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A PHYSICIST WRITES . . .

(May 2009)

It is quite a while since I mentioned the System of Car Control: Information, Position, Speed, Gear, Acceleration ó the sequence that advanced drivers should be muttering under their breath as they approach any road hazard and then travel through it or past it.

Perhaps I ought to confess that I donít often mutter the sequence myself! When I was preparing for the advanced test, my observer didnít really make a big thing of the System. But whenever I do think about the above check-list (in relation to a hazard I am negotiating) it seems to me that Iím getting the items roughly right and in the right order, automatically. Itís a common-sense system.

Itís also a list that has usefully supplied topics for some of these columns. But thereís one thing I havenít focused on before: Gear, or (better for the purposes of this column) Gears. Why do we need them? An engineer might say that they are for converting the torque and the rotary speed of the engine to values that better suit the driving wheels, the inertial load, the frictional drag, the road speed, the acceleration and the gradient. But Iím a physicist who likes to try to explain things more gently than that!

So: why gears? The question takes me back to my cycling days, not only when I was on a single-gear bicycle climbing the hills of Bristol (as I mentioned last month) but also all the rest of my youth, when I rode machines equipped with a number of gears. I guess you probably did too, so I think the best way of exploring the need for gears in vehicles might be to talk first about bicycles...

Picture yourself bowling along the road, moving much faster forward than your feet are moving up and down, as they push (alternately) on the pedals. You wouldnít want them to be whizzing round like a Catherine wheel, so youíve chosen top gear, which sends the bicycle chain around the smallest sprocket on the rear wheel. But hereís a curious thing: the force you are generating between the tyre and the road (to drive the bike along) is actually much lower than the force youíre applying directly to the pedals. Whatís the reason?

It lies in a simple law of machines: power input =power output (plus various losses due to friction, which is why on a level road you have to keep pedalling all the time). And power =forcespeed. So in top gear, because the speed of the bike is much higher than that of your feet, the two forces I described will also be very different (the other way round, of course), hence you canít transmit much thrust to the rear wheel.

Thatís no great problem on the level, but what if youíre facing a Bristol hill? Now you need maximum thrust, so you select a low gear. Generally, bottom gear enables your feet to move at least half as quickly as the bicycle, hence (from my equations) the force on the bike will be at least half your push on the pedals. That should easily get you up the hill!

Or you might want to accelerate (on the flat) from a standing start. This again requires a decent thrust between the tyre and the road, and therefore a low gear. Then as you get faster, you move up through the gears so that the rate of pedalling stays within a comfortable range for your legs.

Itís within this range too that you can deliver the most power from legs to bicycle, when you need to: if you were pedalling more quickly you wouldnít be able to apply a useful force, and if instead you were in too high a gear (therefore pedalling slowly), again you would be up against a force limit on the pedals, namely your own weight!

Enough of bikes ó Iím hoping that your carís gears wonít need much explaining now. The pistons in the engine oscillate much faster than feet on pedals, and there are more of them, but they do the same job. And rather like your legs, the pistons deliver power most efficiently within just a mid-range of engine speed. Different gears match different road speeds to this range, and the job of the driver is to try to choose the right one! And thereís something else too which helps you to get more energy from each drop of petrol: pushing the accelerator pedal a good way down (so I learned to my surprise last year, and then reported here).

But all this is assuming youíre accelerating, or climbing (or both). If you simply want to cruise above 30 mph, then in order to minimize general engine drag you ought to be in the highest gear, depending on road speed, that doesnít Ďlabourí the engine. (In a 30 limit, to avoid the attention of speed cameras itís worth staying in 3rd gear even if you may be burning a little more fuel.)

Iím sorry: Iíve been ignoring drivers of automatics ó I trust that these do always automatically select the optimum gear for you? My experience of them is limited to the two Nissan Micras that Mrs S has owned (giving more than 11 years loyalty to each, I might add). The first one had a three-speed box and seemed to travel satisfactorily, if rather sluggishly. Her current Micra has a larger engine, coupled to Continuously Variable Transmission.

CVT works by running a metal belt round two pulleys which Ďchange gearí by cleverly and smoothly varying their diameters. This is suggestive of a bicycle chain and a set of sprockets! But the driving is certainly nice and lively, especially when you put your foot down: the engine goes straight to high revs and stays there, sounding like a small Intercity 125 moving off, while the car accelerates.

Alas, CVTs have a reputation for being short-lived, and indeed our gearbox gave up last year at 34,000 miles ... what to do? Scrap a well-loved L-reg car? We couldnít! So thank you, 3D Transmissions of Reading, for getting it back on the road (at some cost, admittedly).

Here is one more thought on bicycles: some present-day youths seem to like riding with their knees almost up at chin-level. Have they no notion of efficient pedalling ó or should we be commending them for keeping their childhood bikes unscrapped and on the road too?

Peter Soul

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