Curves
The simplest way of designating a railroad curve is by giving the length of the radius—i. e., the distance from the center to the outside of the circle, or one-half the diameter. The shorter the radius the sharper the curve. The length of the radius is usually stated in feet; but English engineers often state the radius in chains (one chain = 66 feet). The length of the radius of a railroad curve is measured to the center of the track.
Civil engineers designate railway curves by degrees (using the sign ° for degrees and " for minutes, there being 60 minutes in one degree). The sharpness of the curve is determined by the "degree of curve," or the number of degrees of the central angle subtended by a chord of 100 feet. Or, in other words, let two lines start from the center of a circle in the shape of a V, so that the angle at the point of the V is one degree (equivalent to 1/360 of a complete circle), then, if the two sides of the V are prolonged until they are 100 feet apart, any part of a circle made by using one of these lines for its radius is a "one-degree curve." The exact length of radius which with an angle of one degree has a chord of 100 feet is found to be 5,729.65 feet. For sake of convenience 5,730 feet is usually taken as the radius of a one-degree curve. If the angle at the point of the V is two degrees and the sides are prolonged until 100 feet apart, the length of each side is (almost exactly) one-half as long as when the angle is one degree, or one-half of 5,730==2,865 feet. For a three-degree curve the radius is one-third of 5,730; for a four-degree curve one-fourth of 5,730; and so on. For perfect exactness the length of 100 feet should be measured not along a straight line connecting the ends of the V, but along the line of the circle of which the sides of the V are radii—i. e., the arc should be used and not the chord. The difference, however, is so slight for any curves ordinarily used on main lines of standard gauge railroad as to be ignored in practice. But for extremely sharp curves, such as our locomotives both wide and narrow gauge are built for, a considerable mathematical error would be involved by the use of 100-foot chords and calculating the length of the radius by dividing 5,730 by the degree of curve. The ratio of this error increases with the degree of curve, since the error is caused by neglecting the difference between the length of the chord and of the arc (e. g., a 60-degree curve and 100-foot chord mathematically compels 100-feet radius instead of 95½ feet; a 90-degree curve and 100-foot chord, 71+feet radius instead of 63.6 feet).
In practice, however, the formula of dividing 5,730 by the degree of curve (R==5730/D) is almost universally used, and the mathematical error is avoided by using two 50-foot chords for curves ranging from 10 to 16 degrees, and four 25-foot chords for curves ranging from 17 to 30 degrees, and further sub-dividing for sharper curves, since this almost exactly balances the error, and it is also a practical necessity in laying out sharp curves to use short chords.
For extremely sharp curves, or say 100 feet radius or less, it is usual to express the curve by feet radius rather than by degrees. The table following is computed by the formula R==5730/D, and fractions of feet are not taken into account.
Note—The above engineers' method of designating the rate of curvature of a railway curve must not be confounded with the number of degrees of a circle occupied by the curved portion of the track; thus a curved track making a quarter turn, equivalent to a right angle, will always be 90 degrees of a circle (360 degrees—the whole circle) no matter whether the curve is an easy one with a long radius or a sharp one with a short radius.
| Degrees | Radius | |
|---|---|---|
| 1 | 5730 | feet |
| 2 | 2865 | " |
| 3 | 1910 | " |
| 4 | 1432 | " |
| 5 | 1146 | " |
| 6 | 955 | " |
| 7 | 819 | " |
| 8 | 717 | " |
| 9 | 637 | " |
| 10 | 573 | " |
| 11 | 521 | " |
| 12 | 478 | " |
| 13 | 441 | " |
| 14 | 410 | " |
| 15 | 382 | " |
| 16 | 358 | " |
| 17 | 337 | " |
| 18 | 318 | " |
| 19 | 302 | " |
| 20 | 287 | " |
| 21 | 273 | " |
| 22 | 260 | " |
| 23 | 249 | " |
| 24 | 239 | " |
| 25 | 229 | " |
| 26 | 220 | " |
| 27 | 212 | " |
| 28 | 205 | " |
| 29 | 198 | " |
| 30 | 191 | " |
| 31 | 185 | " |
| 32 | 179 | " |
| 33 | 174 | " |
| 34 | 169 | " |
| 35 | 163 | " |
| 36 | 159 | " |
| 37 | 155 | " |
| 38 | 151 | " |
| 39 | 147 | " |
| 40 | 143 | " |
| 41 | 140 | " |
| 42 | 136 | " |
| 43 | 133 | " |
| 44 | 130 | " |
| 45 | 127 | " |
| 46 | 125 | " |
| 47 | 122 | " |
| 48 | 119 | " |
| 49 | 117 | " |
| 50 | 115 | " |
| 51 | 112 | " |
| 52 | 110 | " |
| 53 | 108 | " |
| 54 | 106 | " |
| 55 | 104 | " |
| 56 | 102 | " |
| 57 | 100 | " |
| 58 | 99 | " |
| 59 | 97 | " |
| 60 | 95 | " |
[Rule for Measuring the Radius of a Sharp Curve]
Stretch a string, say 20 feet long, or longer if the curve is not a sharp one, across the curve corresponding to the line from A to C in the diagram. Then measure from B, the center of the line A C, and at right angles with it, to the rail at D.
Multiply the distance A to B, or one-half the length of the string in inches, by itself; measure the distance D to B in inches, and multiply it by itself. Add these two products and divide the sum by twice the distance from B to D, measured exactly in inches and fractional parts of inches. This will give the radius of the curve in inches.
It may be more convenient to use a straight edge instead of a string. Care must be taken to have the ends of the string or straight edge touch the same part of the rail as is taken in measuring the distance from the center. If the string touches the bottom of the rail flange at each end, and the center measurement is made to the rail head, the result will not be correct.
