|
VIII
<br />TABLE IL - Radii, Ordinates -and Deflections. Chord
<br />=100 ft.
<br />Deg:
<br />Radius
<br />Mid
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.`Dor.
<br />Dist.
<br />ef
<br />1 Ft. .
<br />Deg..
<br />"
<br />Radius
<br />Mid.
<br />Ord:
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Dor
<br />1Ft.
<br />18
<br />1° 51'
<br />2° 17'
<br />2° 58''
<br />3° 43'
<br />Ioi. 15
<br />g2°._"
<br />t.
<br />t.I
<br />t,
<br />ft.
<br />3° 58'
<br />0'10'
<br />34377.'
<br />.036
<br />.:145
<br />291
<br />0.05
<br />7'
<br />819.0.1.528
<br />36°
<br />380
<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,;.145
<br />z°" 48'
<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
<br />1:745
<br />0.30-
<br />20-
<br />638.2
<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 />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 />2.618
<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 />.364.1.454
<br />,
<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 />3200
<br />0.55
<br />30,
<br />603.8
<br />2074.
<br />8.281
<br />1G. 56
<br />2.85
<br />2'•r,
<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 />'40
<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 />2.292
<br />9.150'18.30
<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 />.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 />50.
<br />2022.4
<br />;.618
<br />2.472
<br />.4.945
<br />0.85
<br />12
<br />478.3.2.620
<br />10.45
<br />20.91
<br />3.60
<br />3
<br />1910:1
<br />.655
<br />2.618
<br />'5.235
<br />0.90
<br />30.
<br />459.3
<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 />2.949-11.75
<br />23.51
<br />4.05
<br />.30.
<br />1637:.3
<br />..764
<br />3.054
<br />6.108
<br />1.05
<br />'14
<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.G89
<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
<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
<br />1.25
<br />18'
<br />359.3
<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
<br />1.30
<br />'� 30
<br />318.5
<br />.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.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 />1228.1.1.018
<br />4.071
<br />•8:143
<br />1.40'
<br />1S
<br />319.6
<br />3.935
<br />15.64
<br />31.29:5.40
<br />50•
<br />1185.8
<br />1.055
<br />4.217
<br />-8:433'1.45
<br />119
<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 />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 />18.22
<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 />4.814
<br />19:08
<br />38.16
<br />6.60
<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 />41.58'7.20
<br />50.
<br />982.6
<br />1'.273
<br />5.088
<br />10:13:
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<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
<br />1.346
<br />5.379
<br />10:76
<br />1.85
<br />27 ''214.2�6.
<br />.913
<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 />206.7.139
<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 />199.7.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814'11.63
<br />2.00
<br />30
<br />193.2
<br />583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate -in inches for any coi d of length (0) is equal to .0012 C'
<br />multiplied by the middle ordinate taken fromthe above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 10 degree cur-ve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches.; 1
<br />TAsiE III. Deflections'for Sub Chords for Short Radius Curves.
<br />Degree
<br />Radius
<br />50
<br />sub chord
<br />R =s in of g def. angle
<br />Length
<br />of arc
<br />Curve
<br />sin. g def. ang.
<br />. 12.5: Ft. j
<br />15 Ft:
<br />20 Ft.
<br />25_Ft.
<br />for 100 ft.
<br />300193.
<br />18
<br />1° 51'
<br />2° 17'
<br />2° 58''
<br />3° 43'
<br />Ioi. 15
<br />g2°._"
<br />._. 181'.-39- ...
<br />..1° 59"-..--2°
<br />�5'
<br />3°. 1.0i .
<br />3° 58'
<br />101.33
<br />34°
<br />I]I.OI
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />380
<br />161.80.:
<br />153.58
<br />20 13'-
<br />2° 20'
<br />2041'
<br />2° 49'
<br />3° 33 :
<br />3° 44'
<br />4°-261.
<br />4° 40'
<br />1oi.66
<br />1oi.85
<br />40°
<br />146. i,9
<br />2° 27
<br />2° 57'
<br />.3°.55
<br />4° 54
<br />102.06
<br />42°4
<br />.9000
<br />"2° 34'
<br />3° 05'..
<br />4° 07.
<br />50,08
<br />102.29
<br />44° _
<br />133 47..
<br />, .2°,41'
<br />3° 13' .
<br />4° 18'
<br />g° z2'
<br />102.53
<br />46°.
<br />127- 97
<br />z°" 48'
<br />30 21'
<br />4-29'
<br />5° 36'
<br />102.76.
