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VIII
<br />TABUQ II. = Riidii, Qrdinates and Deflections. Chord=100 ft.
<br />Deg_-'
<br />I
<br />! Radius .a'�rd
<br />hLd
<br />Tan.
<br />°
<br />Bef.
<br />)1st.
<br />"Def
<br />11fFf.
<br />.. Deo-,'
<br />Radius
<br />NEI
<br />1Jrd:
<br />Tan. BeI.
<br />. Dist. Dist.
<br />Def•
<br />if Dr
<br />FE.
<br />-
<br />t.
<br />ft.
<br />fc.
<br />ft.-
<br />32°
<br />151.39
<br />it.
<br />ft:
<br />tt, tt.
<br />� 3° 58'
<br />0'.10'
<br />34377.
<br />.036
<br />:145
<br />":241:
<br />0.03
<br />7'.
<br />.0
<br />819
<br />1.5 25
<br />6..105 1;3.21
<br />2.10
<br />20
<br />'17164
<br />.0 3
<br />.201
<br />.:2
<br />530.10
<br />153.58
<br />20'
<br />751.8
<br />1.600
<br />C 95 12.7'
<br />2.20
<br />3O
<br />1145q.'.109
<br />2° 27'.
<br />°436
<br />.873
<br />0.10
<br />30
<br />764.5
<br />1.637
<br />6.511) 13. G3
<br />2.25
<br />40
<br />8504 4
<br />.145
<br />.5S2
<br />1.10E
<br />0.20
<br />40
<br />747.9
<br />1.073
<br />G%`5 13.37
<br />2.'0
<br />50
<br />6875 5'
<br />.1S2
<br />.727
<br />1,:15.1
<br />0.2 5
<br />8
<br />716.5
<br />1.746
<br />:
<br />1:06 13.95
<br />?.§0
<br />1
<br />47296
<br />.218
<br />.S73
<br />1.745
<br />0.30
<br />20
<br />638.2
<br />1.319
<br />7.236 11.53
<br />2.50
<br />10
<br />4011.2
<br />,255
<br />1.018
<br />2.03G
<br />0.35
<br />30
<br />G74.7
<br />1.555
<br />7.411 1.1.92
<br />2.55
<br />20
<br />4297.3.
<br />.291
<br />1.164
<br />2.327
<br />0.40,
<br />40
<br />G61.7
<br />1.592
<br />7.556 15.11
<br />2.60
<br />00
<br />3219-8
<br />327
<br />1.309
<br />2.616
<br />0.45
<br />0
<br />G37.3
<br />1.965
<br />7.646 15.69''
<br />2.73
<br />40'
<br />3437.9
<br />.'61I1.454
<br />2.909
<br />0150
<br />^0.614.6
<br />2.037
<br />8,136 16.27
<br />2.30
<br />50.
<br />31257'-
<br />40011.600
<br />3.200
<br />6.55
<br />:30
<br />GM.8
<br />2 -0rY
<br />8,'2S1 16.56
<br />2.55
<br />2
<br />2864:9
<br />4745
<br />.."
<br />1:
<br />3.490
<br />0.60
<br />40
<br />:,03.4
<br />2.113
<br />5:426 6. S.5
<br />.00
<br />I0'
<br />2044.G
<br />.473
<br />1.091
<br />3:751
<br />0.65
<br />10
<br />5711.7
<br />2.133
<br />5.716 17.43
<br />3.00
<br />20
<br />2455.7
<br />-.509
<br />2.03E
<br />4. -072
<br />0.70',"
<br />30
<br />546.-4
<br />2.292
<br />9.180 1S. 2013.15
<br />30
<br />2292.0
<br />°545
<br />2181
<br />4.363
<br />0.75
<br />11
<br />52t.7
<br />2 A-0'
<br />9.55.; 19.1:;
<br />3.30
<br />40
<br />2145.8
<br />.5S2
<br />2.827
<br />4.654
<br />O.EO
<br />30
<br /><<44.'1
<br />2.511
<br />10:02 20.0113.45
<br />50
<br />2022.4
<br />.615
<br />2,472
<br />4.045
<br />0.3:,
<br />12
<br />479.:1
<br />3.620
<br />10.45 20.91
<br />3.G0
<br />3 ..
<br />1910.1.
