Power stroke from release to launch.

geoffretired

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One aspect of the power stroke that I know I don't understand but would like to, is the part where the string goes tight or straight; somewhere around brace height I suspect.
Quite often the limbs seem to wobble at the end; sometimes that is quite violent and noisy and we try to correct it with brace height changes etc.
If I could show a really slomo version of this, I think we would see one limb carrying on a bit further than the other, and then rebounding, letting that other limb go forwards, and both end up see sawing for a while.
I have read that the limb that carries on further still has more stored energy in it than the other. I can understand that up to a point. With more energy still in it, that limb will over power the other when the string goes tight. The energetic limb will carry on and work on the weaker limb; pulling that limb back slightly. We can mimic this with the bow braced, by pulling one limb tip back and seeing the other limb move the other way.
The bit I don't understand is why the more energetic limb has more energy still it and how that energy gets there. Put another way, when the limbs move forwards on the power stroke, they will both start losing energy(?? )and gaining speed. Or are they gaining energy by moving faster??
At full draw there is a point where the forces are in equilibrium and things settle to a sort of "at rest" state; bow balancing archer's draw force. Are the two limbs storing equal amounts of energy at that stage?
I understand that on release, things change and the arrow has to be moved, and that takes energy.
 


brman

Member
Well, no one else has answered so I will try. But on the basis that, while I am an engineer so think I understand the basic physics, I don't really know how bows work!

The way I see it is that when you draw back you are putting energy into the limbs (so potential energy). Each will store roughly the same but how balanced they are will probably depend on quite a lot of factors - the limbs, tiller, nock point, that sort of stuff? I suspect they are never truly balanced.

On release, the key thing to remember is energy is always being lost from the system, never added (until you pull the string back again). So you are talking about transferring energy elsewhere, from stored (potential) energy to movement (kinetic) energy or even heat. So either to the arrow or to air movement, noise, etc.
When you release that energy is converted to movement. ie. moves the limbs and string and arrow forward. By the time it gets to the "at rest" position we would like all the all the energy to have been transferred to movement in the arrow (so the arrow goes as fast as possible) but it will not be, some will be left in the limbs as they continue to move forward. So the limbs oscillate until they have dissipated that energy and are at rest again.
I assume this is why people tune their brace height for minimum noise, that being where minimum energy is lost in oscillation and so max energy is transferred to the arrow?

So to answer you question: I think there are likely to be a number of factors. eg:
- Tiller, nocking point, how you draw the bow, manufacturer of the limbs etc will mean that there is not going to be an equal amount of energy in each limb at full draw.
- position of the nocking point,how it is released, maybe even arrow flex and probably other factors will mean that the energy is not transferred evenly from each limb to the arrow
End result, when the bow reaches the "at rest" position one limb has more energy than the other, causing them to oscillate unevenly, pulling against each other.
Again, I suspect that if you could tune the bow (and your form?) to minimise this imbalance then you would maximise the arrow speed but I am speculating here!

Am I making any sense?
 


geoffretired

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Hi Brman, Thanks a lot for posting, Yes, you are making very clear sense.
Can I just add a few ideas that you might be able to help me with?
If we use a crossbow instead of a recurve or longbow; the symmetry will allow almost perfect balance between the two limbs and the string, and the arrow will be almost on dead centre of the system, too.
When fully drawn and locked back at the trigger mechanism, I am assuming the energy in each limb is very similar to each other. Tension in each part of the string is equal, the system is in balance,( forces at a point??? I seem to remember from school,)
With the ordinary bow, the asymmetry changes the forces acting around the nocking point at full draw. But are they not in a sort of balance? Equilibrium? I don't mean all forces are the same size, they are at slightly different angles( like a badly fletched arrow) and slightly different size forces; but they cancel each other to create stillness of sorts at the draw fingers.
On release, those differences work to a pattern, and the hope is that the nocking point will be moved forwards in an almost straight line, horizontally.( ignore the string waving side to side.)
Here are some details that I believe are correct. The bow hand, being nearer the bottom limb, makes that limb bend more easily than it would if the hand was on centre. The draw hand is almost on centre so the top limb bends less than the bottom one. Experience shows us that a stiffer bottom limb makes a bow that shoots better. The slightly stiffer bottom limb, is now not so easily bent as it would have been. At full draw, the bends in each limb look about equal. If the bottom limb had been equally stiff we may have noticed an extra bend in that bottom limb.
Is there a simple formula that says how much energy is stored in a spring, when it is bent by a certain amount?
Could we make a rough guess at what the numbers might be? they only need to be rough so we can see that the bottom one stores more energy; or stores the same if that is the likely case.
 


