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Contributed by Yale Peabody Museum of Natural History.
| www.biodiversitylibrary.org
Transcription
VIII
TABLE II. - Radii, Ordinates and Deflections. Chord = 100 ft.
Deg. | Radius | Mid. | Tan. | Def. | Def.
| | Ord. | Dist.| Dist.| for
| ft. | ft. | ft. | ft. | 1 Ft.
0° 10' | 34377. | .036 | .145 | .291 | .05/
20 | 17180. | .073 | .291 | .582 | .10
30 | 11450. | .109 | .436 | .873 | .15
40 | 8594.4 | .145 | .582 | 1.164| .20
50 | 6875.5 | .182 | .727 | 1.454| .25
1 | 5729.6 | .218 | .873 | 1.745| .30
10 | 4911.2 | .255 | 1.018| 2.036| .35
20 | 4297.3 | .291 | 1.164| 2.327| .40
30 | 3819.8 | .327 | 1.309| 2.618| .45
40 | 3437.9 | .364 | 1.454| 2.909| .50
50 | 3125.4 | .400 | 1.600| 3.200| .55
2 | 2864.9 | .436 | 1.745| 3.490| .60
10 | 2644.6 | .473 | 1.891| 3.781| .65
20 | 2455.7 | .509 | 2.036| 4.072| .70
30 | 2292.0 | .545 | 2.181| 4.363| .75
40 | 2148.8 | .582 | 2.327| 4.654| .80
50 | 2022.4 | .618 | 2.472| 4.945| .85
3 | 1910.1 | .655 | 2.618| 5.235| .90
10 | 1809.6 | .691 | 2.763| 5.526| .95
20 | 1719.1 | .727 | 2.908| 5.817| 1.00
30 | 1637.3 | .764 | 3.054| 6.108| 1.05
40 | 1562.9 | .800 | 3.199| 6.398| 1.10
50 | 1495.0 | .836 | 3.345| 6.689| 1.15
4 | 1432.7 | .873 | 3.490| 6.980| 1.20
10 | 1375.4 | .909 | 3.635| 7.271| 1.25
20 | 1322.5 | .945 | 3.718| 7.561| 1.30
30 | 1273.6 | .982 | 3.926| 7.852| 1.35
40 | 1228.1 | 1.018| 4.071| 8.143| 1.40
50 | 1185.8 | 1.055| 4.217| 8.433| 1.45
5 | 1146.3 | 1.091| 4.362| 8.724| 1.50
10 | 1109.3 | 1.127| 4.507| 9.014| 1.55
20 | 1074.7 | 1.164| 4.653| 9.305| 1.60
30 | 1042.1 | 1.200| 4.798| 9.596| 1.65
40 | 1011.5 | 1.237| 4.943| 9.886| 1.70
50 | 982.6 | 1.273| 5.088| 10.18| 1.75
6 | 955.4 | 1.309| 5.234| 10.47| 1.80
10 | 929.6 | 1.346| 5.379| 10.76| 1.85
20 | 905.1 | 1.382| 5.524| 11.05| 1.90
30 | 881.9 | 1.418| 5.669| 11.34| 1.95
40 | 859.9 | 1.455| 5.814| 11.63| 2.00
7° | 819.0 | 1.528| 6.105| 12.21| 2.10
20' | 781.8 | 1.600| 6.395| 12.79| 2.20
30 | 764.5 | 1.637| 6.540| 13.08| 2.25
40 | 747.9 | 1.673| 6.685| 13.37| 2.30
8 | 716.8 | 1.746| 6.976| 13.95| 2.40
20 | 688.2 | 1.819| 7.266| 14.53| 2.50
30 | 674.7 | 1.855| 7.411| 14.82| 2.55
40 | 661.7 | 1.892| 7.556| 15.11| 2.60
9 | 637.3 | 1.965| 7.846| 15.69| 2.70
20 | 614.6 | 2.037| 8.136| 16.27| 2.80
30 | 603.8 | 2.074| 8.281| 16.56| 2.85
40 | 593.4 | 2.110| 8.426| 16.85| 2.90
10 | 573.7 | 2.183| 8.716| 17.43| 3.00
