Einstein’s Horsebow

Every archer knows that a bow’s draw weight increases as you pull it back (I am ignoring compound bows, with their pulleys and cams. I advise everybody else to ignore them as well). Perhaps my favourite fact of all time is that as you pull the string back you also increase the physical mass of the bow.

As every schoolboy once knew (I feel really old…), Albert Einstein proved in 1905 that the energy of an object at rest is equal to its mass multiplied by the speed of light squared. In mathematical notation, this is written as E=mc2, the most famous equation in history, known even to people who have no idea what it means. Since the speed of light, c, stays the same (roughly 300,000,000 metres/second), any increase in energy must lead to an increase in mass.

A bow is a device for storing energy and then releasing it suddenly into an arrow. As you draw a bow it stores the energy that goes into drawing it (some of the energy, anyway). This means that a bow at full draw has more energy than a bow that is braced. Since energy equals mass x a constant (c2), a drawn bow has a greater mass than an undrawn one. As you pull your bow, you make it heavier.

Of course, you don’t notice this effect. That’s because if E=mc2 then m=E/c2. No matter how strong you are, the energy you put into your bow is tiny compared to c2 (90,000,000,000,000,000). The increase in mass when you pull back an average draw weight horsebow is about the same as adding a single bacterium to the bow. That’s about a millionth of a grain of sand.

This is of no relevance whatsoever to the practical workings of bows and arrow, which is what I am going to write about next, but it is a fantastic fact.

And no, Einstein did not have a horsebow.

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