Here's a simple question: which of the three pedals you see above is responsible for the most wasted fuel?If you answered "accelerator", I have some bad news. It's not the accelerator, it's the brake pedal.
To find out why, we need to consider what goes on when you're driving along, and what the purpose of the accelerator and the brake are. The clutch pedal can be safely left out of the discussion for now, although it does have its own uses and misuses.
Most cars weigh something between 1000 kg (a tiny hatchback) and 2700 kg (an enormous 4x4). For the purpose of this illustration I'll deal with a 1700kg car. At 60 km/h this car will have about 470 kJ of kinetic energy. When accelerating to 60 km/h all of that energy has to come from the engine, and when you stop it has to go back in to the engine (engine braking), into the brake pads and discs, and to friction losses (drag, tyre rolling resistance, drive train losses). As it turns out, which of those three mechanisms you predominantly use to dispose of the energy is extremely important with regards to fuel economy.
How you accelerate does have some importance, of course. If you are willing to accelerate more slowly you can save fuel by changing up earlier. This reduces energy losses innate to all piston engines, that is, the back-and-forth motion gets faster and this constant change in direction causes some power to be lost. So even though two people might both end up at 60 km/h, with identical cars, the one that accelerated more slowly would have used less fuel over all, simply because less was wasted in gaining the speed. If both had perfectly efficient engines the slow accelerator would still be slightly ahead (on economy) because he had a lower average velocity, but of course the redneck would get home first.
At constant speed, all other factors being equal, they use the same amount of fuel because they have the same drag to overcome. At constant speed this is the only factor directly related to speed that chews through your fuel. This particular consumption is proportional to the square of velocity, so going a little bit faster actually adds quite a lot of wind resistance (double your speed, say from 30 to 60, and you quadruple the air resistance).
Now we come to the brake pedal.
When you apply the brakes, some of your kinetic energy is converted into heat, and is lost to the atmosphere. Heavy cars need to have big brakes, because these have both more friction to slow the car, and lose heat more quickly so they don't get too hot. It is possible to overheat most types of brakes if you use them a lot in a short space of time, such as slowing from high speed on a steep downhill, or driving around a track. This will cause their friction to decrease and they won't be able to slow the car as efficiently, leading, sometimes, to a crash. That aside, the important point here is that two people, one a redneck thrashing his car, and one a gentle old granny accelerating to 60 km/h in 30 seconds, have identical kinetic energy, all things being equal. So if they both push the brake pedal to come to a stop, both are wasting all the energy they used to get up to speed. All of that energy came out of the fuel in one way or another, so effectively they have both wasted all of that fuel.
Having realised this, what can be done? How can we waste less energy, or even better, recover some of it? The first part, wasting less energy, is possible in any type of car, and it has little to do with how hard you pushed the accelerator 4km ago. The main thing is to take some of the energy that might have been going into the brakes and place it somewhere where it can do something useful, sich as keeping you going along a little way. Most obviously, this means coasting. In gear or out, coasting will be converting some of the kinetic energy into that which is overcoming the drag of the car. You still lose the energy irrevocably, but it is at least keeping you going rather than being converted straight to useless heat. If you are in gear, you also have engine braking going on. This means that the energy the engine would normally need to turn over at the given revs is coming not from fuel but from the kinetic energy of the car or, on a downhill, from the gravitational potential energy as well or instead.
Recovering the energy completely is impossible, but partly, yes, that can be done. If you watch Formula 1 you may know of a system that was used a few years ago: KERS (kinetic energy recovery system). This is a system that uses an electric motor/generator to save some energy when the car slows and spend it out again for a quick burst when the driver wants to overtake another competitor. This type of system is perfectly feasible in a normal car providing that it has an electric motor and battery/capacitor to store the energy. As such, pure electric cars almost always have a system like this, and so do hybrids such as the Toyota Prius, usually called regenerative braking. In an ordinary car (that is, not F1) such a system is very helpful in stop/start traffic, because you can save some of the energy you used to brake and put it to use accelerating again. Slow moving traffic is notoriously wasteful purely because you have to stop and start again so much and hybrid/electric technology helps reduce this energy loss.
Ultimately, the most efficient way to travel will always be at constant speed in top gear, which is why you get much better economy in the country and on freeways than in traffic, even though the drag losses are much greater, but you can get close to that by being gentler in acceleration and braking, and as a result, you'll be safer too. Start slowing down a fair way before a junction or red light. Give the car in front a bit more room, especially if a car behind you is on your bumper. Use both brake pedal and accelerator gently. All of these things will make you a safer driver, and in all likelihood will get you home faster too, since arriving at a light when it is green at 20km/h will put you ahead of anyone who races up to it, stops, and then has to get going again. Hopefully you will have fewer accidents too, which means lower insurance premiums and less hassle. You may also arrive at your destination more relaxed. What's not to like?
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