Virtual Mass revisited

[willie]

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

Kinetic Energy - The energy transferred from the bow to the arrow upon release.

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. 

Potential Energy - The energy stored in the bow at any draw distance.  Potential energy is a function of draw force and draw distance.

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.

Potential Energy of the Bow  =  Bow Hysteresis + Kinetic Energy of the Bow + Kinetic Energy of the Arrow 

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?

[Yooper Bowyer]

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]

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,

  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]

Variances in virtual mass with different arrow weights will point to hysteresis.

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.

[willie]

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

like this?
s1 is a 65" 50 # stiff handled pyramid with strain that drops off steadily toward the tips.
(I can quickly re-draw it any way you like)

[sleek]

Potential Energy of the Bow  =  Bow Hysteresis + Kinetic Energy of the Bow + Kinetic Energy of the Arrow 

The bows efficiency has more losses than only hysteresis.  Its has losses through any tiller less than perfect.  Not just from set or from moisture, but from less than perfect energy transfer due to whip tiller or limbs not being timed exactly.

[sleek]

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

like this?
s1 is a 65" 50 # stiff handled pyramid with strain that drops off steadily toward the tips.
(I can quickly re-draw it any way you like)

I've tillered my bows for years with the thought of a wave being set up upon string release. The idea being the limbs act as a whip, with the energy flowing and being concentrated as it flows from the inner limbs towards the tips. I have the saying, last to bend, first to release. If all the limbs energy releases at once, like an explosion, the energy does not flow and many losses occur.  So I tiller the working limb closer to the tips to bend first as I draw it the bow, and the inner limb to bend last. The inner limb is last to bend on draw but first to release its energy upon string release. This flows like a wave all the way to the tips allowing the most energy efficient delivery of energy possible.

[willie]

sleek,

the equation is from the other site. it shows the basics, but does not include all the ways tillering can be done poorly.


Here is the same  bow with the strain increasing towards the tips. Is this what you mean? Whether any part of the limb bends first or last as it is drawn is an interesting idea, and might depend on string angles. How it returns to brace could be different, as the arrow is accelerating. maybe.. I think you would have to have a slo-mo camera to actually tell.
 

[Badger]

 Willie that is pretty close but I like to keep outer limbs stiff to further reduce working limb area.

[sleek]

sleek,

the equation is from the other site. it shows the basics, but does not include all the ways tillering can be done poorly.


Here is the same  bow with the strain increasing towards the tips. Is this what you mean? Whether any part of the limb bends first or last as it is drawn is an interesting idea, and might depend on string angles. How it returns to brace could be different, as the arrow is accelerating. maybe.. I think you would have to have a slo-mo camera to actually tell.

How it returns to brace IS and SHOULD be the entire focus and good of you to point that out. The way it returns to brace is ideally controlled by the arrow. The moment you let go of that string, the resistance of your fingers no longer is providing the force that keeps the bow in its drawn shape. Its now the arrows inertia ( at rest, it wants to stay at rest ) and the inertia of the limb ( other things too but too many to easily address ) that slow the rate at which the bow returns to brace. The rate it returns, and the orderly fashion in which it does so, has much to do with its efficiency. Too fast and the wave of energy transfers becomes sloppy, or dirty. The effect Steve mentions of Hysteresis also comes into effect here as well. Him coming up with the idea of time sensitive Hysteresis was a stroke of brilliant insight there.


Hysteresis slows the bows ability to provide power to its load, and becomes part of the load in all honesty. Id bet you could calculate it as such if you were to measure the difference in energy of two different weighted arrows. A heavier arrow is well know to carry more energy than a lighter one, because the it spends more time absorbing the bows energy,  vs a lighter arrow. The difference in energy between a heavy arrow and light one could easily be a good indicator of amount Hysteresis in the bow.
Its also noteworthy that the Hysteresis in a bow continues to show up after the arrow is shot. As the limbs relax from the shot the string tension at brace increases. Steve mentioned this same thing earlier. Id like to take a scale ( tensiometer ) rigged to read string tension and see how a bows string tension increases after its been returned to brace, and time it as well.


As for your second drawn bow you show, I dont mean the tips should bend more, or even at all. Im a believer in stiff tips. I mean that the outer working limb ( be it tips or mod limb ) should bend first. One the string angle is increased on them as the bend back, the leverage advantage on them is decreased and they stop bending. The energy of the draw is then focused to the area behind that, and it bends until the string angle relative to it is is beyond any mechanical advantage to cause it to bend further before the wood behind it starts to flex. As it bends, the string angle at the wood closet to the tips becomes even greater loosing even more mechanical advantage, ensuring that the outer wood won't bend any further. I need to get some dial indicators and clamp a bow to a table to test and prove this is how it actually works.

[willie]

Willie that is pretty close but I like to keep outer limbs stiff to further reduce working limb area.

more like this?

[Yooper Bowyer]

Kinetic energy = 1/2mass times speed squared.  This means that if you double the speed of an object, you quadruple its energy.  This means that a bow shooting twice as fast has four times the kinetic energy in its limbs. 
Because heavier arrows cause bows to shoot slower, far less kinetic energy is sunk into accelerating the limbs, which means a larger percentage is put into the arrow. 

This explains why light tips are so efficient.  Because the limb tips are the fastest moving part of the bow, they take a significantly larger share of energy per Oz to accelerate than mid and inner limb areas. 

The kinetic energy of the limbs the moment before departure is not available to the arrow.  Instead, it is converted to limb vibration and handshock.

[scp]

I'm reading the words, but not quite grasping what they are referring to.

Badger: 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.

Sleek: So I tiller the working limb closer to the tips to bend first as I draw it the bow, and the inner limb to bend last. The inner limb is last to bend on draw but first to release its energy upon string release. This flows like a wave all the way to the tips allowing the most energy efficient delivery of energy possible.

To me, they appear to be saying the opposites. Am I wrong?

[DC]

Didn't we decide that you can't get part of a limb to bend first? More or less, yes but not first or last. If you take any snape limb and move the tip 1/4" the inner part of the limb will move, maybe not much but it will move. Like the Parsons carriage.