of the road into account, and generally neither do they make any allowance for the different kinds of surfaces with which the pavements may be constructed. Following are given some of the crown formulas which have been used quite generally in different parts of the country in connection with the construction of city pavements.

The following formula, according to T. J. Powell,* Assoc. M. Am. Soc. C. E., was deduced by Joseph W. Dare:

centage; W = width of roadway in inches.

The distribution of the above crown, when curbs are level,

is obtained by the formula

8 C 0.3 R

=

d, where d

= the transverse

grade, expressed as a percentage, R = width of roadway in feet.

In Fig. 29,

a and b = the elevation at the gutters, expressed in feet and hundredths. In Fig. 29 it is shown that the transverse slope

between the crown and quarter point is just one-half what it is between the quarter point and gutter.

The crown where the curbs are at different elevations is given by the following formulas and Fig. 30. The letters have the same significance as above.

*See Trans. Am. Soc. C. E., vol. 73, page 225.

This method of computing the crowns of streets has been in use in Washington, D. C., since 1894, and is applicable for all widths up to 50 feet. The crowns obtained are for a sheet asphalt pavement. For pavements having a rougher surface,

such as block pavements, Mr. Powell says the formulas can be used with good results by simply adding 1 inch to the crown obtained by the formula.

Formulas devised in 1902 by Andrew Rosewater are as follows:

For brick, stone block, wood block, and compressed European W (100 - 4√)

rock asphalt, C =

6000

It will be noticed that this formula gives the total amount of crown, but nothing relative to its distribution. The total amount of crown being known, however, the elevations at any other points throughout the width of the street can be found by assuming the curve to be a parabola and figuring the ordinates to the curve. The ordinates will decrease as the squares of the distances out from the center.

The following rules were given by George C. Warren* in a paper presented before the American Society of Municipal Improvements in 1909. As will be seen, the rules take into account the grade, width, and kind of surface with which the pavement is built:

"For pavements having smooth surfaces such as asphalt, creosoted blocks, and grouted stone blocks and brick, and having a grade of 2 percent or less, with no car tracks, make the crown I inch to each 6 feet of width between curbs.

"For pavements providing more secure foothold, such as stone blocks and brick, having bitumen filled joints, macadam or bitulithic on streets having a 2 percent or less grade, make the crown I inch to each 4 feet of width.

"If the street has car tracks, deduct the total width outside to outside of rails from the width between curbs and divide the difference (double width between track and curb) by 6 and 4 respectively.

"For grades between 2 percent and 4 percent, provide onehalf the crown provided by the above computation.

"For grades above 4 percent, provide a crown one-third that of the above computation."

To find elevations for quarter points and points midway between the crown and the quarter point and the quarter point and the curb the following rule, suggested by G. B. Zakniser and endorsed by Mr. Warren, is used in connection with the above rules:

"Drop one-eighth the crown at the crown mid-quarter point; drop one-third the crown at the quarter point; drop five-eighths

*See Engineering-Contracting, Nov. 10, 1909.

the crown at the curb mid-quarter point." By quarter point is meant the point midway between the center of the carriageway and the curb or, in the case of streets on which car tracks are placed, it is the point midway between the outside rail and curb.

DRAINAGE AND FOUNDATIONS. The results of the preliminary examination will furnish much valuable information relative to surface and subdrainage and the foundation. A consideration of these subjects, however, will be given in full in their respective chapters.

SELECTION OF TYPE OF SURFACE. There are many essential points relative to the materials used and the methods of construction employed that influence the selection of the type of surface, and for this reason it will not be considered further in this chapter, although it is an important part of the design.

ESTIMATES. When the grade of the road and the form of cross-section have been adopted an estimate can be made of the amount of work to be done.

A template corresponding to the form of cross-section should be cut out of some stiff cardboard or a piece of celluloid, the scale used being the same as the scale with which the crosssections have been plotted. The templates are cut on lines showing the surface of the subgrade. The elevations of points on the subgrade for each 50- or 100-foot station on the center line

www

D

E

Fig. 31.

of the road or street are computed and plotted on the crosssections of the original surface at stations to which they correspond.

In Fig. 31 the ground line of the original surface is shown by the line A B. The line AC DE F, drawn by means of the template, represents the cross-section of the subgrade and sides of the proposed road. The point P corresponds to the elevation of the subgrade. It is seen that the area A C D is in cut and the

area D E F in fill. These areas may be determined by means of a planimeter, by counting the squares included between the lines or by dividing the areas into approximate geometrical figures and computing the same. The method to be adopted will depend upon the form of cross-section or profile paper, the scale used, and the personal equation.

The areas at each 50- or 100-foot station and at those odd stations which mark abrupt changes in the slope of the earth's surface are determined. The yardage is computed by the average end area formula. Let A1 and A2 be the areas in square feet of cut or fill at any two adjacent stations, a distance L feet apart. The volume in cubic yards of cut or fill for this length will then be

If the station interval is uniform the yardage for any desired length can be found as follows: Let A1, A2, A3, etc. . . . An be the areas in cut or fill at the different stations at a uniform interval apart, the total length between the stations A1 and An being L. n equals the number of stations chosen. If the areas are in square feet and L is in feet, the volume for this length will be

A n − 1) + An L.

It is not necessary to estimate the areas closer than the nearest square foot. Except in very heavy work the actual stations defining the line of intersection of the proposed roadbed and the original ground surface, or in other words the true zero of the cuts and fills, need not be found. The station without any area in cut just immediately preceding a station that has such an area may be considered to be the beginning of the cut; the beginning of a fill would be the station preceding one which has no area in fill; in a similar manner the ends of the cuts and fills would be a station immediately following. If the cross-sections are estimated for each 50-foot station, the above method does not involve much error, and the error that does exist makes the quantities larger.