# The "P" (paradox) Factor as it relates to performance...



## limbwalker (Sep 26, 2003)

Okay, it's my term, but I think it fits. Call it "Paradox" factor or "Performance" factor, or whatever. I'll just call it "P" factor.

What am I talking about? Well, the dialogue between Jake K. and myself the other day got me to thinking. How do you really measure performance? I mean, shooting an arrow over a chronograph has always been the primary means of measuring performance, but that only tells part of the story. 

Like Jake eluded to, and myself and others have seen as well, is that some bows need a stiffer or weaker arrow although pulling the exact same draw weight. So while you may be excited that you're getting 2 fps. more speed from a given draw weight, at what cost? If it means you have to jump up a size in spine and shoot a heavier arrow, have you really gained anything?

So I offer this "measure" of performance. The "P" factor. Let's just put it on a scale of 1.0 with 1 being "normal" performance.

Right now, I have four different sets of premium ILF limbs to play with. Samick Masters, W&W Inno Power, SKY carbon/bamboo, and Border Hex-6w (wood core). They are all fantastic limbs from their respective manufacturers, and I'd be happy to take any of them into a competition.

So how do you choose which ones? 

At least for me, I want some numbers to consider. I have a science background, so good, hard, objective data always helps me make a more confident decision. Speed is one thing I look for, as is the shape of the draw force curve as it relates to the feel of "stacking" at the clicker. Feel and sound are very important to me as well, but much harder to measure. So let's go with what we can measure, shall we?

Here's how I set this comparison up... I wanted to compare each set of limbs against one another, but only once I had tuned them all to the exact same arrow - my Nano Pro 500 at 32.5" total length. You see, comparing limbs all set at the same draw weight only tells you part of the story. The rest of the story is decided by what arrow you can actually tune at that draw weight. So, numbers over a chronograph only really matter with a perfectly tuned setup, because that's what you'll compete with.

Here's what I came up with:

The same exact arrow tuned at 44# from the W&W limbs, 45# from the Samick and SKY limbs, and 46.5# from the Border limbs. If you looked at the draw force curves of each of these limbs, you could probably see why this is. At least at my draw length, the W&W limbs stacked the most, followed by the Samick and SKY limbs, with the Border limbs "stacking" the least. In general terms, this means the W&W limbs pushed the hardest at first, while the Border limbs pushed the "softest" on release. The effect is to allow the Border limbs to tune the weakest arrow, and the W&W limbs to tune the stiffest arrow.

So, what do we do with that? Well, what that means in practice is that I can shoot that arrow with a 120 grain point at 46.5# from the Border limbs, and achieve 211 fps. Or I can shoot that arrow from the SKY or Samick limbs at 45# at 202 fps., or from the W&W limbs at 44# at 200 fps. 

Or, I can reduce the point weight of the arrow to 110 grains and tune it at 46.5# from the SKY and Samick limbs at 207-208 fps., or at 46# from the W&W limbs at approx. 204 fps. And so forth.

You see, this gets complicated and no simple feet-per-second figure alone really tells you what's going on.

Sure, I can shoot the same arrow the same exact speed from two different sets of limbs, but I have to give up 10 grains of point weight and a little FOC in the process. Or, I can shoot the same draw weight, but a stiffer (and heavier) arrow from one than the other...

So let's just use the draw weights that actually tune the exact same arrow as a measure of those limbs "P" factor. Since I have long considered the Samick Masters limbs as a worldwide "standard" in ILF limb performance, we'll give it a perfect 1.0. Same with the SKY limbs. A perfect 1.0

However, since the W&W limbs tuned at 44# instead of 45#, we'll deduct the .22% difference and give those limbs a P-factor of .98. Meanwhile, the Border limbs tuned that arrow at 46.5#, a .33% improvement, so we'll give them a performance factor of 1.033 (.33% better).

Not sure if any of this is making sense, but it makes sense to me, so thanks for following along! 

We each have our own preferences for feel and sound, and of course those are very important values to consider too. But as often as "performance" is thrown around, I figured we should at least figure out a common way to measure it, right?

John


----------



## limbwalker (Sep 26, 2003)

Oh, and DChan, go easy on me. I have a Bachelor of Science degree in Forestry. Not engineering...


----------



## limbwalker (Sep 26, 2003)

And the contestants that got to play along...


----------



## limbwalker (Sep 26, 2003)

Each set of limbs had to achieve at least this quality of tune at 30 meters before it was chrono'd...


----------



## Flehrad (Oct 27, 2009)

limbwalker said:


> Sure, I can shoot the same arrow the same exact speed from two different sets of limbs, but I have to give up 10 grains of point weight and a little FOC in the process.


Its not the same arrow if you're changing 10gn of point weight. You should re-clarify in saying that you can shoot the same length and shaft spine, but it by far is no longer the same arrow if you have dropped point weight.

The method you are using to determine your P-factor sounds okay, but you're basing off your decision of using the Samick Masters and Sky limbs as your reference base in terms of behaviour. Variance in manufacture I'm sure between generations of Masters limbs will probably also have some minute differences, so an error range will exist within that. But, it isn't a solid reference base as it is a subjective measure using those limbs.

If we go look briefly at compounds for a certain point, while they do measure FPS a lot as their benchmark, they do so using their IBO standard (30" arrow, 350gn total weight, 70lb, I think?), and that eliminates some aspects of bias towards brands/manufacturers. Of course, then the DFC comes into play with peaks and valley heights and sizes according to cam types, and then people debate about feeling on the wall, hardness of the wall etc, which, are all rather subjective matters.

Any true (scientific) scale and factor (like for example the Moh scale) are based on absolutes with no subjectiveness. The moh scale principle is nice and simple, if X can scratch Y, then X is higher than Y on the scale.

So, going back to the P-factor, scale of performance, I think if you perhaps look at it from a mathematical viewpoint it might work out better.

I myself had some thoughts about this but never had the equipment to really test it.

My perspective was to do a energy efficiency calculation. 
A set arrow length/weight/size, say for argument, a 30" arrow, with 120gn point, and a standard fletch type is used.
- A set of limbs that tunes the shafts (as you have done) will produce a certain shooting weight, as determined by a shooting machine, or best to one (see, archer interaction on recurve is a huge issue)
- Calculate mathematically using real world modelling physics the theoretical FPS that the arrow should be coming out on (for this, your string must also be constant, and the riser constant)
- Compare this to the chronographed FPS
- The performance indicator of theoretical FPS to actual FPS to tune that arrow will provide your performance indicator.

This means that for the fixed arrow (eliminates arrow variation issues), then that particular limb design efficiency is tested against itself from theoretical to actual.

I would expect that with better limb design, the FPS ratio for better limbs would be closer to 1.0 , while poorer limbs with worse performance would be lower than 1.0, as the efficiency to cast the arrow at the tune speed is lower.


----------



## Stash (Jun 1, 2002)

If you must, then why shouldn't straight arrow speed be just as valid with a recurve as with a compound? Same arrow weight, same DL, same DW, and you can have the equivalent of IBO for a recurve. 

Use a standard for bow length, 25" riser and medium limbs for a 68" bow. Brace height at 8 3/4", draw length 28", draw weight 40#, 300 grain arrow, shot with a release out of a machine. 

However, I am of the considered opinion that calculating a "P" factor is a complete waste of time.  The only true indicator of performance is, which gives you the best scores? Tune one set as best as you can, give it a fair test of scoring at long ranges. Repeat with the next set, etc. Whatever scores the most points is the best.

If there's no statistically significant difference, shoot the ones that feel most comfortable. 

If there's no subjective difference there, keep the cheapest and sell the rest.


----------



## limbwalker (Sep 26, 2003)

Actually Flehrad, it is the same arrow. Just different point  ha, ha. But I get what you're saying, and agree that there are probably several ways to measure this.

Stash, you're missing the point. You could easily (as I have before) simply measure speed at a certain grains/lb. of arrow weight and compare those. But that does not take into consideration the effect that the limbs have on the arrow, and what arrow configuration they will force you into - which is ultimately how you compare equipment.

I don't really care if limb A shoots a 350 grain arrow 200 fps. and limb B shoots that same arrow at 205, if only one setup is actually useable.

It's not a perfect formula, I know. Just something to get folks thinking before they just take fps at face value. 

