Archery Question

[--Pete]

Hi,

After reading some of the posts on this topic, I did a little thinking. It occured to me that arrows *are* rocket science. Or at least ballistic missile science :)

Now most of this, a pilot (and even an aviator) would know -- so this is really a general reply to the thread ;)

Any object that is going to fly through the air is either going to fly 'straight' or tumble. If an object tumbles, it doesn't make a good weapon since (without a lot of practice by the thrower, as in knife throwing) it is more likely that it will hit blunt end/side first rather than point first. To ensure that the object will fly straight is a simple exercise in aerodynamics.

Basically, there are two quantities of importance, the center of mass and the center of pressure. In the case of something like an arrow or a spear (i.e., long thin objects) the center of mass is just the point where the object balances. So, for instance, the center of mass of a naked arrow shaft is just the center of the shaft. When the head and the feathers (fletching) have been added, the center of mass is closer to the head of the arrow since the head now weighs more.

The center of pressure is a little more complicated, but essential it is just where the object would 'balance' in the wind. Think of suspending the item so that it is free to pivot horizontally. Now let a wind blow on the item. Move the point at which the item is suspended back and forth until the item has no tendency to line up with the wind. The place where the pivot is located when this happens is the center of pressure. In model rocketry, a simple trick is used to determine the center of pressure. The two dimensional outline of the rocket is cut from uniform carboard. Where the outline balances is the center of pressure of the three dimensional rocket. In the case of an arrow, the center of pressure is towards the tail because the feathers have a greater cross section than the arrowhead does, so there's more there for the wind to catch.

Now, once these two quantities are found, 'straight' flight is simple to figure. An object wants to fly with the center of mass ahead of the center of pressure. A naked arrow shaft is right on the border. If launched without a twist, it might go straight. Firing an arrow, however, always introduces a twist. To achieve true stability, the center of mass has to be well ahead of the center of pressure. Normally this is true.

The conclusions from this simple analysis is that at the front of the arrow we want dense stuff and at the back we want fluffy stuff. Taking a normal arrow, wrapping a bunch of cloth (or grass, or whatever) around the front of the arrow, and soaking it with oil or pitch puts a lot of low density stuff at the wrong end. So, in addition to putting the fire a little further from the archer, this gives another reason why longer than usual arrows would be needed. Add to that the fact that a lot more fluffy stuff will be need to be at the back end to regain stability, and the drag on the arrow becomes monstrous.

Were fire arrows occasionally used? Probably. But they sure don't sound like a Good Idea for general warfare.

--Pete