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TABir II. - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg..
<br />Radius-
<br />-Mid.
<br />Ord.
<br />Tsn.
<br />Dist.
<br />Def..
<br />Dist.'
<br />DeE
<br />' for
<br />1 Ft.
<br />15 Ft.
<br />`
<br />Radius
<br />. Mid.
<br />' Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />If Ft.
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />l0I.15
<br />..,32
<br />.30`
<br />1 59
<br />s 25
<br />t
<br />t
<br />t.
<br />34°
<br />0°10:
<br />34377..
<br />.036
<br />-.145
<br />.291
<br />0.05.
<br />819.0
<br />7°
<br />.5500
<br />1.528
<br />6.105
<br />12:21
<br />2.10
<br />20.
<br />17189.-,
<br />.073.291
<br />2° 20'
<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
<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
<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 />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
<br />1.454
<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 />3125:4.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074.
<br />8.281
<br />16.56
<br />2.85
<br />2
<br />2864.9
<br />.436
<br />1.745;.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 />573.7.2.183
<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
<br />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-`12
<br />478.3
<br />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 />30.459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />20
<br />:1809.6
<br />.-.691
<br />2.763
<br />'5:526
<br />0.95._13.
<br />.-;
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20.c1719.1
<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:•: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 />6.689
<br />1.15.
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4,.50
<br />4 "
<br />1432:7
<br />.873.3.490
<br />6.980
<br />1.20-
<br />.lb
<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 />16 -
<br />359.3
<br />.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 />348.5
<br />3.606
<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
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />is
<br />319.6
<br />3.935
<br />15:64-
<br />31.29
<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 />.155
<br />16.51
<br />33.01
<br />5.70
<br />8
<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.'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 .39.87
<br />6.90
<br />40"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 '41.58
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088.10.18
<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 />5.379'10.76
<br />-
<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 (C) 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.
<br />TABLE XII. Deflections for Sub Chords for Short Radius Curves.
<br />of
<br />Curve
<br />Degreer171-OI
<br />Radius
<br />sub chord - •sin of 's def. angle
<br />Length
<br />of arc
<br />for 100 it.
<br />ef. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. '
<br />25 Ft.
<br />30°.18
<br />511
<br />I° 5i'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />l0I.15
<br />..,32
<br />.30`
<br />1 59
<br />s 25
<br />__3 10
<br />3 58
<br />'-101.33
<br />34°
<br />3
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />io1.48
<br />36°.8o
<br />.5500
<br />2° 13' _
<br />2°.41,
<br />_3°.33� .
<br />:.40 26'
<br />Io1.66
<br />38°-
<br />153, 58
<br />2° 20'
<br />2° 49'.
<br />30 44'
<br />4°_4o;
<br />161.85
<br />40°
<br />.
<br />146.19.,
<br />20 27,-
<br />20 5i,.
<br />-3° 55�
<br />4° 54
<br />102.06
<br />42°
<br />139.52
<br />2° 34'
<br />30 05'-.
<br />4o 07'
<br />So 08
<br />102.29
<br />44° ."
<br />133.47.
<br />20 41'
<br />30 13'
<br />40 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127: 97 .
<br />zo 48'
<br />3° 21'
<br />4° 29'
<br />5° 36' =
<br />162.76.
<br />480
<br />122.02.
<br />.. 2° 55,
<br />30 29' .
<br />40 40•
<br />5°.50'
<br />103.00
<br />Soo •
<br />118.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.24 .
<br />5z°
<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° 16'
<br />3o 54,
<br />5° 131.
<br />"60 31'
<br />103.84
<br />56`
<br />106.5o
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6°:44'
<br />104. 14 .
<br />580
<br />10
<br />30.29"
<br />104.43
<br />4o ld
<br />34'
<br />10.0
<br />60 57'
<br />.5000
<br />40
<br />5o
<br />044
<br />3 .35
<br />4 18-
<br />5 44
<br />7 11 -
<br />164.72
<br />IX
<br />•CURVE FORMULAS
<br />T K tan 2 I R= T cot. Z I chord'
<br />_,5o.tan %-I . - Chord_def.'=._,; R
<br />Sin. z D x R' Sin�� ll
<br />r
<br />Sin. 2 D = R No. chords g
<br />r E R ex..sec a: I D. la
<br />Sin, ' -21 D = ^50: tan
<br />z 1 E = T tan } I `; . Tan. def. _ ; chord def
<br />--The square of anyMistance, divided by •twice, the radius, will equal
<br />`the distance from o --curve, very nearly.
<br />To find angle for a given`distance'and deflection:
<br />Rule i:` -Multiply the given distance by .01745 (def: for•i°.for I ft:
<br />.see Tabl&11.), acid 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. Multiplythe angle
<br />'by -'01745, and the product by the distance.'
<br />GENERAL DATA
<br />'RIGHT ANGLE -TRIANGLES: Square the altitude, divide by twice the
<br />base. Add quotient to -base for hypotenuse.
<br />Given' Base ioo, Alt. 10.102=200=.S. 100-x-.5=.Ioo:S hyp.
<br />Given -Hyp. iioo; Alt. 25.252 126o=3.125. loo-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 />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 0.574d21 where d is the distance. in miles.
<br />The correction for curvature alone is -closely; W. 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 Ed?=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= Ede
<br />1 0.6745 n(n-1)
<br />SOLAR EPHEMERls. 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 iri., 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 />1!:
<br />.0167
<br />Ill
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />511
<br />.8500
<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 />6
<br />I
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833.
<br />4
<br />.0500
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0667
<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 />L 7•..
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<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 />1 .1667 11
<br />20
<br />1 .3333 11
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -Inches
<br />in Decimals of a toot.
<br />1-16 3,32
<br />3-16
<br />% .
<br />5-16
<br />ss
<br />'�
<br />%
<br />%
<br />?�
<br />0052 .0078 .0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />1 2 3
<br />I I
<br />4
<br />I
<br />6
<br />I
<br />7
<br />I
<br />8
<br />9
<br />10
<br />11,
<br />.0833 .1667 .2500
<br />.3333
<br />.4167
<br />.5C
<br />.5833
<br />.6667
<br />.7500
<br />.8333.
<br />.9167
<br />
|