In my previous post, I described how I have been challenged by unnamed parties to score 250 points with 36 arrows at 50 meters on a FITA 80 cm target face with a bare bow, and I have been trying to frame the scope of this problem mathematically.
I already know that I can hit the target with all six arrows in an end, but beyond this, it seems pretty random. I need to state that I have not tested the data for randomness, and do not have enough data to do so. But at a cursory glance, it looks sufficiently random.
So I calculated what my score would be if this were true: a random distribution of six arrows entirely within the area of the target face. Turns out that this would yield an average 6-arrow score of 23.1. So far, my scores have reinforced my suspicion of randomness.
In order to get a score of 250, I would have to get an average 6-arrow score of 41 2/3. How much do I have to improve? It turns out that if I could keep all my arrows within a random distribution boarded by the outer edge of the six-point ring, then this would yield an average 6-arrow score of 43.2.
At 50 meters, an 80 cm target face has an angular diameter of about 0.016 radians, or about 1.1 degrees. The area of the circle described by the 6-point ring is half that, 0.55 degrees, or about the apparent diameter of the full moon. And the area of this circle is only 1/4 of that of 80 cm circle.
If we describe my archery skills by the area of the spread of arrows on the target face, then I have to increase my skills by 4 times in order to achieve this goal.
I’d better put down the pencil an paper and get to work! I am going to cut off the outer five rings of an 80 cm target, and use that for practice.