A Treatise on Highway Construction

1044. Pavements and Horseshoes.-A horse's hoof shod with a heavy iron shoe strikes a blow resembling that struck by a hammer in the hand of man, but with considerably more energy. When the shoes are furnished with sharp toe-pieces and heel-calks, as in the prevailing form, the combined effect of a cutting chisel and hammer is produced. This form of shoe is rendered necessary to obtain foothold on the rough and ill-conditioned pavements generally found in use, but on smooth improved pavements it is not required. Indeed, its use produces exceedingly destructive effects. Brokenstone pavements suffer the most; the surface is excavated and the stones displaced. Block pavements also suffer considerably; the blocks are chipped and rounded until they assume the form of boulders. Wood and asphalt probably suffer the least, unless the blows fall successively in the same place.

The European pavements are not subjected to the destroying effect of this form of shoe. There smooth, flat shoes of light weight are used, and in many localities the form of the shoe is regulated by law.

Flat shoes and wide tires have a large effect in the conservation of pavements, and where improved pavements have been introduced the imposition of a tax would be warranted to hasten their

use.

1045. Annual Cost of Structures.-The annual cost of any structure, or the annual payments required to maintain the structure in perpetuity, is composed of three elements:

(1) Interest on First Cost.-If the structure is built with horrowed money, interest must be paid as a matter of course and charged against the structure. If it be not borrowed, but furnished by the owner, the case is not essentially different. He takes it from some other investment which would pay interest, and is a loser if the new structure does not make him the same return. Any structure which cannot bear this charge of interest, is a bad investment. But if the structure be neither built nor bought, but inherited by its present owner, its first cost to him is what he could sell it for; if it have no market value, its cost to him is nothing, and he may omit the interest charge entirely.

The general principle is that the cost of any structure is the amount of capital which its owner voluntarily keeps in it, and that on this amount the interest must be charged against the structure.

(2) Annual Repairs.-Under this head is included every expense of preserving the property, such as ordinary repairs, watchmen, insurance, etc. If by these means the property is maintained in its original condition, " as good as new," these two elements embrace the whole annual cost. But there are many cases in which this is not true. In spite of the annual repairs, the structure after a time wears out and must be replaced either in whole or in part by a new one. If it be a bridge, it has to be rebuilt; if it be a pavement or a set of rails, they have to be taken up and replaced by new ones. This makes a further payment necessary, viz.:

(3) Annual Payments to the Renewal Fund.-By this is meant the proportion of the sum finally needed to renew the structure chargeable to each year. If this fund be raised all at once when it is actually needed, the amount chargeable to each year is the total sum divided by the number of years in the life of the structure. But the amount of each contribution will be made very much smaller if it is actually paid each year and each payment improved at compound interest after the manner of an ordinary sinking fund for the extinction of bonds. This method distributes the burden equally over the whole term and makes it much lighter than is possible in any other way. Taking it for granted that this is the plan adopted, the formula to ascertain the value of these elements will be as follows:

Let

total annual cost, or the annual payments needed to maintain the structure in perpetuity;

a = first cost:

b =

value of old materials when no longer fit for use in the structure, and also the value of so much of the structure as needs no renewal;

c = cost of annual repairs;

n = number of years the structure lasts before renewal;

m = amount or final value of an annuity of $1.00 com

pounded each year for n years, =

(1 + r)” — 1 ;

The final cost of renewal = a b. If the renewals should exceed first cost, b will equal the excess, and the total cost of renewal will = a + b.

To find the annual payment to the renewal fund, call it p.
Then will 1m::p: a − b.

The annual interest charge will be = ar.

The total annual cost of the structure will therefore be

The factor (1+r)" is the amount of one dollar at compound interest for n years and is given in Table LXXXIX.

As an example of the application of the formula, let the problem be to determine the relative economy of a wooden and an iron bridge for a given place. Let the length of the bridge be 500 feet, or 4 spans of 125 feet each, and let the other data be as follows: For the wooden bridge

$25 per foot.= $12,500;

value of iron when the bridge is worn out;

a = first cost