THE SIGNIFICANCE OF GEAR RATIOS
TIIIS article is to begin with some fairly elementary remarks about gear ratios, and will end with smile I I em e II ts which may not, I hope, he tinily so eommonplaee. It is with considerable diffidence that I embark on the first part. but I have met so many really knowledgeable people %Nilo find the Wiwi(‘ or gear ratios rather confusing, that I believe there may be some justitiea t ion for tackling the subject from the heginning. This looks rather like pretending to special knowledge, which I hasten to disclaim, except to the extent that sums in simple proportion have a peculiar appeal to my otherwise quite umnat I lei natical mind : and stuns of simple proportion are what gear ratios mainly amount to.
To begin with, everyone knows that the effective gear ratios of’ a car are the Product of the gearbox reduction and the back-axle reduction. Top gear generally being direct, the overall top gear ratio is also the back-axle ratio–say 4 to 1, for example. If third in the gearbox is I.25 to 1, the overall third is then 1.25 x 4=5 to I. . One is apt to think of 4 to 1 as a fairly high top gear and 5 to 1 as rather low, het 4 to 1, in conjunction with a 26′ diameter road-wheel is actually lower geared than 5 to 1 with a 33′ wheel ; even the mightiestamong the scribes sometimes overlook this, and it is very ett.sY, too, to get one’s sums wrong. I did so myself, in MOTOR SPORT, quite recently, in connection with the streamlined 1,100-e.e. Fiat. The discovery of this led me to worry out the following simple formula for ascertaining m.p.h. per 1,000 r.p.m. for a given overall ratio and tyre size which, after all, is the only really accurate way of stating gear ratios. 1 here is, of course, a slight difficulty in finding out the true wheel diameter, but the rim size plus twice the tyre width, minus one, is a good rough-and-ready figure (e.g., a 16″ rim and 5″ tyre gives 16 + 5+ 5-1=25″). The formula, which I have not seen stated anywhere else, is
By Cecil Clutton
for the exact effect ive diameter. It is : Wheel diameter in inches ,
= m.p.h. overall (war ratio per f,000 r.p.m. of engine. For example, with a 27″ wlieel and 4.05 to 1 ratio, 27′ x3 4 5 —20 m.p.h. per 1,000 r.p.m. .0 The gearbox serves different purposes on different ears. On an tiverbodied, under-eneined family saloon, it helps the ••••••••••••••••••••••••••••••••••••• Clutton once again presents an absorbing article, and one containing very valuable data, which should be much used, both after the war and by way of an exercise by those now in exile. His views cannot fail to add new weight in favour of the vintage sports car—or is it
vice versa ?—Ed.
thing to drag itself up hills. On a:sports car, which is not unduly worried about bills, it is mainly an aid to acceleration. In racing ears designed for a specific course, the ratios’ maybe plotted to time particular requirements of the cireuit. This is a very important aspect or racing up Shelsley Walsh, and accounts for the long run of successes by cars with FrazerNash-type transmission, which could be ratioed specially for the event. Twice I have seen really knowledgeable people, in print, say, ” We will have nice, close, evenly-spaced ratios of 4, 8, 12, and 10 to 1.” That is to say, they make a gap of 4 between each ratio. What is the result of this ? Supposing the 4 to 1 top gives us a maximum of 80 m.p.h. ; on the 8 to 1 third, the engine will be turning just twice as last at ;IV given mad speed : and assuming the engine can attain peak revs. in top, the maximum in third will therefore be .just half that in top. namely, 4n ni.p.h. Put as a sum
4 40. in simple proportion, –= 8 80
Looking now at third and second, we know that we Cali reach 40 in third, so 8 _26.5. . ? ve have 12 i.e.. the maximum in 12 19.5 second is 26.5 m.p.h. And –in 16=2:5
So our maxima are the remarkably stupid ones of 191, 264, 40 and 80 m.p.h.. and what looked, from a very superficial standpoint. a nice even spacing is, in fact. a very wide spacing between the higher ratios and a very close spacing among the lower ones—just the opposite of what is required.