And if I have time to waste, at least let me do it while learning about archery stuff... kay? 

John


----------



## Hank D Thoreau (Dec 9, 2008)

Very interesting and innovative approach. I like your reasoning. It's great when archers get involved in the testing process. It may not be as scientific as it could be, but it sends a message to the manufacturers demonstrating our resolve to base decisions, as much as possible, on objective measures. I wish I had four great sets of limbs like you have to test.


----------



## limbwalker (Sep 26, 2003)

Hank, I have a few more pairs of traditional ILF hunting limbs that I never even thought to test against these. They are carbon/wood and glass/wood. I may string those up and shoot them to see how they compare.

I'm starting to think that a draw weight vs. speed ratio, at tune, is the answer here. IMHO, this is the first real world way I've seen to really compare one set of limbs vs. another - from a pure performance standpoint.


----------



## Gene M (Nov 16, 2010)

Flehrad said:


> Any true (scientific) scale and factor (like for example the Moh scale) are based on absolutes with no subjectiveness. The moh scale principle is nice and simple, if X can scratch Y, then X is higher than Y on the scale.


As an engineer I'm really interested int these kinds of discussions. Actually, what John is proposing seems like a perfectly reasonable engineering approach to quantifying a complex metric like performance. Engineers do it all the time when we can't come up with analytical equations that can define a metric of interest based on first principles like F=mA or if modelling would be impossible to validate given the available time, money and resources. If the goal is to answer a question like "which one of these 4 limbs should I use if I want the best score tournament after tournament" it probably can't be answered very well with modeling of theoretical risers and limbs or with inhuman shooting machines. 

I'm going out on a limb here (pretty good pun, huh?) but it seems like John has come up with a metric that describes the variation in force that is applied to a specific arrow type for each of his 4 limbs. If we assume draw force is somehow related to performance, the metric is useful. It might also be useful to multiple the draw weight force he measured for each limb type times the speed of the arrow. If I'm doing my math and understanding John's data correctly (and I'm sure some one will point it out if I'm not) draw force X arrow speed = Force X (distance / time) which equals power. If we use the quaint but well known English units, one horse power is the ability to move 550 lbf one foot in one second (lbf is pounds force as opposed to pounds mass). So John's W&W limbs generated 16.0 HP, the Samick and Sky limbs generated 16.5 HP and the Borders limbs 17.8 HP. More than a 10% range in power which is significant for a sport where tournaments are won and lost by fractions of a percent.

John has suggested one metric. The more metrics we come up with the better we'll get at trying to quantify and predict performance. If I may be so bold as to suggest another metric suggested by John's photo of his tuning standard. Mark the target with your best estimate of where the center of your fletched group is (you could calculate the exact center but how painful do we want to make this?). Measure the distance from the fletched group center to each unfletched arrow. Calculate the average (or mean) distance and the standard deviation of the measurements. Do it for enough arrows that you're getting consistent results. If you're some kind of masochist, you could do this for a couple or all of the distances you shoot at. This approach is a stab at trying to quantify real world but extremely hard to define issues like how "forgiving" one set of limbs is given a specific archer's technique (or in my case, lack of technique). Something modelling and shooting machines can't easily address. Of course you could also shoot a bunch or rounds with each set of limbs and just calculate the mean and standard deviation of your scores for each limb.

Just my 2 cents and I'll be happy to make change.

Gene


----------



## Borderbows (Apr 4, 2009)

Yeah... massive topic. and i think your approach seems logical. and at least as good an attempt as we could come up with, as its a complex relationship. one i wouldnt want to tackle alone...

So, i would like to add my 2p's worth on the bows thrust though. 

Smooth bows push harder. for example. 40lbs would drop to 37.7lbs in the first inch, meaning a push is lower by say 2.3lbs. The same holding weight of 40lbs on a smooth bow would then push at 48.1lbs in the second inch, meaning the second inch on the heavier bow is pushing harder.

Though this relationship gets more complex. since your hardest pushing bow could also be said to be the one thats shooting fastest.
so thats a double effect on the severity of the push that the arrow gets.

Thats the concept as we see it anyhow. (hope this doesnt confuse...)


----------



## Gene M (Nov 16, 2010)

I tried to edit in the following to the 2nd paragraph of my post above but didn't meet the 20 minute editing deadline. 

This assumes the arrow speed is related to the speed at which the limbs can apply their draw force which isn't 100% clear to me yet. I can think of more accurate ways to measure limb power but they seem kind of complicated for this discussion.


----------



## Gene M (Nov 16, 2010)

This is indeed a massively complex topic and I like your comment about not tackling this alone. Maybe if enough bright people think about this we'll come up with something useful. 

I should have been more precise in my post above. None of those limbs "generated" the horsepower I mentioned. However, those HP numbers do suggest some relationship about each limbs ability to generate power. The easy way to calculate the actual power generated by a limb is to just multiply the arrow weight by the arrow speed. In any event, I'm kind of intrigued by coming up with a way to quantify to some extent the performance of a particular piece of kit for a specific archer taking into account their particular technique flaws and inconsistencies. How to quantify that in terms of actual points scored on the target should be an interesting conversation.


----------



## Borderbows (Apr 4, 2009)

Gene M said:


> This is indeed a massively complex topic and I like your comment about not tackling this alone. Maybe if enough bright people think about this we'll come up with something useful.
> 
> I should have been more precise in my post above. None of those limbs "generated" the horsepower I mentioned. However, those HP numbers do suggest some relationship about each limbs ability to generate power. To calculate the actual power applied, we'd have to integrate the draw force applied over the distance the force is applied and divide by the time the force was applied. That is what I meant by too complicated for this discussion. In any event, I'm kind of intrigued by coming up with a way to quantify to some extent the performance of a particular piece of kit for a specific archer taking into account their particular technique flaws and inconsistencies. How to quantify that in terms of actual points scored on the target should be an interesting conversation.


I did a thread 2 days or so ago, on limb mass and ILF limb performance.
The mass distribution of the limb is vital to the limbs acceleration (and quality of feel on deceleration)
So you can put a limb on 2 grain scales. limb butt one end and limb tip onthe other.
Just like cars. its horse power per ton. in a bows case you need to include the mass of the working limb. (VERY VERY hard to work out) but this grain scale idea would tell you how the horsepower is applied to the arrow.

Again, this gets complicated, LWs observation is that you can shoot a lesser dynamic spine arrow from a harder pushing bow and still get it to spine right.
I say its Torsional stability not just torsional resistance, but including stability. Hoyt say its less delfex in a riser, but also corresponds to the tri-axial carbon release.
For example.
Hard pushing bows bend the arrow more, this more ill-alignment pulls the limbs out of alignmement. and this makes a bad release worse. but also allows more bend to be applied to the arrow.
Stiff limbs resist this bend, so the arrow tunes differently.
our thinking extends to fast bow closure, tighter straight line limb travel, equals a need for a lower brace height. same single ossilation of parradox, its just its traveled further, with the same amplitude.


----------



## Joe T (Apr 5, 2003)

Historically bow performance has been described in terms of three parameters (stored energy, energy efficiency and muzzle velocity) - see http://www.bio.vu.nl/thb/users/kooi/kobe97.pdf for an application of this approach to various bow designs ( the Border Hex limbs I think would classify between "working recurve" and "excessive recurve").

When it comes to performance of a bow/arrow system i.e. score with target archery you need additional parameters because the arrow properties are very important (thinner, lighter, faster, higher FOC are all terms that you would like to apply to any arrow you can shoot with your draw weight and draw length).

Limbwalker suggested the initial part of the dynamic shoot (as opposed to draw) force curve as a significant parameter - fine but how do you measure this. Another parameter which should be considered is what is usually termed limb torsional stiffness - though really what's meant it's arrow nock torsional stiffness. The lateral stiffness of the bow string at the nock (a variable through the power stroke) will affect the amplitude and flexing rate of the arrow shaft i.e. what's termed its dynamic spine. With the same draw weight and draw length bows with different torsional stiffness will allow use of arrows with different values of diameter, weight etc. which the archer can use has he wishes (speed v FOC etc). Same problem - how do you define, and measure, a "torsional stiffness" number for a bow that you can compare with the "torsional stiffness" number of a different bow. Let's ignore at the moment any limb/string mass effects. 

