|
VIII IX'
<br />TABLE II.-- Radii, Ordinates and Deflections. Chord =100 ft.- - CURVE FORMLTI:AS - - -
<br />Deg.
<br />.Radius
<br />Mid.
<br />Ord.
<br />Taa.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def,
<br />'Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />10I.I$
<br />it.
<br />t.
<br />ft.
<br />ft.
<br />I
<br />101.33
<br />ft,
<br />ft..
<br />it.
<br />ft.
<br />4° 12'
<br />6'10'..34377.
<br />360
<br />.036
<br />-145
<br />.281
<br />0,05
<br />7°
<br />819.0
<br />1.528
<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 />6875.6
<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 />1.745.0.30
<br />6-44 1
<br />20
<br />688.,2'1.819
<br />103.14 3' 29'
<br />7.26E
<br />14.532.50
<br />6° 57'
<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 />2.61,8
<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 />603.8.2.074
<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 />.,
<br />40
<br />693.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2044.6
<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 />2.293
<br />9.160
<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 />.532
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />99.1
<br />2.511
<br />10.02
<br />20.01
<br />3.45
<br />.50
<br />2022.4
<br />.618;2.472
<br />4.945
<br />0.85
<br />12 -
<br />178.3
<br />2.6x20
<br />10.45
<br />"0.91'3.60
<br />8
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />4:59.3
<br />2.730
<br />10.89 -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 />22.0-1
<br />3.90
<br />20
<br />1719.1
<br />.727.2.908
<br />5.817
<br />1.051
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />20
<br />1637.3..764.3.054.
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.053
<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 />6.980,1.20'
<br />30
<br />370.8
<br />3:357
<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 />I3.92
<br />27.84
<br />".80
<br />20
<br />1322.5
<br />.945.3.718
<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 />.9S2
<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 />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 />302.9'4.155
<br />16.51
<br />33.01
<br />5.70
<br />S
<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 />1,8.22
<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 />•1.814
<br />19.08
<br />3S.I0
<br />0.60
<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 />41.55
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088
<br />10.1S
<br />1.75.
<br />;E5
<br />231.0
<br />5.476
<br />21.64
<br />43,25
<br />7.50
<br />6955.4
<br />1'.309.5.234
<br />10.47
<br />1:80,
<br />26222.3
<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 />21.4.2
<br />5.918
<br />23.35
<br />46,69
<br />5.10
<br />20
<br />905.1
<br />1.382
<br />5.:,24
<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 />1.05
<br />29
<br />199.7
<br />6.36025.04
<br />50;07
<br />8.7U
<br />40
<br />859,9
<br />1.455
<br />5.814
<br />11.03
<br />2.00
<br />30
<br />1193.216:583
<br />25.S8
<br />51,76
<br />9.00
<br />The middle ordinate ininches for any cord of length (C) is equal to .0012 C=
<br />multiplied by tho middle ordinate taken from the aiwse 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 2.3Ginches.
<br />TALE III.Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />Radius. snh•cliord
<br />50 A a -sirs of 1, def. angle
<br />Length
<br />of
<br />Curve -
<br />R
<br />sin. a def. ang. 12,5 Ft. 15 Ft. 20 Ft. ---15-Ft,
<br />of are
<br />for 190 ft.
<br />30.°_. .
<br />' 193, t8 1° $i'
<br />2° 17`
<br />'.56'
<br />j° 43'
<br />10I.I$
<br />32°
<br />181.39 10 59
<br />2°25
<br />3° Io'
<br />3° 58'
<br />101.33
<br />340
<br />171.01 2' ob'
<br />2° 3'
<br />3° 21'
<br />4° 12'
<br />loi.48
<br />360
<br />161.8o 2° r3'
<br />2° 4'1'
<br />3'33'
<br />4°26'
<br />1o1.66
<br />38°
<br />153-58 -2° 20'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />fol .85
<br />40°
<br />14b.1g 2° 27' '
<br />2° 57' .
<br />30 55'
<br />4° 54'.
<br />102.o6
<br />• 42°
<br />139.52 20 34'
<br />3' 05
<br />4° 07'
<br />5° 08'
<br />102.29
<br />440
<br />133.47 2° 41..
