# Nusensei's take on arrow placement



## kshet26 (Dec 20, 2010)

I was under the impression that the paradox was caused by the displacement of the string due to the fingers, not the torque of the string. For a RH archer the string deflects left causing the shaft to buckle.


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## b0w_bender (Apr 30, 2006)

kshet26 said:


> I was under the impression that the paradox was caused by the displacement of the string due to the fingers, not the torque of the string. For a RH archer the string deflects left causing the shaft to buckle.


OK it has nothing to do with the torque on the string, it is as you described the string deflecting out around your fingers or alternatively your thumb. He obviously has it correct about what side the arrow goes on but the reason he offers for the "why" is not really the reason why. The cause for the archers paradox is both the deflection around the fingers and the pressure of the string pushing forward that causes archers paradox.

You have all seen this video a hundred times no doubt but it illustrates the point for those who have a confusion about the matter. YOu can clearly see the arrow jumps out around the archers fingers and that is when the arrow begins it's flex.





I'm not sure where nusensei is getting his info from but he has several videos where the details seem a bit sketchy. 
I'm glad he tackled the topic but I'm not sure his explanation was all that well researched or articulated.


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## Zombie_Feynman (Jun 27, 2014)

This is slightly off topic, but it is usually said that the lateral displacement of the arrow is caused by the fingers during the release, and that the spine of the arrow has to be selected so that the lateral displacement is timed correctly for clearing the bow. If that is the case, why do compounds using a release need a particular spine of arrow? As I understand, compounds are usually set for shooting exactly centered, and the release doesn't impart any lateral movement, so a very stiff arrow should work well for all possible draw weights. What am I missing?


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## kshet26 (Dec 20, 2010)

From what I understand, compound arrows shot with a release flex vertically (instead of laterally like with recurve). Which is why the rest is located under the arrow.


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## theminoritydude (Feb 11, 2013)

kshet26 said:


> From what I understand, compound arrows shot with a release flex vertically (instead of laterally like with recurve). Which is why the rest is located under the arrow.


So is the recurve rest.


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## kshet26 (Dec 20, 2010)

theminoritydude said:


> So is the recurve rest.


Ah true! Hmm. Then the mounting location probably takes advantage of the fact that recurves use a plunger? Otherwise, why aren't under mounted rests a thing for recurve? Fletching clearance purposes? The rests for both move in the same axis that the arrow flexes.


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## Zombie_Feynman (Jun 27, 2014)

kshet26 said:


> From what I understand, compound arrows shot with a release flex vertically (instead of laterally like with recurve). Which is why the rest is located under the arrow.


Sure, but it doesn't have to flex to clear the bow, which is the alleged reason for needing a specific spine on a recurve. A very stiff arrow should work for any draw weight on compound.

The reason may be that the arrow can be lighter by going with a weaker spine, but the weight doesn't always increase with spine for all arrows. ACEs, for example, have some spines in which the weaker arrow weights more (one is 720 vs 670).


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## b0w_bender (Apr 30, 2006)

kshet26 said:


> From what I understand, compound arrows shot with a release flex vertically (instead of laterally like with recurve). Which is why the rest is located under the arrow.


Correct the movement a compound has is the nock travel. In most cases the arrow is nocked above center on the string. So when the string moves forward the pressure change on the back of the arrow is in the vertical direction. The arrow then tends to bend upward and the flex in the arrow helps it to stay on plane as apposed to porpoising. A lot of manufacturers are trying to limit the nock travel to reduce the need for spine but in most cases a well spined arrow still performs better.
you can see it in the first 10 seconds of this video and yes it is a lot less pronounced which is why the acceptable window of spine for a compound arrow is so much bigger. You can get away with a lot more on a compound.


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## Zombie_Feynman (Jun 27, 2014)

b0w_bender said:


> Correct the movement a compound has is the nock travel. In most cases the arrow is nocked above center on the string. So when the string moves forward the pressure change on the back of the arrow is in the vertical direction. The arrow then tends to bend upward and the flex in the arrow helps it to stay on plane as apposed to porpoising. A lot of manufacturers are trying to limit the nock travel to reduce the need for spine but in most cases a well spined arrow still performs better.
> you can see it in the first 10 seconds of this video and yes it is a lot less pronounced which is why the acceptable window of spine for a compound arrow is so much bigger. You can get away with a lot more on a compound.