<br />48°
<br />-122.92
<br />2°•55'
<br />3° 29' :.
<br />4° 40"
<br />5° 50'
<br />103,00
<br />50° .:
<br />_ 118.3-1
<br />3° 02'
<br />3° 38'-,
<br />4°.SI.
<br />_ 6° 04'
<br />103.24
<br />52J '
<br />. 114.06
<br />13° 09'
<br />3° 46'..
<br />5° 02'
<br />6° 1j'
<br />103 54
<br />103.84.
<br />540
<br />110. i1'.
<br />30 16' .
<br />3°.54'
<br />5' 13'
<br />60 31'
<br />58
<br />,56°.
<br />166.50
<br />30-22'
<br />4° 02'
<br />5° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14.
<br />'.:'
<br />3 29
<br />4 °.10'
<br />5° 34':
<br />6° 57'
<br />104.43
<br />60' ::
<br />100.00
<br />3° 35'
<br />4.° 18'
<br />5° 44'
<br />7° :I I�
<br />104.72
<br />r- IX
<br />CURVE FORMULAS
<br />T= R tan2 I R= T cot. 2 1 chord'
<br />_ 50 -tan 2.I -- Chord d'ef." = R
<br />T
<br />Sin. 2ll 50
<br />Sin. 2 D 5° R Sim2 D No. chords = I
<br />I2 E = R ex. sec. I
<br />Sin. ;..D 5o tan 2 I'- E:= T fan i L' " Tan, def. 2 chord def.
<br />7.
<br />.The square of auy distance, divided by twice the radius, will equal
<br />"the distance from tangent to curve, yery nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply, the given distance by .01745 (def.--for-1°,for I ftp.
<br />see Table I1.), 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 />RIGFIT• ANGLE'TRIANGLES:' Square,the altitude, divide, by twice•the
<br />base. `Add'.quotient,to base for hypotenuse.
<br />Given Base Y oo,, Alt. 10.102 -.200 = .5. l oo+.5'=100.5 hyp:
<br />Given Hyp. loo, Alt. 25.25?='200-,3.125: 10°-3.125=96.875=Base.
<br />Error in first example, .00'. in last, .045:.;
<br />To find -Tons of Rail'in-one mile of track: multiply: weight per yard
<br />by i i; divide bY7: '. _
<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, _23d2. The, combined corgi
<br />rection is negative.
<br />PROBABLE ERROR: I'f di;-d2;,ds; etc.; are the discrepancies of various
<br />results•from the mean, and if Ed2=the sum of the squares of .these differ-
<br />ences and n =the number of observations, then the probable, error of the
<br />mean .
<br />10.6745 n(n_I)
<br />SOLAR= EPHEMERIS: Attention is called to the- S61ar 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 frorh observatioris.oii'the slin and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLEJV. -Minutes;in Decimals of,a Degree.
<br />1'
<br />.0167
<br />'11' -
<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 />.0729
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0500X43
<br />11
<br />.2000
<br />.23
<br />.3833
<br />33
<br />.5500
<br />'.43 ._.7167
<br />.5833
<br />53
<br />.8833,
<br />4
<br />.0667
<br />_
<br />,. 14
<br />.2167
<br />24
<br />.4000
<br />34
<br />:5667
<br />44
<br />-.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />_
<br />15
<br />.2333
<br />25
<br />".4167
<br />35
<br />.5833
<br />"45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.16 -
<br />.2500
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667-
<br />-56
<br />.9333
<br />7
<br />.1000
<br />17 -
<br />.2667
<br />-.2833
<br />27
<br />•.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />..1167:
<br />18
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1333
<br />-19'
<br />.3000
<br />-''.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49-
<br />.8167
<br />'59
<br />'.9833
<br />10
<br />.1500
<br />1 .1667-
<br />20
<br />1 .3333-
<br />30-
<br />1 .5000 11
<br />40
<br />1 .6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V.
<br />-Inches in Decimals of a root.
<br />1-16
<br />.0052
<br />3-32
<br />.0078
<br />.0104
<br />3-16
<br />.0156
<br />.0208
<br />.0260
<br />%
<br />.0313
<br />.0417
<br />.0521 I
<br />.0625.1
<br />.0729
<br />1
<br />I
<br />2
<br />3
<br />I
<br />4
<br />5
<br />6
<br />I
<br />7
<br />I
<br />8
<br />I
<br />9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />-4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
|