An off the cuff definition suggestion is the area under a torsional stiffness - draw length curve divided by the draw length - a mean torsional stiffness value over the power stroke (as the limb geometry changes the torsional stiffness will change). To measure it using a standard weight, clamp the riser horizontally, vary the draw length with a grip-string centre point brace and measure the vertical deflection when the standard weight is hung from the string centre point.

At the moment have no actual data on how torsional stiffness affects arrow selection - but clearly if it allowed you to change to next arrow spine the benefits would be significant either by changing the arrow or by using a lower draw weight with an existing arrow


----------



## Gene M (Nov 16, 2010)

I hope you're happy with your self Sid, you've got my feeble little mind worked up about this and I can't get to sleep. Luckily I have tomorrow off work. First question: Do you assume that measuring the draw force vs distance when drawing the bow gives essentially the same force as in the opposite direction as the arrow moves down range after release? 

Using your example about draw force as a function of arrow travel it seems like the important question is how much of the 2.3 lbf lost in the first inch of travel (and every inch thereafter) went into accelerating the arrow down range and how much was lost in non-productive work. Ignoring the parasitic loses (air friction, friction in the limb materials, etc.) the only other place for the force to go will be in accelerating the limbs and string and in bending or flexing the arrow. Clearly lighter limbs and string have the advantage here. But if the limb applies too much force immediately after the release, more force will be applied to flexing the arrow because of its inertia. If that is true (and it might not be) it seems like there might be 2 kinds of ways to define smoothness. One would be in the draw direction and one would be in the release (or down range) direction. Smoothness in the release direction might be defined by how much of the limbs energy goes into accelerating the arrow down range and be a function of how well the force curve in the release direction is matched to a given arrow's inertia as it accelerates down range. Does that sound anything like right?


----------



## TheAncientOne (Feb 14, 2007)

John, have you considered using a drawboard and a release to eliminate the "human" factor? That way you don't have to tune the bow for the arrows, you can just graph the results by where the arrows hit. Higher shows increased velocity, left shows relative spine increase, etc. You can also normalize the graph to a 28" draw length and show the differences as draw length increases. Might be approaching Masters Thesis territory though.

TAO


----------



## Gene M (Nov 16, 2010)

My apologies, I seem to be working on new posts and editing old ones while you're posting answers. I need to take a good hard look at what you and Joe T have posted. Thanks for all the information. BTW, I read you're earlier posts on limb mass and it made good sense.


----------



## Borderbows (Apr 4, 2009)

Gene M said:


> I hope you're happy with your self Sid, you've got my feeble little mind worked up about this and I can't get to sleep. Luckily I have tomorrow off work. First question: Do you assume that measuring the draw force vs distance when drawing the bow gives essentially the same force as in the opposite direction as the arrow moves down range after release?
> 
> Using your example about draw force as a function of arrow travel it seems like the important question is how much of the 2.3 lbf lost in the first inch of travel (and every inch thereafter) went into accelerating the arrow down range and how much was lost in non-productive work. Ignoring the parasitic loses (air friction, friction in the limb materials, etc.) the only other place for the force to go will be in accelerating the limbs and string and in bending or flexing the arrow. Clearly lighter limbs and string have the advantage here. But if the limb applies too much force immediately after the release, more force will be applied to flexing the arrow because of its inertia. If that is true (and it might not be) it seems like there might be 2 kinds of ways to define smoothness. One would be in the draw direction and one would be in the release (or down range) direction. Smoothness in the release direction might be defined by how much of the limbs energy goes into accelerating the arrow down range and be a function of how well the force curve in the release direction is matched to a given arrow's inertia as it accelerates down range. Does that sound anything like right?


Maybe's aye, maybe's no... (couldnt resist the joke ballot paper on Facebook the vote on scotish independence)

Well lets confuse things a little further.

The full length of the string is unsupported and allowed to bellow at full length. in a normal geometry bow from release to 20" of power stroke.
this full length unsupported string is a problem if your looking at supporting and reducing parradox.
So when a non-conventional limb catches the string at the 26" mark, the string is supported by 2" of limb at the same 20" mark. this catches some of the sway.
remembering that string grooves are a part of recurve design, and are there to help stabilise the string. or else they wouldnt be there.
so with this in mind, and recurve size being a constant in bows, short bows have a greater % of string supported of thier total length. you end up with funny quotes like this:

Whats your thoughts on arrow paradox on the Ultra?
Well now, this is interesting. We were having some trouble "breaking down the spine" on some shafts to get an extreme weak reaction for the camera. We took a 2016 aluminum shaft and loaded it up all the way with a 300gr point and while it was behaving weak, we weren't getting the extreme "noodling" that I was expecting on the high speed film. Come to think of it none of the shafts we tested out of the BD had the extreme reactions I was expecting. I just thought that my notions of spine were skewed. Do you think your limbs have an effect on paradox?

from this setup:
At my draw length of 29" ( which has grown from 27.5" over the last few months) I am pulling 57# on this bow. My 530gr arrows are chronographing at 193fps with a finger release. About 3-4fps faster with a mechanical release.

full thread here:
http://www.archery-interchange.net/f127/new-me-black-douglas-ultra-22007/index4.html
tested at Lancaster Archery as said in the thread.


----------



## Borderbows (Apr 4, 2009)

we have come to the conclusion that bow forgiveness is like a standard distribution graph (no evedence of this mind) but sensitive bows have a narrow peak of tune. but the tune is easy to find. since its quite obvious where it is. your either on it, or off it.
Bows that are forgiving are hard to tune, since the peak is wide and not so well defined. Spines are harder to select as you appear to be able to get away with it.
We have had several people say that they are having trouble selecting a shaft because of these kinds of observations muddying the waters as to whats weak and whats not.


----------



## limbwalker (Sep 26, 2003)

TheAncientOne said:


> John, have you considered using a drawboard and a release to eliminate the "human" factor? That way you don't have to tune the bow for the arrows, you can just graph the results by where the arrows hit. Higher shows increased velocity, left shows relative spine increase, etc. You can also normalize the graph to a 28" draw length and show the differences as draw length increases. Might be approaching Masters Thesis territory though.
> 
> TAO


With respect, I don't seem to have any problem getting a consistent bare shaft tune - even with my "less than world class" release - so I don't see this as a real issue. Yes, you could just release the same arrow from the limbs set to the same draw weight and graph the impact locations. That would be another way to do this, but I prefer to use real world scenarios because I think it is more meaningful to compare two bows against one another when they are actually tuned. I have a feeling that shooting poorly tuned setups over a chronograph won't tell the whole story as you may get some strange results. And it would be less interesting as someone would always want to point out that "I wouldn't shoot it like that anyway, so why do I care about that result?"

If or when I have time and the money to go back to college, this may well be what I do my masters work on. I think it would be fun.

I'll do some more comparisons this week with my less expensive ILF hunting limbs, just for grins. I figure that I need to get in "x" number of training arrows per week right now anyway, so I may as well be learning something in the process, right? 

John


----------



## limbwalker (Sep 26, 2003)

Incidentally, the next experiment I intend to set up is an investigation of fletching clearance at various brace heights. Not that it hasn't already been done. I'm sure it has, but I can't find it anywhere and I just need to see some things for myself anyway 

But first, I'm going to have to settle on this "P factor" measurement. I feel a formula coming on. My wife teaches physics. Maybe we can make it a class project 

John


----------



## DK Lieu (Apr 6, 2011)

Hello Everyone. Sorry to have been MIA for such a long time. My duties here at the University are sometimes very demanding of my time and effort. This is a very interesting thread, as have been similar preceding threads. It is a pleasure to converse with such a well-qualified scientific and engineering group, as well as high-performance archers. My time is limited, so I will try to make brief contributions as time becomes available. 