<br />.655
<br />2:613
<br />5.235
<br />0.00
<br />30
<br />•59.3
<br />2.730
<br />i0, S� 21.-
<br />3.75
<br />10
<br />1609.6
<br />.691
<br />"G3
<br />5.526
<br />0.95
<br />t3441.7
<br />2.839
<br />11.:1_ �C2.64
<br />3.40
<br />20-
<br />1719.1
<br />.727
<br />2.603
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />2.449
<br />11.75 (22.;1
<br />.0¢
<br />30::;1637.3
<br />.764
<br />3. 05.j
<br />6.109
<br />1.0.6.
<br />14
<br />•110.3
<br />3.0;8
<br />12.15 21.27
<br />4.20
<br />40
<br />1562.9
<br />".SOO
<br />3.199
<br />6.308
<br />1.10
<br />3o
<br />3;,6.2
<br />3.1113
<br />12.62 25.2.1
<br />4.35
<br />50"
<br />1495.0
<br />.836
<br />3.345
<br />G. GSC)
<br />1'.Lj
<br />15
<br />353.1
<br />3.277
<br />13.05 26.11
<br />'1. 50
<br />4
<br />1432.7
<br />°-3
<br />3.490
<br />6.950
<br />t.20
<br />30
<br />370.8
<br />3.387
<br />13.19 26 07
<br />,4.65
<br />10
<br />1375.4
<br />.904
<br />3.633
<br />7:271
<br />1-.25
<br />1G
<br />359.3
<br />.3.45"
<br />13.92 `_`7.81'!
<br />O
<br />20
<br />1.322.5
<br />'.945
<br />3.710
<br />7.5G1
<br />1.30
<br />30
<br />345.°5
<br />3, (MG
<br />11.35 28.70
<br />4.�5
<br />30
<br />1273.6
<br />.032
<br />.",.1)23
<br />7.952
<br />1.35_
<br />17
<br />33S-3
<br />3.716
<br />14.73 29.56
<br />.10
<br />40
<br />1223.1
<br />I.01S
<br />4.671
<br />S. 143
<br />1.40
<br />1S
<br />31'9.6
<br />3.925"'15.34
<br />31._o
<br />5.40
<br />50
<br />1155.9
<br />1.055
<br />4.217
<br />5.433
<br />1.45
<br />19
<br />302-9
<br />•4.155.10,.51
<br />33.Oi
<br />°.7o
<br />b
<br />1146..',
<br />1.00I
<br />4.362'
<br />5,724
<br />1'.50
<br />RD
<br />257.9
<br />4.37.1
<br />17.37 34.73
<br />6.00
<br />10'
<br />1109.3
<br />1.127.4.507
<br />9'.01,1
<br />1.55
<br />21
<br />274.4
<br />4., 59-1
<br />15.22 3G.
<br />G,30
<br />'20
<br />1074.7
<br />1.1;,4
<br />4.653
<br />9.305
<br />1,60
<br />212
<br />202'.0
<br />4.814
<br />19.05 3S.16
<br />6.00
<br />36
<br />1042.1
<br />17200
<br />4.795
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />;19.94 :'4.S7
<br />G.90
<br />40
<br />1011 ;
<br />1.237
<br />4.9-13
<br />4, SSO
<br />1.70
<br />24
<br />249.5
<br />5 255
<br />20.70. 41.:;217
<br />.20
<br />50
<br />982 6
<br />1.273
<br />5.0SS
<br />'10.15.
<br />1.75,
<br />25
<br />231.0
<br />5.576
<br />1 64 43.2
<br />97.50
<br />G
<br />9 a.,f
<br />1309
<br />5.234
<br />10.47
<br />1.891
<br />26
<br />232.3
<br />5.697
<br />22.57 11.40
<br />7.SO
<br />TO
<br />•,929.6
<br />1.346
<br />5•.379
<br />'0.76.-1.85
<br />21
<br />21.1.2
<br />.5.018
<br />23. S5 "5:0
<br />3'.";0
<br />=- 20
<br />005.4
<br />1.352
<br />5.524
<br />11.05
<br />1.90•
<br />':8.
<br />20G.7
<br />6.130
<br />24.14
<br />8.40
<br />30
<br />981-9
<br />1°418
<br />5.669
<br />11.34'
<br />1.95
<br />29
<br />199.716.300
<br />25.04 50-0713.70
<br />40
<br />559.9
<br />1.450
<br />5.514
<br />11.63
<br />12.00 1
<br />30
<br />1 I93.2
<br />6:563
<br />25.55 51.7319.00
<br />The twiddle orcin to is inches for cord of leug6h (C) is equal to.001'2 G'
<br />multiplied by tho middlo ordinate taken from the above table. 'ihi:s. if it
<br />desired to bend a 30 ft. rail to fita. 10 degree curve, its micicile.ordinat0 sl'ould
<br />be .U012X9U0X2.183 or 2°36 inches. -
<br />TABLE .ITT, Deflections for Sub Chords for Short Radius Curves.
