|
VIII r;
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg. ''Radius"
<br />L Radius•
<br />-50
<br />.Mid.
<br />Ord.
<br />•Tan.
<br />Dist.
<br />(Dd. ,.
<br />Dist."
<br />Def..._
<br />' Ft.
<br />-,Deg•
<br />Radius
<br />-
<br />. Mid.
<br />Ord.
<br />- Tan.
<br />.Dish
<br />W.
<br />Dist.
<br />Def.
<br />1 r
<br />2° 17'
<br />t
<br />t
<br />10,1.15
<br />32°_193.
<br />i81.39
<br />1° 59'"
<br />t. '
<br />t.
<br />30 58,
<br />t.
<br />34°
<br />0"LO'
<br />34377
<br />t'- 036
<br />.145
<br />;.231
<br />0 05
<br />"'7°
<br />819(0
<br />1`.528
<br />6:105
<br />12.21
<br />2.10
<br />`20.
<br />7'30
<br />17189
<br />' 073
<br />.291
<br />5S2
<br />'-187.3
<br />0.10
<br />20'
<br />781 8
<br />1.600
<br />• 6.395
<br />12.79
<br />2.20
<br />`40
<br />11459
<br />•'.109
<br />,.436
<br />139.52
<br />0.15
<br />30
<br />764.5
<br />1'.637'
<br />6:540
<br />33.08
<br />2.25
<br />2° 41'
<br />8594.4
<br />:'.14,5
<br />.582
<br />1:164
<br />0.20'
<br />.40
<br />747.91,1.673
<br />3° 21'
<br />6:685
<br />13.37
<br />2.30
<br />50
<br />687,5:5
<br />..152
<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 />11`
<br />5729.6
<br />-:218
<br />'.573
<br />'1.745
<br />0.30
<br />20
<br />683.2
<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 />_
<br />30
<br />140
<br />674.7
<br />1.855
<br />7.411
<br />1.1.82
<br />2.55
<br />-20
<br />74297.3
<br />•,.291
<br />1.464
<br />i 2.327
<br />0.40.
<br />-.,,
<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 />(2.618
<br />0.45
<br />9 '.
<br />637:'3
<br />1.065
<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 />614.0
<br />2:037
<br />;8.136.16.27
<br />2.50
<br />,50
<br />3125. 4400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8,2:074
<br />'8:281
<br />16.56
<br />2.65
<br />2:
<br />2564'9
<br />;.436
<br />1.745
<br />3:490
<br />0.60,
<br />40,
<br />593.:1
<br />2:1'1U
<br />8:426
<br />16.55
<br />2.90
<br />1.10
<br />. 2644.6
<br />',473
<br />f.891
<br />13.781
<br />0.65
<br />10
<br />573.7
<br />2':183.
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2455.7.509'2.036
<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 />.045
<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 />1407
<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 />t50
<br />_2022.4
<br />.618
<br />2.472
<br />14.945
<br />0.85
<br />12 ;
<br />47842:620
<br />10.45
<br />20.01
<br />3.60
<br />3 "r
<br />'1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.,730
<br />1089
<br />21.7 7
<br />3.75
<br />10
<br />.1309.6
<br />.691
<br />2.763
<br />1 5'.526
<br />Ir,.817
<br />0.95:
<br />13 -
<br />441.7
<br />2.839
<br />11:32
<br />22.64
<br />3.90
<br />1'20'
<br />1719:1
<br />-.727.2.903
<br />1.00.
<br />.. 30
<br />425.4
<br />.949
<br />11.75
<br />23.51
<br />4.05
<br />:30.
<br />•1637.3
<br />1.764
<br />3.054
<br />:6`.108
<br />1.05
<br />14
<br />410.3'
<br />.058
<br />12. 18'r
<br />24737
<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--23.24
<br />4..35
<br />.50
<br />-1495.0
<br />--]432.7.:.873
<br />..836
<br />3.345
<br />6t 689
<br />1.15
<br />15
<br />383. 1j
<br />3..277
<br />13.05
<br />20.11
<br />4.50
<br />4''
<br />3.490
<br />`6.980
<br />1.20
<br />30
<br />370:8'
<br />.387
<br />13:49 `
<br />26.97
<br />4.65
<br />110
<br />1375:4
<br />".909
<br />3.635
<br />:7.271
<br />1:25
<br />16
<br />359.3'3.496
<br />13.92
<br />27.54
<br />4.50
<br />20.
