PART I

CHAPTER I.

RESISTANCE TO TRACTION-WHEELS AND WEIGHTS ON THEM.

PREVIOUS to entering upon the subject proper of road construction, it will be necessary to notice briefly the effects of the resistance to traction on a road surface, and the points to be considered in determining the ruling gradient which should be adopted on a proposed road, according to the situation, and the class of traffic likely to pass over it.

The main external forces which offer resistance to the motion of vehicles upon roads are:-Friction, collision, gravity, and air resistance.

1. External Forces affecting the Motion of Vehicles.-(1) Friction. -This arises from the rolling resistance of the wheel tires when in contact with the surface of the road. It involves the consumption of part of the force exerted by the prime mover. Under friction may be considered the resistance of penetration, which is brought about by a yielding road surface, that is, a weak and inferior road, or one on which gravel or loose stones have been spread, also on soft earth. In these circumstances the resistance to traction is less the larger the diameter of the wheels, as larger wheels sink less and spread along a greater surface than wheels of less diameter; the areas of immersion, however, are equal in either case.

Resistance arising from the friction of the axles is nearly constant at all velocities, and may be neglected. It may, however, be mentioned that with wheels of ordinary construction the resistance amounts to from 1 to 10 of the weight on the axle, or 17 to 22 lbs. to a ton of load. Friction of the wheel on its axle is independent of the condition of the surface of a road.

(2) Collision. This may be caused by the want of uniformity or irregular condition of the surface of a road, or may be occasioned by hard substances, such as loose stones, which give a sudden check to the forward movement of vehicles. Considerable injury is done to a road surface by a vehicle surmounting any hard substance, and the wheels descending with great force tend, by repeated blows, to wear holes in the surface, even on roads maintained with the hardest material. By the carriage being

mounted on springs, the power required to draw a vehicle over an obstacle of this kind is lessened, and the damage to the surface of the road is also greatly reduced.

(3) Gravity.-When a road is on an incline, the additional influence due to gravity, which is proportionate to the steepness of the gradient, must be allowed for in arriving at the greatest tractive force which the prime mover is capable of exerting. The resistance due to gravity on an incline is found approximately by dividing the number of pounds in a ton by the rate. of inclination.

(4) Air Resistance.—This varies according to the velocity of the wind, the area of the surface acted upon, the velocity of the vehicle, and the angle or direction at which it impinges against the plane of the surface. At a velocity of 15 miles an hour, equivalent to a pleasant breeze, the force of the wind is equal to 1.107 lbs. per square foot, while at a velocity of 50 miles an hour, amounting to a violent storm, the force is equal to 12.30 lbs. per square foot of surface.

48

1 30

on

2. Tractive Force. The power required to move vehicles along a road depends on, and varies greatly according to, the condition of the surface of the road. The force or pull which a horse has to exert to draw a load on a level macadamized road in ordinary repair may be taken at 3 of the load, but may vary from of the load on roads in the best condition to roads the surface of which is badly maintained, and broken by ruts and hollows. Authorities, however, differ widely on the subject of the tractive power of the horse, and this will be obvious when the varying diameters of wheels of vehicles and the strength and speed of different animals are taken into consideration, along with their adaptability or training for any particular class of work.

The figures in Table I. are now generally adopted in arriving at the relative tractive force necessary to draw a load on different kinds of

material composing a road surface.* Asphalte is taken as the standard of excellence, and in the extended part of table, under A, 15 lbs. is allowed for the force necessary to draw one ton on a level on that class of road.

On a macadamized road maintained in excellent order the table shows that the force put forth by the prime mover is 45 lbs. per ton, or a tractive force exerted of of the gross load. On a road which is only in fair order, slightly cupped, or has an irregular surface, the tractive force exerted rises to 3 of the gross load, while on a road having the surface covered with loose stones the draught or tractive force necessary to be put forth amounts to, at its worst, of the gross load.

33

1 18

3. The following are the general results of the experiments made by M. Morin upon the resistance of the traction of vehicles on common roads :1st. The resistance to traction is directly proportional to the load, and inversely proportional to the diameter of the wheel.

2nd. Upon a paved or a hard macadamized road the resistance is independent of the width of the tire, when this quantity exceeds from 3 to 4 inches.

3rd. At a walking pace, the resistance to traction is the same, under the same circumstances, for carriages with springs and for carriages without springs.

