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Virtual Mass revisited

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willie:
the following quotes are from   https://sites.google.com/site/technicalarchery/home


--- Quote ---Kinetic Energy - The energy transferred from the bow to the arrow upon release.
--- End quote ---
The kinetic energy (KE) of an arrow can be obtained by weighing the arrow with a scale and observing the speed with a chrono, and applying some math. 


--- Quote ---Potential Energy - The energy stored in the bow at any draw distance.  Potential energy is a function of draw force and draw distance.
--- End quote ---
The Potential Energy of a drawn bow can be obtained by counting squares under a plotted force draw curve or calculating the area.

Should you wish to know how well your bow performs, one can compare potential energy of the bow to the kinetic energy of the arrow.  Looking at the equation below, we see our differences or losses broken down and categorized into hysteresis (elasticity efficiency) and energy used move limb mass back to brace height. I should also add that the "Kinetic Energy of the Bow" also includes the string.


--- Quote ---Potential Energy of the Bow  =  Bow Hysteresis + Kinetic Energy of the Bow + Kinetic Energy of the Arrow 
--- End quote ---

On one side of the pond, imperial units are used to describe energy in foot/pounds, while on the other, energy is stated in SI units of Joules. We could also describe hysteresis and limb energy with foot pounds or joules, should we wish.

In the archery world, we like to compare our observed arrow to an imaginary arrow that has the same energy as the bow, and have invented a unit of measure called virtual mass. It is stated in arrow weight. It is the difference in arrow weight, at the same velocity as our actual arrow, that when added to the observed arrow weight, gives the bow and the arrow the same energy. It represents the losses in the bow/string, and is considered to be a unit of measure for bows.

Can this invented unit of measure accurately describe bow/string energy losses?
Can this invented unit of measure accurately describe hysteresis losses?
Can it tell the difference between the two?

Digital Caveman:
Good definitions and equations, but how is this new unit better than the standard efficiency measure (energy out/energy in) or the standard performance measure (FPS per Pound) accounting for GPP?
Regards,

Badger:

--- Quote from: tradcraftsman on September 26, 2020, 12:19:59 pm ---Good definitions and equations, but how is this new unit better than the standard efficiency measure (energy out/energy in) or the standard performance measure (FPS per Pound) accounting for GPP?
Regards,

--- End quote ---

  It can not accurately isolate the amount of Hysteresis in a bow but it can be a very good indicator of how much a bow has. Bow and string losses will remain constant while hysterics losses are time sensitive to how fast a sting returns. Variances in virtual mass with different arrow weights will point to hysteresis.

willie:

--- Quote ---Variances in virtual mass with different arrow weights will point to hysteresis.
--- End quote ---

That seems reasonable with wood bows Steve. Was it Klopsteg who invented the idea? I have read where VM was assumed to stay the same within a range of arrow weights. Perhaps the assumption was reasonable in the fiberglass world? and differences were presumed to come from more/less efficient limb designs?

Badger:
  Willie, one thing interesting about energy losses has to do with limb vibration. To a lesser degree than hysteresis it is also somewhat time sensitive meaning that the faster the bow limbs return the more vibration or limb distortion we get. I have kind of a theory about this. We know the more working limb a bow has the more opportunity for vibration exists. So we need to work toward figuring out the lowest amount of working limb we can get by with before it starts taking set. I have always suspected that a tiller where the limb bent progressively from outer to inner could also help to control this vibration by simply returning to brace over a more extended period.

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