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Working on a giant bow to beat Allen Case!

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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. :D

willie:
Good point Don,
correction made,
thanks

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