Another (rather less superficial) apparently attractive arrangement of the ratios is that whereby one always speeds up the engine by the same amount between each pair of gears. That is to say, if one goes up to 4,500 r.p.m. in each gear, the corresponding engine speed in the next higher ratio is always, say, 3,000 r.p.m. This would mean that the g p between any pair of ratios is as 3 to 2, and it has been followed out in quite a number of famous cars, including the ” 30;98 ” Vauxhall. in which ease the overall ratios of the E type were roughly 3, 41, 61 and 10 to 1. The reason why this sounds attractive is that the engine can always he kept running within a selected range of revs. But what is the effect on the respective maxima ? Let us again suppose that peak revs, can be attained in top and that this gives a maximum of 80 m.p.h. As a change 3 to third produces a step up in revs. of 4 so the maximum in third will be f of top— namely, 53 m.p.h., and so on, giving us maxima of 80, 53, 35 and 23 m.p.h. Thus,
although the ratios are evenly spaced, the maximum read speeds are noticeably bunched together in the lower gears. The result of this is that, in acceleration from rest, you have a terrific step off, rowing away at the gear-lever with tremendous application, till at only 53 m.p.h. you have run out of ratios and are left pinking impotently in top, while that vulgar Frazer-Nos!’ car k just changing up from second to third. Clearly then, this won’t do, either. It has, however, a justification on the family car, where the gearbox is to be thought of in terms of hill-climbing rather than acceleration. For this purpose it is quite good, and gives a nice wide gap between top and bottom.
Incidentally, it is a useful rule of thumb that the number of seconds taken to accelerate. on the level from 10-30 m.p.h. in any one gear is also the gradient which the car will climb on that ratio. I know no reason for this ; it just appears to he a convenient fact.
Reverting to sports cars, which are our principal consideration, it is beginning to look as though we have got to space our ratios unevenly so that the road maxima are more or less equally spaced. To take a case in point, if the E type ” 30/98 ” had had ratios of 3, 4, 6 and 10 to 1, the road speeds at the peak of 3,000 r.p.m. would have been the nice ones of about 95, 71, 47 and 28 m.p.h., instead of the tiresome ones of 95, C3, 42 and 28 . m.p.h., as they are. This is achieved by an uneven spacing of the ratios. Thus, to drop from top to third calls for only a 33Aper cent. increase in revs. From second to third calls for a 50 per cent. increase, and from second to bottom a 06-i per cent. increase.
But beware of thinking. that these figures apply going up ! From bottom to second the revs, drop by 40 per cent. ; from second to third by 33-k per cent., and from third to top by 25 per cent. Quite simple, really, but an easy point on which to slip up. In an ideal fivespeed box arranged on these lines, to get the almost equally spaced speeds of 100, 80, 60, 40 and 24 m.p.h., with a direct drive top, the gearbox ratios would be 1, 1.25, 1.68, 2.5 and 4.15 to 1 and, for example, with a 271″ wheel, 5,000 r.p.m., and a 4 to 1 axle ratio, overall ratios of 4, 5, 6.7, 10 and 16.6 to 1. A properly proportioned four-speed box may use either the lowest four or the highest four of this series of five.
Among other things, there are two factors which largely decide how close the designer can afford to make his ratios, assuming he is going to have the &Riventional number of four. At the top end, he has to decide the maximum road speed of which the car is capable or, putting it another way, the highest ratio upon which the engine will attain peak revs. Alternatively, he may decide that he will put the highest ratio so high that nothing like peak revs, can be attained when it is engaged. The overdrive model RollsBentley and the Frazer-Nash are cases in point. At the bottom end, he has to decide bow steep a gradient the car shall be able to surmount in bottom gear, and upon how steep a gradient it shall be able to restart from rest. The pernicious habit, in latter pre-war reliability trials, of holding restart tests on ridiculously steep hills led designers,
who looked to these events for cheap publicity, to supply their cars with fantastically low bottom gears. They sometimes achieved this by three fairly close ratios and a bottom which was literally 100 per cent. lower than second ; or by a more even spacing which meant very wide ratios all through. Either plan is equally undesirable for all ordinary road use, and it is very doubtful if it is any noticeable divdvantage to be unable to start from refit on even a 1-in-4 gradient. By these ” trials bottoms ” several quite nice little cars were spoilt from the point of view of the ordinary owner, and one hopes that the error will not be repeated.
