The following objections are urged against the curved profile: 1. The greater slope near the side causes vehicles to seek the center, and consequently the road wears unequally. 2. Owing to the ex cess of traffic at the center, the road soon wears hollow and holds water, which is both unsightly and a damage to the road. 3. The slope is so slight near the center that a small settlement of the subgrade causes a depression of the surface, which holds water.
The only objection to a surface composed of two planes is that the flanks wear hollow and hold water; but this objection has less force than any of the three against the curved profile.
Curved Profile. Although the curved profile is usually referred to as being " an arc of a circle or a flat ellipse," it is usu ally laid out as the arc of a parabola. However, the difference of curvature is not material.
To lay out the parabolic arc proceed as follows: In Fig. 47, AC is the crown, i. e., the difference in height between the side and the center. AB represents a horizontal line through the crown. In street pavements A is usually the top of the curb. The curved line BC represents the surface of the finished road. To find the distance from AB down to the line BC, divide the half width of roadway, AB, into any number of equal parts, say, n, and desig nate the distance from the point 1 on AB vertically down to BC by x; then by the principles of the parabola, and the from point 2 down to the road surface is or 4 x, and the distance from 3 is x or 9 x. In practice a string with knots in it to represent the points of division of AB is stretched from the top of the curbs or from stakes driven at the edge of the broken stone, and then the ordinates computed as above are measured with a pocket rule.
There are a number of arbitrary rules for securing a curved profile, of which the following is one of the most elaborate, the most scientific, and the most easily remembered: " Divide the roadway into three equal parts, and starting from the center give a fall of 0.03 ft. per foot for the first part, 0.04 ft. for the second
section, and 0.05 ft. for the last section. If the roadway is ex tremely wide, divide the half roadway into four parts, and give a fall of 0.02, 0.03, 0.04, and 0.05 ft. per foot to the respective sections. If the roadway is very narrow, divide the half roadway into two parts, and give falls of 0.04 and 0.05 ft. per foot to the two sections respectively." This rule gives more slope at the center and less at the sides than the parabolic section, and for roadways of medium width, it gives an average transverse slope of half an inch to the foot or 1 in 24. This rule was used on the road shown in Fig. 50, page 209.
Regularity and evenness of crown is more important than the mathematical form of the cross section. A slight depression be comes very conspicuous when filled with water; and besides the water standing upon the surface softens it and tends to increase the depression. With a little care in filling the low places devel oped during the rolling, it is possible to build a broken-stone road with an almost mathematically exact crown.