In connection with his war work, Dr. Hickman made some more test with featherless arrows. There may be some question as to the stability that an arrow should have. In his tests he only wanted to know how close the center of gravity of a featherless arrow could be placed to the middle of the arrow in order for the stability to be sufficient to damp out all oscillations by the time the arrow reached the ground when shot at a high angle of elevation.
An aluminum arrow 25 inches long was used in the tests. The pile of the arrow was tapped to take a 3-56 rod which was half as long as the arrow. A steel rod 5 inches long which weighed 15.9 grams was placed inside the tube to shift the center of gravity. When the weight was screwed as far forward as possible, the center of gravity was 6.75 inches from the nose. It could be screwed back far enough to bring the center of gravity in the middle. The weight of the aluminum tube was 12.6 grams. The weight of the pile or head was 3.7 grams. The weight of the threaded rod was 10.3 grams. The total weight of the arrow was 42.5 grams (654 grains).
The arrow was shot from bows weighing from 20 to 40 pounds. The stability did not seem to be affected by the weight of the bow. The flight was observed when shot at angles of elevation of 45 to 90 degrees. For angles less than 60 degrees the arrow followed the expected trajectory with decreasing angles of yaw and became quite steady before hitting. For the large angles of departure the arrow had to turn around as it dropped. In some cases it did not have sufficient time to do so and damp out all oscillations.
The position of the weight was shifted two inches at a time. Each step changed the center of gravity from 1/3 to ¾ of an inch. The arrow was quite stable for all positions of the weight where the center of gravity was nine or less inches from the pile tip. Where the center of gravity was nine to eleven inches from the pile tip the stability was fair. The oscillations were being damped out but had not been reduced to zero on striking. When the center of gravity was 11½ inches from the tip it was difficult to be sure whether the arrow would ever have reached a stable condition. For the 12 inch position, the arrow flew broadside throughout its flight regardless of the angle of departure and it always landed broadside.
When the center of gravity was moved further back or when the arrow was shot nock first, (both ends of the arrow were alike. The heads were nocked to take the string.) it would turn completely around and eventually become stable, although in this case the center of gravity had to be well forward otherwise there was not time enough to damp out the oscillations. With the center of gravity 7 to 8 inches from the tip, the arrow would turn through 180 degrees and stabilize on its upward flight and then on falling would again turn 180 degrees and stabilize on its downward flight. For small angles of departure, it would turn only once.
For angles of yaw equal to 90 degrees the center of pressure of the arrow was at its middle. When the center of gravity was 2½ inches or more in front of the middle of the arrow, the stability was good. In other words when the center of gravity was 10 percent of the arrow's length in front of the middle, the stability was good. It is believed that the arrow would stabilize if given sufficient time with the center of gravity 5 percent of arrow length in front of the middle of the arrow.
These tests were not made with any idea of using arrows without feathers. If stability is obtained by shifting the center of gravity forward more spine is needed. In general, however, most arrows are over stabilized. For target shooting the prize paid by over stabilization is not great. In like manner, hunting arrows are most all over stabilized and this has the advantage of reducing the range of the arrow in case of a miss. For flight arrows the stabilizing vanes should be reduced as much as possible. However, if they are made too small it will take the arrow so long to stabilize that considerable energy will be lost in air resistance.