That makes sense. Thanks!


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## theminoritydude (Feb 11, 2013)

kshet26 said:


> Ah true! Hmm. Then the mounting location probably takes advantage of the fact that recurves use a plunger? Otherwise, why aren't under mounted rests a thing for recurve? Fletching clearance purposes? The rests for both move in the same axis that the arrow flexes.


Having an under mounted rest similar to a compound rest (blade) would interfere with the lateral oscillation of the shaft during the launch. That very oscillation is also instrumental in the arrow clearing the bow, so you could say that the problem is its own solution.

Having said that, the way by which many archers fix their arrow rest, makes no difference if they had used an under mounted rest.


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## limbwalker (Sep 26, 2003)

Joe T's comments on column loading are an interesting read as it pertains to paradox.


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## Joe T (Apr 5, 2003)

limbwalker said:


> Joe T's comments on column loading are an interesting read as it pertains to paradox.


I can't take any credit for that one. Basic flexing behaviour of arrows understood for years. Detailed understanding of arrow flexing still not available (as the math is just too d**n complicated).

Recurve arrow shaft bending is an elastic structural failure know as Euler buckling. If you put an arrow shaft in a vice and load it up then at some load the arrow will fail (and bend). This failure isn't terminal and the arrow can recover (see Euler buckling example). When you release the bow string the string axial load on the arrow exceeds the Euler critical load and so the arrow fails i.e.bends. So the fingers really have nothing to do with the arrow bending as such. What the string fingers do affect is what direction the arrow bends in and they can also effect how much the arrow shaft initially bends (weak/stiff tuning behaviour). Say you balance a golf ball on top of an inverted saucer. What determines that the arrow rolls downward is gravity. What direction the arrow rolls down is determined by anything that gives the ball a bias in any particular direction however small this bias is.

So the essential difference with the arrow shaft behaviour between a recurve and compound is that with a recurve the force on the shaft exceeds the buckling load (by design) so the arrow fails and with a compound the force on the shaft doesn't exceed the buckling load (by design) and so the arrow doesn't fail.

Comparison of Euler critical load (pounds) with the Easton draw weight (pounds) from the 2014 arrow selection tables. The critical load is around 70% of the draw weight (though of course the actual force on the arrow is less than the static load).


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## theminoritydude (Feb 11, 2013)

Joe T said:


> So the fingers really have nothing to do with the arrow bending as such.


If I shot a recurve with a d-loop and a calliper release, would the failure still occur? I understand the magnitude of the buckling might be reduced, is there a minimum deflection to qualify as a failure?


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## Warbow (Apr 18, 2006)

Joe T said:


> I can't take any credit for that one. Basic flexing behaviour of arrows understood for years. Detailed understanding of arrow flexing still not available (as the math is just too d**n complicated).
> 
> Recurve arrow shaft bending is an elastic structural failure know as Euler buckling. If you put an arrow shaft in a vice and load it up then at some load the arrow will fail (and bend). This failure isn't terminal and the arrow can recover (see Euler buckling example). When you release the bow string the string axial load on the arrow exceeds the Euler critical load and so the arrow fails i.e.bends. So the fingers really have nothing to do with the arrow bending as such. What the string fingers do affect is what direction the arrow bends in and they can also effect how much the arrow shaft initially bends (weak/stiff tuning behaviour). Say you balance a golf ball on top of an inverted saucer. What determines that the arrow rolls downward is gravity. What direction the arrow rolls down is determined by anything that gives the ball a bias in any particular direction however small this bias is.
> 
> ...


So if the compound arrows are under the Euler Buckling load, does that mean they don't bend at all? And at what point do lateral forces change the Euler load calculation? Intuitively it would seem that if you apply enough lateral force we are no longer dealing with just compressive column calculations :dontknow:


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## Joe T (Apr 5, 2003)

theminoritydude said:


> If I shot a recurve with a d-loop and a calliper release, would the failure still occur? I understand the magnitude of the buckling might be reduced, is there a minimum deflection to qualify as a failure?


