A consideration of the fundamentals of springing on sporting cars, as it effects the propulsive effort required, and therefore their speed. The importance of low unsprung weight is demonstrated in a new manner.
Of all the problems in, on, or around the motor car and its various uses, that of its springing is one of the most fascinating and probably the most difficult. The interest arises, as much as anything, from the variety, the endless variety, of the guises in which the problem presents itself.
Even if we exclude the heavier type of vehicle altogether, and its problems are as intriguing as any, there are still as many types of car and car use to consider as will satisfy the powers of investigation of any enthusiast. Amongst touring cars, for example, there is every type of machine for which to cater, ranging from the light car, the loaded weight of which may be twenty-five or even thirty per cent. in excess of its weight unloaded ; to the heavy high-powered limousine, which rarely conveys a load equal to ten per cent. of its own weight.
The former, the more difficult case to meet, is rendered still more so by the twin handicaps of lack of space and necessity for low cost ; the latter, the easier problem, is still further simplified, generally speaking, by an amplitude of the former, and less stringency in the latter.
The most exacting vehicle, in regard to its springing requirements, is undoubtedly the racing car. Not only is the efficiency of the springing one of the most important factors in the performance of the car as such, but, in considering the racing car as distinct from the touring car, we move into an entirely different region both as to aims and standards.
On a touring car, the object is comfort, and the standard is the opinion of the user— generally formed by experience, but not infrequently lacking that. In the case of the racing car, the aim is speed, and the criterion is a definite statistical one— miles per hour. There may be just cause for a difference of opinion as to a degree of comfort : no expression of opinion carries much weight when the result can be calibrated in such definite terms as miles and minutes.
A Vital Factor.
I think it is a fact that, although every racing man is aware that the efficiency of his springing has a tremendous effect on his speed capacity, there is very little concrete appreciation of the root causes of the effect. The experienced man almost feels in his being that a car’s speed improves with improved springing.
If he expresses Ins belief in any academic fashion at all he does so by reference to the road-holding properties which he Perceives that the car possesses. As a matter of fact, the part borne by the springing in relation to this matter of speed, is as important, almost, as the size of the engine itself.
Actually, the efficiency of the springing directly governs the brake horse power of the car as a whole ; that is to say, for a given size of engine ; and, if other things are equal, the horse power available at the road wheels depends upon the springing.
It is only possible to consider the matter in the proper light if we get right down to fundamentals. The ideal road and wheel conditions for high speed travelling would be such as to obviate the need for springs at all. They would include the existence of a perfectly level and smooth road surface, so hard and strong as not to deflect in the slightest, under the load imposed by the wheel.
The wheel itself would be absolutely hard and unyielding, as well as perfectly circular. So soon as we depart from those conditions, so soon do we begin to lose power. If the road gives under the weight, then depressions are formed into which the wheel is continually falling, and out of which it must be continually climbing as it revolves.
For that continuous climb power is needed. If the wheel itself gives, in the least degree, then more power is expended in causing it to go out of shape. Most but not all of the power lost in this way is restored by the road and wheel, the former as it straightens, giving the wheel a push forward, the latter, as it gains its circular shape, also propelling the car in a forward direction. Some of the power, however, is lost, never to be regained.
Now we engineers could, and would, if required, provide a wheel which would, as near as needs be, fulfil the conditions laid down. Our trouble is that the road makers cannot do their part, or, at any rate, they cannot, at reasonable cost, provide roads which have that perfection, and will maintain it for any appreciable length of time.
We have, therefore, to introduce imperfections into our wheels, fitting them with flexible rims, in the shape of pneumatic tyres, and have to equip our cars with other devices, by the aid of which we are able, to some extent, to counter the depressing effect on car speeds of imperfections in road surfaces.
It is difficult, without going too far back towards the beginning of things, and also without spreading ourselves over a vast amount of mathematical formulae, to express exactly the relation between car speed and power. It will be near enough for our present purpose if we state that there are three governing factors : the internal friction of the car itself, the resistance of the road, and the resistance of the air.
With the first of these three I do not propose to concern myself at all : the third will, I hope, be matter for consideration in the near future : the second, our present interest, is governed by the incidence and dimensions of the obstructions which the road surface presents, so that the larger the obstacles, and the more frequently they occur, the greater is the power required. I should perhaps state that I am leaving out of the question the consideration of hill-climbing capacity, as having no bearing on the present subject.
A solid-tyred vehicle, which is also unsprung, meets all the road obstructions, large and small—and we are considering here the smallest just as much as the largest —full tilt, as it were, and gets all the benefit of them direct, without any discount.
Comfort at Cost of Speed.
The vehicle which is fitted with pneumatic tyres, but which is still unsprung, gets a rebate which varies according to the pressure and capacity of its tyres. It might be possible to equip a car with tyres which, by reason of their dimensions and also because of the comparatively low pressure to which they were inflated, would absolutely absorb all the ordinary road shocks.
It would thus afford comfort, but not speed. It would fail to afford speed because such a very large proportion of the power expended in distorting the tyre, altering its shape from the purely circular, would be absorbed, and would not be returned quickly enough by the tyre as it recovered its shape.