We now come to the much more interesting problem of fitting gear ratios to different shaped power curves, and observation leads one to think that this aspect of the ease is little appreciated by most designers. Notable exceptions have been Frazer-Nashes, W. 0. Bentley and Rolls-Royces (especially in the overdrive Rolls-Bentley). The finer refinements of choosing gear ratios turn upon a combination of two factors :
(a) Does the power curve flatten noticeably at the top end or does it go up in a fairly straight line to peak ?
(b) What is the piston speed at peak revs. ?
While not necessarily the ease, it is generally true that the short-stroke engine has a fairly Straight power curve, and a fairly low maximum piston speed. A very close and extremely interesting comparison can be drawn between the V.12 Lagonda and the 41-litre RollsBentley. The Lagonda (75 x85) has a remarkably straight power curve, and a maximum piston speed Of only 3,100 f.p.m. at 5,500 r.p.m. The Bentley (89 x 114) has a very flat-topped curve, and a maximum piston speed of over 3,400 f.p.m. at 4,500 r.p.m.
The power curves of both engines have been published in various places at different times, and what makes the comparison so particularly interesting is that, on the normal Lagonda axle ratio the road speed per 1,000 r.p.m. is the same as on direct drive on the Mark V Bentley. Furthermore, it is possible to calculate that the total resistance of the Mark V. Bentley and V.12 Lagonda which were roadtested in the Motor during the early part Of the war by Pomeroy, Heal, Clark and Myself (reports also appeared in Moron SPORT) was almost identical in each case.
By stepping up the Bentley engine to a hypothetical 91 x 115, 4k, litres, we are able to compare two diametrically opposed types of engine, of identical cubic capacity, and drawing ears of identical total resistance. This I have done in the appended graph in which horse-power (on the vertical axis) is plotted against road-speed (on the horizontal axis), and also the relevant part of the total resistance curve. As is well known, in a road vehicle the maximum speed varies as the cube root of the power output. In this case, the 44-litre 6-cylinder is assumed to develop 129 b.h.p. and the 41-1itre 12cylinder is assumed to develop 165 b.p.h. In otherwise equal circumstances this gives maximum Speeds of 97 and 105 m.p.h. The curves, as depicted, are believed to bear a close relationship to those of the Bentley and Lagonda.
We now have to find out what ratios to apply to these power curves so as to use them to the best advantage ; a 30″ wheel is assumed in each case, and the 6-cylinder car can be considered first.
What is to be the top-gear ratio ? Now, if the engine is going to be capable of reaching its terminal velocity of 4,500 r.p.m. and piston speed of 3,450 f.p.m., two difficulties confront us. One is that, as the power actually falls off after its peak at 3,900 r.p.m., the best power will not be available at the-greatest road speed, which will suffer to the admittedly negligible extent of 1 m.p.h. ; but acceleration over the last 4-5 m.p.h. will also be affected. A worse snag is that the maximum safe cruising speed will be as low as 70 m.p.h. (3,250 r.p.m. and 2,500
f.p. . ).
As against these two defects we have excellent all-round top-gear performanee and flexibility. Is it net, therefore, worth our while to use a top gear of this kind, and have a separate ratio just to look after the extreme top end of the scale, and to provide high-speed cruising ? Clearly, it would be worth while. The normal top-gear ratio on the lines just mentioned would be 4.2 to I.