The concept of a "P" factor is intriguing, but very complicated. The important factors for P for one person may be different than for another, and different for one application as oppose to another (e.g. indoor vs. outdoor, field vs. fixed distance). Certainly arrow speed has been a traditional measurement of performance. But as Limbwalker has noticed, there is a paradox, since traditionally increasing speed has required a heavier arrow in weight (and spine), which means a slower arrow. But this tradeoff is not necessarily bad, since a heavier arrow would be more resistant to cross winds outdoors. Since Limbwalker's wife is a physics teacher, allow me to propose a simple experiment that may be suitable for a high school or first year college physics class. Have the class measure bow efficiency "E" as the first performance criteria for bow design. This can be done simply by measuring the area under the Draw-Force Curve (DFC), and comparing this to the kinetic energy of the arrow as it leaves the bow. The area under the DFC is the total potential energy (i.e. maximum possible energy) that is available to transfer to the arrow, and 0.5*M*V**2 is the kinetic energy that is contained in the arrow after it is shot. V is the velocity of the arrow, which can be measured on a chronograph, and M is the total mass of the arrow, which can be measured on a grain scale. The ratio of (KE/PE)*100 would be the % efficiency of the bow. I think that you will discover that E improves as the mass of the working portion of the limbs decrease, as professed by BorderBows. The efficiency will also increase as the string gets lighter. Efficiency may even be a function of draw length. Easy experiment to do. More of my thoughts later...


----------



## Borderbows (Apr 4, 2009)

DK Lieu said:


> Hello Everyone. Sorry to have been MIA for such a long time. My duties here at the University are sometimes very demanding of my time and effort. This is a very interesting thread, as have been similar preceding threads. It is a pleasure to converse with such a well-qualified scientific and engineering group, as well as high-performance archers. My time is limited, so I will try to make brief contributions as time becomes available.
> 
> The concept of a "P" factor is intriguing, but very complicated. The important factors for P for one person may be different than for another, and different for one application as oppose to another (e.g. indoor vs. outdoor, field vs. fixed distance). Certainly arrow speed has been a traditional measurement of performance. But as Limbwalker has noticed, there is a paradox, since traditionally increasing speed has required a heavier arrow in weight (and spine), which means a slower arrow. But this tradeoff is not necessarily bad, since a heavier arrow would be more resistant to cross winds outdoors. Since Limbwalker's wife is a physics teacher, allow me to propose a simple experiment that may be suitable for a high school or first year college physics class. Have the class measure bow efficiency "E" as the first performance criteria for bow design. This can be done simply by measuring the area under the Draw-Force Curve (DFC), and comparing this to the kinetic energy of the arrow as it leaves the bow. The area under the DFC is the total potential energy (i.e. maximum possible energy) that is available to transfer to the arrow, and 0.5*M*V**2 is the kinetic energy that is contained in the arrow after it is shot. V is the velocity of the arrow, which can be measured on a chronograph, and M is the total mass of the arrow, which can be measured on a grain scale. The ratio of (KE/PE)*100 would be the % efficiency of the bow. I think that you will discover that E improves as the mass of the working portion of the limbs decrease, as professed by BorderBows. The efficiency will also increase as the string gets lighter. Efficiency may even be a function of draw length. Easy experiment to do. More of my thoughts later...


Also, Lower BH achived by less riser deflex or limb design will also achive higher stored energy. As will limb bolts wound in.
our design prefers a low brace hieght.
LW: point is low brace hieghts loose you clearance. Our point is lower spine arrows increase clearance.
So, this is the start of a massively complex relationship between paradox amplitdue, BH, efficency and overall limb design.
We have spent 10 years getting to this point. and it will take a top shot that is open to parradox, BH and good old archery that came about with the english longbow with no over centre and low bh. Harris Ford was the longbow target shot. wooden arrows english longbows, 5/16 arrows, 6-7" bh, and approx 1/2" over centre with clearance.

remember efficency... is some of the battle. i would rather have 2x the stored energy, same limb mass = low efficency but high speed. than high efficency and low speed., both can be achived.
Efficency is only some of the battle.

but LW is touching on a topic that has puzzled us for ages.


----------



## DK Lieu (Apr 6, 2011)

Here are a few more of my thoughts. There has been quite a bit of discussion in previous threads about how the Hoyt HPX/F7 and the Border HEX 5/6 use a lower that traditional brace height, and also use a weaker spine than what is typically recommended on the Easton charts. There has also been some discussion on the possible affect on arrow clearance from the bow as a result of the lower brace height and weaker spine recommended for these bows.

It has been my opinion that bow clearance and arrow tuning should be considered almost separate issues. Although it is difficult to change one without changing the other, both criteria must be satisfied in order to shoot well. Proper clearance of the bow requires that the arrow bend at the proper frequency. The faster the arrow, the higher this frequency must be. For the purposes of bow clearance, if the arrow speed is the same, it doesn’t matter much where the arrow is released from the string (i.e. at low or high brace height). What matters is the clearance frequency. So why would HPX/F7 and HEX 5/6 require weaker spines? If the arrow goes faster, as claimed by their manufacturers, shouldn’t these bows require stiffer arrows to achieve higher frequencies? Well, here are my thoughts at this time… The requirement for HPX/F7 and HEX 5/6 to use weaker spines are a result of two design changes: the use of a lower brace height and increased torsional stiffness. The lower brace height changes the location where the arrow is release from the string. In my opinion, the best place for the arrow to separate from the string is where the arrow has reached its maximum distortion in its bending cycle. In this configuration, at around 0.75 cycles, the lateral velocity of the nock is zero. In fact, if one backs out the location of this point in the release cycle, this point corresponds amazing well with the traditionally recommended brace height of the string. If a lower brace height is used, a slower frequency (i.e. a weaker spine) is needed to delay the arrow release until the maximum bending (and zero lateral nock velocity) point is reached. So does this affect the ideal clearance frequency? It sure does. The frequency of the arrow is now less than ideal, so the clearance theoretically goes down. But there appears to be good amount of tolerance that is allowed in the clearance frequency, so even though the frequency is not perfect and the clearance is not at its maximum, the arrow can still clear. I suspect that requiring maximum clearance is not so much a problem for expert archers as it is for beginning archers, who tend to have more inconsistent releases and more lateral arrow deflection. Whoops, gotta run to a class. More on the effects of torsional stiff later…


----------



## limbwalker (Sep 26, 2003)

Thanks for that contribution Dennis.

I would really like to find a way to relate all these measurements to a USEFUL ratio for the sake of comparison, and as I've said before, I think that any measure of potential energy is only relevant when compared against a shootable, tuneable, arrow solution.

Of course, there is a tuneable solution for every bow. But the average archer may not be able to use that particular solution, or it may not be a competitive (or the most competitive) tuning solution.

As an example, right now, I find myself right in between two spine sizes. I can go down in weight a lb. or two and comfortably use the 500 spine Nano Pro, or go up in weight a lb. or two and use the 450 spine. That is provided I stick with the same components, which is what I'd prefer to do. There are advantages to either choice, and disadvantages. 

But either way, they are a tuneable solution that I must consider when comparing overall limb performance. If a particular limb dictates the use of one arrow over another, one must consider whether that's really a gain or loss in the end. 

John


----------



## limbwalker (Sep 26, 2003)

Any calculation for "P factor" will have to just accept that the tuning and clearance are acceptable, thereby removing those from the equasion. Otherwise we might be chasing our tails all day with nothing to show for it...


----------



## HikerDave (Jan 1, 2011)

DK Lieu said:


> Here are a few more of my thoughts. There has been quite a bit of discussion in previous threads about how the Hoyt HPX/F7 and the Border HEX 5/6 use a lower that traditional brace height, and also use a weaker spine than what is typically recommended on the Easton charts. There has also been some discussion on the possible affect on arrow clearance from the bow as a result of the lower brace height and weaker spine recommended for these bows.
> 
> It has been my opinion that bow clearance and arrow tuning should be considered almost separate issues. Although it is difficult to change one without changing the other, both criteria must be satisfied in order to shoot well. Proper clearance of the bow requires that the arrow bend at the proper frequency. The faster the arrow, the higher this frequency must be. For the purposes of bow clearance, if the arrow speed is the same, it doesn’t matter much where the arrow is released from the string (i.e. at low or high brace height). What matters is the clearance frequency. So why would HPX/F7 and HEX 5/6 require weaker spines? If the arrow goes faster, as claimed by their manufacturers, shouldn’t these bows require stiffer arrows to achieve higher frequencies? Well, here are my thoughts at this time… The requirement for HPX/F7 and HEX 5/6 to use weaker spines are a result of two design changes: the use of a lower brace height and increased torsional stiffness. The lower brace height changes the location where the arrow is release from the string. In my opinion, the best place for the arrow to separate from the string is where the arrow has reached its maximum distortion in its bending cycle. In this configuration, at around 0.75 cycles, the lateral velocity of the nock is zero. In fact, if one backs out the location of this point in the release cycle, this point corresponds amazing well with the traditionally recommended brace height of the string. If a lower brace height is used, a slower frequency (i.e. a weaker spine) is needed to delay the arrow release until the maximum bending (and zero lateral nock velocity) point is reached. So does this affect the ideal clearance frequency? It sure does. The frequency of the arrow is now less than ideal, so the clearance theoretically goes down. But there appears to be good amount of tolerance that is allowed in the clearance frequency, so even though the frequency is not perfect and the clearance is not at its maximum, the arrow can still clear. I suspect that requiring maximum clearance is not so much a problem for expert archers as it is for beginning archers, who tend to have more inconsistent releases and more lateral arrow deflection. Whoops, gotta run to a class. More on the effects of torsional stiff later…


This is fun. Let me play. (I'm a lowly computer programmer but I do have an engineering degree and experience in motion control.)

