By T. O'CONOR SLOANE, Ph.D.
IN a recent journal of this city an article descriptive of a railroad accident appeared, under the heading, "Derailed by a Sun-Kink." The title doubtless puzzled many readers. The term indicates that the rails were thrown out of line by expansion, due to the heat of the sun. Few accidents are attributed to this cause, though it may be responsible for more than are supposed. It will be interesting to determine a few maxima of distortion that can be thus produced.
The expansion of metals under the influence of heat is very slight. A mile of iron rails, for an elevation of temperature of 100° Fahr., only expands two feet eight and one half inches. This is so little as to be readily taken up by the one hundred and seventy-six joints that exist in that length of rails. If the rails were laid in very cold weather, in solid contact with each other, then, on a warm, sunny day, a consider-able disalignment could be produced. To find the maximum for the mile of rails, we must suppose that the line breaks in the middle, and bulges out like a flattened letter Y. In this condition of things, the broken line of rail, with the original line for base, would form an equilateral triangle. The altitude of the triangle may be calculated by the familiar rule of the reverse of the hypotenuse. It will be found equal to nearly ninety feet. The result, though deduced by the simplest of calculations, is an astonishing one. It is enough to account for any number of "sun-kinks." The books are very prolific of instances of expansion by heat, and always speak of the expansion of rails. They do not, however, allude to the geometrical element of danger; they concern themselves only with the physical one.
It is obvious that a mile of rails would never expand in this way. Disturbances of alignment would be confined to smaller sections. The calculation shows a maximum that would never be attained. The conditions might be fulfilled by four rails. For the given elevation of temperature they would expand about eight tenths of an inch, with a lateral displacement of over two feet. For an expansion through 50° Fahr., the displacement would be eighteen inches.
Two rails would act in accordance with the supposition most readily. Their total expansion, for 100° Fahr., is four tenths of an inch, and the bulge due to such expansion would be twelve inches. For half the number of degrees it would be nine inches. This shows how very small a rise of temperature might produce a spreading sufficient to throw a train from the track. The smaller figures are as impressive as the ninety feet, when it is recollected that four inches displacement of the rails might produce a catastrophe.
The distortion might be confined to a single rail; and, from what