Yes. Historically shooting recurves with release aids was once quite common I believe. Not permitted these days by the rules though I assume some para recurve archers use release aids? The only minimum deflection basis I know of historically was some guy who ran the recurve arrow between a couple of rails so it couldn't bend (a sort of stealth shot plus is suppose  )


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## limbwalker (Sep 26, 2003)

> So the fingers really have nothing to do with the arrow bending as such. What the string fingers do affect is what direction the arrow bends in and they can also effect how much the arrow shaft initially bends (weak/stiff tuning behaviour).


Bingo!


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## Joe T (Apr 5, 2003)

Warbow said:


> So if the compound arrows are under the Euler Buckling load, does that mean they don't bend at all? And at what point do lateral forces change the Euler load calculation? Intuitively it would seem that if you apply enough lateral force we are no longer dealing with just compressive column calculations :dontknow:


Both recurve and compound arrows bend under lateral forces during the shot but nothing to do with Euler buckling. Nothing changes the Euler criteria as it just specifies the failure point. What happens afterwards is a can of worms. For an arm waving attempt at this see My musings Archers paradox in 3 pages I think  .


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## theminoritydude (Feb 11, 2013)

Joe T said:


> Yes. Historically shooting recurves with release aids was once quite common I believe. Not permitted these days by the rules though I assume some para recurve archers use release aids? The only minimum deflection basis I know of historically was some guy who ran the recurve arrow between a couple of rails so it couldn't bend (a sort of stealth shot plus is suppose  )


I've never quite fully understood the phenomenon of buckling during my student days. 

Let's see if I understand it now. For euler buckling to occur, the qualifying points are 1) Critical vertical load (regardless of deflection), 2) When subjected to external lateral load, results in deflection in the direction of the applied lateral load, resulting in lateral load decreasing. 3) Deflection stops when the verbal load is balanced by the stress buildup in the cross section of the material, in elastic deformation range.


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## Warbow (Apr 18, 2006)

limbwalker said:


> > So the fingers really have nothing to do with the arrow bending as such. What the string fingers do affect is what direction the arrow bends in and they can also effect how much the arrow shaft initially bends (weak/stiff tuning behaviour).
> 
> 
> Bingo!


That's a lot of stuff for the fingers affect the bending and still have "nothing to do with the arrow bending," though, isn't it? "Nothing" may not really be the right choice of words...


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## Warbow (Apr 18, 2006)

theminoritydude said:


> I've never quite fully understood the phenomenon of buckling during my student days.
> 
> Let's see if I understand it now. For euler buckling to occur, the qualifying points are 1) Critical vertical load (regardless of deflection), 2) When subjected to external lateral load, results in deflection in the direction of the applied lateral load, resulting in lateral load decreasing. 3) Deflection stops when the verbal load is balanced by the stress buildup in the cross section of the material, in elastic deformation range.


Euler buckling would seem to be harder to calculate based on inertial resistance to a dynamic load. (Of course, any of this is hard to me, I'm not an engineer, not even remotely.)


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## theminoritydude (Feb 11, 2013)

Warbow said:


> Euler buckling would seem to be harder to calculate based on inertial resistance to a dynamic load. (Of course, any of this is hard to me, I'm not an engineer, not even remotely.)


Doesn't seem that difficult. It's basically calculating the critical vertical load that exerts a destabilising force when compared to the resistance that can by generated be the second moment of area for a particular cross-section column for ANY amount of initial deflection up to the point where the resistance increase overcomes the constant load coupled with the amount of deflection (sort of like balancing a pair of moment forces, one of which has a constant force component but a variable arm, the other with a constant arm (i.e. cross section ) but a varying force (i.e. Young's modulus)). Something like that, I guess....


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## Warbow (Apr 18, 2006)

theminoritydude said:


> *Doesn't seem that difficult. *It's basically calculating the critical vertical load that exerts a destabilising force when compared to the resistance that can by generated be the second moment of area for a particular cross-section column for ANY amount of initial deflection up to the point where the resistance increase overcomes the constant load coupled with the amount of deflection (sort of like balancing a pair of moment forces, one of which has a constant force component but a variable arm, the other with a constant arm (i.e. cross section ) but a varying force (i.e. Young's modulus)). Something like that, I guess....