That last inch of brace height can't have too much effect on the timing, because the arrow is moving at its highest velocity.

I think that what happens in that first inch of closure after the release is more important. For a given amount of stored energy, a smoother limb will have less force / acceleration immediately after the release, where most of the time is spent. In a drag race, the stacked limb gets the hole shot and the smooth limb never quite catches up, even with higher acceleration in the middle part of the draw force curve. Both exit the bow at the same speed (because of my stipulation for a given amount of stored energy) but one arrow is behind the other the whole way. Of course, to tune with the same timing along comes limbwalker and cranks the preload on the smooth limb until the arrows once again exit at the same time. Now the smoother limb has an unfair energy advantage and ends up leaving the bow at the same instance but with slightly higher speed.


----------



## Borderbows (Apr 4, 2009)

HikerDave said:


> This is fun. Let me play. (I'm a lowly computer programmer but I do have an engineering degree and experience in motion control.)
> 
> That last inch of brace height can't have too much effect on the timing, because the arrow is moving at its highest velocity.
> 
> I think that what happens in that first inch of closure after the release is more important. For a given amount of stored energy, a smoother limb will have less force / acceleration immediately after the release, where most of the time is spent. In a drag race, the stacked limb gets the hole shot and the smooth limb never quite catches up, even with higher acceleration in the middle part of the draw force curve. Both exit the bow at the same speed (because of my stipulation for a given amount of stored energy) but one arrow is behind the other the whole way. Of course, to tune with the same timing along comes limbwalker and cranks the preload on the smooth limb until the arrows once again exit at the same time. Now the smoother limb has an unfair energy advantage and ends up leaving the bow at the same instance but with slightly higher speed.


lets look at the numbers.
two bows both holding 40lbs.
Bow one (stacks)
Inches into the power stroke
0 inch weight =40lbs
1 inch weight =37.7 (2.3lbs drop)
2 inch weight = 35.4 (2.3lbs drop)
3 inch weight = 33.2 (2.2lbs drop)

Smooth bow
0 inch weight =40lbs
1 inch weight =38.2 (1.8lbs drop)
2 inch weight = 36.4 (1.8lbs drop)
3 inch weight = 34.7 (1.7lbs drop)

so after 3 inches of thrust, the smooth bow is pushing with 34.7 pounds of force, while the stacky bow is pushing with 33.2lbs This means that the smooth bow is pushing harder.

is that what you meant?


----------



## Borderbows (Apr 4, 2009)

DK Lieu said:


> Here are a few more of my thoughts. There has been quite a bit of discussion in previous threads about how the Hoyt HPX/F7 and the Border HEX 5/6 use a lower that traditional brace height, and also use a weaker spine than what is typically recommended on the Easton charts. There has also been some discussion on the possible affect on arrow clearance from the bow as a result of the lower brace height and weaker spine recommended for these bows.
> 
> It has been my opinion that bow clearance and arrow tuning should be considered almost separate issues. Although it is difficult to change one without changing the other, both criteria must be satisfied in order to shoot well. Proper clearance of the bow requires that the arrow bend at the proper frequency. The faster the arrow, the higher this frequency must be. For the purposes of bow clearance, if the arrow speed is the same, it doesn’t matter much where the arrow is released from the string (i.e. at low or high brace height). What matters is the clearance frequency. So why would HPX/F7 and HEX 5/6 require weaker spines? If the arrow goes faster, as claimed by their manufacturers, shouldn’t these bows require stiffer arrows to achieve higher frequencies? Well, here are my thoughts at this time… The requirement for HPX/F7 and HEX 5/6 to use weaker spines are a result of two design changes: the use of a lower brace height and increased torsional stiffness. The lower brace height changes the location where the arrow is release from the string. In my opinion, the best place for the arrow to separate from the string is where the arrow has reached its maximum distortion in its bending cycle. In this configuration, at around 0.75 cycles, the lateral velocity of the nock is zero. In fact, if one backs out the location of this point in the release cycle, this point corresponds amazing well with the traditionally recommended brace height of the string. If a lower brace height is used, a slower frequency (i.e. a weaker spine) is needed to delay the arrow release until the maximum bending (and zero lateral nock velocity) point is reached. So does this affect the ideal clearance frequency? It sure does. The frequency of the arrow is now less than ideal, so the clearance theoretically goes down. But there appears to be good amount of tolerance that is allowed in the clearance frequency, so even though the frequency is not perfect and the clearance is not at its maximum, the arrow can still clear. I suspect that requiring maximum clearance is not so much a problem for expert archers as it is for beginning archers, who tend to have more inconsistent releases and more lateral arrow deflection. Whoops, gotta run to a class. More on the effects of torsional stiff later…


on the maths side of things, if the arrow is setup 1/2" over centre as a example. then the column loading on this arrow is out of sorts... The bend on the arrow will become exagerated. this exagerated bend will influence the frequency of the parradox in my mind. so how does this centreshot adjustement come about for perfect launch position.
in my mind the resisntace and angle of resistance from the arrow under acceleration will force the strings path to change?


----------



## Borderbows (Apr 4, 2009)

limbwalker said:


> But either way, they are a tuneable solution that I must consider when comparing overall limb performance. If a particular limb dictates the use of one arrow over another, one must consider whether that's really a gain or loss in the end.
> 
> John





limbwalker said:


> Any calculation for "P factor" will have to just accept that the tuning and clearance are acceptable, thereby removing those from the equasion. Otherwise we might be chasing our tails all day with nothing to show for it...


these two are linked i think.


----------



## HikerDave (Jan 1, 2011)

Borderbows said:


> lets look at the numbers.
> two bows both holding 40lbs.
> Bow one (stacks)
> Inches into the power stroke
> ...


I turned the comparison around to suggest an equivalent stored energy. So the smooth bow starts out at 0 inch with something like 36 pounds to get the same stored energy / arrow velocity.

Once the smooth bow is preloaded to the same poundage I guess you could say that it pushes harder, but only after a short distance. And it's that short initial distance in which much of the time is spent, which is why the faster bow can have an arrow with equivalent timing / spine.


----------



## TheAncientOne (Feb 14, 2007)

limbwalker said:


> With respect, I don't seem to have any problem getting a consistent bare shaft tune - even with my "less than world class" release - so I don't see this as a real issue.


No comment on your technique intended. I'd show you videos of my release but you may not be able to stop laughing afterwards.

TAO


----------



## Vittorio (Jul 17, 2003)

It is now around 8 years I have written the article "Telling limbs from limbs" that was published by Archery Focus magazine and in 2005 become a chapter of THA. A lot of testing with many different limbs carried on by my son brought to conclusions about how to compare limbs in terms of efficiency, that I have verified several times in the years and had no change.
The basic of the comparison was the "perfect" arrow, or the arrow that in any case you would like to use because is perfect for you in terms of weigh and FOC. Then, you simply had to tune at best any sort of (similar) limb you have with that unique arrow you have choose to use, and see what poundage you need to get it in an almost perfect tune. What we found was that :
1) the perfect tuning was giving exit speeds very similar from any kind of limbs
2) the remaining real difference was only the poundage used to propel the arrow at that speed
3) At almost constant kinetic energy in the arrow, the parameter obtained from the comparison was the real efficiency of the limbs.

