Virtual Mass revisited

[Badger]

Virtual mass has very little relation to actual mass

I think kevin has a good point, Steve. My guess is that you are pointing out that arrow mass, or the virtual arrow mass,  is not directly comparable to bow mass, as in grains and ounces.

Not at all, virtual mass is a measure of the amount of energy not going into the arrow. It doesn't have much to do with arrow mass or bow mass although bow mass can effect it obviously.

[DC]

I gathered some arrows 300,400,500,550 and 560 grains and shot them through the chrono. Then I graphed the results and got a pretty much straight line except for a little jog with the 550 that I can't explain yet. Then I made a heavy Ocean Spray arrow that is 650 grains. I marked on the graph where I thought it would end up and it was right on. Speeds went from 175 to 240 fps. Does this straight line tell me anything?

[Digital Caveman]

That's very interesting, I'd love to see the data.  I wish I had a chrono and could do these experiments myself.

Depending on the measurement precision, gentle curves could look flat if their not spread out over a wide enough range of data.  What if you shot a 900 or 1000 grain arrow?  What about a flight arrow? 

The math is looking more and more complex, I fear integrals in the near future... 

[sleek]

I gathered some arrows 300,400,500,550 and 560 grains and shot them through the chrono. Then I graphed the results and got a pretty much straight line except for a little jog with the 550 that I can't explain yet. Then I made a heavy Ocean Spray arrow that is 650 grains. I marked on the graph where I thought it would end up and it was right on. Speeds went from 175 to 240 fps. Does this straight line tell me anything?

From knowing the 300 grains shot the 240 fps I calculated  38.36 foot pounds of energy in the arrow.  With the 650 grain arrow doing 175 fps it has 44.19 foot pounds of energy.  It illustrates that heavier arrows take more energy away from the bow. That supports whats being said about Hysteresis being time sensitive. The longer the arrow is on the string, the more energy it sucks from it, and the internal frislction of the bow ( Hysteresis  ) is reduced.

If you are familiar with non newtonian fluids, you know that they solidify as energy increases through them, providing more resistance to an object trying to move through them. So the slower the object moves through it the easier it can move. Compare that to a bows limbs. They behave in a non newtonian way. The faster they move, the more they dont want to due to internal friction. Im certain inertia of mass has a bit to do with this as well.

If you post the arrow weights and corresponding speed, I can calculate the energy of each arrow, and when you plot that, you may notice the energy is not a linear increase. Id posit that the energy increases tangental to the arrow weight increase.

[sleek]

Virtual mass has very little relation to actual mass

I think kevin has a good point, Steve. My guess is that you are pointing out that arrow mass, or the virtual arrow mass,  is not directly comparable to bow mass, as in grains and ounces.

I was incorrect in my answer and quite honestly,, distracted when I made my reply. Im sorry about that and have edited my reply to note the fact.

[Badger]

I gathered some arrows 300,400,500,550 and 560 grains and shot them through the chrono. Then I graphed the results and got a pretty much straight line except for a little jog with the 550 that I can't explain yet. Then I made a heavy Ocean Spray arrow that is 650 grains. I marked on the graph where I thought it would end up and it was right on. Speeds went from 175 to 240 fps. Does this straight line tell me anything?

 if your graph was based on Virtual mass the predictability would mean little hysteresis. What was your graph based on? You got 240 from a 300 grain arrow? Excellent! I think a clean shot from a 300 grain arrow going 240 fps would get you over 400 yards.
 

[DC]

My graph was just weight vs speed.

[Badger]

  Using virtual mass I came up with these. 400 grains 215 fps    500 grains 195 fps     550 grains 188 fps.    How close is this to what you have. I had to estimate your stored energy.

[DC]

 400 was 215, 500 grains was 200, 550 was 198. I did a 560 and it was 191. I'm thinking that if there was a lot of hysteresis the line would have been curved?? I'm not sure which way. The arrow weight weren't exactly even numbers but they were within a grain or two. I think the 300 was actually 305. It's bed time

[bownarra]

By the way guys - what exactly is it you are trying to work out?

I WAS WRONG IN THE STATEMENT BELOW, BUT AM LEAVING IT BECAUSE IT WAS REFERENCED IN OTHER REPLIES. sorry for yelling

Exactly how much wood is required to make a bow. Or more specifically, how little we can get away with.

I think you need to set out a theory first then try to prove it or not
At the end of the day wood has hysteresis.....you can't change that. Now what do you intend to do about it and what can you do differently that will help 'offset' these losses?

[Tuomo]

DC - what was the bow and its parameters? Draw weight and length (from back or belly, if back, how thick handle), brace height (belly or back)? I think that hysteresis is very low, but need those parameters for calculations.

[sleek]

By the way guys - what exactly is it you are trying to work out?

I WAS WRONG IN THE STATEMENT BELOW, BUT AM LEAVING IT BECAUSE IT WAS REFERENCED IN OTHER REPLIES. sorry for yelling

Exactly how much wood is required to make a bow. Or more specifically, how little we can get away with.

I think you need to set out a theory first then try to prove it or not
At the end of the day wood has hysteresis.....you can't change that. Now what do you intend to do about it and what can you do differently that will help 'offset' these losses?

I think you may have missed where I stated I posted that while distracted. I thought this question I was answering was referencing actual mass, on another thread.  I really made myself look foolish there.

As for what to do about Hysteresis,  I feel with out the ability to provide a concrete argument, that it can be dealt with via efficient energy transfer..The way nature does it is via wave transmission. Im pretty set on my wave theory and seeing as how it works in so many other applications, I feel a limb tillered to release its energy via a sine wave, flowing from handle towards tips, will minimize hysteresis loses best.

I do reserve the right to be wrong...

[Badger]

By the way guys - what exactly is it you are trying to work out?

I WAS WRONG IN THE STATEMENT BELOW, BUT AM LEAVING IT BECAUSE IT WAS REFERENCED IN OTHER REPLIES. sorry for yelling

Exactly how much wood is required to make a bow. Or more specifically, how little we can get away with.

I think you need to set out a theory first then try to prove it or not
At the end of the day wood has hysteresis.....you can't change that. Now what do you intend to do about it and what can you do differently that will help 'offset' these losses?

 Bownarrow, I did some extensive testing several years ago on hysteresis. What prompted the tests was seeing how much more efficient shorter draw bows were. Wood has almost no hysteresis until fibers start to get crushed ( set) the virtual mass testing was used to isolate hysteresis from vibration losses. As it turns out it is one of the biggest controllable losses. 

[DC]

DC - what was the bow and its parameters? Draw weight and length (from back or belly, if back, how thick handle), brace height (belly or back)? I think that hysteresis is very low, but need those parameters for calculations.

50#@28" from the back, handle 1 1/2" thick, BH 6" back.
A little more accurate arrow weights and speed
306-240 and 236
405-215
501-200
548-198
556-191
653-175

[Badger]

  It looks like your 650 grain arrow was a little slower than it should have been and your 548 grain arrow was too fast.