|
VIII
<br />TA13LU IL - Radii, Ordinates and Deflections. Chord -100 ft.
<br />Deg.
<br />Radius
<br />Mid,
<br />Ord.
<br />Tan.
<br />Diet.
<br />DeF•
<br />Dist.
<br />D'
<br />IFt
<br />Deg.
<br />Radius
<br />Mid
<br />Ord
<br />Tsa'
<br />Dist_,.
<br />Dd.
<br />Dist.
<br />�'
<br />i Ft.
<br />2°.,17'
<br />t.
<br />It.
<br />ft
<br />tL
<br />181.39
<br />1.059'
<br />ft.
<br />ft.
<br />ft,
<br />t.
<br />340
<br />0`10'
<br />34377,
<br />.036
<br />.145
<br />•291
<br />0,05'
<br />71
<br />819.0
<br />1.528
<br />6,105
<br />12.21
<br />2. to
<br />20
<br />17189,
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395.12.79
<br />2° 27'
<br />2.20
<br />30
<br />11459,
<br />.109
<br />.436
<br />.873
<br />0.15
<br />130
<br />764.51.637
<br />i° o8
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8591.4
<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 />1
<br />5729.6
<br />.218
<br />.873'•1.745
<br />3° 09'
<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 />1.555
<br />7.411
<br />14,88
<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 />7.556
<br />15.14
<br />2.60,
<br />30
<br />3819.8
<br />.327
<br />1.309,
<br />2.618
<br />0.45
<br />9
<br />637.3.1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2.909
<br />0,50
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />1G. 27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.53
<br />30
<br />603,8
<br />2.074
<br />8.281
<br />16.56.2.85
<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
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />5164.4
<br />2.292
<br />9.150
<br />18.30
<br />3.16
<br />30•
<br />2292.0
<br />.545
<br />2.1S1
<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 />.562
<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 />18
<br />478-3
<br />2.620
<br />10.45
<br />20,91
<br />3.60
<br />a
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />439.3
<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 />1!
<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 '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 />7.271'1.25
<br />10
<br />3559.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322,5
<br />.945
<br />3.718
<br />7.561'1.30
<br />30
<br />348.3
<br />;606
<br />14.35
<br />28.70
<br />4.93
<br />30
<br />1273.6
<br />.952
<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 />.935'16.64
<br />N.
<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 />237.9
<br />4.:374
<br />17.37'.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 />18.22
<br />36.44
<br />fr,W
<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 />6.640
<br />30
<br />1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.6
<br />5.035
<br />19.94.
<br />39.87
<br />6.90
<br />40
<br />1011.5
<br />1-237
<br />4.943
<br />9.686
<br />1.70
<br />24
<br />340.5
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />5D
<br />982.6
<br />1.273
<br />6.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.25
<br />7.50
<br />6
<br />955.4
<br />1.309
<br />6.234
<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 />6,018
<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 />200.7
<br />6,139
<br />24,19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1,.418
<br />b: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 />51.7n
<br />9.00
<br />The middle ordinate in inches for any cord. of length (C) is equal to 0012 C'
<br />multiplied by the lrliddle ordinate taken froln the above table, Thus, if it
<br />desired to bendel. 30 ft, rail to fit a 20 degree curve, its middle ordinate should
<br />be .0012X900X9.1B3 or 2.36 inches.
<br />TASI:E III.' Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius,
<br />50
<br />2 sub chord - sin of 'x' def. angle
<br />R'
<br />Lcngth
<br />of arc
<br />for 100 ft,
<br />din: i def. anx.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30'193.18
<br />51'
<br />1°.SI,-
<br />2°.,17'
<br />2°58'
<br />•3°43'
<br />101.15
<br />32°
<br />181.39
<br />1.059'
<br />2°.25
<br />3° 10
<br />3'58'•
<br />lor.33
<br />340
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3°21'
<br />4 .T2'
<br />101.48
<br />36°
<br />161.80 '
<br />2°:I3`
<br />2, 41'
<br />3° 33'
<br />4°26'
<br />1oI.66
<br />380
<br />153.58 "
<br />2° 26'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />101.8.5
<br />40°
<br />146-19•
<br />2° 27'
<br />2° 57
<br />3° 55'
<br />4° 54'
<br />102.o6
<br />42°
<br />134.52 -.