<br />Degree .
<br />of
<br />Curve
<br />Radius
<br />50
<br />sub chord
<br />R =sin of z def. a_agle
<br />Len,Ea
<br />of arc
<br />� for Ivo ft.
<br />sin.I def. ang.12.5•
<br />Ft.
<br />45 1 t.
<br />ZD Fc.
<br />25 Ft.
<br />•30°
<br />193: i8_
<br />1°;5:1-,
<br />-1°
<br />_° 17,
<br />2° 58,
<br />3'_43'
<br />1ol.13
<br />32°
<br />151.39
<br />59
<br />2°'25'
<br />3° lo'
<br />� 3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />'° 33'
<br />3° 71'
<br />° 12'
<br />IOI.48
<br />360 1
<br />16.1- So .
<br />20 13'
<br />° 41'
<br />3° 33'
<br />4° 26'
<br />lot, 66
<br />3$°
<br />153.58
<br />2° 20'
<br />2° 49'3°
<br />44`
<br />4° 40'
<br />toI.85
<br />40°
<br />146.19
<br />2° 27'.
<br />2° 5T
<br />3° 55`
<br />4° 54'
<br />ro2.06
<br />42°
<br />- 139.52
<br />2° 34'
<br />3° 05`
<br />4° 07`
<br />5° 08
<br />102.29
<br />44°
<br />133.47
<br />"° 4t'
<br />3° 13'
<br />4° z$'
<br />S° 2_+
<br />102.53
<br />46°
<br />127°97
<br />2° 48
<br />3° 21'.'
<br />4° 29'
<br />56 3G'
<br />102.76
<br />4$°
<br />122.92
<br />2° 5-1
<br />3° 29+
<br />4° 40'
<br />S° 5�'
<br />103.00
<br />50°
<br />168.31
<br />3° 02,`
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />1o3.24
<br />52°
<br />114.06.'
<br />3° 09`
<br />3° 46'
<br />5° 02'
<br />6° t7.'
<br />103.54
<br />54°
<br />IIo. I I
<br />3° 16'
<br />3° 54'
<br />13
<br />6° 31
<br />103.84
<br />56°
<br />to6.50
<br />.3° 2'-'
<br />4° 0'--'
<br />S° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.'14
<br />3° 29' -
<br />.4° 10'
<br />5° 34'
<br />6° 57'
<br />104.43
<br />600
<br />t00.o0
<br />3° 35'
<br />4° is'
<br />S° 44'
<br />70 11'-
<br />104-72
<br />IX
<br />:'CURVE _ FORMULAS '..
<br />T = I2 tori I chord2
<br />R T cot. I
<br />,I = �o.talt I 'Chard def. _.. R
<br />_Sin. } D 50
<br />50 R Sin. a D I
<br />Si.. 'r D. _ ' r - l IN o. chords = -
<br />E = R. ex. sec I D
<br />5o tan a. I 1
<br />E = T tan j I tan. def. = � chord def.
<br />The square of 'any: distance, divided bi 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 1. - T,4ultiply the given distance by .61743. (clef. for z° for i ft:
<br />see Table II.), and divide given -deflection_ by the product.
<br />Rule 2. 17ultiply given deflection by 57.3; and divide the product by
<br />toe 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 />RiGaT A_,Tr _: TRIAKCLEs. Square the altitude, divide by ti ice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base ioo, Alt. ro.Io2=2oo=.5. 100=.5=100:5 hyp.
<br />Given Ily-p. ioo, Alt:25.252-2oo=3°125. 100-3°125=96.375=Base:
<br />Error in first example, .00--; in last, .045.
<br />To find Tons of Rail in onc,mile of tracl.:• nwltip€y ,vcight ncr yard
<br />by i t, and divide by 7.
<br />LEVELIIG. The correction for curvature and refraction, hi .feet
<br />ar.d decimals of feet•is equal to 0.574d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, 3,1;1. The combined cor-
<br />rection is r-egative. w
<br />PrcrAimn'ERROiZ. If d„ da, d,,;etc. are the discrepar-eies of v::
<br />
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