As written at that time and still valid today, this is just a way to compare efficiency (call it speed, if you want) of the limbs, but his does not give any idea about the other "magic" parameter everyone is looking for: forgiveness. 
Forgiveness is commonly related to torsional stability, and surely is, but that is not the only factor. Vertical stability is also a very critical factor, and limbs curve is influencing drastically both. 

So, at the end, only after some real testing (shooting them quite a lot) you can decide if a pair of limbs is stable enough or not. An not all pairs are made equal, independently from brand, model and name on them. But you can surely compare them in terms of efficiency, and system is still very valid even considering "very new" limbs and riser designs. For instance, very "new" bow design has generated the need to increase more than 3 pound the power in order to get same arrow previously used with an "old" bow to tune. Frankly, it was not an "efficient" solution, IMHO, despite being very new... 

John, doubts on arrows are quite easy to solve: poundage can be a limited variable in +-1#, but FOC should be as high as possible, so with Nano Pro, 120 gr Tungsten is a must. 
That’s all you need to choose your perfect arrow. Surely a 500 will be lighter, faster and with better FOC than a 450, but if you wil have to drop too much in poundage to use it, than the advantage will be gone. 

One more important point: forgiveness in release is very related to poundage on fingers. An archer with 55# on fingers will have a more forgiving release with any kind of limbs than an archer with 45# on fingers. No need to explain why. So be sure to compare apple with apples. Results from limbs used at that sort of poundage are definitely of no reference for those that have to use 10 or more pounds less...


----------



## DK Lieu (Apr 6, 2011)

Vittorio said:


> As written at that time and still valid today, this is just a way to compare efficiency (call it speed, if you want) of the limbs, but his does not give any idea about the other "magic" parameter everyone is looking for: forgiveness.
> Forgiveness is commonly related to torsional stability, and surely is, but that is not the only factor. Vertical stability is also a very critical factor, and limbs curve is influencing drastically both.


Vittorio, I think you have precisely hit upon one of the most important, if not THE most important aspect of equipment design. It's something that I have been thinking about for a long time, and I have even built in my mind a machine to test and quantify that magical property called forgiveness. For bow design, torsional stability of the limbs, as you have noted, is certainly a contributor to forgiveness, as is draw weight. Many other factors related to tuning and clearance are all efforts to increase the forgiveness of the shot, so when the archer makes a error, the arrow still goes to the center.


----------



## limbwalker (Sep 26, 2003)

> 1) the perfect tuning was giving exit speeds very similar from any kind of limbs
> 2) the remaining real difference was only the poundage used to propel the arrow at that speed


Vittorio, great post, as usual. My results are aligned with your findings, except for the Border limbs. The difference in poundage was certainly there, but so too was the difference in speed. 

And (slightly off-topic) the Nano Pro with 120 grain tungsten point is most definitely the "perfect" arrow. 

John


----------



## Borderbows (Apr 4, 2009)

DK Lieu said:


> Vittorio, I think you have precisely hit upon one of the most important, if not THE most important aspect of equipment design. It's something that I have been thinking about for a long time, and I have even built in my mind a machine to test and quantify that magical property called forgiveness. For bow design, torsional stability of the limbs, as you have noted, is certainly a contributor to forgiveness, as is draw weight. Many other factors related to tuning and clearance are all efforts to increase the forgiveness of the shot, so when the archer makes a error, the arrow still goes to the center.


Torsional stability includes supported string lengths. Torsional resistance is just a limb feature.
one is the ability of the limb to resist twists.
the other is how it helps support the nocking point path.
what we think makes a stable bow is any aspect that keeps the NP path constant.
Riser deflex puts the pull forces inside the bow rather than round the pivot point.
Vertical stability in the string helps control the up and down issues, and manifests itself with quick closure and low limb flap.

somehow these issues need addressing to assess the forgivness value in our opinion.


----------



## Borderbows (Apr 4, 2009)

Vittorio said:


> It is now around 8 years I have written the article "Telling limbs from limbs" that was published by Archery Focus magazine and in 2005 become a chapter of THA. A lot of testing with many different limbs carried on by my son brought to conclusions about how to compare limbs in terms of efficiency, that I have verified several times in the years and had no change.
> The basic of the comparison was the "perfect" arrow, or the arrow that in any case you would like to use because is perfect for you in terms of weigh and FOC. Then, you simply had to tune at best any sort of (similar) limb you have with that unique arrow you have choose to use, and see what poundage you need to get it in an almost perfect tune. What we found was that :
> 1) the perfect tuning was giving exit speeds very similar from any kind of limbs
> 2) the remaining real difference was only the poundage used to propel the arrow at that speed
> ...



Vittorio, The same arrow will tune at the same speed, and the same brace height out of the same kind of design. in 2005 all limbs were very very similar.
Check them out. Limb mass, DFC, profile width. All identical. so back to LW's other thread, where has the R&D money gone to.
I think it would be restrictive if we designed a bow to an arrow.
Id much reather match the arrow to the bow.
What your saying is that there is a perfect tyre, so lets restrict race cars to tyres.
If the perfect tyre was the cheapest, then 60mph would be max since remoulds are cheapest.

I firmly do not beleave inthe perfect arrow but do think there is an optimal tune for a set bow. This is the feedback we are looking for since we have developed the skills to control (within reason) vertical and horizontal NP stability, so now to control launch point.
If the three concepts can be controlled then energy is the key. Its about lower BH, more mechanical advantage. etc.
We think recurve technology has only just had its doors opened. and mass production techneques as we have seen dont lend themselves to limb profile changes.
for this reason we think recurves are about to have a new lease of life.
the energy delivery on some limbs are very very different to others. and im not talking 2-3% difference. this is going to effect parradox and there for launch point

Speed is also a benefit, as is momentum.
Momentum will get your arrow to the target in better shape. and speed will open up access angles to the target. so pushing 50lbs and your competitor is hitting the target harder than you with 47lbs seems like a winner.


going up 1.5lbs in bow weight to shoot 7fps faster with the same arrow plus smoother through the clicker is a neat trick dont you think?


----------



## Joe T (Apr 5, 2003)

Sid



> LW: point is low brace hieghts loose you clearance. Our point is lower spine arrows increase clearance.


Dennis



> It has been my opinion that bow clearance and arrow tuning should be considered almost separate issues. Although it is difficult to change one without changing the other, both criteria must be satisfied in order to shoot well.




Those two comments alone are worth the price of admission!

One could also almost historically consider brace height as a measure of bow performance. e.g. Longbow ~ 5", Early glass limbs ~ 7", current top end carbon limbs ~ 9".
As bows have improved in performance the BH has got bigger, for the reason mentioned by Limbwalker clearance. The faster the same arrow is going the more time (hence distance) it needs to flex out of the way of the riser.
However if the arrow has a high amount of curvature in it as it leaves the string it doesn't need the full 0.25 cycles to clear. It can get away with less, hence the BH starts to reduce. 


As regards forgiveness you are dealing with two items:

Arrow forgiveness - basically aerodynamic flight characteristics
Bow forgiveness - lateral and vertical stability and energy storage/efficiency

You need both but I would regard the arrow as the more important in terms of the wanted result (highest score, furthest distance.. whatever)


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> Sid
> 
> 
> 
> ...


now for what i think is the crux of the topic.

Hi performance bows are simply all the same because of the lack of innovation. Earl hoyt being the only name. Name me another innovator in Target bow geometry?
Yet bows have got faster, and the same brace still applies (what was the original GM geom & bh, vs RX). this is a Vertical string stability remit, along with noise levels and not much else.
Now, the Torsional stability needed in each of the designs longbow, through to modern target bows are VERY VERY different.
hence the limb width changes. this change in remit, changes the speed of the bow. and the resulting sway allowed in the limb
As torsional stability changes, so does parradox. and if parradox changes then so does BH.
so if you can multiply the torsional stability of the design 4 fold, then surely the speed of the bow is only half the equation. as the parradox has changed too?


----------



## limbwalker (Sep 26, 2003)

> Name me another innovator in Target bow geometry?


That's so easy Sid, I'll give you two:

http://www.w4wc.org/bill_stewart/home.htm

http://www.bowmaker.net/index2.htm

Okay, perhaps not "target" archery manufacturers specifically, but certainly innovative bowyers who pushed the design limits. 