30 | 546.4 | 2.292| 9.150| 18.30| 3.15
11 | 521.7 | 2.402| 9.585| 19.16| 3.30
30 | 499.1 | 2.511| 10.02| 20.04| 3.45
12 | 478.3 | 2.620| 10.45| 20.91| 3.60
30 | 459.3 | 2.730| 10.89| 21.77| 3.75
13 | 441.7 | 2.839| 11.32| 22.64| 3.90
30 | 425.4 | 2.949| 11.75| 23.51| 4.05
14 | 410.3 | 3.058| 12.18| 24.37| 4.20
30 | 396.2 | 3.168| 12.62| 25.24| 4.35
15 | 383.1 | 3.277| 13.05| 26.11| 4.50
30 | 370.8 | 3.387| 13.49| 26.97| 4.65
16 | 359.3 | 3.496| 13.92| 27.84| 4.80
30 | 348.5 | 3.606| 14.35| 28.70| 4.95
17 | 338.3 | 3.716| 14.78| 29.56| 5.10
18 | 319.6 | 3.935| 15.64| 31.29| 5.40
19 | 302.9 | 4.155| 16.51| 33.01| 5.70
20 | 287.9 | 4.374| 17.37| 34.73| 6.00
21 | 274.4 | 4.594| 18.22| 36.44| 6.30
22 | 262.0 | 4.814| 19.08| 38.16| 6.60
23 | 250.8 | 5.035| 19.94| 39.87| 6.90
24 | 240.5 | 5.255| 20.79| 41.58| 7.20
25 | 231.0 | 5.476| 21.64| 43.28| 7.50
26 | 222.3 | 5.697| 22.50| 44.99| 7.80
27 | 214.2 | 5.918| 23.35| 46.69| 8.10
28 | 206.7 | 6.139| 24.19| 48.38| 8.40
29 | 199.7 | 6.360| 25.04| 50.07| 8.70
30 | 193.2 | 6.583| 25.88| 51.76| 9.00
The middle ordinate in inches for any cord of length (C) is equal to .0012 C²
multiplied by the middle ordinate taken from the above table. Thus, if it
desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate should
be .0012x900x2.183 or 2.36 inches.
TABLE III. Deflections for Sub Chords for Short Radius Curves.
Degree | Radius | sub chord = sin of ½ def. angle | Length
of | 50 | 12.5 Ft. | 15 Ft. | 20 Ft. | 25 Ft. | of arc
Curve | | | | | | for 100 ft.
30° | 193.18 | 1° 51' | 2° 17' | 2° 58' | 3° 43' | 101.15
32° | 181.39 | 1° 59' | 2° 25' | 3° 10' | 3° 58' | 101.33
34° | 171.01 | 2° 06' | 2° 33' | 3° 21' | 4° 12' | 101.48
36° | 161.80 | 2° 13' | 2° 41' | 3° 33' | 4° 26' | 101.66
38° | 153.58 | 2° 20' | 2° 49' | 3° 44' | 4° 40' | 101.85
40° | 146.19 | 2° 27' | 2° 57' | 3° 55' | 4° 54' | 102.06
42° | 139.52 | 2° 34' | 3° 05' | 4° 07' | 5° 08' | 102.29
44° | 133.47 | 2° 41' | 3° 13' | 4° 18' | 5° 22' | 102.53
46° | 127.97 | 2° 48' | 3° 21' | 4° 29' | 5° 36' | 102.76
48° | 122.92 | 2° 55' | 3° 29' | 4° 40' | 5° 50' | 103.00
50° | 118.31 | 3° 02' | 3° 38' | 4° 51' | 6° 04' | 103.24
52° | 114.06 | 3° 09' | 3° 46' | 5° 02' | 6° 17' | 103.54
54° | 110.11 | 3° 16' | 3° 54' | 5° 13' | 6° 31' | 103.84
56° | 106.50 | 3° 22' | 4° 02' | 5° 23' | 6° 44' | 104.14
58° | 103.14 | 3° 29' | 4° 10' | 5° 34' | 6° 57' | 104.43
60° | 100.00 | 3° 35' | 4° 18' | 5° 44' | 7° 11' | 104.72