Why can installing feathers improve flight stability?

If you have ever shot an arrow with a broken tail feather or no tail feather at all, you will find that the arrow has rolled or swung, while the arrow with intact tail feathers will not have these two situations. Therefore, we can say that with the existence of tail feathers, the arrow can be more stable during flight. (Picture from the Internet) Similar to the principle of badminton, the feather area is large and the air resistance is large. During the flight of the arrow, the tail part is pulled behind by the force of the air because of the large force, so the arrow can fly straight.
If there is no feather, the arrow will fly vertically and rotate during flight. (Picture from the Internet) At the moment the arrow is shot, the force applied to the tail of the arrow shaft will cause the arrow shaft to deform instantly, that is, the arrow in the slow motion becomes S-shaped. If there is no tail feather, then this deformation will cause the arrow to swing left and right for a long time, and eventually deviate from the target.
In addition, the tail feather can provide rotation, and the arrow moves forward during rotation, which can correct this left and right swing. In addition, the arrow is heavier, and the arrow tends to swing the tail rather than the arrow head during rotation, so that a relatively stable flight trajectory can be completed, making it easier to aim at the target.
According to different placement methods, the tail feathers can be divided into three types: straight, offset, and spiral: Straight
Straight tail feathers The straight type means that the feathers are parallel to the arrow shaft. This type of tail feather has the fastest flight speed, the smallest air resistance, and is easy to bond, and can match various arrow rests. However, the ability to maintain a flying posture over a long distance is relatively weak, and the balance is not good when using an arrow with an arrowhead.
Offset tail feathers The offset type means that the bottom bonding point of the arrow feather is straight and parallel to the arrow shaft, but the upper part of the arrow feather is deflected at a certain angle to the arrow shaft, generally 4°.
This type of tail feather has less air resistance, can match most arrow rests, and can maintain a good flying posture at a longer distance. However, this type of arrow feather will reduce the speed of the arrow and affect the kinetic energy of the arrow. Spiral tail feathers The spiral type means that the bonding of the arrow feathers has a relatively large rotation. Both offset and spiral arrows will rotate themselves when flying in the air. Arrows equipped with spiral tail feathers can maintain stability throughout the flight process, significantly improving the accuracy of the arrow. However, it will also reduce the flight speed of the arrow, thereby reducing the kinetic energy of the arrow. Moreover, this type of arrow can only be matched with some arrow rests.