|MadSci Network: Physics|
Question: A modern bullet vs. a medieval arrow which would have more strength behind it? Wouldn’t it be the bullet since it's made of metal while the arrow is simply made of wood? Dear Krystina, thank you for your question. It is not an easy one since there are so many things to consider in both the case of bullets and of arrows. I’m no expert in armaments but I’ll point out some of the things you need to think about. You used the words “force” and “strength” and although we know what you mean, we should take some care to use measures of the behaviour of arrows and bullets which would let us compare the two on a fair basis. Let’s be honest, both bullets and arrows are used to cause damage, usually to animals including humans so we need a measure of this capability to cause damage. In order to cause damage the projectile must use its kinetic energy, the energy it need to travel at speed, to split crush and deform the material being hit. Often we use the ability of the bullet or arrow to penetrate a solid material. At least that is a good starting point. Let’s look at bullets first. They are propelled by an explosion within the gun barrel and the expanding gases force the bullet down the barrel and out towards the target. Guns often need to be carried easily so the size of the cartridges and bullets is a compromise between causing the maximum damage and being easy to handle. The kinetic energy of the bullet ( and arrow ) is ½ x M x V ^2 where M is the mass, and V the velocity. The mass depends on the size and density of the bullet and the velocity depends on things like the amount of explosive, the mass of the bullet and the design of the gun. Arrows on the other hand are projected by a bow which has been drawn by the archer’s muscles. This web-site has some interesting information about the history of the long-bow:- http://www.history-magazine.com. We can define energy as the force applied times the distance over which the force is applied. In the case of a bow, the archer pulls back the string using at first a small force but as the bow bends the force needed to pull further builds up. Some say that a medieval bow could require 160lbs “draw strength” which is the force needed for the last part of the draw where most of the energy is stored up. On release of the string, most of the stored energy is transferred to the arrow. Arrows could be up to 3 feet long so even though they were made largely of wood this weight of wood plus the weight of the normally metal arrow-head could be much greater than a rifle bullet. This is a factor which results in the arrows traveling more slowly than bullets which usually travel faster than sound. Once the projectile is on its way, it can only lose energy through air resistance. This energy loss is important because it is the energy on impact not the firing energy that counts. The bullet and arrow are again very different. Because the arrow travels more slowly, the air resistance due to pushing air out of the way is lower. On the other hand the shaft and particularly the flights will cause frictional drag. ( The fact that the drag due to the flight is greater than the tip is how flights keep the arrow straight ! ) The final amount of energy depends on these losses and therefore of course how far the projectile travels before impact. I should think arrows lose a smaller fraction of their energy. This may help to explain why arrows can penetrate solid materials so well. Another factor is their shape. The arrow-head is very sharp, that is it has a very small cross sectional area at the tip. The size builds up slowly and this is good for air resistance and particularly good for penetrating solids. Arrows shot by the famous Welsh bowmen at around the time of Henry the Fifth in Britain could penetrate solid oak, four inches thick and poke through by over six inches. Hope that helps even though there is no clear winner – at least not as clear as Henry was against the French thanks to the Welsh ( how did you guess I was Welsh ? ). [note added by MadSci Admin: If you can find some information, maybe on the Web, about typical bullet masses and velocities, and typical arrow masses and velocities, the kinetic energy could be compared.]
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