On Our overdrive, we want to put Our cruising speed as high as possible and to arrange for the peak power output to occur where the power curve crosses the ‘total resistance line. This seems to suggest a ratio of 3.5 to 1. Actually, these two ratios conform very closely to the Mark V Bentley ratios of 3.6 and 4.3 to 1. A word, in passing, about this vexed question of cruising speed, which really is vital to our argument. In the first place, one should try to frame a definition of the term, and this is very difficult Hoping for better suggestions from readers, I propound the following :—
“Cruising speed is the maximum road speed which the engine can sustain for long periods, and at a sufficiently reduced throttle opening to ensure silent and smoot h operation. It must coincide with crankshaft and piston speeds compatible with reliable and economical operation.”
The partial throttle opening is, I think, an essential characteristic. It leaves a margin of power to tackle minor gradients without a .gear change, while an engine operating at full throttle is always relatively rough and noisy. This applies less to inefficient engines, with small, low-lift valves, which are therefore able to cruise comfortably on agreater throttle opening than in the case of a high-efficiency engine.
One hears a lot about cruising at a maximum of 2,500 f.p.m. piston Speed, and one is apt to wonder what special merit lies behind this apparently arbitrary figure. The answer is easily shown in a graph to illustrate the power losses in an engine at varying speeds. The loads in an engine go up as the square of the speed, and the losses go up accordingly. At very high speeds the engine is therefore having to devote a relatively large amount of its energy to pushing itself around. This naturally means uneconomical operation ; and it happens that a piston speed of 2,500 f.p.m. is just about the point above which the loads and losses begin to become excessive. The actual speed at which the piston rubs along the cylinder walls is
in itself of little importance ; but it is an exact measure of the rate of increased loading in the engine. This is not true of crankshaft speeds, which leave the ‘moth of stroke out of account. If and when the weight of reciprocating parts can be considerably reduced, the 2,500 figure may become out of date, but at the present state of development it must be regarded as pretty well an outside figure for touring machinery.
On our 3.5 gear, then, the cruising speed occurs at 87-88 m.p.h., and the graph suggests that this is very nicely placed to meet the various requirements. Some American cars have at last been forced to adopt an overdrive gear (the average American power curve is remarkably flat-topped), but they frequently make much too wide a gap, involving a 33i per cent. drop in revs, from top to overdrive. As has been shown, this defeats the object of the thing to a large extent. In our example it would have meant a 2.8 to 1 overdrive, whieh would have put the theoretical cruising speed
much higher than the engine could conveniently cope with. It is, I think, the essence of an overdrive ratio that it should be fairly close to the normal direct drive. The Mark V is a splendid example of how the thing should be done, and the Frazer-Nash was another (a typical set of ratios was 3.8, 4.8, 7 and 11.75 to 1). Now, how about the short-stroke, 12cylinder engine ? The problems at once become much easier of solution. In the first place, the straightness of the curve raises no difficulty in attaining maximum revs, at maximum speed. In this particular instance, the Lagonda maximum of 5,500 r.p.m. has been assumed, which gives a piston speed of only 3,100 f.p.m. The resistance curve and power curve cross at 105 m.p.h. and 5,250 r.p.m., which gives a slight margin against overrevving in top. Owing to the low piston speed, the maximum cruising speed is 88 m.p.h., which is the same as on the overdrive of the 6-cylinder car. It will therefore he seen what a tremendous advantage in performance is gained by a
short-stroke (not more than 85 mm.) engine and a straignt power curve. It achieves on one ratio what the long-stroke, (1cylinder engine requires two gears to do— and then stiff falls short. 1 his does not necessarily imply that the Bentley type of curve is a bad thing ; it does, in tact, provide an exceedingly pleasant sort of performance, especially in conjunction with such an exquisite gearbox as the Bentley’s ; but it does follow that for an engine of the Bentley type to equal the Lagonda performance, without resort to special tuning, a capacity of nearly 6 litres would be required. Alternatively, a mild supercharge is remarkably ettective at stidening up a power curve which tends to droop at the top end. The 2-litre V.I2 Grand Prix Delage affords a remarkable illustration of this. In its unblown, 1923 form, it developed its maximum power of 115 b.h.p. at 6,000 r.p.m. and fell off to 106 b.h.p. at 7,000 r.p.m. In its 1924 supercharged form the curve went straight up to 190 b.h.p. at 7,000 r.p.m., at which point it was still rising steeply.
