So much has been written and said regarding the phenomenon long ago christened "The Archer's Paradox," that mysterious twist which brings an arrow back on its path after starting off on a tangent; that it hardly behooves one to bring forth any further ideas and brand them as new. However, the results of the following experiments have proven so interesting and have brought to light so many whimsical traits in the flight of an arrow from a bow that I shall endeavor to pass them on for what they may be worth.
In the first place I have been able to demonstrate that our paradox contains or is accompanied by several minor and similarly freakish actions contrary to what we might expect, which had to be dealt with as they presented themselves.
These experiments were conducted over a mechanical archer or shooting machine designed to reproduce as nearly as possible the effect of shooting by hand. In the work we used many different kinds of bows, both wood and metal, including one with a very narrow handle only one-fourth of an inch wide made up to my design for experimental purposes, which proved to be a very interesting study. Arrows of various weight and spine with large and small feathering all had their effect upon the results, but the fundamental characteristics remained the same.
We have all wished for a slow motion picture which would show the flight of an arrow from the moment of release. We will attempt to show with some degree of certainty, the path of the string, the movement of the bow at the hand and at the tips, the path of the arrow as it bends around the bow and the antics of the arrow as it leaves the bow and gets away on its flight. The exact position of the arrow in the air with relation to its original line of flight is easily demonstrated at any desired distance by the simple means we have employed in this work. We will start with the path of the string from full draw. Assuming that the path of the empty string if released without any lateral impulse would follow a direct line through its point of rest to the middle of the bow shown as (a) Fig. 1. In shooting an arrow we have to deal with, first, the lateral impulse imparted to the string and arrow by the releasing fingers, second, with the acute angle of the arrow and the path of the empty string, also with the center of gravity of the arrow. Bear in mind that we have to consider many and varied forces released and spent in an extremely short space of time. To be more or less exact according to my crude method of measuring its bow velocity the arrow travels its length in about l-65th of a second, varying of course with the cast of the bow and weight of the arrow. In Fig. 1 the path of the string is shown as (c) with the dotted line (a) representing the center or path of the empty string. Line (b) is a continuation of the side of the arrow next to the bow at full draw. These illustrations are drawn to scale and not exaggerated. As the string and nock speed forward they perform the arc to the left of center, swinging back across the line at about five inches and enter into the long curve to the right, again crossing line (a) just beyond the point of rest (d). This swing to the right is the results of the center of gravity of the arrow endeavoring to travel forward at an angle less than that of the arrow and the center line of the bow and the interference of the bow. This force as the arrow travels forward increases until the balancing point of the arrow passes the bow and then begins to decrease.
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Fig. 1, Fig. 2 and Fig. 3.