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Bow Design
Part 4 of 4

The above points are practical and all easily demonstrated mathematically but we need look no further than many of the long shooting bows of our own and previous generations. If there is not a decided tendency toward wider, flatter and shorter limbs, my eyes are sure growing undependable. Distance means basically "cast"; in other words, an efficient, powerful bow plus the proper arrow combination. The various long shooting bows I have seen in "the flesh" or on paper are progressively flatter as their range increases. Oriental bows apparently could reach up towards 800 yards according to pretty definite records left us (I believe there are about a dozen over 500 yards).

These bows departed from the rectangular section no more than is explained by the slight increase in stress that may be safely imposed on a fiber that is supported by adjacent fibers. This padding a flat rectangle is apparently feasible near the center of back and belly with a slight relief of the corners, as shown in Figure 2a. If different materials are used, or, as is usually the case, the wood is stronger in tension than compression, the trapezoidal form logically follows. From the fact that crysalling develops on the belly, it seems certain that there is excess strength on the back. Therefore, any bow designed to the limit and not carrying useless weight should have a cross-section somewhat like Figure 2a.

I have made ¼-inch diameter "Bureau of Standards" test bars of yew and osage and they regularly will pull up to 15,000 pounds and 30,000 pounds per square inch respectively. Few bows are strained much over 12,000 pounds per square inch figured stress. Incidentally, these tests show that wood which is one-tenth the weight of steel has about one-half its strength —a clue as to why no steel bow can hope to equal a wooden one in cast or flight shooting.

There are many arguments and probably actual laws that make the long bow popular. I believe they will ultimately be found in the analysis of the path of the rear end of the arrow. We know that gripping the bow tightly is wrong, as any twisting tendency, either horizontally or vertically, throws the arrow off. Such tendency, whether conscious or unconscious, exists with a tight grip and its possible effect is easily demonstrated by a definitely applied twist when releasing an arrow. If the loose grip or in effect, a "one point" contact at the handle is used, the path of the rear end of the arrow depends on its location on the string and the relative energy and weight in the two limbs. Undoubtedly skill in the art of bow design (not the science) consists of approaching a correct combination of these elements by long experience. Possibly the longer the bow the easier it is to achieve the right combination. When we get some ultra slow motion pictures of the rear end of an arrow we will know a lot more of the internal action of bows and will be able to explain a lot of the varied reports of aiming point location with different bows. Any bow that forces the rear end of an arrow downward or below the original line of the arrow, by reason of distribution of work and weight in the upper and lower limbs, naturally has a better apparent "cast" or a lower aiming point. Many of these 40-pound bows that hold on the gold at 100 yards evidently can do so because of some accidental or unsuspected inequality rather than from any magic "cast" obtained by cut, seasoning or design of the bow.

That indefinable term "cast" will probably long be with us. As applied to material, it is probably completely contained within three basic tools of engineering design, i.e., modulus of elasticity, weight and strength. A complex cellular and laminated structure like wood will never yield to as exact detail analysis as does steel but overall analysis is easily obtained. The weight and strength are fairly simple except strength in compression and crysalling gives us data on that. The bow itself gives us direct data on the overall modulus of elasticity as it is fixed by the relationship between bending moment and curvature.

The bow designed theoretically above conforms to experience on one brand of yew and the modulus of elasticity is about 1,000,000 pounds per square inch (all steel is about 30,000,000 pounds or about 30 times as stiff). This results from the mathematical relationship between a stress of 10,000 pounds per square inch and the combination figure of 50 obtained by dividing the radius of curvature by the thickness of the section. Any one wood or any other homogeneous material will have its own combination figure which one cannot go below without incurring excessive stress. Yew is apparently about 50 and Osage possibly higher.

Here's hoping that these "feints" will evoke some real "counter."

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