|
VIII Y
<br />TABLE IL - Radii, Ordinates and Deflections. Chord="100 ft.
<br />'Dec. .
<br />.iiadrus.
<br />Ord
<br />Dist.
<br />Dist:
<br />l.
<br />fof. r'..
<br />1 Ft.
<br />±Deg...
<br />Radicis
<br />a
<br />Mid
<br />-Ord.--
<br />-Tan.
<br />Dist:
<br />Def. "'Doi
<br />Dist.
<br />1 Ft.
<br />193.18.
<br />I°. 51'
<br />2° 17'2°
<br />'
<br />58'
<br />3° 43'
<br />I01.15
<br />_320.. _
<br />t,
<br />t.
<br />t._
<br />t:_
<br />_30 58'"
<br />9' W
<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 />-..2W
<br />17189..'):073
<br />101.66
<br />.291.582
<br />153.58-
<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••.436
<br />.4 54 1.
<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 />145.582
<br />3o i3..
<br />(1:164
<br />0.20T.
<br />40-747.9
<br />.6000
<br />1.673,
<br />6:685
<br />13.372.30
<br />40 29'
<br />i• 50.6875:5
<br />102.76
<br />1 182
<br />.727
<br />;1454
<br />0.25L
<br />6
<br />716.8
<br />1:746''.6-.976
<br />50. "-
<br />13.95
<br />2.40
<br />1'�
<br />5729.6
<br />'.218
<br />.873
<br />1.745
<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 />1.411
<br />14.82
<br />2.55
<br />20;;4297:3..291
<br />158°
<br />103-14
<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 />1.1309
<br />.2.618
<br />0.45 ;
<br />'-i 9 1
<br />637.3'
<br />1,:965'
<br />17-.846
<br />15.69
<br />2.70
<br />40:
<br />3437,9
<br />:'.364
<br />1.454
<br />'2.909
<br />0.501'-
<br />20
<br />614.6
<br />2.037:,8:136
<br />16.27
<br />2.80
<br />-'50--
<br />3125.4
<br />1.400
<br />1.600
<br />3.200
<br />0.55,.,,1,
<br />'30'
<br />603.8
<br />2.4
<br />07.
<br />8:281
<br />16:56
<br />2.85
<br />2 .
<br />2864:9.'.436
<br />1.745
<br />:3.490
<br />0.66
<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:.8:716
<br />17.43
<br />3.00
<br />" 20'24557
<br />'.509
<br />2.036
<br />4.072
<br />0.70
<br />`' 130
<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 />I1
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40.'
<br />; 214878
<br />.582
<br />2,327
<br />"4.654'
<br />0.80';;
<br />d ' '` 30,
<br />499:.1
<br />2:511.
<br />10:02',,
<br />20.04
<br />3.45
<br />f.50[12022.4
<br />..618
<br />2.472
<br />14.945
<br />0.85,';12,
<br />1'
<br />478.3
<br />2.620,.10:45•;20.91
<br />3.60
<br />3 "T1910:1
<br />'.655
<br />.2•.6185:235
<br />0.90r j.'
<br />' 30,
<br />459.3
<br />2.730.10.89_21.77.
<br />3.75
<br />..,10'
<br />; 1809.6
<br />1..691,
<br />2.763
<br />X5:526
<br />0.95"
<br />113
<br />441.7
<br />2:839
<br />11-.32_•
<br />22.`6
<br />1719:1
<br />3.90
<br />,!.20c
<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::1637:3
<br />' .764
<br />3.054.
<br />61108
<br />1.05'
<br />114', '
<br />410.3
<br />3.058
<br />12.18'::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 />.143217
<br />•5.873
<br />3:490
<br />*6:980
<br />1,20`
<br />-` 30.
<br />370.8
<br />3.38713.49`
<br />26.97
<br />4.65
<br />} 10,
<br />1375.4
<br />!.909'3.635
<br />7.271
<br />1.25"
<br />16
<br />359.3
<br />3.496'13'.92
<br />27.84
<br />4.80
<br />20f;1322.5
<br />".945
<br />3.718
<br />7.561
<br />1.30
<br />30;
<br />318.5
<br />3.606
<br />141,35.
