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ARCHERY: COMPUTER MODEL of BOW, ARROW and HUMAN BEHAVIOR (forma parte de Arqueria)
Humanism, Sport, Mechanics, Arrow Flight.
ABSTRACT: From the past to the modern times, a human attitude, a type of Man has pervaded History: critical, polished, cultivated, competent in Letters, Techniques and Arts, the Humanist. His tool is now the computer, a computer capable of offering degrees of subtlety compatible with his. It must be his prolongation, his arm, as such it should incorporate many of his qualities and features. In this paper the author shows some of his software applications which illustrate, he believes, this humanistic flavor. They are related with Nature, Sports, Perception, Art, Poetry, Music and Beauty.
A simulation of archery has been developed, where many features and parameters, including the human, cooperate to show the behavior of a whole session of shooting. The main factors are the bow, the arrow, the air, the target and the archer, each one with its own parameter set.
The bow is defined by its weight (drawing force when extended), fistmele (distance of arch center to the string), the string weight and the bow spatial position, defined by its horizontal and vertical angles. The opening scope of the bow will be governed by the arrow length. The sight situation is also a parameter of the shooting ( the sight is a little circle on a perch attached on the bow side, that protrudes from it and on which the sight can be displaced in horizontal and vertical directions.
The final direction of the shot depends on the relative eye and bow sight positions, which will fix both hands position, left on the bow center and right drawing the string back, with the feathered arrow extreme between the fingers. All this determines two angles with the horizontal and vertical references.
The arrow is defined by its length, its weight and a friction factor depending on the transversal area that counters the air when flying.
The air medium is characterized by its friction factor and the dependence of this factor on the arrow velocity - a 2nd. degree polynomial expression.
The target is the usual one, composed by several concentric circles, on a plane surface, whether vertical or slightly tilted. It is defined by its size (diameter), position and situation (distance, height) with respect to the archer.
The archer is simulated by some movement of the arrow direction, defined by two random horizontal and vertical variables with a Gaussian distribution law. These direction increments are multiplied in their effect by the distance to the target, producing a volley of impacts around the reference point, which can be centered or not on the target center (the yellow, from the inner circle color).
The flight of the arrow is simulated point by point, calculating changing arrow direction, velocity and position in it, by an integration of the corresponding differential equations. These equations are different for rising and falling directions due to the coincidence or opposition between the gravity and acceleration directions in both situations. The equations equally change depending on the exponent of velocity in the friction force expression.
So the trajectory of the arrow is represented in real time, after evaluating the computer speed on which the program is run. For each point of this path, arrow height, distance to archer, direction, velocity and acceleration can be recovered and printed. The trajectory, drawn in this way, varies between the theoretic parabolic one – when there is no friction – and the popular empiric one, which believes arrows to fall vertically at the end of a high fly.
The impacts on the target ( if any !) are represented as well. Scores are computed shot by shot, according to the weight attributed to each circular frame/color (five colors, ten circles valued from 1 to 10). If no target is used, or if situated out of the arrow paths, there is no score and the reach of the system bow-arrow is obtained.
The session or round is characterized by a determined number of arrows at a determined number of target distances. The outdoors international are those adopted by the FITA: 144 total shots, 32 arrows for each of four distances (men: 30, 50, 70 and 90 meters; women: 30, 50, 60 and 70); the first two distances using a target external diameter of 80 cm and the other two, one of 122 cm. Indoors the distances and diameters are: 18 (diameter: 40 cm). and 25 meters (60 cm), 30 arrows per distance. In USA some other rounds are also used.
After the whole set is shot there is the possibility of correcting the reference direction of the bow, using the information that the impact cloud suggests to the (simulated) archer. Eventually, the program itself is able of this correction, in horizontal and vertical orientations, improving the performance as much as its random (human or mechanical) movements allow. The program show thus how to center the bow during an actual shooting, from the not always obvious information that the cloud provides.
Computing by the human for the human can no longer be an activity separated from human flowing life. Technology and Humanities must grow together from now on: technology cannot develop without taking into account the human requirements and needs; Humanities cannot either grow without extensively using technological tools, as it has been always done. Now computers allow humanistic activities to use huge resources to help the finer human qualities express, learn and teach. We hope this paper has shown a small part of them.
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