<br />2?'34'
<br />30 05
<br />40 07
<br />i° o8
<br />102.29
<br />44°
<br />133 47
<br />2° 41'
<br />3 13'
<br />4° 18,
<br />5° 22''
<br />102,53
<br />460
<br />127.137
<br />2° 48'
<br />3° 21'
<br />3 29'
<br />5° 36'2.102,76
<br />.9333
<br />480
<br />122.92.
<br />2° 55'
<br />3° 29`.
<br />4° 40
<br />5° 5o'
<br />103.0 0
<br />50°
<br />I18.3I
<br />.3° p2'
<br />3° g8'
<br />4° 5T`
<br />6°.04'
<br />103.24
<br />52°
<br />114, 06
<br />3° 09'
<br />3° •46'
<br />,5° 02'
<br />6° 17'
<br />163-54
<br />54°
<br />110,11
<br />3° 16',
<br />3° 54'
<br />•5° 13'
<br />6° 31'
<br />103.84:
<br />56°..
<br />1o6. 5o
<br />3° 22' '
<br />4° 02'
<br />5° 23'
<br />60 44'
<br />104-14 ,
<br />580
<br />I03.14
<br />3° 29'
<br />4° Io'
<br />5° 34'
<br />6' 57'
<br />104-43-
<br />600
<br />loo . oo
<br />3' 35'
<br />4° is'
<br />5* 44
<br />7' 11.
<br />104 - 72
<br />ix
<br />CURVE FORMULAS
<br />T Wtan i I R, = T cot..; I chord'
<br />5o tan I Chord def. _
<br />T 0:..5 I) 50
<br />54It
<br />R=
<br />Sin, z : go Sin. ; L)
<br />D No, chords = L
<br />R E. = R ex. sec a f D'
<br />50 tan..= ] -
<br />Sin. ,l U' ' E = T tan J 1 Tan. def. = ;chord def.
<br />P.
<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 fora giveli distance and deflection.
<br />Rule I. : Multiply the given distance_ by .Or745 (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 Ar1GLE THrnxcLEs. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given
<br />'Base too, Alt, to. to' =zoo=.5. too+.5=too-5 hyh•
<br />Given Hyp. too, .alt: 25.252-200=3.125..500-3.125=96,875=13c1se.
<br />Error in first example, .002; in last, .045.
<br />To find Tons of Rail in one mile of track: multiply•weight'.ler yard.
<br />by I1, 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 />PRnnARLE ERROR. If di, d2, da, etc. are the discrepancies of various
<br />results from the 'mean, and if Ede =the suns of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean Zdz_
<br />-0,6745. n(n-1)
<br />SOLAR,EPI-IEMERIs. 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, 3N6 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 />IF
<br />„0167
<br />lie
<br />.1833
<br />21'
<br />.3500
<br />31Y•
<br />.5167
<br />411
<br />'.6833.
<br />51'
<br />'.850D
<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 />.7167.
<br />'53
<br />RR33
<br />4
<br />.0667
<br />14
<br />,.2333
<br />24
<br />,4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9DOD
<br />5
<br />.0833
<br />1.5
<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 />,1157
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9.100
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.96D7
<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 />S333
<br />60
<br />1.0000
<br />TAnl.r•, 1'. ---Inches in Dccinla9s of a Foot.
<br />1-16 3-32? yr 114 s s -
<br />Y 3-16 1 5-1s e s s i,
<br />0.052 .0078 .0101 .01,56 .0208 I .0260 .0313.0.117 .0521 .0625 .0729
<br />1 ? 3 4 5 ti 7 5 9 10 II
<br />.0833 .1667 .2500 .3333 .4167 .5000 8833 .6titi7 .7500 `� .8433 .411 D7
<br />
|