It is only by very rapidly returning to its original shape when released from contact with the road that a tyre can and, as regards a good tyre, does return to the car, the power which has been spent in flattening it. Roughly speaking, the smaller the tyre, and the more it is inflated, the more quickly does it spring back to shape. (This capacity for rapid re-formation after flattening, is often quite wrongly called resilience).
We are, therefore, in tyre equipment, between conflicting fires. If we fit tyres which are soft enough to absorb all the road shocks, then we shall, in that way, relieve ourselves of the direct loss of power from a rough road surface, but lose, at the same time, very nearly the same amount of power owing to the tyres own inertia.
If we fit a tyre which will absorb a minimum of power in itself, then it is also the case that it will absorb a minimum of road shocks, and thus fail in achieving our object. This aspect of the matter is more important than is thought possible by the majority of motorists, for there is no doubt whatever that the correct place to absorb road shocks is at the rim of the wheel, and when some bright genius solves the problem of providing efficient means of so absorbing them, we shall be approaching very closely to perfection in springing.
The wisdom of arranging the springing at the rims of the wheels is demonstrable in this way. The three factors which govern the power consumption of a car, to which I referred earlier in this article, are indicated in the following formula as a, b and c: a being a constant for the internal friction of the mechanism of the chassis, b representing the road resistance, and c the air resistance. If F be taken as the force needed to propel the car, W be the weight, and v its velocity, then the formula is—
F = W (a + bv + cvv
Of this formula we are concerned with the (bv) portion, and for us the expression might just as well be F varies as Wbv, meaning that the force required to propel the car increases or decreases as the velocity, as the road resistance, and as the weights of the portions which are effected by that resistance.
Now, if all the road shocks were absorbed at the rims of the wheels, then no part of the weight of the car would be affected by the road resistance, and everything would be for the best in the best of all possible worlds. To use a familiar and well understood term : there would be no unsprung weight at all.
Since it is not practicable, for the reasons stated, to absorb all road shocks at the rims of the wheels, provision is made to absorb such as pass the tyres, at points near to the rims of the wheels as is possible, and up to now this has invariably meant the use of shock absorbing media of one kind or another located between the axles and the frame of the chassis.
If the combined effects of the tyre and this second means of absorption were perfection and if nothing reached the chassis itself, then we should be in the fortunate position of only having to reckon, in our formula, the weights of the axles, besides being able to calculate on a considerable proportion of the shock being taken by the tyres.
Our formula would then become F1, varies as Wbv, in which this F, is less than the old F because W, which formerly, as W meant the weight of the whole chassis, now means only the weight of the axles, and b, instead of being the full intensity of the road resistance represented in the original formula by b as imposed by having to surmount all the obstacles by a rigid wheel, is now less because some of that resistance has been absorbed by the tyre.
Actually, of course, the combined shock absorbing powers of springs and tyres together do not suffice to relieve the chassis of all road resistances, and the matter is more complicated than is stated. If we ignore, as for our present purpose we reasonably may, the power lost in the actual flexion of the tyres and springing devices, then we have a formula in three parts.
A Definite Formula.
There is first of all one which embodies the full road resistance. The tyres have to meet this, in the first place, so that, if we express the force due to this cause by Ft, then Ft, varies as Wt x bb x v, the factor b is here at a maximum, but as the weight of the tyres is, comparatively small, almost negligible in fact, the effect is not great on the whole.
Then there is the resistance to motion of the axles, which meet the full shock b, less anything absorbed by the tyres. We can call this resistance b–t, a term which is mathematically incorrect, but illustrative of my meaning. The tractive force required for the axles, F., then varies as W., the weight of the axles, multiplied by b—t, and by v. Now b—t, although less than b itself of course, is still a considerable factor, while W. the weight of the axles, depends on the design of the car, that is to say, on the degree to which the designer realises the almost acute importance of reducing the unsprung weight. Finally, there is that proportion of the road resistance which is not absorbed at all : that which remains after the tyres and springing has done all that they can towards its reduction. This portion of the resistance is felt by the whole car less the wheels, axles, and tyres. It can be represented—reading the formula nonmathematically—by b —1—s, and, with efficient springing, is comparatively small. The formula by which allowance can be made for this is = W c(b S)7.1
the symbols having meanings corresponding to those already used. On these bases, the total effort needed to propel a car can be calculated, with the exceptions noted, by the use of the following formula, which is compounded of the above three Wb — 1(W Wc)
That is to say, it is equal to the whole effort which would have been required had there been no springs or tyres at all, less the proportionate shock absorbing effect of the tyres, multiplied by the weight of the car, less that of the tyres, less, again, the proportionate shock absorbing action of the springs, multiplied by the weight of the car, less axle and tyres, i.e., the ” sprung ” weight. For the necessary propulsive effort to be a minimum, the second and third factors must be maxima. The second cannot be greatly altered. The absorption properties of tyres, having in mind the need for them to have rapid recuperative powers, are almost so invariable as to deserve the name “constant.” Moreover, as the weight of the tyres is small, it has already the maximum effect. The third factor is the important one, and it clearly becomes greater and greater as the unsprung weight bears a less and less proportion to the weight of the complete car. The importance of reducing unsprung weight, so as to reduce the propulsive effort needed for a car, and thus to increase Us speed for a given power, is thus demonstrated.
In a future article I propose to deal in a more concrete way with the actual rproblems of springing as they are affected by the need for speed.