Working on a giant bow to beat Allen Case!

[willie]

I wonder if a limb could employ airplane wing technology.

To some degree there might be ways that maximizing stiffness/weight ratio might be applicable to bow builds, but in esssence, the primary goal in wing design is to build a light limb limb that does not bend too much while our goals are more about bending and energy storage.

Of course, a sponsor with deep pockets and an unemployed aircraft engineer looking for new challenges would be an interesting  team to have onboard

[Badger]

  I was just thinking in terms out adding light weight ribs to a hardwood back and belly, might be worth a simple test. Maybe something like 2/3 of the center empty 1/3 of the space occupied by ribs. Might be an easy way to preset tiller at the same time

[willie]

Always worth an experiment. I think your challenge is going to be shear forces inside the limbs
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Del might have have an observation or two, as I think he was working on a hollow crossbow limb earlier this winter.

[avcase]

The giant bow should not be able to throw an arrow any faster than a regular size bow.  Somewhere north of 200 fps with a reasonably sized arrow would be a major success.  But the trajectory of the huge arrow from the huge bow should travel much farther than the same speed arrow at normal scale.  Air resistance will be much less a factor on the big arrow trajectory. 

Alan

[Badger]

The giant bow should not be able to throw an arrow any faster than a regular size bow.  Somewhere north of 200 fps with a reasonably sized arrow would be a major success.  But the trajectory of the huge arrow from the huge bow should travel much farther than the same speed arrow at normal scale.  Air resistance will be much less a factor on the big arrow trajectory. 

Alan

   Allen, that's what I was coming up with. Even the dry fire speed calculations were disappointing. The only way to make the giant bow short that I can think of is to have an extra long draw length. I was hoping for 500 fps plus and it doesn't look like I will even come close to that.

[sleek]

The draw length will be what makes the difference. The longer the better.

[willie]

The giant bow should not be able to throw an arrow any faster than a regular size bow.  Somewhere north of 200 fps with a reasonably sized arrow would be a major success.  But the trajectory of the huge arrow from the huge bow should travel much farther than the same speed arrow at normal scale.  Air resistance will be much less a factor on the big arrow trajectory. 

Alan

   Allen, that's what I was coming up with. Even the dry fire speed calculations were disappointing. The only way to make the giant bow short that I can think of is to have an extra long draw length. I was hoping for 500 fps plus and it doesn't look like I will even come close to that.

I took a few minutes to refine the previous calculation a bit. Accounting for a spectra string that has a breaking strength at 5 times draw weight, the arrow speed drops down 4%

The initial calc also assumed a 10% energy loss for hysteresis.  I should mention that the sheet is estimating a max and min spread for kinetic energy and arrow speeds , perhaps giving a broad definition to what constitutes hysteresis? Nevertheless, I have to use a value of 60% energy loss to hysteresis, to bring a 10GPP arrow speed down to 226 FPS at the lowest estimate of it's speed, and an 80% loss for average speed. 5 GPP speeds are of course higher.

Perhaps  a reasonable vibration loss for a "normal" bow is lumped in with hysteresis to create the hi/low spread, at any rate with the exponentially high energy storage, something else is not scaling very well. I would prefer to suspect that  hysteresis is what doesn't scale, otherwise there might be some potentially limb shattering vibrations in a bow 10 time normal size.

Steve, can you refer me to your source of the formulas for the dryfire calcs? It would be interesting to see which method scales better.

[Badger]

  Willie, my estimates on speed were based on 100,000# stored energy at 60% efficient at 1/800 arrow weight of stored energy. From that I established a virtual mass not accounting for any additional hysteresis which I know I would have. I did all my figures on a scratch pad which I trashed but can easily do them again

[willie]

I did find some examples of virtual mass calcs, let me see if I can duplicate your results, just for the sake of a learning exercise.  what did you get for the fps?

125 lb arrow? if I understand you correctly?

[Badger]

  I don't remember now, I just remember I was disappointed

[avcase]

Here’s my quick & dirty estimate:

The estimate for stored energy of the giant bow is pretty straight forward. Simply take the energy stored by a 80”X2” bow, and scale it by volume.

Drawn to a conservative 28 foot draw length would be the equivalent of a 28” draw on the 80” bow. Assuming the 80” bow draws 50# at 28”, the stored energy would be conservatively around 45 ft-lb.

So for the giant bow, stored energy, SE = 45 ft-lb * 12 * 12 * 12 = 77,760 ft-lb

The same scaling applies to the arrow. A 300 grain flight arrow for the 80” bow becomes: 80 x 12 x 12 x 12 = 518,400 grains giant arrow = 74 pounds.

Virtual mass of the bow also scales by volume. If the 80” bow has 200 grains of virtual mass, the. The giant bow has VM = 200 x 12 x 12 x 12 = 345,600 grains.

Velocity for the giant bow 74 pound flight arrow: V = sqrt((2 * 77,600 ft-lb) / ((518,400 grains + 345,600 grains) / (7000 * 32.2)) = 206.2 fps

Dry fire speed = 339 fps.

But, the distance the giant bow flings the giant Flight arrow could easily be 100 yards farther than the equivalent 80# with its flight arrow, but this would be just over 400 yards at the best.

Alan

[Badger]

  We are pretty similar Allen, I had a higher virtual mass I believe and came out with lower numbers for distance. But I do believe they are within a reasonable range of reference.

[willie]

Has any one seen actual usage of virtual mass formulas that scale bow size? My research only uncovers the method being used to proportion energy between arrow and bow. Klopsteg said that a bows virtual mass remained constant, but isn't a scaled up bow a different bow?

just thinking out loud here,

if ......
a typical bow is said to have a a limb deflection of 1/3 the draw length?  let's say for instance,  10".
a  typical powerstroke is said to take 1/40 th of a sec, or 25ms
then.....
the tip speed when shooting our arrow is 10 x 40 = 400 inches/sec, or 33 FPS

If the bow is 12 times as long, and the powerstroke has to be of the same duration to produce comparable velocities, then the limb tip speed now has to be 10 x 12 x 40   or  400 FPS

is wood strong enough to survive these accelerations?
can wood actually accelerate itself that fast?  What is the hysteresis of wood trying to unbend at these velocities?
or perhaps the powerstroke does not have to be 1/40 of a sec to provide comparable velocities?

[DC]

Willie, I've found that tip movement is only about 1/3 of draw length. Confused me foe a while but I think the brace height uses a third that we don't get to use. I reserve the right to be wrong.

[willie]

Good point Don,
correction made,
thanks