<br />3' 13'
<br />4° i8'
<br />$° 22'
<br />102.53
<br />46°
<br />127.97. 20 48'3°21'
<br />.7500
<br />4°2g'
<br />$°36'
<br />102- 76
<br />48°
<br />122.92 2° 55r
<br />3° 29,
<br />4° 40
<br />S° 50'
<br />103-00
<br />,.500
<br />118.31 3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.24
<br />52°
<br />114.06 3° 09`
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />540
<br />Ilo.lt 3° 16'
<br />3° 54'
<br />5° 13
<br />6° SI!
<br />103.84
<br />56°
<br />Io6.5o 3° 22'
<br />4° a2'
<br />5' 23'
<br />6-44 1
<br />104.14
<br />58°
<br />103.14 3' 29'
<br />4' 1o'
<br />5° 34'
<br />6° 57'
<br />104.43
<br />6o°
<br />100.00 3°35'
<br />4°18'
<br />5°44'
<br />7°11'
<br />104.72'
<br />T =__ o tan I. R= T cot: r I Chard def. =chorda
<br />T 50 R
<br />R� Sin. j IJ i
<br />Sin. 1] =. R Sin. D No.chards = I
<br />I = R ex. sec: I D
<br />Sin. D• = 5o t r '2 I E = T tan if Tan. def. _ ch©rd 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 7.' Multiply the given distance by .oi745 (def. for.l° for 1. ft.
<br />see Table II.), and divide given deflection by the product: ' ,
<br />Rule 2. ' Multiply given deflecti6n 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 Tx1ANG1.Es.. Square the altitude, divide by twice the
<br />base. Add. quotient to base for hypotenuse.
<br />Given Base loo, Alt. io.IO2=2oo=.5. 100-x-.5=loo.5 hyp.
<br />Given Hyp. loo, Alt.sS_252^.00 =3:125, ioo-3.128=46.87)=Base.
<br />Rrror in.first example, .o62; In last, .
<br />To find Tons of Rail in one mule of track: multiply weight per+yard
<br />by I1, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in. feet
<br />and decimals of feetis equal to 0.574 d2, where.d is the distance in miles.
<br />The correction for curvature alone is closely," P. The combined cor-
<br />rection is negative.
<br />PROEASLE ERROR. If d1, d,, da, etc. are the discrepancies of various
<br />results from the mean; and if Y42 the sum of the squares of these -differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean = + 0.6745 �' s a
<br />,1 n (n-1) .
<br />SOLAR EPEEINIERis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel d Esser Co., and furnished free of
<br />charge upon request, which is 3.1,-x58 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 oa the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of INTumbers.
<br />TABLE N. - Minutes in Decimals of a Degree. '
<br />1'
<br />0167
<br />11'
<br />.1533
<br />21'
<br />, 3500
<br />31'
<br />.5107 '
<br />41'
<br />.6533
<br />51"
<br />.9600
<br />2
<br />.0333
<br />12
<br />.2600
<br />V.
<br />,3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />58
<br />.5667
<br />3
<br />0500
<br />13.2167
<br />1
<br />23
<br />.3 8.333
<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 />64
<br />,9000
<br />a
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.91G7
<br />6
<br />.1000
<br />16
<br />-2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.70567
<br />56
<br />.9333
<br />7
<br />.1167
<br />11
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />1s
<br />.3000
<br />28
<br />.4667
<br />3S
<br />•6333
<br />48
<br />.8000
<br />58,
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4533
<br />39
<br />.5500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333 11
<br />30
<br />.5000
<br />40
<br />.0667
<br />50
<br />.8333
<br />1 68
<br />1 1.0000
<br />TABLH V. - Inches in Deciml is of a Foot.
<br />1-16
<br />3-32
<br />3-16
<br />516
<br />fg
<br />i§
<br />is
<br />.0052
<br />.0078
<br />.0101
<br />.0156
<br />.0203
<br />.O2G0
<br />.0313
<br />.0417
<br />.0521
<br />.0025
<br />.0720
<br />1
<br />2
<br />3
<br />45
<br />6
<br />7
<br />3
<br />9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />,5833
<br />1 .6667
<br />1 .7500
<br />.8333
<br />.9167
<br />
|