Del the Cat

Active member
Wot brman said.... :)
Potential energy becomes kinetic energy... the chances of everything being perfectly balanced are zero.
All systems oscillate...
If you factor in the geometry of small angles (different for each limb).... the difference in string length between a 6" brace and a 7" inch brace is very small, less than the amount of stretch as the limbs slam home... thus the limbs can easily overshoot by that inch and oscillate, the string will also oscillate.
You have two stable states... full draw and brace...going from one to t'other will always give rise to some oscillation, exacerbated by the search for ever increasing arrow speeds which leave more energy in bow.
Try shooting a 1/2" diameter 32" Oak shaft with a forged head... that'll dampen it down a tad ;)
Del
 


dvd8n

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I don't know if I'm right, but I have always seen it as a timing/geometry problem in that one limb reaches its 'at rest' position before the other limb and hence overshoots it slightly. Thus when the string straightens and the system comes to rest one limb is slightly past it's at rest position and the other hasn't quite reached its. The system then vibrates as it stabilizes.

So, if you can adjust the limb preloads so that the two limbs arrive at their equilibrium point at the same time then that will minimise vibration? Well, maybe not as to get that to happen maybe one limb would need to move a little faster than the other and then the momentum of the two limbs would be different and that in itself would cause vibration as it all equalised.

So I think that all you can reasonably do is to experimentally adjust the tiller until vibration is minimised.

But maybe I'm completely wrong?
 


geoffretired

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Thanks Del and dvd8n,
I understand that there is no perfect "stop" with no oscillation, but we do try to reduce the really bad ones.
If I alter the preload on one limb; then I also alter the preload on the other. That is not the same as having one limb deliberately made stiffer than its partner, is it?
If we alter preload at the bottom for example, that alters the angles of the limbs to the string. Is that new difference in string angles part of why the bow reacts differently? Or is it the nocking point being moved down( or adjusted back to compensate) or both?
 


dvd8n

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My understanding always was that yes, it's a system, but the altering of the tiller screw on one limb does affect that limb more than the other. But now you've got me wondering what the effect really is.....
 


dvd8n

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Ok, had a think and drew some sketches, and my theory is that the limbs are moving around when the bolts are adjusted such that the string exits the string groove on the recurve in a different spot which due to the nature of the recurve will have a slightly different stiffness. Which as a result will let you adjust the relative stiffness of the limbs.

But threats just a thought experiment and I may be talking rubbish.
 


Del the Cat

Active member
Thanks Del and dvd8n,
I understand that there is no perfect "stop" with no oscillation, but we do try to reduce the really bad ones.
If I alter the preload on one limb; then I also alter the preload on the other. That is not the same as having one limb deliberately made stiffer than its partner, is it?
If we alter preload at the bottom for example, that alters the angles of the limbs to the string. Is that new difference in string angles part of why the bow reacts differently? Or is it the nocking point being moved down( or adjusted back to compensate) or both?
Everything is interactive ... so both.
Even on a simple bow, with it on the tiller, if you remove wood from one limb it effects the load and curve of the other.
Like a see-saw .. put another kid on one end, it goes down and the other end goes up...
Take a kid off one end it goes up and the other comes down.
Nothing can be adjusted independently.
Even raising the nocking point effects the balance of pull on each limb slightly.... that's why all changes need to be small.
One of my mantras is... always remove half as much as you think!
Del
 


Timid Toad

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The geometry of all bows is different.
Most recurves have the pressure point - throat of the grip - near the centre of the bow. Compounds have it below the bow.
This puts the arrow, rest and np above centre in a recurve, compound close to or dead on, centre.
The two limbs working as uniformly as possible is desirable not just from the pov of limb flap but of vertical nocking point oscillation.
It's a closed system so it should be possible to bring about a stable finish *within the consistencies of the archer* through tillering and np movement, taking into account things like the size of the archer's hands, arrow diameter etc, however most bows will have a sweet spot of a few mm positive tiller and a few mm above square np.
 


dvd8n

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To be honest I've always had the most success setting the tiller to the manufacturer's recommendations then not messing with it.
 


geoffretired

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dvd8n,thanks for that.I think "different stiffness" is about right. I know that the string angle makes a lot of difference. If you clamp a limb butt in a vice and add a string to the limb tip then start pulling the string with a spring balance tied to the other end, you can get different readings according to which direction you pull the string. If you pull when the string is at right angle to the limb; as you would when bending a ruler over a desk to make it twang; it bends quite easily. If you pull with the string lying close the the limb butt; as it is when stringing the bow, the tension is much higher; it's a stiffer limb now... apparently. This is one reason why it is difficult to string a recurve bow without a stringer. The stringer pulls on the limbs at a much greater angle.
So altering tiller bolts does change both angle making one harder to bend and the other easier.
One aspect of all this that I struggle with is knowing what to call the energy in the limbs. I know potential is stored at full draw. I understand kinetic energy is when it is moving. Is that increasing as the speed of the limbs increases?
When the string goes tight, what form of energy is acting? Is it the differences in each limb speed causing the overshoot, or something else?
 