In practice it will be found best to make trials on different parts of the curve to allow for irregularities. It is best not to measure across from one end of the curved track to the other even when the curve is so located that this is possible, since if any portion of the straight track at either end of the curve is included the result will be incorrect. This rule does not apply to curves of over one-half circle if the line is drawn connecting the two ends of the curve. It is a good plan to make the measurement on the inside of the outer rail of the curve, as this is often more convenient. In this case one-half of the width of gauge should be deducted from the radius when calculated, as the radius of the curve should be measured to the center of the track.
Example—Let A C be a 20-foot string; half the distance, or A B, is then 10 feet, or 120 inches. Suppose B D is found on measurement to be 3 inches. Then 120 multiplied by 120 is 14,400, and 3 multiplied by 3 is 9; 14,400 added to 9 is 14,409, which, divided by twice 3, or 6, equals 2,401½ inches, or 200 feet 1½ inches, which is the radius of the curve.
| A B2 plus B D2 | ||
| The formula is thus stated: | == R. | |
| 2 B D |
| 1202 plus 32 | ||
| Or applied to the above example, | == 2,401½ in. == 200 feet 1½ inches. | |
| 2 times 3 |
MATERIAL FOR ONE MILE OF TRACK
| Weight per Yard | Tons per Mile | ||
|---|---|---|---|
| 8 | lbs. | 12 | 4-7 |
| 10 | " | 15 | 5-7 |
| 12 | " | 18 | 6-7 |
| 16 | " | 25 | 1-7 |
| 20 | " | 31 | 3-7 |
| 25 | " | 39 | 2-7 |
| 30 | " | 47 | 1-7 |
| 35 | " | 55 | |
| 40 | " | 62 | 6-7 |
| 45 | " | 70 | 5-7 |
| 50 | " | 78 | 4-7 |
| 52 | " | 81 | 5-7 |
| 56 | " | 88 | |
| 60 | " | 94 | 2-7 |
| 63 | " | 99 | |
| 65 | " | 102 | 1-7 |
| 70 | " | 110 | |
| 75 | " | 117 | 6-7 |
| Number complete joints per mile 90 per cent, 30 ft. and 10 per cent, short length rails, 358. | |||
| Size Under Head | Average per Keg | For Rail Weighing | Kegs per Mile | |||||
|---|---|---|---|---|---|---|---|---|
| 6 | × | 9-16 | 320 | 75 | to | 100 | lbs. | 32 |
| 5½ | × | 9-16 | 375 | 52 | to | 75 | " | 30 |
| 5 | × | 9-16 | 400 | 45 | to | 60 | " | 26 |
| 5 | × | 1-2 | 450 | 35 | to | 45 | " | 23½ |
| 4½ | × | 1-2 | 530 | 25 | to | 40 | " | 20 |
| 4½ | × | 7-16 | 680 | 25 | to | 40 | " | 15½ |
| 4 | × | 1-2 | 600 | 20 | to | 35 | " | 17 2-3 |
| 4 | × | 7-16 | 720 | 20 | to | 35 | " | 14¾ |
| 4 | × | 3-8 | 1000 | 16 | to | 30 | " | 10½ |
| 3½ | × | 1-2 | 800 | 16 | to | 25 | " | 11 |
| 3½ | × | 7-16 | 900 | 16 | to | 25 | " | 12 |
| 3½ | × | 3-8 | 1190 | 12 | to | 20 | " | 9 |
| 3 | × | 3-8 | 1240 | 12 | to | 20 | " | 8½ |
| 2½ | × | 3-8 | 1342 | 8 | to | 16 | " | 7⅛ |
[We are prepared to furnish to exceptional advantage—]
- BRIDGE BUILDING MATERIALS
- STRUCTURALS
- UPSET RODS
- BOLTS AND RIVETS
- LIGHT AND HEAVY FORGINGS
- STEEL CASTINGS
- MALLEABLE IRON CASTINGS
- GRAY IRON CASTINGS
- JOURNAL BEARINGS
- CAR WHEELS
Quotations and Specifications furnished on Application. Special Attention given to Rush Orders.
The following well known corporations are among those who have purchased equipment of us and availed themselves of our Service Department:
- NORTHERN PACIFIC R. R.
- O. W. R. & N. R. R.
- C. M. & ST. P. R. R.
- OREGON ELECTRIC RY. CO.
- SPOKANE & INLAND R. R.
- STONE & WEBSTER
- B. C. ELECTRIC RY. CO.
- PENINSULAR RY. CO.
- U. S. GOVERNMENT
- TIENTSIN-PUKOW R. R.
- SUN NING RY.
- YOSEMITE VALLEY R. R.
and hundreds of the leading logging, milling, mining and contracting concerns of the Pacific Northwest and Alaska.
SEATTLE CAR & FOUNDRY CO.
UNION PRINTING Co. SEATTLE
Compiled by Foulser Advertising Service
[TRANSCRIBER'S NOTES]
The List of Subjects on p. [7] includes Bunks, McLafferty yet there is no corresponding section in the text.
The page title for p. [62] split the paragraph. Moved the page title to a position immediately prior to the first illustration.
There was no item number 66 on p. [17].
[Most pages had a decorative rectangular border with "Seattle Car _and_ Foundry" at the top.] [Most of the other pages had a simple triple line rectangular border.]
![[Most pages had a decorative rectangular border with "Seattle Car _and_ Foundry" at the top.]](#4423115570811699203_frame_002.jpg.id-1453906133559283255.wrap-0.html.html){kind=link}
![[Most of the other pages had a simple triple line rectangular border.]](#4423115570811699203_frame_001.jpg.id-5393100630817579662.wrap-0.html.html){kind=link}
Silently corrected simple spelling, grammar, and typographical errors.
Retained anachronistic and non-standard spellings as printed.