Energy storage and light arrows

[DC]

I've been reading and I keep seeing things that say that the lighter the arrow is the less energy from the bow is transferred to it. Can someone explain why in simple English?

[Pat B]

I guess more energy is stored with heavier mass than with light mass. It takes more energy to push a heavy arrow than a lighter arrow.

[sleek]

A bows limbs have a maximum speed they can snap back to. Any weight on the string ( an arrow ) slows them down. The heavier the arrow, the slower the limbs return. If you put a 1 grain hypothetical arrow on the string and shoot it, the bow will accelerate the one grain arrow until the limbs have reached their maximum speed. With an arrow so light, the max speed will be reached before the end of the power stoke of the bow. For this hypothetical arrow, lets say that its full speed after the first 6 inches of release. All the energy after that is not being used and will be re absorbed by the bow and let off as vibration. With enough energy the bows vibrations can cause it to break. 

With a heavier arrow, say 100 grains, it may take half the power stroke to reach max speed. With a 500 grain arrow, idealy with a 50 pound bow ( 10 grains arrow weight per pound of draw weight AT 28 INCHES ( many forget or dont realise that part ) the arrow will reach maximum speed at the last inch of poeer stroke, right when the string snaps tight at brace height.

Because the formula for energy envolves mass and speed, and speed, the heavier arrow has the most energy because it reached maximum speed with the most weight. It took all the bows energy stored up during the draw and turned it to kenetic energy rather than leaving  any of it behind in the bow.

[DC]

Thanks Sleek, I think that's what I was looking for. It makes sense.

[TSA]

very well explained.
tell me what you think for draw lengths over 28", what should a person be looking at for GPP- or do you still work on 10gpp- divisible by 28' multiplied by your draw length- whether it is over or under 28".
thanks Sleek!

[Badger]

     There are actually a few different reasons at play why heavy arrows are more efficient. With wooden bows they have a double wammy because they also have hysteresis which is time sensitive. So the faster the limbs are moving the more hysteresis they have. Another big reason is that heavy arrows have more leverage against the momentum of the moving bow limbs especially in the final few inches of the power stroke. Bow limbs do not reach a dry fire speed until they are actually dry fired, any amount of weight will slow the limbs. We often use a number called virtual mass when attempting to extrapolate speed potential. It really only works with bows that don't have hysteresis. But suppose a bow didn't have hysteresis. If a bows virtual mass is 200 grains it will stay 200 grains regardless of arrow weight. This means that a 500 grain arrow will shoot the same speed as a 700 grain arrow if the bow were 100% efficient. The same bow would shoot a 200 grain arrow the same speed as a 400 grain arrow if it were 100% efficient. As you can see 200 grains is 1/2 of 400 grains so it will drop down to 50% efficiency. The same 200 grains is less that 1/3 of 700 grains so the bow will be 74% efficient.

[willie]

 you start shooting a heavy arrow over a chrono,
then as you successively lighten it, it leaves the bow faster and faster up to the point the limbs can go no faster

isn't that more to do with the bow than the anything else? how does the 28" arithmetic work?

I think I am beginning to understand virtual mass... a little bit anyway  ... thanks steve

[Badger]

  Willie, there is no point the limbs will stop going faster, all the way until there is no arrow. They will never reach a dry fire speed before they are actually dry firing

[willie]

With an arrow so light, the max speed will be reached before the end of the power stoke of the bow.

from sleeks explanation.  sounds reasonable.........    but is this different from your experience, Steve?

[sleek]

  Willie, there is no point the limbs will stop going faster, all the way until there is no arrow. They will never reach a dry fire speed before they are actually dry firing

I know there is more to it than I wrote, but to explain it completely would have required almost a book. I know hysteresis is a friction factor that slows down a limb, and the angle the limb is at relative to the load ( leverage ) which is why a bows limb changes its speed due to levearge agaimst its own weigh on a dry fire ( i reserve the right to be wrong ). I just wanted to say there is a max speed without going into the detail of why and the factors involved. Also the max speed of the limb does change as a heavier arrow is used, speed is not a consyant in this, it is a variable,  changing with the arrows weight. There is probably more to that than I understand.  So, Willie, i dont think Steves point disagrees with mine, only he is further explaining a part of it I didnt go into at all, and clarifying  ( where he mentions dryfire speed and arrow speed will never be the same  ) things i didnt go into detail about.

If im wong on anything, i sure hope he points it out. And any disagreement between me and him, defere to him, he has forgotten more than I know probaly, and I doubt he forgets much.

[Del the cat]

Easy way to look at it... some energy goes into the limbs and some into the arrow.
If we ignore all the fancy stuff and say for the sake of argument that the limbs and the arrow weigh effectively the same and that half the energy goes into the arrow and half into the limbs.
The energy is getting shared in 2 parts 1 part to the limbs, 1 part to the arrow
So if we make the arrow weigh twice as much then the energy gets shared in 3 parts, 1 part in the limbs and 2 parts in the arrow.
So the arrow now has a bigger share of that energy.
Exactly the same logic applies to lightening the limbs.

Of course this is a huge simplification just to illustrate the principle.
Del

[willie]

The energy is getting shared in 2 parts 1 part to the limbs, 1 part to the arrow
So if we make the arrow weigh twice as much then the energy gets shared in 3 parts, 1 part in the limbs and 2 parts in the arrow.

That looks like a good way to start understanding the concept. There are explanations out there on the web that are heavy on the math...... a full understanding might take a while.

Can someone illustrate a practical usage of the principle? Seems like the calculation would only be useful for small changes in velocity or weight. that is, where efficiencies remain relatively constant?

[willie]

And any disagreement between me and.........

Not looking at disagreement at all, just trying to understand.

ok, compare two scenarios

the first, a very heavy arrow leaves a bow at limited velocity . from sleeks example, it is an arrow that reached its velocity during the first half of the powerstroke, with the implication being that the last half of the powerstroke was ineffective or a wasted opportunity. For that bow, a slightly lighter arrow that accelerates thru the full powerstroke will be more efficient

in the the second, a much lighter arrow is shot. It continues to accelerate right up to the moment it leaves the string. In this case, the bow is only as efficient as mass of that arrow lets it be, the implication being if a slightly heavier arrow could have also been accelerated  to the same moment of release (with of course a slighty lower velocity), the bow would be more "efficient" with the slightly heavier arrow.

the bowyers job is to design and tiller a bow that delivers acceleration thru the full powerstroke, to an arrow of the design weight, no more, no less?

[Badger]

 Willie, all of them accelerate all the way through the power stroke, the last 1/2 of the power stroke has less weight pushing but gives the arrow better leverage over the limbs sucking the power back out of them. The bowyer can try to reduce string angles in the last 1/2 of the stroke to improve the leverage the arrow has.

[willie]

Willie, all of them accelerate all the way through the power stroke

well ok, then I suppose that there might be a difference between a strong  usable acceleration (one that adds the final 20 or 30 fps,) and an acceleration that only nominally increases the arrow speed during the last part of the power stroke.

I read somewhere, (but I can not remember where at the moment), about using a chronograph when tillering out the last 6 inches or so of a new bow. something about seeing if the bow is coming in as expected, and using speed readings to help with decision making during the final tillering. Have you ever tried anything similar?