Plane and Simple

If, like me, you take a modicum of interest in the way that the physical world works, then the inclined plane is one of your base units of knowledge, or should be. If you don't think that you are interested in such things, or the terminology puts you off, please read on for a bit, and allow yourself to be surprised. I find it hard to learn java, a programming language, because when I start to look for a definition for one term, I find it usually leads me to several more terms that I don't understand, so then I have to find the meaning of them and process that... and so on. But somewhere in that process I usually find myself in territory I understand and things start to link together: I understand something new.

My point is simply that terminology itself can often be a little frightening. "Inclined plane" sounds a bit alien and abstract. "Knife" or even "Blade" is much more familiar. Indeed, a knife is a very good example of an inclined plane. Any edge tool is. The point of using an abstract term is that it applies to all devices that use a common technique, not just specific ones. In other words, there are many items that we use that contain or are in themselves inclined planes that are not knives, and might not be thought of as blades either.

So what is an inclined plane, and why is it useful? The simplest example is a hill. It is easier for you to get to the top of the hill by walking up the gentle slope, rather than to take the most direct route, up the sheer cliff face. This is intuitive and obvious to us: from the memories we have we can almost feel the effort involved in taking certain routes before we take them.

So, anyway, that's the idea behind an inclined plane. You don't do any less work by walking up the slope than you would be scaling the cliff, but the work that you do is far easier. (Thank you to David Macaulay for his wonderful book, The Way Things Works, where demonstrates this point by drawing primitive people pushing boulders up a ramp, to drop onto the heads of mammoths, in order to stun and hence capture them.) Naturally, the steeper the slope, the harder work it is. Wheelchair ramps are ideally built at an angle of about 5 degrees, meaning 12 foot of ramp for every foot gained in height: a lot of ramp!

Another example. The wedge. Typically used for holding doors open, splitting logs or raising a heavy object off the ground, a wedge is a beautifully simple device. It is really no more than a portable ramp. Rather than push the object to be lifted onto the ramp, you push the ramp under the object. In the case of splitting, of course, we are not lifting anything off the ground. But we could look at the process of splitting a log as lifting one section of the log away from another part. The two billets of wood are glued together by lignin, so it's chemical rather than gravitational forces we are acting against, but the principle is the same.

You will notice that the work done in splitting involves hitting the wedge, edge on, towards the wood, while the work that that wedge is doing, pushing the two pieces apart, is perpendicular (square) to that. So the wedge is not only magnifying the force applied, it is changing it's direction. In this case the long downward movement of the sledgehammer that strikes the wedge is converted into a very powerful sideways force. If you look at splitting wedges, you will see that they are much steeper in angle than wedges for simply holding something open, so that they split the wood more quickly, but of course need more effort to drive in.

So what other things in our world depend on the same principles? Screws, for one, which are shafts with an inclined plane spiraling around the side. You typically turn the screw several times to drive it a short way into the wood. The number of times the thread is wrapped around the shaft governs it's angle, how quickly it will drive into the wood and thus how much effort is required to turn it. Is that the only use of a screw? No, a screw is also used to power a ship. The shape might have evolved due to experimentation, and the peculiarities of fluids (apparently the modern ship's propeller was invented by accident, when a more conventionally shaped screw broke and the boat moved faster!), but essentially a ship's propeller is a screw that turns, driving the boat into the water. In fact the blades of propellers are aerofoils, which are more complex than simple inclined planes, but share important characteristics.

Any mechanical cutting machine works on the principle of the inclined plane. So without the inclined plane, chances are that the Amazon forest would be a lot larger, and in fact that most of England would be forested too! And people would be a lot furrier, although I suppose wax might have been invented. We would be very hampered in our attempts to get around quickly. Zips, cylinder locks, ploughs and a zillion other items we take for granted could not exist. So thank you to Mr. Inclined, the inventor of the inclined plane. I'm off to cut some bread for breakfast.