Resistance to speed
F. W. Roberts analyses three factors which affect high performance
This article is an attempt to provide a few notes detailing the main cause’s of power loss, since, in general, the whole of the engine output is absorbed in the following ways:–
1. Acceleration.
2. Gradient climbing.
3. Transmission losses.
4. Tyre drag.
5. Air resistance.
The first is outside the scope of this article, while the second is inevitable unless all motoring is done upon level roads. The remainder are all, theoretically at least, susceptible to reduction, and we will consider them in a little mare detail.
Leaving item (3) for the time being, we will tackle the tyres. There have been a number of excellent articles in various technical journals on this subject, in particular a paper read before the S.A.E. in 1941. Taking fairly liberal extracts from this, we find that the percentage loss due to the tyres is not extremely large, except at low speeds. Numerous factors affect the amount of power the tyres consume and which they convert into heat. The loss is increased by increase of speed and load. Larger rim diameters and increased slip-angle of the front wheels when cornering will increase the loss, while higher inflation pressure and wider rims decrease it. Some tyres have a four-ply base while others have six-ply; the latter consume more power, the increase being roughly 7 per cent. at 30 m.p.h., falling to 4 per cent. at 60 m.p.h.
Drag due to the tyres is commonly expressed in lbs. per ton load, or lbs. per 1,000 lb. load; the latter is American practice, but as it is a very convenient notation it will be used here. Curves were published in Motor Sport last month – in the article on a method of measuring power output – which showed for a few typical tyres the effect of speed on drag. Those curves were, strictly speaking, applicable to 16-in, diameter rims, and can be converted to h.p. by using the formulae given in the same article. Typical figures, for comparison, are about 3 1/2 h.p. at 30 m.p.h. and 9 h.p. at 60 m.p.h. tyre loss for a car weighing 3,500 lb. and shod with 6.00 x 16″ tyres. If smaller rims (15″) were used, the power loss would decrease to 90 or 93 per cent. or the value for 16″ rims. Now that there is a tendency to use wider rims, it is of interest to note that the paper mentioned (S.A.E. 1941) quotes a decrease of loss to 85 or 95 per cent. of its previous value when changing to the widest rim then available; exact sizes are not mentioned. The saving is due to the decreased tyre deflection with the extra rim width.
Various authorities, including the S.A.E. and, in this country, Dunlops, have published data concerning the saving both in power and rubber due to high inflation pressures; rubber wastage data seems conflicting, but the curves reproduced here give average values for both power and material loss (Figs. 1 and 2). There is no particular virtue in taking the 100 per cent. values at 28 lb./sq. in. except that that is a common pressure. If your recommended pressure is some other value, alter the figures in proportion, making 100 per cent. whatever is the correct inflation for your tyre. It should be noted that it is not recommended that the pressures be increased much above their correct values, as the tyre makers suggest that other troubles would then be experienced.
A few miscellaneous items are worth noting. Part-worn tyres, in general, have less loss than new ones, the saving being of the order of 14 per cent. A new type of tyre, having rayon in place of cotton in the carcase, saved something in the neighbourhood of 3-5 per cent. The effect of power being transmitted by the rear wheels is interesting; in general, the increase of h.p. output from zero to 25 h.p. increased the loss in the rear tyres by about 10 per cent. Finally, there is the question of the slip angle of the front tyres. The S.A.E. paper gave two curves, one at 30 m.p.h. and one at 60 m.p.h. Taking a few points from these, we find that at 30 m.p.h. the power loss varied from 1 h.p. at zero angle to 21 h.p. at 3 degrees, and rose to over 10 h.p. at 8 degrees. Similarly, for a speed of 60 m.p.h. the losses at the same angles were 3 h.p., 5 h.p. and some very high value at 8 degrees. At 6 degrees and 60 m.p.h. the loss was nearly 14 h.p. The moral clearly is: do not expect good tyre life if you corner at high speeds.
Leaving the tyres for the moment, let us consider wind resistance. This is the predominant loss at speeds much over 30 m.p.h., and the efforts to reduce it have resulted in various forms of streamlining. The subject was discussed in another paper read before the S.A.E., also in 1941, and from which some of the following is extracted. The paper stresses that streamlining would be much easier if very long tapering tails could be added, and rear passengers would lie down rather than sit up. This tapering tail effect is so important compared with the frontal shape that experiments even proved that a typical saloon had less air drag in reverse than when going forward, since, in reverse, the bonnet was a sort of tail. Commonly used formulae in connection with air resistance are:
Drag = k x A x m.p.h. 2 lbs.
k x A x m.p.h. 3
Power = horse power
375
In these formulae, “A” is the frontal area in square feet, while “k” has various values. A simple flat plate – the worst case – has a “k” value of about 0.0032 a very perfectly streamlined solid has a “k” value of about 0.00008. Common values for “k” were suggested in the article in Motor Sport mentioned earlier.
Before considering what relationship these losses bear to each other, a very tentative suggestion is made for transmission losses. The writer has not been able to get any authoritative data on this subject except the fact that gearboxes are very nearly ideally perfect and have an efficiency usually better than 97 per cent. Rear axles are an unexplored subject as yet, and until data are collected the curve given in Fig. 3 might be tried as a rough approximation. It should be noted that high torque – i.e. hill climbing, on low gear at low speeds – will pull the rear axle efficiency down, due to high gear-tooth pressures, while high speed, even at low torque, will also give a comparatively low efficiency due to oil churning.
Now to compare the relative magnitudes of these losses. Take as our example a car weighing 2,000 lb. and having a frontal area of 5′ x 4′ i.e. 20 sq. ft.; its “k” could be taken as 0.002. We might assume that the tyre loss is in accordance with the 5.00″ line of Fig. 1 in last month’s article. We can now make up a table of tyre, air, and approximate transmission losses thus:
The column for maximum engine output is added here purely for comparison and is not derived from the other columns. Let us plot some of these figures on squared paper to a base of m.p.h. as in Fig. 4.
The first thing to note is that the engine output is above the total loss line until a little over 70 m.p.h. is reached. At that point the two curves cut, and therefore that is the expected maximum speed of the car. The next and more pertinent thing to notice is that at the higher speeds the “Tyres+ Air” line lies considerably above the “Tyres only” line; the increase is due solely to air resistance. In percentages, we can express this by saying that although at 10 m.p.h. air drag absorbs only about 1 1/4 per cent. of the available engine output, and at 30 m.p.h. it. takes 8.5 per cent., at 60 m.p.h. it has increased to take over 40 per cent. The method of calculating the power absorbed by acceleration and by hill climbing appeared in the previous article.
In conclusion, therefore, in order to put up your maximum performance, reduce your weight to lower the tyre loss and at the same time improve your acceleration; reduce the rear axle loss by careful assembly and use of the correct oil at the correct level; most important of all, reduce your frontal area and taper off the tail if possible so as to decrease your air resistance drag. A smooth under surface is also very helpful in this connection.
Incidentally, if any reader can augment the estimates made for transmission losses, he will be performing a valuable service.