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Useful Charts and Tables. No. 5.

28th February 1907
Page 5
Page 5, 28th February 1907 — Useful Charts and Tables. No. 5.
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Which of the following most accurately describes the problem?

By George Watson, A.M.I.Mech.E.

Road Resistance, Gradient and Tractive Effort.

The resistance to the motion of a motor vehicle is, usually, referred to as the tractive resistance, and the effort required to overcome this resistance is spoken of as the tractive effort. The tractive resistance of roads varies, considerably, and is as low as 8, or to, lb. per ton, for railroads, and as high as 560 lb. per ton, for loose-sand roads; that is to say, a pull, or eflort, of 8, or 56o, lb. would be required, in order In move one ton along a road surface with a corresponding resistance.

The tractive effort required to move a gross weight of " W " tons, along a road having a tractive resistance of " R " lb. per ton, = WR, assuming that the road is a level one. If the road surface makes an angle " a " with the horizontal, and rises, vertically, one foot for a base-line of M " feet, then Tan. " a " = — and the conditions of traction along such a road are very different from those on the level, as, here, the force of gravity has to be overcome, in addition to the resistance of the road to traction; therefore, the formula now becomes (R cos. " a " 2,240 sine " a "). Where T = Tractive effort, in pounds. W = Total load, in tons.

R = Tractive resistance, in pounds per ton. a = Angle of inclination to the horizontal.

It is, however, much more convenient to express an incline as i in M than by giving it in degrees; therefore, the formula undergoes still another change, in order to make it more handy for the use of the motor engineer. It is usually expressed as follows : 2,240 '1= W (R --) Where M = 'The length of road, over which the load would roll while being raised one foot.

From this formula, a chart has been prepared, and, from it, the tractive effort for any given load, resistance, and gradient, may be obtained, without any calculation. A reference to chart No, 1 will, also, show, at the extreme right, a table giving the resistance to traction of various classes of roads.

EXAMPLE i (showing the use of this chart) :—

A vehicle weighing 3 tons, and carrying a load of 3 tons, is required to travel along a road having a tractive resistance of 6o lb. per ton, the gradient of the road being x in 12. What must be the tractive effort, at the road wheels?

Commence at 6o lb., at the left of the chart, and trace along the horizontal, until the vertical for i in 12 15 CU; -now, follow the diagonal, guide line, to the top of the chart, and, then, drop, vertically, to the point where it cuts the 'diagonal for 6 tons. Now, trace across the chart to the 'ht, and find the answer = 1,500 lb.

The tractive effort is independent of the speed of the vehicle and, if this is, also, to be taken into account, reference must be made to chart No. 2, which, in addition in speed, takes into account the efficiency of the transmission, and the brake horse-power required, in order to ensure a given tractive effort at the road wheels.

EXAMPLE 2.—Taking the same figures as in example but assuming that a speed of 6 miles an hour is required, and the transmission, from motor to back wheels, is through 4 shafts, includingthe driving axle, what brake horsepower will be required at the motor? Assuming that the shafts are running on plain bearings, take the figure, 1,500 lb., obtained from chart No r, and commence, with this figure, at the left of chart No. 2Trace across to the point of intersection with the diagonal for 6 m.p.h.; then, trace, vertically, up to-the point of intersection with the diagonal for 4 shafts, and, then, read across to the right for the answer = 38 b.h.p. (nearly).

If the vehicle were fitted with ball bearings, the efficiency of the transmission would, of course, be much higher; in fact, it would be, approximately, in the proportion of r : 1.38,

A table of ratios, or constants, for r, 2, 3, 4, 5, or 6 shafts is given at the extreme right of chart No. 2.

The efficiency of transmission is based on the assumption that the co-efhcient of friction between metal and metal, lubricated, is o. r. This may appear rather high, at first sight, but, when the conditions of dust and grit under which motor vehicles are expected to work, are considered, it will be agreed that the figure is not too high. The co-efficient of friction for ball bearings has been taken as 0.02. This figure has been arrived at by a few simple experiments, and, in the absence of more reliable figures, the writer lsas used this value, and has found that the results obtained in actual practice, are very near the mark.

In using this chart, for a vehicle fitted with ball bearings, it will be necessary either to divide the tractive resistance, obtained from chart No. x, by the constant for the number of running shafts, or to divide the b.h.p., obtained from chart No, 2, by the same constant. Thus :- EXAMPLE 3.—Taking the same case as in example 2, Litt assuming that the vehicle is fitted with ball bearings, what b.h.p. will be required?

First, divide the tractive resistance, 1,500, by the constant for 4 shafts, 1,38 : the result is 1,087 lb. (nearly), and, using this corrected tractive resistance, in the same way as for eaampIe 2, it will be found that the required b.h.p. will be 28 (nearly), If, instead of dividing the tractive resistance by the constant, we divide the b.h.p. obtained from the chart, the same result will be arrived at :-38 ÷ 1.38 = 28b.h.p. (nearly). These examples will suffice to show the principal uses of the charts, but they may be used for obtaining, any one factor when the others are known.

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