The 630 Inch-Pound Rule for Crossbows - James Prescott
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The 630 Inch-Pound Rule for Crossbows
Copyright © 1992 James Prescott
[ Note: This article concerns combat archery safety within the Society for Creative Anachronism (SCA). ]
[ Note: The 630 inch-pound limit mentioned here was later reduced to 600 inch-pounds. ]
As the probable author of the 630 inch-pound rule used for crossbows in the IKCAC rules and elsewhere, let me briefly describe the physics behind that number, and back it up with the results from a simple experiment. I have never written a paper on this subject, so this is perhaps the first written commentary. It will be a summary only. As to my qualifications, I hold a BSc With Distinction in Physics and Mathematics.
As many of you probably know, if you plot the pull weight (vertically) against the power stroke (horizontally) for a longbow, a recurve bow, or a crossbow, the curve is always below the diagonal line, with the straightest line being the one for a good modern recurve. The power stroke is measured from where the string lies at rest to the point of full draw, and has also been called the draw distance. See, for example, Robert Hardy's Longbow, Mary Rose Trust, 1986.
Simple physics tells us that the energy stored in the bow when it is drawn is the area under the curve. If the plot were a simple diagonal, the area would of course be 1/2 the pull weight times the power stroke. A good modern recurve is closest to this, with the other bow types storing the same or less energy for a given pull weight and power stroke.
When a bow is shot, all of the stored energy is expended, and a percentage of the energy goes into the missile. For a good modern recurve firing a heavy SCA blunt arrow the proportion of the stored energy that goes into the arrow is in the range from 85% to 90%. The proportion (assuming that a bolt is lighter than an arrow) is lower for a crossbow, and is significantly lower for a longbow.
So, we see that the greatest energy for a given pull weight and power stroke will be put into a missile by a good modern recurve. We have already seen that bruising is directly proportional to the kinetic energy in the missile (Thorvald Grimsson and Garrathe Ravenswood, "Bruising and SCA Missile Combat", typed article, 1987). It is also inversely proportional to the frontal area, but we assume here that all missiles have the same frontal area. Any bow that puts the same or less kinetic energy into the missile than a good modern recurve is acceptable for SCA combat.
The energy that a good modern recurve puts into an arrow is therefore very approximately 1/2 the pull weight times the power stroke. Because it is a factor common to all bows, the 1/2 may be dropped. We can then restate the principle as: "the acceptability of any bow for SCA combat is proportional to the pull weight times the power stroke".
When I first developed this formula, I measured the best modern recurve I knew, Garrathe Ravenswood's, which had a pull weight of 30 pounds at a 21 inch power stroke when used with a standard 28 inch war arrow. 21 inches times 30 pounds gave the mystical figure of 630 inch-pounds that has since been widely used. Garrathe's bow was admittedly exceptional (my own excellent bow would have given an equally mystical 555 inch-pounds).
I recently carried out a penetration test such as is commonly prescribed in the SCA for testing crossbows, in which kinetic energy is proportional to penetration. It is essential for this measurement that the tip of the missile not protrude from the back of the target. I fired a 28 inch arrow from my recurve and a bolt from my crossbow at point-blank range into adjacent locations in a newly-tightened straw archery mat. The two missiles had identical field points. I measured the penetration of the arrow and the penetration of the bolt. This was repeated 13 times at different places on the mat. The mean penetration ratio (bolt penetration divided by arrow penetration) was 0.80 with a sample standard deviation of 0.06.
My recurve has a pull weight of 30 pounds with a power stroke of 18.5 inches, for a product of 555 inch-pounds. My crossbow has a pull weight of 65 pounds with a power stroke of 6.75 inches, for a product of 439 inch-pounds. The theoretical penetration ratio (crossbow product divided by recurve product) is 0.79.
The experimental ratio was 0.80, and the theoretical ratio was 0.79. The penetration test therefore offers excellent support for the theory.
Yeoman Master Thorvald Grimsson, OP, OL, OGGS
Additional later comments:
But "really accurate" methods are not necessary.
As originator many years ago of the inch-pound method of rating crossbows, my reasoning was as follows:
1) The archery books available to me all suggested that a good quality modern recurve was more efficient than a crossbow.
2) The Society had said that a 30 pound recurve at 28 inches was by definition legal.
3) Mildly technical comment -- see an archery book such as Hardy's
_Longbow_ if necessary
4) Garrathe's recurve was 30 pounds, and with a 28 inch combat arrow fitted had a power stroke of 21 inches. The area of the triangle was half of 30 times 21. For simplicity it is possible to drop the "half" everywhere, so we had a recurve with less than 630 inch-pounds of "energy".
5) By paragraph 1 above, a crossbow with an inch-pound rating of 630 inch-pounds would *always* have less energy than Garrathe's recurve. In addition, because most bolts are lighter than arrows, a lower percentage of that energy would be transferred to the bolt than would be transferred from the bow to the arrow.
6) Several years ago the 630 was rounded down to 600 inch-pounds because someone thought it was a more aesthetically pleasing round number.
Some years later, in order to check whether the above theory bore any relationship to reality, I undertook some simple field tests. An arrow penetrates into something in proportion to its kinetic energy. I had a fairly new Saunders matt. I made up an arrow and a crossbow bolt with identical shaft materials and heads, though with different lengths.
I fired the arrow and the crossbow bolt (in alternating order) into the matt at various places side-by-side. I discarded any pair in which a head had come out at the back of the matt. I measured the depth of penetration into the matt for each shaft.
When I had enough measurements, I analyzed them. They supported the theory that draw weight times power stroke is an acceptable predictor of the relative energy of an arrow fired from a bow versus a bolt fired from a crossbow.
The measurements did not support the secondary hypothesis that a crossbow bolt would have less energy.
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