|
lix
<br />TABLE II. -Radii, Ordinates a,nd Deflections. Chord =100 ft. ' • CURVE: FORMULAS _
<br />Deg.
<br />Rarlius
<br />Mid
<br />Ord.
<br />Ina.
<br />Dist,
<br />Def:
<br />Dist. _
<br />for
<br />1 Ft: -
<br />Deg.
<br />Radius
<br />' Mid.
<br />Ord.
<br />Tan..
<br />Dist_.
<br />Def.
<br />Dist.
<br />Def
<br />'
<br />1 Ft.
<br />'-° 17'-'
<br />1t,
<br />it.
<br />ft--
<br />ft.
<br />r-
<br />1° 59'
<br />-ft,
<br />! It.
<br />'ft.
<br />ft.
<br />r
<br />a-10'
<br />34377
<br />-;036.14.5
<br />'
<br />- .291
<br />0:05
<br />7"
<br />819.0
<br />1:528,6.105
<br />2° 41''
<br />12.21
<br />2.10
<br />20
<br />17189
<br />:073
<br />.291
<br />{ :582
<br />0.10
<br />120'
<br />781.$
<br />1.600
<br />63:395
<br />12,71)
<br />2.20
<br />30.
<br />11459
<br />.309
<br />.436
<br />:873
<br />0.15
<br />30
<br />764.5
<br />1.631
<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 />76i970_.13.95
<br />-3°-38`
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.873
<br />1,743
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />;1t2GG
<br />14.53
<br />2.50
<br />10
<br />4011.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />074.7
<br />1.855
<br />7:411
<br />14.82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.3270.40
<br />104.43
<br />40
<br />061:7
<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 />6337.3
<br />1!965
<br />.7.846'15.69
<br />2.70
<br />40
<br />3437.9
<br />.361
<br />1.454
<br />t2:909
<br />0.50
<br />20
<br />G14.6
<br />2:037
<br />'•8.136
<br />1n^.27
<br />2.80
<br />50
<br />3 125. 4
<br />'..400
<br />1.600
<br />•3.200
<br />0.55
<br />30
<br />-003.8
<br />21074
<br />8:281
<br />16.56
<br />2.85
<br />2 ;
<br />2864-9
<br />.4381
<br />1.745
<br />3.490'0.60
<br />40
<br />593.4
<br />2:110
<br />'S.426
<br />16.85
<br />2.90
<br />'10
<br />2644.6
<br />.473
<br />1.S91
<br />3.781
<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
<br />:50!1'2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />15.30
<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 />9.585'19.16
<br />3.30
<br />40-:'2148.8
<br />.582
<br />2.327
<br />.4.654
<br />0-80
<br />30
<br />499.1
<br />3.511
<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 />11
<br />478.3
<br />2.620
<br />10.45
<br />'20.91
<br />3.60
<br />S -
<br />1910.1
<br />.655
<br />2.618
<br />5.231
<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
<br />11.75
<br />23. 51
<br />4.05
<br />30
<br />1637.3
<br />-764
<br />3.054
<br />?6:10S
<br />1.05
<br />14
<br />410,3
<br />3.058
<br />12.18`
<br />24.37
<br />4.20
<br />40
<br />1662.9
<br />.800,3.199
<br />'6.393
<br />1-10
<br />30
<br />356.2
<br />3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />..836
<br />3.345
<br />6.639
<br />.1.15
<br />15
<br />383.-A
<br />3.277
<br />13.05
<br />2G It
<br />4.50
<br />3
<br />1432.7
<br />.573
<br />3.490
<br />6.980
<br />1.20
<br />39
<br />370.8
<br />3.387
<br />13.49
<br />263.97
<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 />3.496
<br />13.92,
<br />27. S4
<br />4.80
<br />20
<br />1322..5
<br />..•9453.719
<br />7.561
<br />1.30
<br />130
<br />348-5
<br />3:000
<br />14:35'
<br />25.70
<br />4,05
<br />30
<br />1273.6
<br />.082
<br />3.926
<br />7.852
<br />1-35,
<br />17
<br />338.3
<br />3.710
<br />14.78
<br />20.56
<br />5.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8:143
<br />1.40
<br />18
<br />319.0
<br />3:035
<br />154.64
<br />31.29
<br />5.40
<br />50
<br />1185.5
<br />1.055
<br />4.217
<br />-8.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />$
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20•'
<br />287.0
<br />4.374
<br />17.37
<br />34.73
<br />0.00
<br />_
<br />;0.
