archery - The Phillosoph Blog

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Recently I got to thinking about archery. In particular, I was curious about the time of flight of arrows and quarrels. This seemed quite a practical thing to know. I was a little surprised at how little information on this could be found on the internet.

Most modern archers are target shooters, so not particularly interested in how long the arrow takes to reach a static target.

They also shoot at ranges that provide very little insight into, say, bows being used on medieval battlefields.

If you play role-playing games, arrows probably hit in the same turn, which may be the same second, of firing.

You would think there was considerable discussion of flight times among bowhunters, but not according to my search engine.

One target site did inform me:

“Recurve bow arrows can travel up to 225 feet per second (fps) or 150mph while compound bow arrows can travel up to 300fps (200mph). Longbow arrows travel slower due to the weight of the arrows. Even at 300fps, it takes around a second to reach a 90 metre target. You hear your release first followed by the thud of the arrow hitting the target a second later (you can’t see it unless you use a telescopic sight).”

More trawling found me this article, with the following table:

I also remembered an old book I had, which gives the following table:

90 metres in the first second sounds like a good rule of thumb, although I would like to know how this changes beyond this range.

Why does it matter?

If in an emergency situation a bow may be one of your options for defence or food gathering. Much of the information relevant to arrows will also apply to other hand-thrown missiles such as spears or rocks.

Contrary to what you see in action movies, bows are not “silent killers”. Some of the energy stored up in a drawn bow is released as sound.

Your arrow will travel at 100-200 fps, while sound travels at about 1,100 fps. The animal you are shooting at will hear you before the arrow arrives. Many animals survive by being paranoid, so there is a good chance it will begin moving before your arrow arrives.

Thus, you need to lead your target. For this, you need to know time of flight. Calculating lead and other parameters is covered in my book on survival weapons.

While there was very little discussion of time of flight, it seemed initial velocity and kinetic energy seemed to be of great interest to bowhunters.

The V0 of a bow is the equivalent of the muzzle velocity of a gun. Most bows don’t have muzzles.

Arrows lose energy at a pretty steep rate. One of the above sites uses a working figure of 3% per 10 yards. This means that the terminal velocity of an arrow is going to be very different from the V0. Failing a really strong tailwind, V0 is the one velocity your arrow will not be at!

As discussed elsewhere, kinetic energy is something of a red herring when predicting bullet performance. It is popular in the gun press. It is far more impressive to say a round has 2,352 ft/lbs of energy than that it has 1.7 ftlb/sec of momentum!

Terminal performance of arrows is somewhat easier to estimate than for bullets. Arrows mainly rely on cutting to produce blood loss.

Given similar size and configuration of arrow heads, it seems reasonable that the more effective arrow will be that that penetrates more. Just for fun, I ran some figures using the following formulae:

Energy (ftlbs) = [(Velocity (fps))^2 x Weight (grains)] ÷ 450,240

Momentum (ftlbs/sec) = Weight (grains) x Velocity (fps) ÷ 225218

From the above chart, I selected a 450 gr arrow at 130 fps and compared it to a 350 gr arrow at 147.4 fps. These would both have a kinetic energy of about 16.89ftlbs. Since weight is different, so will momentum be.

The heavier arrow is at 0.2597 ftlb/sec while the lighter is 0.225 ftlb/sec. That is about 15% difference.

One would expect the arrow with more momentum to penetrate more due to its higher inertia, but would the difference be significant in real world applications?

Something to think on.

Reading through my file collection the other day I came across an old (1930’s?) article on how the North American Indians made their bows. I have some knowledge of English and Asian bows but this was a field I was less familiar with. One of the reasons that this article so interested me was that I am currently reading Edgar Rice Burroughs’s Pellucidar series. Many of the characters in these books use bows and there are frequent references to them constructing new weapons after escaping from capture. The Indians tended to favour flatbow designs and I have heard it suggested that such a bow is easier to construct under field conditions than the D-section English Longbow.

I will not bother to reproduce the entire article since there are some excellent websites on the topic available on the internet. Some interesting points from the original article were:

- The best time to cut wood to make bows was February since the sap had not yet risen into the wood. This was defined in the article as “when the geese return”.
- The wood of choice was Osage Orange. Where this was not available a number of other woods were used including ash, hickory and yew.
- Like the English Longbow, the bowstave needed a considerable period of seasoning before any carving could be done. Bowstaves were hung high up in the tepee above the fire to gently season in the heat. Arrowshafts and other items were seasoned in the same way. The bark side of the stave was used for the "back" of the bow: the part that faces away from you.
- Bow length varied with tribe, intended use and probably the individual. Bows of six foot or longer were known, as were bows of only a few feet. A suggested measure for a bow was the distance from the left hip to the right hand when the hand was held out horizontally to the side. This is about four feet. Some readers will recognize this as illustrated in Lofty Wiseman’s “The SAS Survival Guide” and doubtless this book and the article drew from a similar source. The bow illustrated in that publication is a flatbow.
- Arrows were often marked with three lightning bolt carvings. Practical purpose of these may have been to reduce the tendency of the arrow to warp. It was also suggested in the article that the grooves might have encouraged blood loss.
- Arrowheads were bound into the end of the arrowshaft. Some war arrowheads were constructed so that impact with the target would cut the bindings, leaving the head in the target even if the shaft was pulled out.
- Hard sinew (from the neck of a buffalo) was sometimes used as an arrowhead. The stated advantage of this was that such heads had a tendency to deflect from the ribs of an animal and slip between them while flint or iron heads would stick, shatter or bend.

ERB does not give us any description of the type of bows his characters use, although David Innes in “Land of Terror” does tell us:

“A species of the genus Taxus is more or less widely distributed throughout Pellucidar; and I had discovered that its wood made the best bows. For arrows I used a straight, hollow reed that becomes very hard when dry. The tips which I inserted in the end of the reeds were of wood, fire-hardened.

A modern archer of the civilized outer world would doubtless laugh at the crude bow I made then at the edge of the Valley of the Jukans. If he uses a yew bow, the wood for it was allowed to season for three years before it was made into a bow, and then the bow was probably not used for two more years; but I could not wait five years before eating; and so I hacked the limb I had selected from the tree with my stone knife and took the bark from it and tapered it crudely from the center toward each end. I prefer a six foot, eighty pound bow for a three-foot arrow, because of the great size and formidability of some of the beasts one meets here; but of course my bow did not attain this strength immediately. Every time we had a fire, I would dry it out a little more, so that it gradually attained its full efficiency. The strings for my bows I can make from several long-fibered plants; but even the best of them do not last long, and I am constantly having to renew them.”

In “Return to Pellucidar” in the anthology book “Savage Pellucidar”:

“Fruit and nuts grew in abundance on the trees and shrubs of the little canyon; but fighting men require meat; and one must have weapons to have meat. These two had not even a stone knife between them, but the first men had no weapons originally. They had to make them.

Innes and Hodon went into the little stream and hunted around until they found a large mussel. They pried it open with a sharp stone, and each took a half shell. With these they cut two pieces of bamboo-like arborescent grass to form the hafts of two spears. Searching again they collected a number of stones: soft stones, hard stones, flat stones, stones with sharp edges; and with some of these they chipped and scraped at others until they had fashioned two spear heads and a couple of crude knives. While Hodon was finding the toughest fibers with which to bind the spear heads to the hafts, Innes made a bow and some arrows, for this was one of his favorite weapons.”

Since Pellucidar was constantly under an unmoving noon-day sun it presumably had no seasons and the trees would have always been filled with sap. Perhaps that was why the bow was so rare on Pellucidar!

The Boy Scout Handbook (1911) has a nice section on archery.