Accommodation summits have to be introduced between street intersections—first, in hilly localities, to avoid excessive excavation; and second, when the intersecting streets are level or nearly so, for the purpose of obtaining the fall necessary for surface drainage.
The elevation and location of these summits may be calculated as follows: Let Abe the elevation of the highest corner; B, the eleva tion of the lowest corner; D, the distance from corner to corue- ; and R, the rate of the accommodation grade. The elevation of the summit is equal to The distance from A or B is found by subtracting the elevation of either A or B from this quotient, and dividing the result by the rate of grade. Or the summits may be located mechanically by specially prepared scales. Prepare two scales divided to correspond to the rate of grade; that is, if the rate of grade be 1 foot per 100 feet, then one division of the scale should equal 100 feet on the map scale. These divisions may be subdivided into tenths. One scale should read from right to left, and one from left to right.
To use the scales, place them on the map so that their figures correspond with the corner elevations; then, as the scales read in op posite directions, there is of course some point at which the opposite readings will be the same: this point is the location of the summits; and the figures read off the scale its elevation. If the difference in elevation of the corners is such as not to require an intermediate sum mit for drainage, it will be apparent as soon as the scales are placed in position.
When an accommodation summit is employed, it should be form ed by joining the two straight grade lines by a vertical curve, as described in Part I. The curve should be used both in the crown of the street and in the curb and footpath.
Where the grade is level between intersections, sufficient fall for surface drainage may be secured without the aid of accommodation summits, by arranging the grades as shown in Fig. 49. The curb is set level between the corners; a summit is formed in the gutter; and receiving basins are placed at each corner.
Transverse Grade. In transverse grade the street should be level; that is, the curbs on opposite sides should be at the same level, and the street crown rise equally from each side to the center. But in
hillside streets this condition cannot always be fulfilled, and opposite sides of the street may differ as much as five feet; in such cases the engineer will have to use his discretion as to whether he shall adopt a straight slope inclining to the lower side, thus draining the whole street by the lower gutter, or adopt the three-curb method and sod the slope of the higher side.
In the improvement of old streets with the sides at different levels, much difficulty will be met, especially where shade trees have to be spared. In such cases, recognized methods have to be abandoned, and the engineer will have to adopt methods of overcoming the difficulties in accordance with the conditions and necessities of each particular case. Figs. 50, 51, and 52 illustrate several typical arrangements in the case of streets in which the opposite sides are at different levels. Transverse Contour or Crown. The reason for crowning a ment—i. e., making the center higher than the sides—is to provide for the rapid drainage of the surface. The most suitable form for the crown is the parabolic curve, which may be started at the curb line, or at the edge of the gutter adjoining the carriage-way about one foot from the curb. Fig. 53 shows this form, which is obtained by dividing the ordinate or width from the gutter to the center of the street into ten equal parts, and raising perpendiculars the length of which will be determined by multiplying the rise at the center by the respective mnnber of each perpendicular in the diagram. The amounts thus obtained can be added to the rod readings; and the stakes, set at the proper distance across the street, with their tops at this level, will give the required curve.
The amount of transverse rise, or the height of the center above the gutters, varies with the different paving materials, smooth pave ments requiring the least, and rough ones and earth the greatest. The rise is generally stated in a proportion of the width of the carriage-way. The most suitable proportions are: Stone blocks, rise at center, ,16 width of carriage-way.