<br />30
<br />1322:5
<br />1273.6
<br />'.945
<br />.932
<br />3.718
<br />3.9267.852
<br />7.561
<br />X8.143
<br />1.30
<br />1.35
<br />30
<br />17
<br />348.5
<br />33S.3
<br />3.606
<br />3.716
<br />14.35
<br />14.•78
<br />28.70
<br />29,56
<br />4.95
<br />5.10
<br />40'
<br />1'50
<br />1228.1
<br />1.018
<br />4.071
<br />1.40
<br />18 ''
<br />319.6,3.935
<br />15.64
<br />31.29
<br />5.40
<br />1185:8
<br />1.055
<br />4.217
<br />'4.362
<br />8.433
<br />1.45
<br />19
<br />302.9,4.
<br />155
<br />16.`51.
<br />33.01
<br />5.70
<br />8
<br />1146.3
<br />1.091
<br />8.724
<br />1.50
<br />20 :
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10.1109.3
<br />20•.
<br />-1074,7
<br />1.127
<br />1,164
<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 />130
<br />1042.1
<br />1.200
<br />4.653
<br />4.798
<br />9.305
<br />9.596
<br />1.60
<br />1.65
<br />22 s
<br />23
<br />262:0
<br />250.8
<br />4.814
<br />5.035
<br />19:08
<br />19.94
<br />38.36
<br />39.87
<br />6.60
<br />6.90
<br />40•
<br />1011.5
<br />1_.237
<br />4.943
<br />9:886
<br />1.70
<br />24 ' .,240.5
<br />5:255
<br />20.79
<br />41.68
<br />7.20
<br />50.
<br />082.6
<br />1.273
<br />5.088
<br />10:18
<br />4.75
<br />25
<br />231.0
<br />5.•476
<br />21:64
<br />43.29
<br />7.5U
<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 />7.80
<br />10
<br />929.6.1.346
<br />5.379
<br />10:76
<br />1.85
<br />27
<br />214.2
<br />1.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />6.524
<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
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />5L.76
<br />9.00
<br />The middle ordinate in inches for any cord, of length (0) 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. 1, 1,
<br />TALE III. :Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />L Radius•
<br />-50
<br />sub chord
<br />R = sin of I def: angle
<br />Len th
<br />of arc
<br />for 100 ft.
<br />sin.II def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. y
<br />25 Ft.
<br />-30?
<br />193 _1_8
<br />1° 51'
<br />2° 17'
<br />2° 58' M
<br />3° 43'
<br />10,1.15
<br />32°_193.
<br />i81.39
<br />1° 59'"
<br />- 2° �5.
<br />_ 3°-I o,
<br />30 58,
<br />_ 1or.33
<br />34°
<br />171.01
<br />20 o6'
<br />2° 331
<br />3° 21'
<br />4° 12'
<br />101,48
<br />36°
<br />161.80 -
<br />2° 13,.
<br />2° 41'
<br />3°-33'
<br />; 4°26' -
<br />tor.66
<br />38° .
<br />.-153.58
<br />2° 20'
<br />20 49,
<br />3° 44'
<br />4°, 40'
<br />161.85
<br />40°
<br />146.19_
<br />i° 27'
<br />2° 57,
<br />30.55'
<br />4° 54
<br />r62.66
<br />42°
<br />139.52
<br />2° 34"
<br />3° 05'
<br />4° 07'
<br />5° 08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13,
<br />4° 8'..
<br />5° 2z' •
<br />102.53..
<br />46°
<br />127-97
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />5036'
<br />102.76
<br />480
<br />122.92
<br />2° 55'
<br />3° 29'
<br />;1° 40',
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />30 38,
<br />10 51'
<br />6-04 1
<br />103.24
<br />52`
<br />114.o6
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110.11
<br />3° W
<br />3° 54,
<br />9° 13,
<br />6° 31'
<br />103.84
<br />56°
<br />1o6.!5o
<br />3° 22'
<br />4° 02'
<br />5' 23
<br />6° 44
<br />104- 14
<br />}
<br />580,
<br />103.114
<br />30 29'
<br />40 1o',
<br />5a 34'
<br />60 57'
<br />104'• 43
<br />60
<br />100.00
<br />3 35
<br />4 18
<br />5 44
<br />7 ]I
<br />104.72
<br />IX,
<br />•
<br />"CURVE" FORMULAS
<br />T= R tan ; 1
<br />T R= T t. z l chord'
<br />'So tan i I. - . coChord def. = o
<br />Sin. ; D _ 50
<br />RSin: 8 D I
<br />Sin. ; D = 50 No. chords = D
<br />R E- R"ex. sec z 1
<br />i ' 5o tan . I_ . Tan. def. = i chord def.
