I stopped at the gas station on the way home from work today. With gas prices at $1.034/L, the $40 worth that I purchased barely filled 3/4 of my tank. Being the cheap bastard that I am, I was immediately reminded of an article I recently came across on Treehugger that recommends conserving gas by driving the speed limit. It’s good advice but, as an engineer, I found their expanation somewhat lacking. So here is my best attempt at explaining, in the language of high-school physics, why driving slower uses less gas.

There are two parts of driving that are worth considering. First, how much energy is spent getting a vehicle up to speed, and second, how much is used to sustain that speed.

Let’s consider the first: accelerating to full speed. If you remember from your high school physics classes, the kinetic energy of a moving object is proportional to the square of its velocity, or e=mv^{2}/2. What this means is that to go twice as fast requires four times as much energy. For example, to accelerate from 0-100km/h requires in your car requires four times as much energy, and therefore four times as much gasoline, as accelerating from 0-50km/h.

And that’s just the energy to get up to speed. In a frictionless and air-resistanceless world, you wouldn’t need any more energy, the car would just coast forever. But we don’t live in such a world, which brings us to the second point, sustaining the velocity.

Air resistance and internal friction increase propotionally with the speed that you drive. If you drive twice as fast, the air pushes twice as hard against you. This shouldn’t come as a shock to anybody who has held their hand out the window of a moving vehicle. So how does that translate into fuel consumption?

If you followed the link to the Treehugger article, you’d already know that fuel consumption is proportional to the speed you drive. But how? Think back again to your high school physics class: work is equal to force times distance, or w=fd. You’ll also remember that work and energy are the same thing. So if you drive faster, you’ll have to apply a force against a higher air resistance. Over the same distance, driving faster will require more work, which is energy, which is gasoline, which is dollars at the gas station. Driving twice as fast requires twice as much gasoline over the same distance.

So there you have the basic physics of how it’s cheaper to drive the speed limit (or less) from a cheap bastard of an engineer.