FOC, center of pressure and performance

[avcase]

Alan, are you still describing your bamboo hex shaft arrows, where the outer skin on the bamboo is presumably denser than the interior?

It seems like this should be worse for a shot that leaves the bow misaligned, because the arrow has high inertia for the fletching to overcome.

The inertial force causing yaw?

I have been giving some thought to similar mass distributions, ie, heavier footings, both front and rear, or both, on some designs I hope to make soon.

Willie,
Yes, I was referring to the split cane bamboo arrows. I leave the thickness of the wall thinner in the middle and thicker at the ends. It is a similar effect as footing a wood shaft at each end.

Alan

[willie]

"It is a similar effect as footing a wood shaft at each end"
 
"However, this higher inertia should be better if we are talking about a “floater”".

Alan, Do you have a hypothesis for why such a mass distribution might act this way? Maybe the "high inertia to overcome" works both ways? Once the arrow gets going straight the end weighted arrows are harder to disrupt from straight flight?
Just a guess on my part.

[avcase]

"It is a similar effect as footing a wood shaft at each end"
 
"However, this higher inertia should be better if we are talking about a “floater”".

Alan, Do you have a hypothesis for why such a mass distribution might act this way? Maybe the "high inertia to overcome" works both ways? Once the arrow gets going straight the end weighted arrows are harder to disrupt from straight flight?
Just a guess on my part.

There is a disadvantage in the initial flight of a higher inertia arrow since it takes more fletching action to get a misaligned arrow on course. But, once on course, it should want to stay there.

The trajectory of the arrow is also constantly changing the direction the arrow travels. This requires the arrow to be redirected, particularly as the arrow approaches the descent portion of the trajectory.  At the top of the trajectory, the arrow speed has slowed, and the center of pressure starts creeping forward closer to the center of gravity of the arrow, reducing stability.


If the arrow has zero spin, this increasing misalignment with the arrow to the trajectory will create a reactive force in the fletching, forcing the arrow to start pitching down.  It will usually overreact, requiring the fletching to react the opposite way, and the arrow pictches nose up again.  This pitching up and down continues until the arrow has regained speed on the way down. This is not a good thing, and probably a major reason why distances sometimes suffer with arrows that have a CG behind center.

But, what happens if the same arrow is shot again at the same angle and speed, except the fletching is changed to induce a mild amount of spin?

It takes awhile for the arrow to spin up, during which time hopefully most of the launch misalignment issues are sorted out. But as the spinning arrow arcs across the top of its trajectory, the rotation of the arrow should be just enough that it doesn’t start pitching up and down. Instead, it reacts more slowly to the changing trajectory path. In other words it is descending a bit nose up, causing drag. This drag slows the descent, keeping it in the air longer and giving it more time to travel a little farther before it picks up enough speed that the fletching becomes more effective again and forces the arrow back into closer alignment with the trajectory.

I don’t know if that makes any sense.

Too much spin combined with not enough aerodynamic stability will create too much drag and can lead to excessive angles of attack on the descent. This can cause the fletching to stall and loseeffectiveness, and the arrow will turn 90 degrees and fall to the ground. This is not good either.

Alan

[willie]

So having the mass distributed towards the ends of the arrow seems to attenuate pitching (as does the spin), or helps the arrow to keep it's nose slightly up with less spin?  Quite a lot to consider when one wants the arrow to "float" at the top of its trajectory, seems like lots of tradeoffs when the COG is so close to the CP (center of pressure).

On a different note, I was reading about FOC experiments done by Clarence Hickman. I cannot find the full text of his paper, just this synopsis from Barry Groves. 

With all fletch sizes, distance fell slightly as the CofG moved backwards. With the CofG behind the center of the arrow, the distances achieved fell markedly. The greatest distance he achieved was with the CofG at 32% and the arrow unfletched.