Now, back to how to calculate "P" here...

Going to give this some more thought. Need to relate draw weight to KE of a properly tuned arrow, I think, with the arrow having some particular standards for point weight, FOC, etc. So as not to get too far outside the practical.

John


----------



## limbwalker (Sep 26, 2003)

And a third, just for fun  :

http://www.skyarchery.com/sky_home_target.htm


----------



## Borderbows (Apr 4, 2009)

limbwalker said:


> And a third, just for fun  :
> 
> http://www.skyarchery.com/sky_home_target.htm


Authenic Earl Hoyt Limbs and riser ive just read on the same presses.


----------



## Borderbows (Apr 4, 2009)

limbwalker said:


> That's so easy Sid, I'll give you two:
> 
> http://www.w4wc.org/bill_stewart/home.htm
> 
> ...


Do you see these on target lineups?


----------



## Borderbows (Apr 4, 2009)

limbwalker said:


> Now, back to how to calculate "P" here...
> 
> Going to give this some more thought. Need to relate draw weight to KE of a properly tuned arrow, I think, with the arrow having some particular standards for point weight, FOC, etc. So as not to get too far outside the practical.
> 
> John


John, Calculating "P" is a tough call, very good call, but tough none the less. You have a very valid point, and i dont know how to create a base value for it.
How do you select the ultimate arrow? For example heavy mass arrows suit longbows better, GPP vs FPS, and its possible to tune light arrows or heavy ones to any bow.

I can see hundereds of variables which makes my head gag at making a rule.

you do have a fantastic point, which is particular to your shooting i think. everyone has this, but they might come to a different conclusion, due to draw length, and release (depth of hook/slowness of release etc) dictating the final spine/point weight

i think the average outcome of this would benefit the faster bow everytime though.
if the bow has the power and construction benefits, in many respects you cant hide raw power. 
(is your point that sometimes when looking at limbs the difference is small enough that the spine choice dictates the performance difference?)

could this be why 4fps is deemed a "significant improvement" in bow design. since <4fps = a spine choice deciding factor?


----------



## Joe T (Apr 5, 2003)

limbwalker said:


> Going to give this some more thought. Need to relate draw weight to KE of a properly tuned arrow, I think, with the arrow having some particular standards for point weight, FOC, etc. So as not to get too far outside the practical.
> 
> John


If you consider tuning as grouping characteristics and believe grouping relates to arrow alignment and rotation than there is no connection between arrow KE and tuning. (excluding clearance issues of course). Arrow vibration also relates to such a small relative amount of energy that there is no connection between arrow KE and arrow vibration either.

Relationship between KE and draw weight is the standard geometric one. What this discussion has been about recently is how limb design can change this geometrical relationship e.g. torsional stiffness/limb mass changing the arrow flexing amplitude and frequency.


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> If you consider tuning as grouping characteristics and believe grouping relates to arrow alignment and rotation than there is no connection between arrow KE and tuning. (excluding clearance issues of course). Arrow vibration also relates to such a small relative amount of energy that there is no connection between arrow KE and arrow vibration either.
> 
> Relationship between KE and draw weight is the standard geometric one. What this discussion has been about recently is how limb design can change this geometrical relationship e.g. torsional stiffness/limb mass changing the arrow flexing amplitude and frequency.


Jake K is saying its the reduced deflex in the riser is changing the flexing aplitude.

It also corresponds with the launch of thier tri-axial fiber orientation.
The biased carbon and UD carbon also gives a 3 way fiber orientation.
Cross weave carbon can be run in a bi-directional alignment, giving less TS gains, since one direction is in alignment with the UD. This is what appears to be in the F4 limbs as far as we can see. So the HPX in all its merit ie including the F7 limbs, could proove to be Torsionally stiffer. but i have personal doubts as to the parradox change being down to the less deflex. more the F7's Tri-axial carbon.
if ive read the blurb right.


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> If you consider tuning as grouping characteristics and believe grouping relates to arrow alignment and rotation than there is no connection between arrow KE and tuning. (excluding clearance issues of course). Arrow vibration also relates to such a small relative amount of energy that there is no connection between arrow KE and arrow vibration either.
> 
> Relationship between KE and draw weight is the standard geometric one. What this discussion has been about recently is how limb design can change this geometrical relationship e.g. torsional stiffness/limb mass changing the arrow flexing amplitude and frequency.



in Sailing, a full sail is a benfit. a sail with a fluttering edge is less efficent. so a arrow fluttereing will effect speed. Thes Correction of vector is done through drag
the more the arrow ossilates the more the fletchins will present side drag as the ossilations will be dependent on tune and spine selection?


----------



## Borderbows (Apr 4, 2009)

John, Can i take your first post and start another thead/debate/thought...


----------



## Vittorio (Jul 17, 2003)

I personally don't see any real innovation in limbs shape and riser geometry design in the last may be 20 years. Materials have evoilved a lot, not shapes. 
For instance, by design all Hoyt limbs had to be shot with lower BH since the FX (but many were using successfully high brace with them), and the most reflex riser design was the Bernardini MITO, back in the 1994, while the high deflex design is probably the Fiiberbow 5.99 that is already 6 years old (anyone noted Matteo Fissore getting third place in Indoor World cup finals with it and G3 Hoyt limbs few days ago in LV?).
Advanced curve was introduced in modern designs by Border with ML10 limbs in around 1999 (but the Turkish cavallery was having similar designs some hundred years ago).
Hoyrt is claiming with F7 to be back to FX design, and results are really comparable to them... 
Lets make it easy: when an arrow is flying, it will never know what sort of bow have shot it, but foir sure it wil have a kinetic energy "inside". better it is , better is the bow. 
The only one time in the last 20 years I have really seen much faster arrow from same bow/poundage has been when McKinney II have been used. Arrow weight dominates speed, in a world were the dynamic spine must be a constant. 
All other things are theories, as surely you can get a very ligh arrow with very light point going very fast, but no one will score any reasonable result with it. 

No, definitely none of the existing bows will perfectly tune a larger spine (usually lighter) arrow at same poundage. If it happens, it only means that the arrow comes out form the bow with lowre KE, that means the bow is reall not so efficient. 

P.s.
The search is still going on for the perfect arrow, not for the perfect bow, as the arrow has to go 70 mt far in cross wind and still group, while the bow limbs will only have to travel for less than 30". Koreans (and many others) have found it to be an X10 450 of around >28" lenght with 120 gr tungsten point. I'm still trusting the 430 ACE with 120 grains one piece steel point in > 29" lenght, But a Nano pro 450 for >29" lenght with a 130 gr tungsten point may be an alternative ...


----------



## Borderbows (Apr 4, 2009)

Vittorio said:


> Advanced curve was introduced in modern designs by Border with ML10 limbs in around 1999 (but the Turkish cavallery was having similar designs some hundred years ago).
> 
> ...


if 5 is the shape of a hoyt limb and 1 is a reflex/deflex longbow. then aliken the XP10 to be a 5, the ML2 to be a 5.5, innos to be like a 5.5, hex4 to be a 6.5, hex5 to be an 7.5, and hex6 to be 8 if thats any kind of comparison.
if you are under the impression that the ML2 was a advanced recurve compaired to Earl hoyts design, the hex series would make you fall off your chair.


----------



## limbwalker (Sep 26, 2003)

Sid, go for it. I think we've gotten a little off track from my initial concept of the "P" factor...



> when an arrow is flying, it will never know what sort of bow have shot it, but foir sure it wil have a kinetic energy "inside". better it is , better is the bow.


Vittorio,

The reason I started this thread was exactly because an arrow DOES know what kind of bow it has been shot out of. An arrow can be shot from two different bows, with the same resulting speed and KE, but if only one of them is tuneable, then only one is useable for our purposes. The other bow would require a different arrow, and provide a different result.

Not sure if this is making any sense, but we cannot simply compare the same arrow shot from two different bows at the same holding weight and declare a clear winner when possibly only one of them is a tuneable combination.

And this is the dilemma I am faced with at the moment. I can shoot the same arrow from one bow drawing 45# and another drawing 46.5# giving me significantly different speeds. It would be a simple decision if the gain in draw weight were really of no consequence, but every increase in draw weight has a consequence on the endurance of the body. Otherwise, we'd all be shooting 60# bows.



