SECTION OF THE RAIL.

286. A good rail must be able to act as a girder, or supporter, between the ties, as a lateral guide upon curves; and must possess a top surface of sufficient hardness and size to resist the rolling wear of the wheels.

		Lbs. per yard.	Tons per mile. (2,240 lbs.).
One square inch	of rail section weighs,	9.9	15.72
Two inches	of rail section weighs,	19.8	31.42
Three inches	of rail section weighs,	29.7	47.14
Four inches	of rail section weighs,	39.6	62.84
Five inches	of rail section weighs,	49.5	78.56
Six inches	of rail section weighs,	59.4	94.28
Seven inches	of rail section weighs,	69.3	110.00
Eight inches	of rail section weighs,	79.2	124.50
Nine inches	of rail section weighs,	89.1	140.01
Ten inches	of rail section weighs,	99.0	155.57
		Single line of rails.	Double line of rails.

Thus, at sixty dollars per ton, each square inch of section costs $943.20 per mile, or $94,320 per one hundred miles, whence the necessity of rolling the rail to the form which shall give the greatest strength with the least weight.

The sections most in use in America are shown in fig. 136, and 137.

Fig. 136.

Fig. 136 gives the most direct bearing, is compact, and brings the fibres at top and bottom more directly in opposition with the compressive and extensive strains. The top of the rail being curved to a radius of ten or twelve inches, the load is applied nearly to a single point; whence the whole resistance in fig. 137, depends upon the lateral resistance of the piece a b c d to being pushed down.

An objection is sometimes made to fig. 136, on the ground that it splits off on the line n n: this will not be the case when the head is joined to the web by a proper curve, as in fig. 136. This splitting off happens full as often in fig. 137 as may be seen where it is in use; and it might be supposed to act in that manner; because if the weight is transferred at all from the point of application to the web, it must be in the direction e f.

Fig. 137.

The rails in present use upon our roads, weigh from fifty to seventy-five lbs. per lineal yard; and are laid upon cross ties placed at a distance of from two and one half to four feet from centre to centre.

OF THE ACTUAL DIMENSIONS OF RAILS.

Digesting carefully the results of the experiments of Barlow, Fairbairn, and Hodgekinson, and the experience of Mr. W. B. Adams, and other English engineers; also the conclusions arrived at by the Berlin Convention of 1850, appointed to determine the best form of section, we come to the following limiting dimensions.

THE HEAD.

Mr. Barlow limits the width of head at two and one half inches as the maximum; the Berlin Convention, at two and one fourth inches; W. B. Adams, at two and one half; and all of the above recommend supporting the edges of the head well from the rib.

THE VERTICAL RIB.

The experiments of the Prussian engineers fix the thickness for a rail four inches high, at one half of an inch, and a rail four and one half inches high, at 0.6 or 6
10 inch. Mr. Barlow makes it six tenths of an inch for a four and one half inch rail, and 0.75, or three fourths inch for a rail four and five eighths inches high, and for four and three fourths inches high, 0.8, eight tenths inch.

THE BOTTOM FLANGE.

The use of this is more for bearing and fastening, than for supporting strength. The Prussian engineers make three and one half inches an ample base for a rail five inches high. The edge for one half or three fourths of an inch, should be nearly horizontal, or parallel with the base, to allow the spike to have a good bearing.

OF THE INCLINATION.

As the tread of the wheel is conical, the top of the rail must be inclined to fit this cone, otherwise the wear will come upon the inner edge of the rail only. This may be done in two ways; by placing the rail base level, and inclining the vertical axis of the cross section of the rail, and making the tread square with that axis; or by making the rail section true, and inclining the base, either by cutting the tie, or by a wedge placed between the rail and the tie.

OF THE HEAD CURVATURE.

If the top surface of the rail were perfectly flat, and the wheel tire does not happen to fit it exactly, (from want of the proper position of the rail, by settling, or other cause,) the wheel will bear entirely upon one edge, and would soon destroy the rail. To remedy this, a slight convexity is given to the top. Mr. Clark (in R. R. Mach.), recommends the top to be curved to a radius of ten or twelve inches.

OF THE VERTICAL DEPTH (HEIGHT) OF THE RAIL.

Mr. Barlow’s general results are as follow:—

Distance from inside to inside of tie.	Height of rail.
3′ 0″	4½″
3′ 9″	4⅝″
4′ 0″	4¾″
5′ 0″	5″
6′ 0″	51 16″

In the London edition (1836) of Barlow’s Strength of Materials, page 402, in a report to the London and Birmingham Railway Co., upon the best form and upon the strength of rails; after a carefully conducted set of experiments, and an elaborate theoretical deduction of results, the writer comes to the following five sections of rails possessing the maximum strength, with the least weight.

Dimensions.	No. 1.	No. 2.	No. 3.	No. 4.	No. 5.
Height,	4½	4⅝	4¾	5	55 16
Breadth at top,	2¼	2¼	2¼	2¼	2¼
Depth of top,	1	1	1	1	1
Thickness of rib,	0.6	0.75	0.8	0.85	1.0
Width of lower flange,	1¼	1½	1½	1⅔	1⅔
Depth of lower flange,	1	1	1	1⅛	1½
Weight per yard,	51.4	58.8	61.2	67.4	79
Distance C. to C. of ties,	3′	3′9″	4′	5′	6′

This table shows the ratio of material which should be placed in the top and bottom.

With the above dimensions, and joining the curve of the head to the rib at two and one fourth inches from the top of the head, we obtain a strong and well-shaped rail, with the least material possible. See fig. 136.

As an example of the application of the above, the table below has been formed, showing four standard forms, which will be found to unite all of the requirements of good rails; the general form being that of fig. 136.

Dimensions.	The weight of the rail being, in lbs.,
	60	65	70	75
Width of head,	2½	2½	2½	2½
Rad. of top,	12	12	12	12
Height of rail,	4	4¼	4½	4¾
Thickness of rib,	0.6	0.6	0.65	0.7
Breadth of base,	3½	3½	3¾	4
Depth of head at point A B,	2¼	2¼	2½	2½
Thickness at edge of lower web,	½	½	½	½

and the following figures show the weights which should be applied to differently spaced sleepers.

Distance centre to centre of tie.	Distance clear.	Weight of rail.
1½ feet,	1 feet,	60 lbs. per yard.
2 feet,	1½ feet,	60 lbs. per yard.
2¼ feet,	1¾ feet,	60 lbs. per yard.
2½ feet,	2 feet,	60 lbs. per yard.
2¾ feet,	2¼ feet,	65 lbs. per yard.
3 feet,	2½ feet,	65 lbs. per yard.
3¼ feet,	2¾ feet,	70 lbs. per yard.
3½ feet,	3 feet,	75 lbs. per yard.

The amount of inclination or bevel to be given to the cross section of the rail, depends directly upon the cone of the wheel, and indirectly upon the gauge of the track. (See Chapter XIV. part 2.) The radius of curvature being averaged at 2°, or 2,865 feet,

	Feet or	Inches.

For the 4′ 8½″ gauge it should be	.0017	.020
For the 5′ gauge,	.0017	.020
For the 5½′ gauge,	.0019	.022
For the 6′ gauge,	.0021	.025

in the width of the rail, or two and one half inches.

The above dimensions embrace all of the best results of experiment and experience, and at the same time satisfy the conditions demanded by the mechanical and physical nature of the material—iron.