More about Gear Ratios
Cecil Clutton’s article in the February issue gives rise to some miscellaneous comments, including interesting data on the ratios obtainable with Wilson and Cotal boxes.
ENTHUSIASTS everywhere must have welcomed Cecil Clutton’s magnificent article on gear ratios. Let us hope that manufacturers will take equal interest and benefit accordingly. The present comments are intended only by way of an amplifying postscript by one who holds very similar though not necessarily Identical views. The formula that Clutton uses, m.p.h. per 1,000 r.p.m. =3 x effective tyre diam. gear ratio, is a valuable approximation that deserves to be better known. Owing moreover to wheel-spin and the difficulty of measuring effective diameter nearer than + in., it is mathematically more ” honest” than
the classical . Diameter 1000 Gear Ratio x 336
from which it derives, and is less likely to lead to quibbles over whether five thou. represents 119.8 or 120.1 m.p.h. Decimal points should be barred from speeds over 10 m.p.h. As a rule it is over-optimistic to translate maximum r.p.m. into maximum m.p.h. on top gear by strict proportion (though it is, of course, quite legitimate to calculate r.p.m. from observed m.p.h.). Obviously any road speed (a) above that corresponding to maximum revs., or (b) exceeding that represented by the point of intersection of the engine power curve and the total power needed to maintain a steady velocity, whichever is the lower, is beyond reach. Hence the curious anomaly of the early Anzani Nashesif I remember rightly, 71 on third, 74 on top (or was it vice versa?) instead of the 90 on top predictable from the ratios. Top gear was in those days too high for the engine to attain maximum revs., although low enough to provide a reasonable reserve of power up to 65 m.p.h. Performance up to the admittedly limited maximum velocity was, however, particularly satisfying. For road work there is undoubtedly a peculiar charm in sensibly equal maxima on top and third, say 85 and 80 for a fast tourer with full load and equipment, and I am surprised more has not been made of it. It implies, of course, top and third gears that are close on either side of whatever theoretical ratio would give the absolute maximum road speed, and this is a tricky business to arrange
really satisfactorily. Maximum revs. must be only just unattainable on top (or overdrive) and maximum velocity only just unattainable in the next lower ratio. Talking of overdrives, too many, as Clutton points out, have been ruined by
an excessive gap between ” top ” and o.d., the result being an annoying attack of staggers on engaging o.d. under anything but free-wheeling conditions. The importance of (1) plenty of reserve urge on direct drive, and (2) a close ratio between o.d. and direct, seems obvious enough, but has not apparently penetrated some manufacturers. An o.d. should be a real twin top, giving about the same ultimate road speed as direct drive, but at about 15 per cent. less piston speed, with, naturally, 15 per cent. less urge, which must therefore be comfortably sparable if the o.d. is to be wholly satisfactory.
The desirable ” expanding progression ” of ratios is most readily obtainable with the normal type of gearbox favoured by the majority of gentilshommes sport ifs. Owing to the facts that, bar mishaps, each pinion has a whole number of teeth and that one tooth less on one pinion of a pair means one tooth more on the other, it is not always possible to get precisely the ratio aimed at ; but the approximation is usually close enough for practical purposes. Epicyclic gearboxes are more difficult. In the Wilson epicyclic box, bottom gear is obtained by holding the bottom gear ring stationary ; second and third by rotating the bottom gear ring in the direction of drive at increasing predetermined rates by means of the second and third gear assemblies and top by locking the lot solid. This is mechanically sound in that it gives minimum tooth-loading and and a light, compact box, but in its usual commercial form with similar sized pinions throughout, the choice of ratios is limited. A uniform progression of, say, 50 per cent. drop lietween gears is easier to obtain than the 25-33-50, or 33-50-66, that we want. A good compromise can be made, however, despite epicyclic blind spots” or gears that cannot be got on account of mechanical considerations. I have in mind two Wilson boxes, designed for sports cars that were apparently never produced, with gearbox ratios :
1, 1.38, 2.2, 3.4 to 1 and 1, 1.30, 1.7, 2.27, 4.0 to 1, i.e., a ” drop ” between gears of respectively, 38, 59, 55 per cent., and 30, 30, 33, 76 per cent.
The Cotal electro-magnetically-gripped box is basically different and rather simpler, consisting of two 2-speed epicyclic trains in series. Call them A and B, and let a and b represent the reduction afforded by each separately. Top gear is obtained by locking both A and B solid to give a direct drive. Third and second gears involve locking one assembly and taking advantage of the reduction afforded by the other. Bottom gear uses both assemblies together. The available gearbox ratios are, therefore, 1, a, b, ab to 1. This means that the Cotal box will readily give uniform spacing of gears but not a regular expanding progression ; the spacing between bottom and second is necessarily the same as between third and top, with an awkwardly uneven gap between second and third, unless wide spacing or a very high bottom gear can be tolerated. Numerical examples will make this clear. Suppose (conveniently ignoring possible blind spots) one epicyclic train gives a reduction of 1.5 and the other 2.25 to 1, then we have ratios of 1, 1.5, 2.25, 3.75 to 1, i.e., with a 4: 1 final drive, the overall ratios would be 4, 6, 9, 13.5—adequate but uninspiring. Top and bottom are all right, but the others would be better at 5.2 and 7.5. This just cannot be done. Suppose a=1.3, and b=2.25, 2.0 or 1.7, we get the following overall ratlos : 4 5.2 9.0 11.7 4 5.2 8.0 10.4 4 5.2 6.8 8.84 (even spacing)
In each set, except the first, bottom gear is too high in relation to top for anything but racing ; but the spacing is painful ; second gear is virtually wasted. Perhaps the best way out would be No. 3, with an additional sliding gear to provide an emergency reduction for sticky going (forgetting that this gives eight speeds forward and reverse). Or perhaps Major Wilson and Monsieur Cotal could get together to give us an electrically-operated box that provides expanding ratios and avoids preselection. J. R. EDISBURY.