BACKGROUND INFO: The law of Conservation of Energy states that energy cannot be created or destroyed; it can only be changed from one form to another. The total amount of energy in a system remains constant. A compound bow is a machine that is specifically designed for the purpose of changing one kind of energy into another. But your bow can't make energy, it can only change it. As you draw back your bow, the bow transfers the biomechanical energy supplied by your muscles into the bow's limbs (as potential energy). Then when you fire the bow, the bow transfers that stored energy into the motion of the arrow (kinetic energy). Easy enough!
Unfortunately, the process of transferring all this energy into the arrow isn't 100% efficient. Some of the energy gets changed into forms of energy we don't necessarily want, like heat from friction, or unwanted motion (recoil, vibration, noise, etc.). So even though you may supply an exhausting 80 ft-lbs of muscle-energy drawing your bow back, you might only get 60 ft-lbs of that energy successfully transferred into the forward motion of your arrow. The remaining 20 ft-lbs gets essentially wasted (though it's not destroyed).
The more wasted energy, the LESS efficient the bow is at launching arrows and the MORE efficient the bow is at producing noise, recoil, and heat. So efficient bows tend to be fast, quiet, and smooth upon release; inefficient bows tend to be slow, noisy, and can have heavy recoil upon release. So it's up to bow designers to find ways to limit the energy lost to friction and unwanted motion.
The winner of this round is the bow that's most energy-efficient. That is, the bow that makes the MOST out of the energy YOU supply. Once we have all our data, we'll use this simple formula for find each bow's total efficiency.
order to compute our bow efficiencys, we'll need to know how much energy
it takes to draw each bow back and how much energy each bow actually
transfers into the arrow. So let's begin with ENERGY-IN.
Both of our bows are set for 30" draw length and 70# peak weight.
However, since our bow's powerstrokes are considerably shorter than
their draw lengths, and the draw weight of the bows don't remain
constant at 70# throughout the draw cycle (they only PEAK at 70#),
finding our energy input isn't as simple as we might expect.
So essentially we'll need to find the area UNDER the curves to know how
much energy each bow requires during it's powerstroke.
Fortunately, we'll not need any Calculus today. We can get a very
good estimate by breaking the big problem into many small easy problems,
computing ft-lbs at every 1/4" measurement (LBS/48). Then at the
end, we can just add them up. The graphs below, converted into
simple bar graph format, represent our total energy in.
If you would like to
see our data and computations, please
download our spreadsheet (MS Works 4.5A *.wks format).
So in the closing seconds of our 6th round, we just need to compute overall efficiency to finish-up.
ROUND RESULTS: Bowtech earns another victory in round 6. At nearly 80% efficient, the Liberty puts more of it's stored energy into the arrow and requires less effort on the part of the shooter. Although the Diablo did have about 8% more knock-down power, it required approximately 13% more energy to complete the draw cycle. The Liberty wins the efficiency round 10/9.
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