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FOC, center of pressure and performance

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avcase:
A model rocket is a lot like an arrow in a lot of ways. The same physics are at work. A rocket requires a little more stabilization, but it will fly stable as long as the center of gravity is forward of the center of pressure.  There are a number of model rocket builders that have altitude competitions that resemble our flight archery competitions. The model rocket builders are also looking for that perfect balance of center of gravity to center of pressure. They need enough stability to keep the rocket on a straight upward path. An over-stable, point heavy rocket does not do as well because it tends to weathervane into every fluctuation of the wind currents that it passes through.

I do pay attention to the angle the arrows strike the ground. Every arrow seems to have a hard limit in how far it can be thrown. There comes a point where faster launch speeds from the bow makes little difference in how far the arrow can be thrown. If you start to notice the arrow starts landing at a very steep angle, like 75 or more degrees from horizontal, then this is a sign that the only way to progress is to work to improve the arrows.  I experienced this first hand a couple of years ago at one of our Salt Flats events. I launched about 20 arrows from different bows over a wide range of launch speeds, launch angles, and wind conditions, and every arrow landed within +/-15 yards distance of each other!  The arrows launched at high speeds went a little bit further, but landed almost vertically. The arrows launched at slower speeds landed at a little shallower angle, but still went nearly as far.  It was as if there was an invisible wall that these arrows were not allowed to cross. 

This led to a long process of trying to figure out how to break past this barrier. I was able to rule out atmospheric conditions by running into this same distance limit at completely different shoot locations and atmospheric conditions. I started playing around with arrow geometry and test shot my arrows alongside arrows made by past flight archers (arrows made by Harry Drake, Ike Hancock, and George Alavekiu). I found each of these groups of arrows had their own limits. Some were better than others. I considered an arrow topped out if it landed at an angle greater than 75 degrees. Faster launch speeds were a waste of time beyond this.

I even went as far as creating computer models of these flight arrows, and I used a fairly sophisticated model rocket program to shoot these virtual flight arrows at various launch velocities and angles. Funny thing is that these simulations showed the exact same symptoms that indicate the point of reaching the performance limits of a flight arrow.

The hard part is to figure out what to do to get the most out of an arrow. All I can say for certain is that there isn't a simple formula to make a great flight arrow. There are several factors that all interact with each other. I played around with several experiments to try to find some breakthrough. I tried an experiment shooting numerous arrows from a shooting machine that were identical weight, and identical nock and fletching geometry, but with different shaft geometry. Some were barreled with more thickness toward the rear, others barreled with more thickness to the front, others barreled with greatest thickness to the center.  About the only consistent result from this indicated that the barelled arrows with more thickness at the rear performed worse than the rest. Also, arrows with more radical barrel tapering performed worse than arrows that had less radical barrel tapering. But it is kind of hard to isolate if this performance difference is due to the geometry differences, or due to shifts in the center of gravity due to the shape differences.

There's much more to this, but this post is long enough already. I will say that I did manage to break through the performance limit that I ran into a couple of years ago, but I am also sure there is still much to learn. For example, I cannot figure out how Harry Drake shot as far as he did using the equipment he had. I've ruled out the bows. They were very good, but not magic. It had something to do with his arrows and how they were shot. Pictures indicate Drake's record footbow arrows landed at pretty exceptionally shallow angles at distances exceeding 1-mile, but I don't understand how this was achieved. Drake's arrows were barreled with more of the thickness toward the front, and this pushes the center of pressure toward the front of the arrow. Drake's footbow arrows did not have metal points, but had a metal nock and steel razor blade vanes, which pushes the center of gravity rearward.  My farthest flying arrows have similar properties, so maybe there is something to this. 

Alan

Badger:
  Very interesting post Allen, I enjoyed every bit of it. I also appreciate greatly the work you have done over the last decade and more. And congratulations on breaking the 1 mile barrier, that is a great achievement.

  Arrow knowledge is the key to great flight shooting. My experience matches yours to a tee, it doesn't seem to matter what launch speed some arrows take off, they seem to have an upper limit. The best comprehensive approach to arrow design I could come up with was to rent an apt. near the flats and spend about a year their making and shooting arrows. The few arrows we launch each year for distance are not enough to tell us much if anything. At this time I am favoring slight tapers from front to back, no opinion on spine I really need to work on that, I have had some good flyers from arrows I thought were weak but I have also had some good flyers from arrows I thought too stiff.
I could pull my hair out just thinking about arrows!

Del the cat:
Great thread from everyone, great post Alan
Del :)
(Mrs Cat has vetoed the wind tunnel in the living room  ;) )

JNystrom:
That's good idea to check the arrow angle at ground level! If the arrow angle changes quickly, shouldn't this be because of,
a) too much drag
b) too much FOC
?
In extreme, badminton ball leaves fast from the racket, but drops fast like hitting the imaginary wall. Because of drag and low mass.

Shouldn't one always use vellum vanes only if he want's to shoot far? They surely are thinner and have less drag. I don't have any yet, so i would be interested in trying paper vanes saturated with superglue, which should act similary.

Yep, it's excellent we have a discussion about flight arrows! Its always bows, bows.

BowEd:
Great post fellas.As just an interested observer of the knowledge commented here way more then my experience for this competition but making my own arrows.The greater front of center degree I thought was mostly for better penetration reasons hunting without any concern for distance.With not as much concern for the extra stiffness needed on the shaft flight shooting too.
My related thoughts when making arrows with more front of center degree were of a javeline being thrown for farther flight though.A javeline is very front heavy.
Arrow making for this competition is far more involved then just making hunting arrows.

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