I'm sure top archers can say that about hitting the 10 at 90M, too :-D 

Also, your cat is probably just a sociopath :wink:


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## theminoritydude (Feb 11, 2013)

Warbow said:


> Also, your cat is probably just a sociopath :wink:


I have ruled that out prior.


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## Joe T (Apr 5, 2003)

Warbow said:


> Euler buckling would seem to be harder to calculate based on inertial resistance to a dynamic load. (Of course, any of this is hard to me, I'm not an engineer, not even remotely.)


The (simple  ) complications re Euler buckling of an arrow shaft are:
1. That you don't have a static load. The force on the arrow shaft is derived from the arrow acceleration by the string force (force = mass*acceleration)
2. The mass of the arrow has two elements; the mass at the "top" the point and the distributed mass of the arrow shaft (taken as total mass as half way up the arrow shaft).
3. Because the axial stress in the shaft varies along the shaft, because of the acceleration, the "dynamic spine" of the arrow varies along the shaft. Whereas with traditional Euler buckling the bending of the column is uniform along its length, with an arrow because the the variable dynamic spine the bending of the column is biased towards the rear end. (This is why with barreled arrows the "barreling" is biased towards the rear of the arrow and why cutting shafts from the rear has a bigger impact on the shaft dynamic spine then cutting shafts from the front).

Basic notes on this topic here: https://groups.google.com/forum/#!topic/archery-folk/d8mUU68e8tI


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## theminoritydude (Feb 11, 2013)

I have learnt much from this thread. Thanks Joe.


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## theminoritydude (Feb 11, 2013)

And yeah, like you guys, I think Nusensei was mistaken about the reason for arrow placement.


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## b0w_bender (Apr 30, 2006)

Joe T said:


> So the fingers really have nothing to do with the arrow bending as such. What the string fingers do affect is what direction the arrow bends in and they can also effect how much the arrow shaft initially bends (weak/stiff tuning behaviour).
> View attachment 2193033


Hi Joe thanks for your input and correct me if I'm wrong because I want to make sure that the posts I make are relatively factual when talking techno geek stuff. I take a minor exception to the above statement only in that I think the fingers play a critical role but I'm hoping you can set me straight (so to speak) 

Since the fingers are deflecting the string or in the case of a compound the nock travel is angled in relation to the travel of the arrow. Doesn't that nonlinear force increase the likely hood of the Euler buckling?
In other words in the case of a finger release the force of the string is no longer inline with the shaft of the arrow so wouldn't that make it far more likely to buckle than if the force were centered perfectly behind the arrow and the vector of the force was perfectly inline\parallel with the travel of the arrow?

I'm looking at the video and the force being applied to the back end of the arrow looks like it is traveling basically in the shape of a sine wave. 
If the force were linear and directly in line with the arrows travel then I would think that spine would become immaterial. And the amount of force to create the Euler buckling would need to be far greater?


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## Joe T (Apr 5, 2003)

Euler buckling is the consequence of structural instability. There is no requirement for *any* other forces for buckling to occur. Other factors like the nock weight, the bow torsional stiffness, tab friction etc. etc. etc. will all effect *how the arrow shaft behaves* as it buckles and hence the string torque on the arrow and hence the tuning.

In the video referenced above the load is straight down the column (no fingers etc.) and the column buckles. There are other videos were the weight on the column is made slightly asymmetric (e.g. on a tilt table) so you can demo how the direction of buckling can be controlled as happens with the fingers or thumb ring.

*If the force were linear and directly in line with the arrows travel then I would think that spine would become immaterial.*

This a very common mistake. People think only in terms of collapse being a material failure. With a slender column there is an additional (elastic) failure mode. In the video when the weight is removed the column just straightens up again. Arrow spine is one of the main factors that dtermine the Euler critical load.


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## b0w_bender (Apr 30, 2006)

Warbow said:


> That's a lot of stuff for the fingers affect the bending and still have "nothing to do with the arrow bending," though, isn't it? "Nothing" may not really be the right choice of words...


That was kind of my thought without that lateral force a lot of arrows wouldn't even buckle. In other words it requires a lot more force to cause the buckling if the force is directed straight down the shaft as apposed to non-symmetrical force path that a string takes. Of course I'm not an engineer either but I believe that is correct?


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