When a projectile is thrown by hand, the speed of the projectile is determined by the kinetic energy imparted by the thrower's muscles performing work. However, the energy must be imparted over a limited distance and therefore over a limited time, so the limiting factor is not work but rather power, which determined how much energy can be added in the limited time available. Power generated by muscles, however, is limited by Force velocity relationship, and even at the optimal contraction speed for power production, total work done by the muscle will be less than half of what could be done if the muscle were contracting over the same distance at very slow speeds, resulting in less than 1/4 the projectile launch velocity possible without the limitations of the Force-velocity relationship.
When a bow is used, the muscles are able to perform work much more slowly, resulting in greater force and greater work done. This work is stored in the bow as elastic potential energy, and when the bowstring is released, this stored energy is imparted to the arrow much more quickly than can be delivered by the muscles, resulting in much higher velocity and, hence, greater distance. This same process is employed by frogs which use elastic tendons to increase jumping distance. In archery, some energy is dissipated through elastic hysteresis, reducing the overall amount released when the bow is shot. Of the energy remaining, some is dampened both by the limbs of the bow and the bowstring. Depending on the elasticity of the arrow, some of the energy is also absorbed by compressing the arrow, primarily because the release of the bowstring is rarely in line with the arrow shaft, causing it to flex out to one side.
This is because the bowstring accelerates faster than the archer's fingers can open, and consequently some sideways motion is imparted to the string, and hence arrow nock, as the power and speed of the bow pulls the string off the opening fingers. Even with a release aid mechanism some of this effect will usually be experienced, since the string always accelerates faster than the retaining part of the mechanism. This results in an in-flight oscillation of the arrow in which its center flexes out to one side and then the other repeatedly, gradually reducing as the arrow's flight proceeds; this can be clearly seen in high-speed photography of an arrow at discharge.
Modern arrows are made to a specified 'spine', or stiffness rating, to maintain matched flexing and hence accuracy of aim. This flexing can be a desirable feature, since, when the spine of the shaft is matched to the acceleration of the bow (string), the arrow bends or flexes around the bow and any arrow-rest, and consequently the arrow, and fletching, have an un-impeded flight. This feature is known as the archer's paradox. It maintains accuracy, for if part of the arrow struck a glancing blow on discharge, some inconsistency would be present, and the excellent accuracy of modern equipment would not be achieved.
The accurate flight of an arrow is dependent on its fletching. The arrow's manufacturer can arrange fletching to cause the arrow to rotate along its axis. This improves accuracy by evening pressure buildups that would otherwise cause the arrow to "plane" on the air in a random direction after shooting. Even though the arrow is made with extreme care, the slightest imperfection, or air movement, will cause some unbalanced turbulence in air flow. Consequently, rotation creates an equaling of such turbulence, which, overall, maintains the intended direction of flight i.e. accuracy. This rotation is not to be confused with the rapid gyroscopic rotation of a rifle bullet. If the fletching is not arranged to induce rotation, it will still improve accuracy by causing a restoring drag any time the arrow tilts away from its intended direction of travel.
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