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Old 11-14-2011, 10:47 AM
Nontypical Buck
Nomercy448's Avatar
Join Date: Oct 2009
Location: Kansas
Posts: 3,765
Default Mathematically...

If you consider the mathematics, heavier bows really show their advantages. The "percent change" versus "value change" becomes pretty evident.

The simple example is that if something weighs 3lbs and I increase the weight by 20%, it only means a difference of 0.6lbs. If something weighs 300lbs and I make the same 20% increase, now we're talking about 60lbs. 0.6lbs isn't much, but 60lbs is a lot, even though they're proportionately the same 20% increase.

Similarly, we can compare the numbers for bows. In my opinion, there are two critical values for a bow ENERGY and MOMENTUM, both of which hinge on arrow weight and speed. In my experience, ENERGY has a lot to do with the level of damage done, and MOMENTUM has a lot to do with penetration and ability to fight off wind, but both are coupled together.

Kinetic Energy: KE = 1/2 (Mass) * (Velocity)^2, off the cuff, we calculate ft.lbs. KE by (arrow weight in grns) * (velocity in fps) / 450380

Momentum: P = (Mass) * (Velocity), again, off the cuff, I calculate momentum in terms of lb.ft/s by (arrow weight in grns) * (velocity in fps) / 7000

By design, a bow will ONLY ever deliver approximately the same energy level, because the draw weight curve and efficiency is constant, so the bow will store the same potential energy, and deliver the same kinetic energy no matter what arrow is used, but the momentum of the arrow will change.

So, a 50lb bow that pushes a 250grn arrow at 300fps (being generous, most 50lb bows IBO well under 300). That's a KE of 49.96ft.lbs. and a momentum of 10.71 lb.ft/s. Say I want to go black bear hunting, and I want to increase my arrow weight by 20%, that means my arrow jumps up to 300grns. From that, I can back calculate that the new velocity of the 300grn arrow will drop to approx 274fps (273.8612788 fps for those of you holding a calculator). The new momentum will jump up 9.6% to 11.74 lb.ft/s.

Ultimately, a 20% increase in arrow weight meant 50grns, no change in KE, and 1.03 lb.ft/s improved momentum.

Comparing that to a 70lb bow that shoots a 350grn bow at the same 300fps (being conservative, most modern 70lb bows IBO over 300fps). That's a KE of 69.96ft.lbs. and a momentum of 15.0 lb.ft/s. Increasing my arrow weight by 20% means the new arrow will weigh 420grns and fly 274fps (same as the 50lb, because KE is held constant, 20% increase in mass means 8.7% decrease in velocity, and both started at 300fps), and carry 16.43lb.ft/s momentum (energy unchanged).

So ultimately, it gets an increase of 70grns, and 1.43 lb.ft/s improved momentum.

Both bows increased arrow weight by 20%, decreased velocity by 8.7%, and increased momentum by 9.6%, but relatively speaking, that 20% change in 50lbs isn't as important as a 20% change at 70lbs. The same "20% increment" meant 40% more difference in arrow weight (70grns vs 50grns) and 40% more difference in momentum (1.43 vs 1.03).

The moral of the story is that making changes in arrow weight to improve performance will make MORE improvement for a heavier bow, making the heavier bow more versatile. A 60-70lb bow can come down low enough to be comfortable and have enough power hunt deer, but still go up high enough to hunt anything on the planet.
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