Archery Question

[Doc]

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
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Adding to what Pete said, flaming arrows were also fired practically straight upwards, because they really didn't fly. They would come straight down from above. Pointing said arrow upward was what was dangerous, all that fuel dribbling down.

Taking this into account, the reality is on the battlefield, you didn't fire these at oncoming armies. You waited till they were literally right at the walls in most cases, as these missiles had little to no flight capability, and firing them skyward didn't allow for much distance. Tar and pitch arrows were, relatively speaking, the safest, but also the heaviest. And they dropped like lawn darts. Tar arrows had no heads or tips usually. A blob of tar or pitch was far to much wieght on the front end to begin with. Tar arrows also burned up the wood. They didn't stay long in the air, but the intense heat would burn down quite a bit of the shaft. They were kind of like flying matchsticks. Often the tarball would burn off, dropping in one place, while the remainder of the burnt shaft would land elsewhere. Rag arrows had greater flight abilities, contrary to what you might think. I can't explain why, they just do. Wrap the rag tightly around the shaft, and form a knot at the tip. Rag arrows usually didn't have arrowheads, they had stone or lead or some sort of scrap bob on the tip for wieght. When lighting a rag arrow, you only light the knot at the end. The flight causes the flames to spread backward along the length.

The real revolution in warfare with missile launchers was the crossbow. You could launch a flaming bolt with quite a bit of distance, fired forward, with some small degree of acuracy. In what can only be described as cruelty, you could stick a ball of burning tar about 3 inches behind the tip of a metal bolt, fire it into somebody's armor, where it would punch clean through. With a barbed tip, it was nearly impossible to pull out, and the burning ball of tar would be right at the surface of the skin and armor, heating it, burning it, with flames that could not be extinguished. There was plenty of damn good reasons that crossbows were outlawed as cruel uncivilized weapons. There were crossbows made for the express purpose of firing flaming missiles, with elaborate metal guards and shields to protect the wielder from the dangerous flyback. I am not sure that any of these worked as well as their creator hoped. The fact that it never became standard practice to fire flaming bolts tells me that to many mishaps happened for it to become commonplace.