|
VIII
<br />TABLE IL - Radii, Ordinates -and Deflections. Chord=100 ft.'
<br />Deg.
<br />Radius .
<br />Mid.
<br />Ord
<br />Tan. '
<br />Diat,
<br />Def.'
<br />Dist
<br />D f*
<br />1Ft.
<br />' Deg,
<br />Radius
<br />Mid.
<br />Ord:'
<br />Tan..
<br />. Dist.'
<br />Def.
<br />Dist.
<br />Da '
<br />1 Ft.
<br />2° 17'
<br />2° 58'.
<br />3° 43
<br />IOI. 15 '
<br />32°-
<br />181.39
<br />1°'59'
<br />t,
<br />t.
<br />t 1
<br />77-
<br />34°
<br />0'10'
<br />34377.
<br />.036
<br />"•.145
<br />.291
<br />0.05
<br />7'
<br />819.0
<br />1.528
<br />6.105
<br />12.21.2.10
<br />26'..
<br />-20
<br />17189..
<br />;.073
<br />.291
<br />.582
<br />010
<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 />..188
<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 />5729.6.218
<br />52o
<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 />`.30
<br />4297.3...291
<br />4° IO'
<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 />-104.:72
<br />3819.8
<br />x.327
<br />1.300
<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 />614.6-2.037
<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 />8.2S1'16.56
<br />2.85
<br />2.'
<br />2864.9
<br />.436
<br />1.745
<br />•3.490
<br />0.60
<br />=` 40
<br />593.4,2:110
<br />16.85
<br />2.90
<br />16'
<br />2644.6
<br />'.473
<br />1.891
<br />3.781
<br />0.65
<br />10 .-
<br />573.7
<br />2.183
<br />.8.426
<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 />2.827
<br />4:654
<br />0.80
<br />30
<br />499.3
<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
<br />2.620
<br />10.45,
<br />20.01
<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 1441.7
<br />2.839
<br />11.32.'22.64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />30.425.4
<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_.
<br />14, . ,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 />306.2
<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
<br />26.11
<br />4.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.080
<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 />'16
<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 />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 />18
<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 />4.155'16.51-'33.01
<br />5.70
<br />b
<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 />.594
<br />18.22.,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.'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
<br />7.20
<br />50
<br />' 982.6
<br />1.273
<br />5.088
<br />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 />10.471.80
<br />26
<br />222.3
<br />6.697
<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
<br />214.2
<br />'.918
<br />23.35'
<br />46:69"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 />.139
<br />24.19
<br />48.38
<br />5.40
<br />30
<br />881.9
<br />1:418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7.6.360
<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 l`n inches for any cold of length (0) ''equal to .0612 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 III. ' Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />34 sub chord = sin of $def, angle
<br />R A
<br />Length
<br />of arc
<br />for 100 ft..
<br />sin, I def. ang.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft..
<br />- 25 Ft.
<br />30°
<br />193.18
<br />1° 51'
<br />2° 17'
<br />2° 58'.
<br />3° 43
<br />IOI. 15 '
<br />32°-
<br />181.39
<br />1°'59'
<br />_2°25,_.
<br />..3°.,10,_
<br />3°58,...
<br />101.33'
<br />34°
<br />171.01,
<br />20 06' `
<br />20 33'
<br />3° 21'
<br />4° 12'
<br />I01.48 .
<br />.36°
<br />161.80
<br />20 13'
<br />a 41'
<br />3o 33'
<br />26'..
<br />io1.66
<br />3$°
<br />153:58
<br />2° 20'
<br />2° 49'
<br />3° 44',
<br />-40
<br />4° 46'
<br />`161.8,5
<br />40°
<br />146. 1g
<br />io 2j'.
<br />2° 57 .
<br />3° 55'
<br />4o 54'
<br />fo2.06 '
<br />4 -?'139.52
<br />.
<br />25 -
<br />20 34'
<br />•3° 05'
<br />'4°. 0
<br />50 08'
<br />1102.29
<br />44° '.
<br />133.47
<br />2° 41'
<br />3° -13'
<br />.:4° 18S°.22'
<br />.2667
<br />_ 102.53
<br />46°
<br />127,97
<br />2° 48'
<br />3° 21'
<br />4°.29,
<br />5° 36, :
<br />102,.76 ,
<br />.48o
<br />122.92 '
<br />2° 55'
<br />3° 29'
<br />.:4° 40'
<br />5° 50'
<br />103.00•.
<br />50°
<br />118:31
<br />3° 02'-.3°
<br />38'
<br />4' gi'.
<br />G° 04'
<br />103.24
<br />52o
<br />1'14.06
<br />110-11,
<br />3°.09,30
<br />46,
<br />5° oz'
<br />6° 17' :
<br />103. 54'
<br />54o;
<br />58
<br />3° 16
<br />30 54'.:
<br />5o 13'
<br />60.31'
<br />163.84
<br />56
<br />Io6:50
<br />3 22
<br />4 02
<br />5 23
<br />6 44
<br />104.14
<br />58°
<br />103.14
<br />3° �9'
<br />4° IO'
<br />S° 34'
<br />6° 57'
<br />-104-43-
<br />600,
<br />100.00
<br />3035
<br />4° 18'
<br />S 44'.
<br />70 11'
<br />-104.:72
<br />IX
<br />CURVE FORMULAS
<br />= R tan z I
<br />- R = T cot. 2'1 I chord'
<br />T _ 50 tan ,
<br />2-I Chord -def.
<br />Sin. -z D R = 50 R
<br />Sin. s D = So Sin. ;,ll I
<br />No. chords =
<br />R E= R ex. -sec ; I D
<br />5o tan 2 I a
<br />Sin. 2'D = T E = T tan } I Tan. def. = 2 chord def.
<br />The square of ani -distance, divided by twice the radius, will equal
<br />the distance from tangent to'curve, very nearly.
<br />To find'arigle fora given distance and deflection.
<br />Rule I. Multiply the given distance by .01745 (def. for I° 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 find deflection for a given angle and distance. Multiply the angle
<br />-by .61745, 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 1oo,-Alt.'10.102=Zoo=.5. 100+-5=100.5 hyp.
<br />Given Hyp. loo, Alt. 25.25'-200=3.I25. 100-3.125=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 ? 1,'and'divide by 7:
<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, 8d'. The combined cor-
<br />rection is negative. '
<br />. . PROBABLE ERROR. I141, d2, der 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= Ed 2
<br />-0.6745
<br />SOLAR EPHEMERIS. 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 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; arithrrietic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree. 0
<br />1t
<br />.0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />51,
<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 />-.8833
<br />�3',
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />-8
<br />4
<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 />.0833
<br />15
<br />.2500
<br />.
<br />25 -
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6-
<br />.1000
<br />36
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7;;
<br />.1167
<br />''17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />41
<br />.7833
<br />57
<br />.9500
<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 />10
<br />.1667
<br />20
<br />.3333
<br />- 30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V.
<br />-Inches in Decimals of a -Foot. -
<br />- -
<br />1-163-32
<br />Y
<br />3-16
<br />%
<br />5-16
<br />%
<br />Y2
<br />%
<br />%
<br />..0052.
<br />.0078
<br />.0104.
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />1 I
<br />2
<br />3 I
<br />4 I
<br />5 I
<br />6 I
<br />7
<br />-8
<br />I 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 />
|