It is not necessarily the ease that the long-stroke engine has a Hat-topped curve, and vice versa ; factors such as valve timing and breathing efficiency are also of prime importance ; but it IS generally the case. It is also generally true that an engine like our u-cylinder example gives excellent power at low revs., and this is evident from the graph. Even with its smaller engine, the standard 4f-litre Bentley engine has a greater power output than the V.12 Lagonda up to about 3,000 r.p.m. It is, therefore, only above 60 m.p.h. in top that the Lagonda has the advantage. It is, indeed, a remarkable feature of the Lagonda performance that the low-speed performance, although quite good in itself, compares so unfavourably with the really electrifying top-end acceleration as to appear definitely inferior. To make the most of the potentialities it is therefore necessary to do a lot of gear shifting to keep tile revs, in the top half Of the range. So although the short-stroke engine can do without an overdrive, thus saving some gear-changing, it probably calls for more gear-changing on balance. The remaining two gear ratios on the 6-cylinder car are not so tremendously important (the Mark V ratios of 3.6, 4.3, 6.15 and 10 to 1 are beautifully chosen), but they have to be very carefully selected on the 12-cylinder type. The Lagonda ratios (on the middle of the three available axle ratios) are 4.45, 5.56, 7.43 and 14.46 to 1, which means that second and third are fairly close ratios, ensuring a vivid performance from 35 m.p.h. upwards. Bottom is largely an emergency ratio, on which 35 m.p.h. can just he reached ; it is very nearly twice the second gear ratio. This implies that unless by running up to peak revs, in bottom there is rather a blank space around 30 m.p.h., and this was also true of 3and 41-litre old-school Bentleys fitted with “A ” or ” 1) ” type gearboxes. Probably a rather higher bottom gear would be the best all-round solution. But however one looks at it, the short-stroke engine needs a lot of gear-changing, and some effortless gearshift, such as the total, seems definitely to be called for. In this connection it seems a dreadful pity that the Cotal box
has such painfully wide ratios. As generally supplied a 50 per cent. increase in revs, is called for between top and third, and between third and second, like the old “30/98.” One is informed that this is inherent, but I should very much like to see a convincing explanation of the reason, because it is not the case on the Wilson-type box which is basically similar. On the Squire, the change from top to third only called for a 25 per cent. rise in revs., and on the Alta, 33f per cent., the Alta box conforming very closely to the 3, 4, 6, 10 series mentioned earlier. It is therefore very much to be hoped that a close-ratio Cotal box will be put into production after the war.
An interesting gear-ratio variant was that applied by Burgess to the 1914 T.T.
Humber, in which he evidently considered both third and second in relationship to top, and very little in relationship to each other. And for racing purposes there is much to be said for it. Assuming a 3 to 1 top, then the ratios of top, third and second would be 3, 4 and 5 to 1. Bottom would be largely a getting-away ratio of about 9 to 1. This is also very much the spacing on the “A” and ” D ” type Bentley boxes, ;and W. 0. Bentley has not entirely deserted it, even on the V.12 Lagond a. The underlying idea apparently was that if one had to slow down into the middle speed-range, say, 30 to 45 m.p.h., a drop into the close-ratio third would not be very effective. Burgess therefore made second a sort of wide-ratio third,
and the two could be treated as alternative rather than supplementary. On the Humber this was carried to its logical conclusion by placing both second and third at the front end of the gate. The change from top into either was therefore very easy, but from second to third called for a U-shaped movement of the lever. It is a delightful arrangement in practice, except for the lack of ratios around 25-35 m.p.h.
I hope enough has been said to open up this interesting subject for any readers who may have previously regarded it as rather formidable. One could go on amplifying and refining ad nauseam—or has the nauseam stage already been reached ?