Methods of Determining Waterway

Talbot's Formula.

This formula was proposed by Prof. A. N. Talbot in 1888,t and is the one most generally employed by engineers. It is: in which C is a coefficient which varies from 1 to }. Data from various States give values for C as follows: "For steep and rocky ground, C varies from to 1. For rolling agricultural country subject to floods at times of melting of snow, and with the length of valley three or four times its width, C is about i; and if the stream is longer in proportion to the area, decrease C. In districts not affected by accumlated snow, and where the length of the valley is several times the width, 4 or or even less, may be used. C should be increased for steep side slopes, especially if the upper part of the valley has a much greater fall than the channel at the culvert." The author has tested the above formula by numerous culverts and small bridges in a small city and also by culverts under high ways in the country (all slightly rolling prairie), and finds that it agrees fairly well with the experience of fifteen to twenty years. In these tests, it was found that waterways proportioned by this formula will probably be slightly flooded, and consequently be com pelled to discharge under a small head, once every four or five years.

In both of the preceding formulas it will be noticed that the large range of the "constant" C affords ample opportunity for the exercise of good judgment, and makes the results obtained by either formula almost wholly a matter of opinion; in other words, the above formulas with their variable coefficients should be regarded as giving the probable maximum and minimum area of waterway, and should be used more as a guide to the judgment than as an infallible mathematical rule.

Direct Observation.

Valuable data on the proper size of any particular culvert may be obtained (1) by observing the existing openings on the same stream, (2) by measuring—preferably at time . of high water—a cross section of the stream at some narrow place, and (3) by determining the height of high water as indicated by drift and the evidence of the inhabitants of the neighborhood. With these data and a careful consideration of the various matters referred to in § 1117, it is possible to determine the proper area of waterway with a reasonable degree of accuracy.

Ordinarily it is wise to take into account a probable increase of flow as the country becomes better improved. However, in con structing any structure, it is not wise to make it absolutely safe against every possible contingency that may arise, for the expen diture necessitated by such a course would be an unjustifiable extravagance. Washouts can not be prevented altogether, nor

their liability reduced to a minimum, without an unreasonable expenditure. It has been said—and within reasonable limits it is true—that if some of a number of culverts are not carried away each year, they are not well designed; that is to say, it is only a question of time when a properly proportioned culvert will perish in some excessive flood. It is easy to make a culvert large enough to be safe under all circumstances, but the difference in cost between such a structure and one that would be reasonably safe would probably much more than overbalance the losses from the washing out of an occasional culvert. It is seldom justifiable to provide for all that may possibly happen in the course of fifty or one hundred years. One dollar at 5 per cent compound interest will amount to $11.47 in 50 years and to $131.50 in 100 years. Of course, the question is not purely one of finance, but also one of safety to human life; but even then it logically follows that, unless the engineer is prepared to spend $131.50 to avoid a given danger now, he is not justified in spending $1 to avoid a similar danger 100 years hence. This phase of the problem is very important, but is foreign to the subject of this volume.

In the construction of a new railroad, considerations of first cost, time, and a lack of knowledge of the amount of future traffic as well as ignorance of the physical features of the country, usually require that temporary structures be first put in, to be re placed by permanent ones later. In the meantime an incidental but very important duty of the engineer is to make a careful study of the requirement of the permanent structures which will ulti mately replace the temporary ones. The high-water mark of streams and the effect of floods, even in water courses ordinarily dry, should be recorded. With these data the proper proportioning of the water way of the permanent structures becomes a comparatively easy task.

Most of the older railroads, as a result of their experience, have tables or formulas for waterways which are quite accurate for their particular territory and forms of culverts. For several such formulas and tables, see Bulletin No. 108 of the American Railway Engineer ing and Maintenance of Way Association, February, 1909, page 89-146.