Sci: Speeding arrows

Estimation, unlike history, is a part of mathematics, and it is an important one, if you are relying on a calculator, where a slip of the finger can move the decimal point. Estimation is also useful for scientists when they don’t have complete and reliable data.

For example, until about 1600, most military firepower, aside from the odd cannon, used to batter walls from a distance, came from bows and arrows. In reality, up until the mid-1800s, it would have made more sense to keep on using archers, because a skilled bowman could fire more shots faster, doing greater harm at the end of their range, than a soldier could do, equipped with a rifle or a musket.

The key point is that an archer had to be skilled, and those who used longbows had to be strong. On the other hand, the skill and strength needed to fire a crossbow were low, like those needed to discharge a firearm. Crossbows fired fewer shots per minute than longbows, but they were more damaging than muskets.

The Aiming of the Shrew.

In October 1415, the small English army of King Henry V, some 6000 men, was faced at Agincourt with an army of 50,000 Frenchmen. The difference was not as great as you might think, because 5000 of the Englishmen were skilled archers. The French army was mainly composed of cavalry, and facing a rain of arrows, the French cavalry turned back into the French infantry, causing confusion that is bad for winning battles.

A good archer could fire off ten arrows a minute, each of them leaving the bow at 60 m/s (more than 200 km/h), and arriving a few seconds later, still carrying three quarters of that speed. All of these are estimates, of course, but we know that in 1590, Sir Roger Williams complained that only 10% of archers could do harm “12 or 14 score off”, which is at 240 to 280 yards, or 220 to 260 metres. Even at Waterloo in 1815, muskets had a range of less than 100 metres.

Much of the armour used at Agincourt was thin metal, perhaps 1 mm thick, and tests have shown that arrows would go through 1 mm steel. Some armour was up to 4 mm thick, and that would have withstood arrows, but not crossbow bolts.

The crossbow has the advantage that it can be loaded in advance, and used when necessary. More importantly, it fires a heavy bolt with real killing power, and no real training is needed to use one, because the operation is intuitive: point, steady the bow and shoot. After a ranging shot or two, most operators can be accurate enough to be dangerous.

The crossbow bolt would have been slower at first, but later ones are credited with ranges of a quarter of a mile (400 metres) and more. Allowing for air resistance, the bolts must have reached at least 75 m/s, close to 300 km/h. The rate of fire of the crossbow was comparable with that of a trained musket user, with less chance of a misfire, making the changeover to firearms (when it happened) a bit odd, because arrows, even crossbow ones, were still better. Perhaps the people in charge believed Zeno’s Paradox?

That same argument can also be applied with appropriate changes to an arrow approaching a target, but Zeno also said that if we divide the time into tiny enough segments, in each of them, the arrow is not moving. Either way, it will never reach the target. Remember the bumblebee!

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