Why toast lands buttered side down

In one of the very first posts on this blog, we tackled the question of how cats always land on their feet. Now, two years later, it’s time to tackle another species with a similar skill: namely toast.

Animated clip of a piece of toast falling from a plate on the edge of a table, turning in the air and landing butter-side down
A demonstration of the typical behaviour of falling toast. It’s physics, not bad luck, that causes it to land butter-side down.

As with the cats, the answer turns out to be physics – and not, as you may have expected, Murphy’s Law, which is more of an engineering principle.

You see, Murphy’s Law is frequently taken as a pessimistic prediction that things will always go wrong. This is clearly not true: the principle says “anything that can go wrong will go wrong”, but usually there are many, many things that can go wrong, and they can’t all happen at once.

A more charitable interpretation – which was supposedly one of the original meanings when the law was named for USAF Captain Ed Murphy, who built rocket sleds in the 1950s – is that if there’s a known flaw you should try and rectify it, rather than just leave it and hope that it won’t happen.

To give an example, consider the Death Star. It was built with the engineering fault of an exhaust vent that, if you hit it just right, would cause the whole thing to explode. But Grand Moff Tarkin apparently just assumed that the Rebels would never be good enough shots to hit it (perhaps he was used to the lousy accuracy of Imperial Stormtroopers, not to mention targeting computers). If he had have known of Murphy’s Law, he might have decided to put a cover over it instead.

But enough sci-fi nonsense: back to toast. As I mentioned, this is actually straightforward physics, first documented by Robert Matthews of Aston University, an achievement for which he won an IgNobel Prize (Matthews RAJ 1995, “Tumbling toast, Murphy’s Law and the fundamental constants”, European Journal of Physics, vol. 16, no. 4, p. 172, doi:10.1088/0143-0807/16/4/005).

Toast usually falls by tipping over the edge of something, like a plate or the edge of a table. When it does, it teeters first, rotating about the edge of the plate/table, before dropping down. It continues to rotate while in the air, and under typical conditions does a half-turn and lands upside-down.

Diagram of the dynamics of falling toast, showing the angular rotation forces of gravity, friction, reaction of the table
Diagram of the dynamics of falling toast, taken from “The Anthropomurphic Principle”, by Roland Krenn

I say ‘typical conditions’ because the amount it rotates depends on a number of factors, like the height of the table, the amount the toast is overhanging the edge when it’s released, how fast it’s moving horizontally, the friction between the toast and the table, and the size of the toast.

It’s fairly straightforward to model a simplified scenario where the toast doesn’t slip against the edge of the table (see Roland Krenn 2005, “The Anthropomurphic Principle”, Karl Franzens Universität Graz). In the no-slipping case, the toast doesn’t fall until it’s aligned vertically (θ = 90° in the diagram above).

Using those calculations, you can show that you’d need to drop the toast from a height of about 3 metres for it to do a full rotation and land right-side up again. Needless to say, this rarely happens.

When you add in the slipping it gets more complicated, and you need sophisticated computer modelling to do the calculations. Fortunately, people have done just that (Bacon ME, Heald G & James M 2001, “A closer look at tumbling toast”, American Journal of Physics, vol. 69, no. 1, pp. 38-43, DOI: 10.1119/1.1289213, PDF 475 KB).

They found that slipping causes the toast to rotate faster, but for small amounts of overhang – which is realistic for natural toast dropping – it will still land upside-down.

So, going back to Murphy’s Law, how can we save our toast from dirty butter? Well, the experts have a number of suggestions:

  1. carry the plate above your head at about 3 metres high
  2. equivalently, only use toast about 2.5 cm wide (maybe that French mini-toast)
  3. when the toast starts to fall, pull the plate away quickly so it doesn’t rotate.

Considering that last point, I have an alternative idea: if you are able to pull the plate away, you should also be able to push it back under the plate. Why let it fall at all?

Murphy would be proud.

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