<br />1.127
<br />4.507
<br />,9.014
<br />1.55
<br />21
<br />274':4
<br />4.594
<br />18.22
<br />30.44
<br />0.30
<br />20
<br />_1109.3
<br />1074.7
<br />1.104
<br />4.653
<br />'9.305-1.60
<br />22
<br />262.0
<br />4.814
<br />19-.08
<br />38.10
<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 />30.87
<br />6.00
<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 />41.55
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088
<br />10.1.8
<br />1.75
<br />'25
<br />231.0
<br />5.476
<br />21.64
<br />43.23
<br />7.50
<br />B =••'-'
<br />'055. 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.G
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />48.639
<br />8.10
<br />20
<br />905.1
<br />1'.382
<br />5.524.11.05
<br />1.90
<br />26
<br />206.7
<br />6.139
<br />24.19
<br />48.33
<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 />3.70
<br />40
<br />859.911.45
<br />5
<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 -e ual to .0012 O'
<br />multiplied -by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 90 ft. rail to fit a 10 degree curve, its iniddle ordinate should
<br />r •.be .0012X900X2.183 or 2,36 inches.
<br />TAIILE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />!radius j
<br />50
<br />� sub chord
<br />It = sin of i def -`angle -
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. l def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18.
<br />1:_51. _
<br />'-° 17'-'
<br />2'-58'
<br />- 3° 43�
<br />101.15
<br />32°
<br />181.39
<br />1° 59'
<br />2° 258
<br />3° 10'
<br />3° 58'
<br />101.3,
<br />34°
<br />17;.,01
<br />2°06'
<br />2°.J3',-
<br />'
<br />4° 12-'
<br />.101,48
<br />361
<br />161:8o
<br />2° 13'-
<br />2° 41''
<br />3° 33'
<br />40 26'
<br />fol .66
<br />-380
<br />153.58 -
<br />.2° 20'
<br />2° 49'3°
<br />44'
<br />4° 40'
<br />101.85
<br />40°
<br />146: i9:
<br />2° 27'
<br />2'-5-1"
<br />3° 55'
<br />4° 94'
<br />i02.06
<br />42
<br />139 •,52
<br />'-° 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° 18''
<br />S° 22'
<br />102.53
<br />lob°
<br />,
<br />127-:97
<br />2° 48'
<br />3° 2I'
<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°5a',
<br />103.00
<br />50°
<br />118:31
<br />3°02'
<br />-3°-38`
<br />4° 51'
<br />6°04'
<br />103.24
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46'
<br />5° oz'
<br />6°.17'
<br />103.54
<br />54°
<br />110.11
<br />3°16'
<br />3° 54'
<br />130
<br />6° 3i'
<br />103.84.
<br />56°
<br />1o6. 5o
<br />3° 22'-
<br />4° 02
<br />S° 23'
<br />6° 44' .
<br />r04.14
<br />58°
<br />103%J4
<br />3° 29'
<br />4°ro'
<br />.. 5° 34'
<br />6° 57'
<br />104.43
<br />60°• .
<br />100.00
<br />3° 351
<br />4' i8'
<br />50 44--
<br />... 7°.i I'
<br />104• 72
<br />T= R tan � I R= T cot. z I chorda
<br />T= So tan 8-I Chord def. = R
<br />Sin. v 50 -. .. . f
<br />5o
<br />R" = Sin. 2, D I
<br />Sin. D = 'R _" . No. chords = --
<br />1 = IZ-ex. sec 1 D
<br />;Sin. 51)t- T '- E='Tuan-§ I Tan..def. = chord def. .