(CofG is percentage of total arrow length that COG locates behind the point, not FOC).
Can you comment if this has proven out in any of the flight records? Or are any shooters competitive with arrows designed around the high FOC/minimal fletching concepts.?

Thanks for taking the time to share, Alan. Almost every thing I have read about arrow exterior ballistics admits  "not much has been researched" about arrow flight.

[avcase]

It’s funny that I just Hickman’s report on his FOC experiment last night. Hickman created an arrow with an internal weight that he could adjust to shift the center of gravity of the arrow without affecting its shape. The arrow was initially fletched with large straight-fletched feathers that he could trim down to see if the fletch size affected anything. The bow was set in a shooting machine with a mechanical release and set at 45 degrees. Hickman used a pretty light bow and the arrow was pretty heavy in order to keep the distances within reason (less than 140 yards for the farthest shots). The procedure was as follows:

With the full size feathers, shoot several times with the weight forward to give a high forward balance, then neutral balance in the center, than rearward balance. The distances were recorded for each shot.

Then he would then trim the feathers down and repeat the shot sequence and measure the distances. He continued this to the point where he was shooting a bare shaft with no fletching at all.

Hickman’s results showed that there was little difference in distance for different FOC with the large fletched arrows. But as the fletching was reduced, the shots with the forward center of balance out distances the arrow with rearward center of balance.  At yet smaller fletch size, the arrow with rearward balance was completely unstable, and the forward balance configuration outdistanced the center balance configuration. Finally, with no fletching, only the forward balance configuration flew stable.

It was also no surprise that the distance of the farthest flying arrow increased as fletching size was reduced. The farthest shots of the test were with the unfletched arrow with a forward center of balance. He concluded that the floating arrow theory was busted and that a rearward CG was not beneficial to long distance arrow Flight.

But there was one important detail missing in his experiment. Did you happen to notice what that was?

Alan

[Badger]

   My first thought would be how various speeds affected the arrows but that was not part of this test. Good question? Fun trying to figure out what he forgot.

[Badger]

 He didn't use medium settings of balance, only the extremes and center.

[Selfbowman]

Going out on a limb here. The arrow was not barrel tapered.  Arvin

[willie]

Going out on a limb here. The arrow was not barrel tapered.  Arvin

what arvin mentioned, and not sure how hickman accounted for changes in dynamic spine in his continuously modified test arrow

[avcase]

Okay, here is where I think Hickman may have missed something. I didn’t see where he included the effect of arrow spin. A straight fletched arrow with little to no spin should do just what he reported.  It should get a little erratic as the fletch size is reduced and weight moved rearward.

I am actually not yet completely sure that moving the center of balance rearward and inducing a moderate spin is a good strategy for longer arrow Flight, but I do think I too is worth investigating further. I have seen some evidence of this with my foot bow arrows. The nose-heavy arrows flew predictably, and buried themselves deep in the ground. The arrows with their center of gravity further rearward landed more erratically, and often didn’t go any farther. But when I induced a small amount of spin (by altering the shape of the vanes), I had a few very long flying arrows.  Unfortunately, I haven’t been able to test this out in a very controlled way yet.

Alan

[willie]

In addition to the gyroscopic benefits of spin, perhaps there is also a beneficial reduction of turbulence? or thickness of the boundary layer?

http://sci-hub.bz/10.1063/1.2885330

[Selfbowman]

Ok I won't ask for the math anymore. Ifen I was to understand it though I could shoot farther arrows than you guys. .  Arvin

[willie]

Ok I won't ask for the math anymore.

LOL......... Arvin, Its not like I try to follow the calculus either, I am too old to remember how.
 
I find the basic principles described to be of interest, but will leave it up to experimentation to see if the extra friction from a faster spin is a net gain or loss when glueing and trimming feathers on an arrow.

[TSA]

i came across this info- and thought i would just drop it here
http://www.turkishculture.org/lifestyles/turkish-culture-portal/turkish-flight-arrows-554.htm