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Arrows and the Archer's Paradox
Part 1 of 4

Earlier in this article certain facts were mentioned regarding the strength and other characteristics of wood which make it especially suitable for arrows. The high acceleration— several hundred times that of gravity—encountered by the arrow as the string urges it forward makes stiffness imperative and strength desirable. Buckling of the "column effect" type should be minimized; but if buckling does take place there should be no breakage. On the other hand, the arrow must not be too stiff, otherwise it will deviate from the line of aim. It will also deviate from this line if it is not stiff enough. These comments regarding stiffness may be summarized by saying that, with respect to stiffness and mass, the arrow must be matched to the bow if it is to fly accurately in the direction in which it is aimed. The reason for these requirements will appear as we consider the phenomenon which for a century or more ha been known as the archer's paradox.

Imagine a bow to be held vertically with an arrow on the string passing the bow on the left side of the latter as the string is drawn back. Suppose further that at full draw the bow and arrow are so oriented in azimuth that the axis of the arrow lies in the vertical plane containing the mark to be hit. Now suppose the bow to be maintained rigidly in that position and the string to be let down gradually by diminishing the force. The string moves forward in the median plane of the bow. Observing the tip of the arrow, we note that as the arrow approaches the undrawn position its tip moves markedly to the left. The axis of the arrow therefore points very appreciably—perhaps 5° to 7° —to the left of where it was aimed. Now, if ail conditions are kept as they were except that the arrow is fully drawn and loosed in the regular manner, it will fly accurately to its mark. The archer's paradox is the fact that it does fly to its mark instead of on a line represented by its axis when the string has been gradually let down. This is illustrated in Fig. 10.

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Fig. 10. Illustrating the archer's paradox.