4th. Upon hard macadamized roads and upon paved roads, the resistance to traction increases with the velocity-the increments of traction being directly proportional to the increments of velocity above the velocity 3.28 feet per second, or about 2 miles per hour. The equal increments of traction thus due to equal increments of velocity are less as the road is smoother, and as the carriage is less rigid or better hung.

5th. Upon soft roads, of earth, or sand, or turf, or roads fresh and thickly gravelled, the resistance to traction is independent of the velocity.

6th. Upon a well-made and compact pavement of hewn stones, the resistance to traction at a walking pace is not more than three-fourths of the resistance upon the best macadamized roads, under similar circumstances. At a trotting pace, the resistances are equal.

7th. The destruction of the road is, in all cases, greater as the diameters of the wheels are less, and it is greater in carriages without than in those with springs.

4. Experiments were carried out by Sir J. Macneil on the road between London and Shrewsbury to ascertain the tractive forces required there, and measured by an instrument devised by him for the purpose. The general results, reduced to that on a level, as given by Telford,† are presented in Table II.

* Vide Report of the Society of Arts on the application of Science and Art to Street Paving and Street Cleansing of the Metropolis, 1875.

+ Seventh Report, etc., p. 13.

5. It appears from experiments carried out at the Royal Agricultural Show at Bedford in 1874, by means of a horse dynamometer, made by Messrs. Easton & Anderson, that 1 lb. of draught was expended on moving every 35.1 lbs. of weight resting on a wagon with fore wheels of 41 inches in diameter, while on the hind wheels having a diameter of 60 inches it was 58.7 lbs. In the former case it was thus equal to a tractive force of 64 lbs. per ton with the smaller size of wheel, compared with 38 lbs. for that of the larger one, which latter figure practically agrees with those in the above table. Of the other trials at the same place with loaded wagons, having tires 2 to 4 inches wide, the average draught was of the gross load, or nearly 46 lbs. per ton. For single horse carts, loaded to about 30 cwt., the wheels of which were from 52 to 62 inches in diameter, and the tires 3 to 4 inches wide, the tractive force was found to be on a level macadamized road at a walking pace of the gross load, or 34 lbs. per ton. With other carts having wheels of slightly larger diameter and a greater load, the average draught under similar conditions was found to be 1 of the gross load, or 44 lbs. per ton.

6. There can be no question that the smoother and harder the surface of a road is, the tractive force or draught necessary to move a vehicle will be less. It must also be apparent that the work of one horse on a level and well maintained road, may be easily increased two or three times, if the surface of the road is inferior in condition, by reason of any inequalities or ruts on the surface. In other words, four horses are enabled to do the work of five, or three of four, by keeping the roads in an efficient state of repair.

7. Gradients. In ascending an incline the prime mover has to exert an additional force which has to be added to that of resistance on the level. This is approximately equal to the gross load divided by the rate. of gradient. It can be shown diagrammatically what additional resistance is occasioned when the road is inclined against the load instead of being level.

In the accompanying diagram fig. 7, the whole weight is supposed to

be supported on one pair of wheels, being the simplest form in which this additional resistance may be investigated, and which can be shown in the following manner.

Let AB represent a part of an inclined road, D a vehicle sustained in its position by a force acting in the direction DG, DW the weight of the vehicle and load or the force of gravity acting vertically downwards. It is evident that the vehicle is sustained in equilibrium upon the inclined plane by these two forces, and, in addition, by the resistance of the road surface to the pressure of the vehicle acting at right angles to the incline of the road. To determine the relative magnitude of these three forces, draw the horizontal line BC and the vertical line AC; then since the two lines DE and AC are parallel and are both cut by the line AB, it follows that they must make the two angles DEF and BAC equal; likewise, the two angles DFE and ACB are equal; therefore, the remaining angles EDF and ABC are equal, and the two triangles DEF and BAC are similar. As the three sides of the former are proportional to the three forces by which the vehicle is sustained in equilibrium, so also are the three sides of the latter; viz., AB or the length of the road is proportional to W, or the

weight of the vehicle and its load; AC or the vertical rise is the same to E, or the force required to sustain the vehicle on the inclined plane; and BC or the horizontal distance in which the rise occurs, to P, or the force with which the

And if BC be of such a length that the vertical rise AC of the road equals one foot, then the force DG will be represented by

in which B is the angle ABC.

These formulæ reduced to words are as follows:

To find the force requisite to sustain a vehicle upon an inclined road, the effects of friction being neglected, divide the weight of the vehicle and its load by the inclined length of the road, the vertical rise of which is one foot, and the quotient is the force required.