<br />28:70
<br />4.95
<br />30"
<br />1273.61'.982
<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 />319.6
<br />3.935
<br />15:64_•
<br />31.29
<br />5.40
<br />" 50•+1185:8
<br />1.055
<br />4.217
<br />'8.433
<br />1,45•-
<br />_18,
<br />19.
<br />302.9
<br />:155
<br />16.51'-"33.01
<br />5.70
<br />5
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />201
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />r 10-"•1109.3
<br />1.127
<br />4:507
<br />9.014
<br />1.55
<br />21•
<br />274.4
<br />.594
<br />18.22
<br />36:44
<br />6.30
<br />20,1074:7
<br />1.164
<br />4:653
<br />9'.305
<br />1,60
<br />22
<br />262:0
<br />4.814'19:08'
<br />38,16
<br />6:60
<br />30
<br />1042.1
<br />1.200,
<br />T. 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 />1.237.4.943
<br />9.886
<br />1.70,_
<br />-24
<br />240.5
<br />5:255.20:79-
<br />41.58
<br />7.20
<br />= 50
<br />982.6
<br />11273
<br />5.088.10.18
<br />1.75
<br />'25
<br />231.0
<br />5.476
<br />21.64 -43.28
<br />7.50
<br />6; .=
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80•'-26
<br />222.3
<br />51697
<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
<br />1.455
<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 (U) is equal to .001`2 U'
<br />multiplied by the middle 'ordinate' taken from the above table. Thus, if it
<br />desired to bends 30 ft, rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X900X2 ,183 or 2:36 inches.
<br />TABLE TIL r.Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />i Radius
<br />50
<br />sub chord = sin of $def. angle ;
<br />I R +
<br />Length
<br />of arc
<br />Curve
<br />sin. a def. ang.
<br />12.53 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />300
<br />193.18.
<br />I°. 51'
<br />2° 17'2°
<br />'
<br />58'
<br />3° 43'
<br />I01.15
<br />_320.. _
<br />'--181.-3'9-'-
<br />.�Iou59'-
<br />-_,i° 25'
<br />_ 3°-10'._'-'
<br />_30 58'"
<br />-461:33
<br />340
<br />171,01
<br />2° o6'
<br />2° 33
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°/161-.-80
<br />.7167
<br />z° 13, :
<br />?� 41,
<br />3° 33' -
<br />.4° 26' -.:
<br />101.66
<br />38o
<br />153.58-
<br />z° 20'
<br />2° 49'
<br />3° 44'
<br />-v
<br />4° 46"'
<br />ioI.85
<br />40
<br />.
<br />146.19
<br />_
<br />z 'zj "r
<br />2 -57 -
<br />_
<br />3 55.
<br />.4 54 1.
<br />"l0i:o6
<br />42o
<br />139 52
<br />'° 34'.
<br />,30 05,
<br />4o 071.
<br />.5a 08,
<br />-.102.29
<br />"440 t,
<br />' 133.47
<br />2° 41,
<br />3o i3..
<br />4° 18.
<br />.'5° 22'
<br />102.53
<br />.6000
<br />1-27.97
<br />z° 48'' '.
<br />3° 21'
<br />40 29'
<br />5° 36'
<br />102.76
<br />48o'''
<br />122.92:
<br />20 55'.
<br />`. 30. 29
<br />- 40 40- '
<br />- 5a W
<br />163.00
<br />50. "-
<br />? 118.31
<br />i
<br />3002
<br />3 38
<br />4 5i
<br />6 04.
<br />103.24
<br />5i°' ,
<br />11406'
<br />r 3° 09' ;.
<br />30 46'
<br />5° 02'..
<br />. 60.17'
<br />103.54"
<br />,54°
<br />110. II
<br />30 16
<br />3° 54,
<br />5° 13' '
<br />6° 31'
<br />103.84
<br />56°
<br />Io6.5o
<br />3° 22'
<br />4° 02'
<br />S° 23'
<br />6° 44'
<br />104,14
<br />158°
<br />103-14
<br />3' 29'
<br />40 10'
<br />50 34'
<br />60 57' ':._
<br />104.43
<br />609.
