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A PHYSICIST WRITES . . .

(September 2008)

I donít know if what I write stays with you for long, after you have read it, but some things certainly stay in my own head, worrying away until I feel I have to focus on them again. Last February, I compared accelerating from 0 to 60 in twenty seconds with doing it in ten (then staying at 60 mph). I calculated that the difference was just five secondsí journey time. So my advice was: take it easy!

Afterwards it occurred to me too that adopting the slower take-off might save fuel. On the other hand, you are putting the same amount of kinetic energy into the car whatever the rate of acceleration (as someone pointed out to me), so maybe thereís no difference in consumption. Ever since, Iíve wondered which really is the most economical: accelerating fiercely, or just Ďbrisklyí or ó my own instinct ó gently?

This is not a question of physics only, and Iíve been lucky to find a contact in the automotive industry to supply the answer (I decided not to complicate the question by asking him about hybrids!). I wasnít surprised to learn that several different factors come into play.

A petrol engine runs most efficiently when the throttle is wide open and the speed of the engine is near the middle of its working range. In other words, these conditions convert each drop of fuel into the greatest amount of Ďmechanicalí energy. But you have to remember that much of this is used up in overcoming rolling friction and (especially) combating air drag on the vehicle. The latter becomes seriously large at higher speeds.

Now, if you go for maximum acceleration, first you are taking the engine to high revs, and then youíre travelling a greater distance while up at your cruising speed, pushing against the air drag. This isnít so good! Therefore I was right to think that it is rather more economical (in terms of miles per gallon) to accelerate less fiercely ó that is, with the pedal still a good way down but not over-revving the engine.

But what about accelerating more calmly still? Doing this, you are definitely running the engine inefficiently, because the throttle will be half open or less. So the message is: if thereís a clear road ahead of you, get a bit of a move on. Similarly you wonít be wasting fuel if, for example, thereís a tailgater behind and you put your foot down for a second (when they least expect it, if possible) hoping they will then stay clear: see my January 2007 column.

Anyway, having absorbed this message Iím certainly in the habit of accelerating more briskly than I used to (while still aiming to move the pedal slowly to avoid jerky travel), which compensates somewhat for the time lost through my other habit ó when I remember to apply it ó of lifting off early to slow down, in order not to waste more fuel.

The problem with this livelier acceleration is that you tend to reach the speed limit sooner than you realize! And donít forget, thereís no escaping the rule that the higher your cruising speed, the lower your overall mpg will be. This applies even to diesel-powered vehicles, whose engines (I was told) have a more constant efficiency than petrol engines, over a range of speeds and accelerations. The overriding reason is the increasing air drag as you go faster.

From acceleration to deceleration: last year our newsletter editor gave us his opinion of the yellow lines you encounter (often with a bump) across the carriageway on a fast approach to a roundabout. He complained that as they get progressively closer together, they distort your judgement of how quickly you are slowing down. Also (he said to me later), the bumps must affect your braking capability in an emergency.

They may be gentle, but in bouncing your wheels even slightly they surely do increase your braking distance, even if (I guess) ABS systems take them in their stride. You sometimes meet thinner bump-lines similarly getting closer together as you approach a 30 mph sign. There, absurdly, they are laid right across the road ó so if they have any effect on you at all, then when you are leaving town in the other direction they must make you think youíre not speeding up fast enough!

Worse still, in Fleet where the A323 arrives from the north-west you find not one but two vicious rumble-strips, each one slowing you down whether you are entering the 30 limit or trying to accelerate in the opposite direction.

But the ultimate silliness, I think, is on the edge of Fittleworth in West Sussex, where they laid bump-lines on the approach to a 30 sign and then later they moved the sign out to beyond the lines. So now you get not only a late reminder to slow down but also, in the other direction, an early encouragement to accelerate. I suppose, though, that this matches how most drivers tend to react to speed-limit signs anyway, and many signs are probably sited a bit further away from town than they would otherwise be, to allow for it.

As for the magnitudes of speed limits, you often feel these are chosen without rhyme or reason. Well, things are very different on the continent, it seems: the limits there are adjusted most carefully to the road conditions. One consequence Iíve heard about is that a certain grande route in the South of France has no less than eighteen changes of speed-limit in 25 km, switching between 50, 70 and 90 kph. Within one half-kilometre the limit alters three times! Iím told that even with the presence of repeaters in the 50 and 70 stretches, one forgets trŤs facilement la limitation actuelle de vitesse.

Peter Soul

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