geoffretired

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Hi TT, I understand what you are saying. Thanks for that.
And Del, I get what you are saying, too.
It isn't the connections between all the variables that bothers me. It is really what is the energy called; how do I describe this to others?
My current method is to say the two limbs are racing back to brace height. One is faster/stronger but has further to travel. The faster/stronger one is playing catch up all the time, and given enough distance in the race, it will catch up. So, we set up the bow (by different means) so both limbs " cross the line" together.
In that simplified explanation I am left with one limb travelling faster across the line; or with more energy in it.... so it causes the overshoot.
If I tweak something I can make the overshoot smaller. Let's say I shorten the race with a higher brace height. Now what happens? The string will go tight again, but further away from the riser this time.
The race is shorter and the stronger limb is trailing behind still. That's where I run out of ideas.
 


dvd8n

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Energy can neither be created or destroyed.

When you pull the string back you do 'work' which is the measure of energy transfer when a force (F) moves an object through a distance (d).

F is the pull you exert on the string and d the length of the pull. So by pulling the string you do work which puts potential energy into the bow system. Potential energy is the energy stored in a system due to its state which in this case is the limb tension.

When you let go of the bowstring the potential energy is converted into kinetic energy which is the energy inherent on the system due to its motion.

When the string stops the energy has to go somewhere so it goes into the arrow and the arrow flies away with that energy. If there is no arrow the energy has to go somewhere so it goes into sound, heat and the destruction of the limbs. Which is why you shouldn't dry fire your bow.
 


dvd8n

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Bow, not boss. I don't seem to be able to edit my posts all of a sudden. The forum and to be throwing away my paragraphing too...

Edit: And the edit button's back.. Go figure :confused:

And I fixed the misprints and paragraphing.
 


geoffretired

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Hi dvd8n, so at the point where the string goes tight there is quite a lot of kinetic energy. Much goes into the arrow, and the residue has to be wasted in the string stretching, limbs still flexing along with all the other bits that wobble about... even the bow arm.
Bow, not boss. I don't seem to be able to edit my posts all of a sudden.
On that topic, I read "boss" in my email notification, but I see "Bow" in your post at present. How was that edited?
 


dvd8n

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As well as the energy of the system, the system has momentum. Which is mass x velocity, plus it has direction. The momentum of a system is always balanced so if the two limbs have the same momentum and the string is perfectly inelastic then the limbs would come to a dead halt and 100% of the energy would go into the arrow.

If the string was elastic to some degree then the limbs would overshoot their equilibrium point and the string would vibrate with the limb tips moving in opposition; the energy would bleed away in the audible twang;

If the string became straight when the limbs weren't at their equilibrium point then some energy would be lost moving to the equilibrium point as if you had twanged the string vertically; the energy would bleed away in the audible twang.

If the momentum of the limbs is not the same at the equilibrium point with the string straight then the tip with more momentum would continue in its path and drag the other limb after it, again as if you had twanged the string vertically, taking energy from the arrow with the tips oscillating together. Eventually the tips would stop vibrating with the energy bleeding audibly.

Combinations of these effects would be possible.
 


geoffretired

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dvd8n thanks again, yes, I can see all that.
The point where the string goes tight, is the point that I am trying to visualise. I can see how the two limbs can reach that tight string position in different conditions. Top has more energy and goes on ahead. Bottom has more energy and goes on ahead. Both of those conditions result in the twanging and the see sawing movement. If they both had the same energy I could imagine the string stretching and both limbs flexing, little or no see sawing. This is the condition we get closer to when we try to tune out the twanging,yes? As it is possible to make the twanging worse and also better, there must be something happening at the point that changes as a result of our tuning tweaks.
Perhaps there is something in the definitions of Kinetic Energy and Momentum that I am missing or unable to process.
KE =1/2 mv" ( " replaces the little 2 required for squared)
Momentum P=mv.
Apparently two items can have the same momentum yet have very different KE. Perhaps this is in some way responsible for two different limbs having different closing velocities but same momentum. Perhaps this is why the limbs can come to an almost dead stop even though one is travelling faster.
 


Timid Toad

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Presumably you have kinetic energy in 2 different planes. Vertical when the limbs are not in sync, which is wasted energy and undesirable, and horizontal, which is the force behind the arrow.
 


geoffretired

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Hi TT that sounds interesting, cheers.
That gets me thinking that it might possibly feature in the way the limbs reach the "at rest" position, either together or not quite in sync.
Would the string waving side to side along with the arrow also play a part in dispersing the last bits of energy?
 


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