<br />The square of any distance, divided by tea ice the radius, will equal
<br />the distaned from tangent to curve, very nearly...
<br />To find angle for a given distance:and'deflzction.
<br />Rifle I. iflultiply the given distance by .101745 {def. for 1' for i ft.
<br />see Table Il.);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 />(' RIGHT ANGLE TRIANGLES.: Square the altutude, divide by twice the
<br />base. - Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 10.102-200=.5."z_om-f-.5=100.5 hyp.
<br />Given_ Hyp. loo; Alt. 25.25'-* 200 3,125. 10073.121=•96.875=,Base.
<br />Error in first example, .002; i4 last, .045..
<br />To find Tons of Rail in one mile of trach: multiply weight per yard
<br />by I I, and divide by. 7. -
<br />1' LEVELINd. The correction .for curvature- and refraction, in- feet
<br />I and decimals of feet is equal to 0.574d°, where d.is the distance in miles.
<br />I The correction for curvature alone is, Closely, J42. The combined, eor-.
<br />I rection is negative. • • ' - '
<br />PROBABLE ERROR. If dt d.,, dc, etc. are the discrepancies of various
<br />i results from the mean, and If. id2-the sum of the squares of these differ-
<br />eneds and r_ -the number of observations, than the probable error of the
<br />mean= +0.63745 7_d
<br />n (n-1)
<br />SOLAR EPHEaIERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and•furnlshed free of
<br />charge upon'request, which is 34x58 in., with about -!DO pages of datavery
<br />useful to -the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directions and tables for determining the meridian
<br />and the latitude from observations on the suli and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers. -
<br />- TABLE IV. - Minutes in•Decimals of a Dd�rce.
<br />• 1' -:0167 11' .1833 21' .3500 31' .5167 41' .6833 51' .8500
<br />2,• .0333 12 .2000 22 .36637 32 .5833 42 .7000 52 .8667
<br />3 .0500 13 .2167 23 -3833 33 .51506 43 .7167 53 .8833
<br />4 .0667 14 .2333 24 .4000 34 .C667 44 .7333 54 -.9000
<br />A
<br />TABLE V: - Inches in Dnima.ts of a Foot.
<br />1=1G
<br />3-323-16
<br />%
<br />5-,6
<br />�a
<br />�s
<br />.0052
<br />.0075
<br />.0104
<br />,015E
<br />.0203
<br />.0-60
<br />V'1=3
<br />.0313
<br />.0117- .0521
<br />0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5'
<br />0
<br />7
<br />8 9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500,
<br />.3333
<br />.4167
<br />.5000
<br />.5S$3; 1
<br />.6667 .7500 =.8333
<br />.9167
<br />b
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.833
<br />45
<br />.7500
<br />55
<br />•9167
<br />0.1000
<br />iG
<br />.2667
<br />26
<br />.4333
<br />36
<br />,60100
<br />46
<br />.7667
<br />56
<br />•9333
<br />7'
<br />.1167
<br />1.7
<br />.2833
<br />27
<br />.4500
<br />37
<br />C167
<br />47
<br />.7833
<br />57
<br />•0500
<br />8
<br />.•1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />63'33
<br />48
<br />.8000
<br />58
<br />.9667
<br />9 -
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />GN0
<br />49
<br />.8167
<br />59
<br />.9883
<br />10
<br />.1667
<br />1 20
<br />.3333 11
<br />30
<br />1 :5000 11
<br />40
<br />1 6661 11
<br />50
<br />, s32311
<br />60
<br />11.0000
<br />A
<br />TABLE V: - Inches in Dnima.ts of a Foot.
<br />1=1G
<br />3-323-16
<br />%
<br />5-,6
<br />�a
<br />�s
<br />.0052
<br />.0075
<br />.0104
<br />,015E
<br />.0203
<br />.0-60
<br />V'1=3
<br />.0313
<br />.0117- .0521
<br />0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5'
<br />0
<br />7
<br />8 9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500,
<br />.3333
<br />.4167
<br />.5000
<br />.5S$3; 1
<br />.6667 .7500 =.8333
<br />.9167
<br />A
<br />
|