NOTE B. Page 65. THE resistance produced by collision is seldom a constant retarding force; loose stones, or hard substances, are sometimes met with, and will give a sudden check to the horses, according to the height of the obstacle: the momentum thus destroyed is often very considerable. The power required to draw a wheel over a stone or other obstruction may be thus determined:-Suppose ABD to represent a carriage wheel 52 inches in diameter, the axis 2.5 inches in diameter, the weight of the wheel 200 lbs., and the load on the axle 300 lbs. Let a stone or other obstacle four inches high be represented as at S: the power necessary to be applied to the axle to draw the wheel over the stone is thus found:— Suppose P the power which is just sufficient to keep the wheel balanced, or in equilibrio, when acting from the centre C in the direction C P. The force acting against this power is gravity, and is equal to the weight of the wheel and load on the axle, acting from the centre Cin the direction CB. These forces act together against the point D in the direction CD. Gravity acts in the direction CB with the energy or length of lever D B, and the power acts in the direction C P, with the leverage BC; and the equation of equilibrium will be W DB PxCB. In this equation, CB the radius of the wheel diminished by the height of the obstacle, and BD equals DC-BC; hence the Wx/DC-BC2 power P = DC-DS -: in the present example, the road to Lichborough to the upper angle of Mr. Drayson's osier plantation, and the lowering of the summit at Foster's Booth would extend into Cold Higham Fields, nearly similar to that in the first plan. All the rest of the road would remain as at present. If this improvement were made, the mean expense of drawing one ton over it between the sixty-fifth milestone and the Crown Inn at Foster's Booth, would be 79.8450 pence, as shown in p. 416.: the saving, therefore, per ton, would be 2.2207 pence, and for 170 tons it would be 377.5190 pence; which would be interest for 11,4201. The estimated expense of this improvement, as detailed in p. 421., is 14,1717. The difference is 2,7517.; which shows the amount of loss the public would sustain by completing the work here described. PLAN, No. V. By this plan it is proposed to raise the valley forty feet, to lower the summit at Foster's Booth twentyseven feet, and the summit at the Angel eighteen feet. If this improvement was adopted, the new line would run. along the south side of the present road to near the sand pits, where it would cross it obliquely, and entering a small ravine on the opposite side, it would cross the valley in a straight line for the upper angle of the osier plantation. At this point it would again cross to the south side of the present line, and follow the direction described in the first plan. The saving in expense of drawing a ton over this line of road, when made as above described, would be 5.0200 pence (p.417.), and for 170 tons it would be 475.39 pence, which would be interest for 25,8157. The estimated expense of this improvement, as detailed in p. 422., is 19,607. The difference is 5,2087., which shows the amount of profit the public would acquire by completing the works here described. Expense of drawing one ton by a stage coach over the present line of road from the sixty-fifth milestone to the Crown Inn at Foster's Booth. |