<br />100:00
<br />3°.35'
<br />40 18'
<br />S° 44'
<br />7o 1-I�
<br />104:72
<br />IX
<br />CURVE 'FORMULAS
<br />T R tan Z I- R= T cot. ` 1 chord=
<br />1 "5o tan 2 I Z_ '. Ghord~def. R
<br />-- Sin. z D R = 50 -
<br />Sin. ; D = 5o Sin: D No. chords = I
<br />r. R. E=Rex.aecr,-I D
<br />1 5o tan 2 Tan. df. chord def.
<br />1 e = a
<br />Sln: z D T E =`.T tan }• I s
<br />i The,'square of; any -distance, divided by twice the radius, will equal
<br />the distance frorli tangent.to curve, very nearly.
<br />To find'aligle for a given distance and deflection.
<br />Rule I.-'' Multiply the given distance by .01745 (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 filid deflection for7a'given angle and distance. Multiply the angle
<br />by bi745, and the product by the distance.
<br />GENERAL DATA
<br />"- .'RIGHT ANGLE- TRIANGLES.' Square the altitude, divide'Wtwice the
<br />`base "Add quotient to base for hypotenuse. _; i
<br />-Given-Base "loo, Alt. 1o.102=200,=.5:.1004-.5=1oo.5 hyp.
<br />Given Hyp. loo, Alt. 25.252 200=3.125: Ioo.-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 />il, anddivide by 7..
<br />LEVELING. -'The correction for rcurvi ture and refraction, ;in' feet
<br />and decimals of feet is -'equal to 0.574d2, where d,is.the distance in -mile 's.
<br />The correction for- curvature 'alone ' is'.closely, . ,d2: ` The, combinecor.,
<br />rection is negative.
<br />PROBABLE ERROR: If di; "d2 d2, etc are•the discrepancies'of various
<br />results�•from the mean, and if Ede=the sum of the'squares of'
<br />these differ-
<br />ences and:n=`the number of observations, then.the.probable error of the
<br />mean ids
<br />10.6745 n(n 1)
<br />:SOLAk- EPHEMERIS.. Attention is=called to. the Solar Ephemeris for
<br />the current year, published by.Keuffel & Esser.Co., and furnished upon
<br />request'_ Thisl 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,"
<br />etc.
<br />TART.Ii TV --Minutes in Decimals of a Dea'ree. '
<br />1t
<br />':0167
<br />"111
<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 />i.2000
<br />-22�
<br />.3667.
<br />-32
<br />.5333
<br />42
<br />'.7000
<br />52
<br />,8667
<br />3
<br />13_
<br />.2167'
<br />23
<br />.3833
<br />33
<br />:5500,'
<br />'143.,
<br />.7167
<br />53 -
<br />:8833'
<br />4'
<br />_.0500'.
<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 />15
<br />'.2500
<br />25
<br />.4167
<br />35
<br />'.5833
<br />45
<br />..7500
<br />55
<br />'.9167
<br />6 =
<br />.0833
<br />.1000,
<br />16
<br />.2667
<br />• 26-
<br />.4333
<br />36,
<br />.6000
<br />;46:.
<br />.7667
<br />56
<br />-.9333
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />-47
<br />.7833
<br />-57-,
<br />.9500
<br />.7
<br />8
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9,
<br />.1333
<br />:1500
<br />19
<br />':3167
<br />29
<br />:4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />.101-
<br />".1667-
<br />.
<br />20
<br />.3333
<br />30
<br />.5000
<br />40'
<br />..6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />-'
<br />-. -- -TABLE V.
<br />-Inches In l)eclmals Ol a foot.
<br />-
<br />1-16
<br />3-32 Y8
<br />3-16
<br />%
<br />5-16
<br />A
<br />0052
<br />..0078 .01304
<br />.01456.
<br />.0208
<br />.0660
<br />.013
<br />.0817
<br />05921
<br />06025
<br />0119
<br />1
<br />I
<br />I
<br />0833
<br />.1667 .2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />8333
<br />.9167
<br />
|