<br />Sin. z D ,= T E= T tan } I
<br />'I'he ,square of_ a6y' distance, divided by twice the radius, will equal
<br />the'distance from tangent to curve, very nearly.
<br />To find anglc fo'r.a,given distance and deflection.
<br />Rule i. Multiply"the given distance by .01745 (def. for I for L 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' fiiid deflection for, a gly the, angle and distance. Muitipangle
<br />by: 61745, and the product by the'distance.
<br />r
<br />GENERAL. DATA
<br />RiGHT ANGLE TRIANGLE'S. Square the altitude, divide by twice the
<br />base._. Add quotient to base for hypotenuse. • ,
<br />Given Base,ioo; Alt. 10.102-'200=.5. Iood-.5=1oo.5 hyp.
<br />Given Hyp.'ioo, Alt. 25.252_200=3.I25. i00-3.i25=96.87=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 0.574d2, where d is the distance in miles.
<br />The correction" for curvature alone. is closely, ,d?. The 'combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, d2, da, etc. are -the discrepancies of 'various
<br />results from the mean, and .if Bd2=the sum of the squares of thesg'diffcr-
<br />ences arld n=the number of observations, then the probable error of -the
<br />mean= ., .. Ede
<br />10.6745 n(n_I)
<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 sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc. ' _/1
<br />-,-..,. ,, nF _1%4;nntPS ;n Deririials of a Devree.
<br />1/
<br />.0167
<br />111V,.1833
<br />-Inches 1n Decimals of a Foot.
<br />217.
<br />.3500
<br />311
<br />.5167
<br />417
<br />.6533
<br />51'
<br />52
<br />.8500
<br />2
<br />.0333
<br />12
<br />..2000
<br />22
<br />23
<br />.3667
<br />32
<br />33
<br />.5333
<br />42
<br />43
<br />.7000
<br />.7167
<br />53
<br />.8667
<br />.8333
<br />3
<br />4
<br />.0500
<br />13
<br />14
<br />.2167
<br />24
<br />.3833,
<br />.4000
<br />34
<br />.5500
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5.0833
<br />.0667
<br />l5
<br />.2333
<br />'.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />46
<br />.7500
<br />55
<br />56
<br />.9167
<br />6
<br />.1000-
<br />16
<br />..2667
<br />26
<br />27,
<br />.4333
<br />36
<br />37
<br />.6000
<br />.6167
<br />47
<br />.7667
<br />.7833
<br />57
<br />.9333
<br />.9500
<br />7
<br />8
<br />.1167
<br />.1333
<br />.1[7
<br />l8
<br />.2833
<br />.3000
<br />28
<br />.4500
<br />.4667
<br />38
<br />.6333
<br />48 .
<br />.8000
<br />58
<br />59
<br />.9667,
<br />. 9 ',
<br />,.1500
<br />l9
<br />..3167.
<br />29
<br />30
<br />.4533
<br />39
<br />40
<br />.6500
<br />49
<br />50
<br />.5167
<br />.8333
<br />60
<br />.9333
<br />1.0000
<br />-10
<br />.1667
<br />1 20
<br />1 .3333 11
<br />.5000
<br />.6667
<br />TAI)LE V.
<br />-Inches 1n Decimals of a Foot.
<br />1-16,
<br />3-32
<br />5F
<br />3-16
<br />%
<br />5-16
<br />°�
<br />.0313
<br />%d
<br />.0417
<br />.0521
<br />.0625
<br />r.�
<br />.0729
<br />.0052.
<br />1
<br />0833
<br />.0078
<br />2
<br />I .1667
<br />.0104
<br />3"
<br />.2500
<br />.01,%
<br />4
<br />.3333
<br />I .0208
<br />.4167
<br />1
<br />I .0260
<br />6
<br />.5000
<br />7
<br />.5833
<br />8
<br />I .6667
<br />9
<br />.7 500
<br />10
<br />.8333
<br />Il
<br />.9167 .
<br />
|