Monday, May 6, 2013

On the Physical Principles of Graminoid Elimination

On Facebook this past Saturday I commented that I had “mastered E&M and multivariable calculus, but can’t seem to figure out how to start a lawnmower.” Leaving aside the image of a pasty nerd being carried off by an out of control garden tool, I think it’s interesting that the relatively basic physics introduction I’ve been given over the past two semesters is sufficient to explain almost completely how a lawnmower works. So I’m going to share that neatness with my dear and devoted reader(s).

It starts with the starter cord (no surprises there). Pulling the cord almost literally spins the engine’s crankshaft into motion. The crankshaft pulls the piston, which lets fuel and air into the cylinder. The crank continues to turn, the piston compresses the mixture and then, well, then Faraday’s law happens.

There are some chemicals that ignite on contact with air. There are other chemicals that ignite when they are compressed to any degree. Gasoline is not one of those chemicals. Gas is volatile, but not too volatile, which makes it a good method of storing energy. In order to get energy out of gas, you have to mix it with air, compress it, and then raise its temperature all at once.

I don’t want to get too much into the process of combustion, partly because that’s more chemistry than physics, and partly because I don’t understand it very well. But the very basic principle is something Dr. Dave Goldberg explained to me a few years ago when I asked why matter and anti-matter annihilate. His answer: because they can. Essentially, because matter and anti-matter are oppositely charged, it’s very easy for them to disappear and be replaced by electrically neutral photons with the same amount of energy.

The same principle applies to combustion. Oxygen doesn’t have enough electrons, and gasoline has electrons to give. So when you mix the two together, gasoline gives up electrons, breaks down into simpler compounds, and releases energy, because it can. That energy heats and expands the mixture, pushing the piston out and turning the crankshaft, which subsequently turns the lawnmower’s blade.

Why this releases energy is complicated. The simple explanation is that more energy is stored in the system than it takes to release that energy. The usual analogy is to a ball sitting at the top of a hill. When you kick a ball, you transfer kinetic energy from your foot to the ball, and the ball moves away from you until that kinetic energy has been lost to friction and air resistance.

But if you kick a ball so that it rolls down a hill, the energy you provide is enough to “release” the gravitational potential energy stored in the ball, so that by the time it gets to the bottom of the hill it has way more kinetic energy than you provided from your foot alone. So gasoline, because of its structure (yes, that’s a copout), has a lot of potential energy just waiting to be released if you give it a big enough push.

The key is that gasoline is less likely to give up the electrons that form its chemical structure than it is to give up the electrons that bond one molecule of gas to another, so you need more energy to get at those deeper electrons. This energy is provided in the form of a spark that raises the temperature of the mixture.

Where does the spark come from? The spark plug, of course. A spark plug is essentially just a capacitor that is designed to fail. As I explained a couple posts back, charging a capacitor creates an electric field. If the electric field gets too strong, the insulating material between the capacitor plates ionizes. That is, its electrons are stripped away, which turns it into a conductor, causing all those stored electrons in the capacitor to flood across the gap at high speed, producing lightning. This lightning is a spark. But where does a tiny gas-powered lawnmower get the necessary voltage to produce lightning?

This guy:

Courtesy Wikipedia

Lawnmowers use a device known as a magneto. As the engine spins, it rotates a permanent magnet inside a coil of wire. This changing magnetic field induces a current in the coil. But with every turn of the engine, that current is interrupted by a contact breaker, so the current drops down to zero.

Or it would, if it weren’t running through a coil of wire. This coil acts like an inductor, and inductors create electromagnetic fields whose strength is determined by how quickly the local electromagnetic field is changing. So even if there is only a very small current through an inductor, if that current is immediately cut off then the change in current is very large, which in turn produces a very strong electromagnetic field.

But we're not done there. After the magneto comes this:

What would I do without you, Wikipedia?

There’s a second stage, a transformer, which increases the voltage even more, enough to induce a spark in the spark plug. The other pole of the permanent magnet has its own set of wires coiled about it, but it has far more windings than the first set. When the magnetic field produced by the inductor changes due to the broken contact, this induces an electric field in the secondary coil.

But the interesting thing about Faraday’s law is that it talks about changing magnetic flux rather than just a changing magnetic field. Flux is the flow of magnetic field lines through an area. The larger the area, the greater the flux. And the area we’re dealing with here is the circle formed by a loop of wire. But if you have a hundred loops of wire, you have a hundred times the area as far as Faraday’s law is concerned, which means the voltage induced is a hundred times larger.

So by exploiting Faraday’s law to create a rapidly changing magnetic field through a very large area, pulling on a starter cord can induce a large enough voltage to create lightning, which ignites the fuel in the lawnmower’s engine. Pretty cool.

I also wanted to look at converting the chemical energy of gasoline into the rotational energy of the lawnmower blade, but I think this post is long enough already. So tune in next time and there might be a discussion of energy density, thermodynamics, and angular momentum.

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