 />c• 20.1..4297-.3-
<br />58°
<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 />..3271:309
<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 />.3641,454
<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 />.4001.600
<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 />2864.9.436
<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 />.401.
<br />2148'.8
<br />;.582
<br />2:327
<br />4.654
<br />0.80:.
<br />' 30,
<br />499.1
<br />2.511.10.02
<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 />S..
<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 />.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 />-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 />'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 />1.351
<br />17
<br />338.3
<br />3.716'14.78
<br />29.56
<br />5.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />1S
<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 />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 />274.4
<br />.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='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 />1.7525
<br />231,0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />6
<br />956.4
<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 />859-9,1
<br />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 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 TIL : Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />50
<br />LJ sub chord = 'sin of 's 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 />25 Ft.
<br />for 100 ft.
<br />30°
<br />193.18
<br />1051'
<br />20 17
<br />20 58';
<br />30 43'
<br />101.15
<br />320-`
<br />181:39'
<br />--'1° 59'
<br />20-�5'
<br />-30-10'-
<br />3.58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />20 33'
<br />3° 21'
<br />4° 12'
<br />I01.48
<br />360
<br />161.80;,';
<br />-2° 13!
<br />2° 41'
<br />3033"
<br />' 4° 26'
<br />'lof .66
<br />380
<br />-153 .58
<br />20 20'
<br />2° 49'�
<br />3044
<br />4° q0'
<br />IOI.85
<br />40
<br />146.19.
<br />2 27
<br />_,2 57.
<br />=
<br />3 'S5,
<br />;4 5
<br />102.06
<br />42°
<br />4139 52
<br />-03'.17
<br />2° 34'1
<br />3' 05,- ,
<br />40,07'
<br />5° 08 .
<br />102.29
<br />44°
<br />.::
<br />20 41'
<br />.3..05'--'
<br />30 �3,-.
<br />40 18'
<br />, .'5° 22'
<br />102.53
<br />460
<br />127.97- ,
<br />. 2° 48'
<br />3° 21, .
<br />40 29,
<br />.5° 36:
<br />102.76
<br />48°.'
<br />.122:92, .
<br />20 55'
<br />. 30 29.
<br />4° 40'
<br />5°:50'
<br />103.00
<br />50° '
<br />118:31
<br />3.° 02':
<br />30 38,
<br />4o 51,
<br />6o 04'
<br />103.24
<br />520
<br />114,06"'
<br />3°,09'
<br />3o 46' ..
<br />5o O2'
<br />•6° 17'
<br />103.54
<br />540
<br />: 11 0-11I
<br />30 16'
<br />30 54'
<br />60 131
<br />=. '60 31'
<br />103-84
<br />39
<br />14
<br />49
<br />.8167
<br />59
<br />44f
<br />104-14
<br />58°
<br />i 103,
<br />3° 29'
<br />4° 10'
<br />50 34'
<br />60 57'
<br />104.43
<br />50,
<br />100.00
<br />3°:35'
<br />4018'
<br />S°.44'
<br />7°'I I'
<br />104.72
<br />T R tan z I R= T cot. ' I chord$
<br />50 tan T I 2. Chord def. ,
<br />T R
<br />50
<br />R -
<br />in. z D :_
<br />=
<br />Sin. I D _ 5o Sin. I D No. chords I
<br />R E = R ex."sec 8.I D
<br />Sin. z D. = 50• t 1 I E ._ -T tan } 1. Tan. def. _ } chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />i 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.t Multiply given deflection by 57.31 and divide the product by
<br />the given distance.
<br />>. To -find deflectiomfor a given, angle and distance. Multiply the angle
<br />by :01'745,"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 Ion; Alt. Io.102=200=_5. I00+-5=Io0.5 hyp-
<br />Given Hyp: loo, Alt. 25.252=2oo=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 1; 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 curpature alone'is, closely, 8d2: ' The combined cor-
<br />rection is negative. -
<br />.-PROBABLE ERROR."If d,, dz, da; etc. are -the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares bf,these differ-
<br />ences'and n=the number of observations, then the probable error of the
<br />mean = ids
<br />-0.6745 n(n-1)
<br />SOLAR EPHEMERIS. Attention i. .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 />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 />' -8667
<br />;3,
<br />.0500-
<br />13
<br />,.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />"
<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 />-7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />_47
<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 />--10 -
<br />,1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50,
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -Inches
<br />in Decimals of a Foot.-_ -
<br />1-16
<br />3-32
<br />y
<br />3-16
<br />X
<br />5-16
<br />5s
<br />%
<br />%
<br />?4
<br />",0052
<br />.0078
<br />.01304
<br />.014.56
<br />.0'08.0860
<br />.0
<br />.0 g17
<br />..0921
<br />.06025
<br />.Oi19
<br />[.1667
<br />X13
<br />I
<br />I
<br />.0833
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
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