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The Center of Gravity of an Arrow and its Flight
Part 3 of 4

About a week after the foregoing tests were made, they were repeated using straight cut feathers. The feathers were kept at a constant length of 4 inches and the height reduced from one inch in steps of 1/8 inch until a height of ¼ inch was obtained.

Mathematical investigations indicate that the air resistance of a feather is proportional to the length and to the height. If this is the case, it should not make any difference whether a short tall feather is used, or a long low one. From a practical point of view, however, it is much easier to fletch an arrow with symmetry with a long low feather than a short tall one. Then too, the tall feather does not have sufficient strength to keep its shape when subjected to high velocities. For this reason I have always thought that there were very good reasons for using the long low feather.

The tests which were made indicate that the range is not reduced by using such a feather. The steadiness of the arrow in flight seemed to be equally as good as for the balloon type feather.

If tall feathers are to be used it is quite important that the forward part of the feather be lower than the rear part. If the forward portion of the feather is tall it will not stand the air force without puckering. The puckering would do no harm if each of the three feathers puckered in exactly the same manner.

In both tests, the loss in range with increase in size of the feather was approximately proportional to the area of the feather used. If the long low feather had the same area as the short taller one, the flight of the arrow seemed equally as steady. This being the case the former is preferable for it will keep its characteristics longer than the latter.

In the second set of tests, a stop watch was used to measure the time of flight. This time was 4½ seconds for the largest feather and 5.8 seconds for the smallest feather.

TABLE 1
Location of center of gravity.

 Position Distance From Distance Ratio of Dist. from pile Rod Wt. pile From nock to length of arrow (27") 1 8.95 18.05 .322 2 9.65 17.3 5 .357 3 10.55 16.45 .390 4 11.70 15.30 .435 5 13.00 14.00 .482 6 14.12 12.88 .521 7 15.40 11.50 .571

TABLE 2
Range of Arrow as Function of Size Feather and Location of Center of Gravity.

 Position Length of feather and height and area. Rd. Wt. 4" x l" 3 ½ x 7/8 3"x ¾" 2 ¾ x 5/8 2 3/8 x ½ 2"x 3/8 0 2.77 1.96 1.55 1.14 .81 .52 0 1 107 113 117 124 126 128 133 2 106 3 104 111 116 124 126 128 4 103 5 103 109 115 124 125 127 6 103 122 123 7 100 106 107 109 103 93