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Analyzing the Paradox
Part 3 of 6

Now for the flight of the arrow. By tracing the string in Fig. 1 we follow the nock and the heavy dotted line in Fig. 2 shows the path of the inside of the pile as it bends around the bow. In traveling the first three or four inches the pile end bears against the bow with a sudden pressure due to the lateral impulse of the loose acting against the resistance of the center of gravity. The arrow then springs away and is carried forward in many cases free of contact with the bow for almost half its length where it is again driven back forcibly against the bow as the balancing point passes forward. When the nock occupies the extreme point in the path to the right, about 14 inches, the pile then begins a sudden swing outward as is shown by the dotted curve about 14 inches forward of the bow. This force piles up as the arrow speeds forward sending the bow hand to the right and bending the arrow as may be visualized from the diagrams. The arrow begins its recovery from this bend about the time the string jerks out of the nock, the effect of these fortes starting the arrow away on its flight shivering from end to end, which is plainly shown by the reverse curves of the patterns on the targets in Fig. 2.

This wriggling of the arrow I had detected while charting them on the range and may be seen by sighting along the arrow's path on its initial jump. The targets shown in Fig. 2 are individually sighted shots through paper targets stretched upon a wooden frame, through which the arrow cuts its path, the point entering at the lower right and the nock emerging at the upper left. The sight was taken along the right side of the arrow against the vertical line and the lower side on the horizontal line, and by means of micrometer adjustments on the machine very accurate sighting was possible. The numbers in Fig. 2 indicate the distance in inches from the bow.

In Fig. 2 the position of the arrow in flight is shown with the pile 36 inches from the bow. Notice its relation to line (b) which is an extension of its inner edge at full draw, the arrow in dotted lines gives its relation to an extension of the lower side of the arrow at full draw, and shows, its vertical deflection at this point. The tail is about the same distance above and to the left of the line, swinging rapidly outward and upward with the pile twice as far to the left as it is above the line.