Ok, I have conducted 2 amateur experiments. I remain unbiased and did my best to control what variables I could.
First, I went to an indoor archery range. It was very busy on Saturday morning, and I was not able to take my time and set things up the way I wanted. Still, I did what I could. I was shooting a 45# recurve bow using aluminum arrow shafts with field tips. The target was a big foam block that seemed to me might have a somewhat uniform density. I shot 2 arrows at 4 yards, 2 at 8 yards, and 2 at 20 yards. The arrows I shot were NOT uniform in terms of spine stiffness. I also was not able to take my time an measure how far each one penetrated. It was obvious the 4 yard arrows did have the most energy. I've never shot a target that close. It made a loud THWAP when hitting the target. The 8 yard arrows were not as loud but they "seemed" to go in to the target just a bit more. The 20 yard arrow obviously did not penetrate as deeply. I was interested in the 4-8 yard difference so I decided to do a more controlled experiment at home.
I made a target from a 9x12 box and PACKED it with papers so it was uniform density. It was like a paper brick lol. Kind of like a really thick phone book. I got 3 arrows that were identical in stiffness and weight. I shot 3 arrows at 1 yard and 3 at 8 yards. The 1-yard arrows all penetrated exactly 13/16ths of an inch. Of the 8-yard arrows, two arrows penetrated exactly 1 inch, and one was 1+1/16th inch.
The differences were small, but in this 2nd test they were consistent. The arrows penetrated more at 8 yards than at 1 yard. I also think I know why. Something I observed at the very close shots (1 & 4 yards) was that the arrow stuck out of the targets at and angle once they were shot. I attribute this to the previously discussed "wobble". I've modified my mspaint pic to illustrate this. While in both cases all the energy of the arrow is transferred to the target, I think the energy is transferred at slightly different angles. This may so explain Why the very close shots produced more noise. The part in the box shows what I mean.
Pic
In conclusion, I think there is a point somewhere along the arrow's flight where it can transfer maximum energy to the target in a "stabalized" state which allows it to penetrate the best. I don't think this point is "point blank" but somewhere between 4 and 15 yards, depending on the bow and arrows used.
tidbit: did you know the term "point blank" (pointe blanc) come to us from ye olde time archery lingo?
Some other thoughts:
1. A medieval war bow could have a draw weight from 80-120 lbs...way more than my 45# bow. This may mke a difference. Then again it may make these results more pronounced. The field tips I used are designed to just penetrate a target and then slow down so they don't go too far in.
2. I don't hunt, but I've heard bow hunters say that an arrow shot from a 50# or 60# bow, with a broadhead attached, routinely go STRAIGHT THROUGH deer and other large game animals if it doesn't hit a large bone like a shoulder blade. In this light I think only armored targets would benefit from being further away/closer to an archer in terms of negating damage (in game or irl).
3. Lastly I encourage people to try this out or suggest other ways to test. My experiment was really small, but at least it gives something to think about!
edit:
pics for proof.