John


----------



## DK Lieu (Apr 6, 2011)

The improved torsional resistance of the HEX 5/6 and the F7 may also contribute to why these limbs seem to tune better with weaker arrow spines. When an arrow is released, its bending deformation is determined not only by the force pushing it forward (from the string) but also by the amount of initial lateral deflection at the nock, as produced when the string goes around the fingers. If you take your bow and move the string laterally, e.g. side-to-side, you will notice that the limbs will deform not only back and forth (as intended), but also twist. There is a minute amount of lateral deflection as well, but this is usually too small to be of significance. By increasing the torsional rigidity of the limbs, the amount of lateral deflection can be decreased. The lateral deflection cannot be eliminated altogether, because the limbs still have to move back and forth for the bow to operate. But increasing the torsional resistance should reduce the lateral deflection, which will reduce the bending deformation of the arrow and make it behave stiffer. I spent some time going around my club, simply twisting by hand limbs of various makes. The difference in torsional rigidity on HEX 6, when compared to more conventional designs was quite evident.


----------



## Borderbows (Apr 4, 2009)

DK Lieu said:


> The improved torsional resistance of the HEX 5/6 and the F7 may also contribute to why these limbs seem to tune better with weaker arrow spines. When an arrow is released, its bending deformation is determined not only by the force pushing it forward (from the string) but also by the amount of initial lateral deflection at the nock, as produced when the string goes around the fingers. If you take your bow and move the string laterally, e.g. side-to-side, you will notice that the limbs will deform not only back and forth (as intended), but also twist. There is a minute amount of lateral deflection as well, but this is usually too small to be of significance. By increasing the torsional rigidity of the limbs, the amount of lateral deflection can be decreased. The lateral deflection cannot be eliminated altogether, because the limbs still have to move back and forth for the bow to operate. But increasing the torsional resistance should reduce the lateral deflection, which will reduce the bending deformation of the arrow and make it behave stiffer. I spent some time going around my club, simply twisting by hand limbs of various makes. The difference in torsional rigidity on HEX 6, when compared to more conventional designs was quite evident.


if you measure the lenght of lever aswell, you will notice the ts is huge per inch of lever over normal limbs.
carbon is a wonderfull material. its just hard to work with.


----------



## Joe T (Apr 5, 2003)

Borderbows said:


> in Sailing, a full sail is a benfit. a sail with a fluttering edge is less efficent. so a arrow fluttereing will effect speed. Thes Correction of vector is done through drag
> the more the arrow ossilates the more the fletchins will present side drag as the ossilations will be dependent on tune and spine selection?


What I meant here Sid was that the arrow vibrational energy (~ 0.03NM) was tiny compared with the arrow KE so irrelevant. For sure in flight the arrow vibration (as in amplitude) is a significant contributor to drag, but this amplitude is determined by the need for the arrow to wiggle around the riser. Only flight variable is how fast the arrow vibration amplitude damps out.

Torsional stiffness has a Jekyll and Hyde effect on the arrow. Restricting lateral movement reduces amplitude (stiffer) while at the same time reducing frequency (weaker). In theory the former effect allows you to pump more energy into the arrow while having the same bend, the latter effect allows for a longer or stronger power stroke putting more KE into the arrow. So higher torsional stiffness allows you get higher speed of out a tuned bow. Still baffled by how you can reduce brace height though


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> What I meant here Sid was that the arrow vibrational energy (~ 0.03NM) was tiny compared with the arrow KE so irrelevant. For sure in flight the arrow vibration (as in amplitude) is a significant contributor to drag, but this amplitude is determined by the need for the arrow to wiggle around the riser. Only flight variable is how fast the arrow vibration amplitude damps out.
> 
> Torsional stiffness has a Jekyll and Hyde effect on the arrow. Restricting lateral movement reduces amplitude (stiffer) while at the same time reducing frequency (weaker). In theory the former effect allows you to pump more energy into the arrow while having the same bend, the latter effect allows for a longer or stronger power stroke putting more KE into the arrow. So higher torsional stiffness allows you get higher speed of out a tuned bow. Still baffled by how you can reduce brace height though


dont get me wrong im no harmonics expert.

Though, i would have thought that the angle the arrow resists forward acceleration would also dictate the amplitude. just like the pole of a pole volter takes the forawrd movement and pushes it upwards.
This and the acceleration would dictate the end position of a "perfect launch cycle". so im baffled as to how all these vairiables are all part and parcel of BH being the same for a set speed. I would have thought that the bows speed, and its ability to hold a line would dictate the Bh, and this is showing us that not all bows shoot the same spine at the same speed but also have different poundages to achive different speeds using different spines?
Not being a guru in maths, but knowing there are more vairables than bow weight, arrow frequency, and output speed makes me wonder how a BH can be derrived. 
my mind says that its also part of the bows ability to retain a striaght line and limb mass is also a factor in the equation... and the style of power stroke. massaging the scale, and style of parradox you get?


----------



## Joe T (Apr 5, 2003)

To summarise bracing height is a derived value, a consequence not a creator. What determines it are three factors.

1. You want the arrow to leave the bow with the COM going in the direction the arrow is pointing. This means the nock has to separate from the string when it's on/close to the bow center line.
2. You want a slick (torque free) nock-string separation. Put an arrow on the string at an angle to the bow plane and puch forward - TWANG. This is what you want to avoid by aligning the string travel with the alignment and travel path of the nock at separation.

Items 1) and 2) relate to the power stroke characteristics of the bow. High torsional stiffness allows you a longer power stroke (more KE) and the ability (I think) to put more bend energy into the arrow while still being tuned.

3. You want enough distance from the nock leaving the string for the arrow to flex sideways around the riser. The conventional relationship (which agrees fairly well with experiment) is that BH = V/4*F where V is the arrow speed and F is arrow vibration frequency. This is based on the arrow going through 0.25 cycles from leaving the string to passing the riser. For the same speed in order to reduce brace height you need a higher frequency (i.e. a stiffer arrow) - but a stiffer arrow means a heavier slower arrow, with same construction, so you go nowhere. Only other option is to increase arrow vibrational energy hence increasing amplitude so instead BH = X*V/4*F where X (<1) relates to free-free vibration amplitude. Higher torsional stiffness may allow you to increase the free-free amplitude (energy) while keeping a tuneable arrow. Just guessing but only option I can think of.


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> 1. You want the arrow to leave the bow with the COM going in the direction the arrow is pointing. This means the nock has to separate from the string when it's on/close to the bow center line.


The on or close to centre is the part i dont agree with.

How can an english longbow archer shoot a straight arrow, straight in the direction they are aiming, and still have clearance the bow is 1/2 thick from a centre line with no window at all?

even more comon these days are Flatbow, or American longbows. The rules state the bow cannot be cut past centre. Yet can still be tuned to bare shaft, and still provide clearance.

this close to or on Centre is a theory that in my head doesnt apply to reality. therefor the forumals (again in my head) dont work in all clases.

There are plenty of bows where the window is cut to centre, putting the point/arrow centre 5/32" out of plane with the bows centre. again these bows can be bare shaft tested to tune.


----------



## Joe T (Apr 5, 2003)

Borderbows said:


> The on or close to centre is the part i dont agree with.
> 
> How can an english longbow archer shoot a straight arrow, straight in the direction they are aiming, and still have clearance the bow is 1/2 thick from a centre line with no window at all?
> 
> ...











COM is on line between nodes. Direction of travel is (hopefully via tuning) along the red line. All you need is enough flex to jump the fence. With longbows you have a higher fence to jump so more bend required (weaker arrow).


----------



## Borderbows (Apr 4, 2009)

Joe T said:


> View attachment 1287361
> 
> 
> COM is on line between nodes. Direction of travel is (hopefully via tuning) along the red line. All you need is enough flex to jump the fence. With longbows you have a higher fence to jump so more bend required (weaker arrow).


So you can have nodal alignment along the bow plane with weaker arrows and more over centre by way of button, and more parradox supplied by flexy limbs.

or can you have nodal alignment with waker arrows more over centre and paradox supplied by the more flex in the arrow.

all this related to bow speed dictating BH? or as John posted, More speed provided with the same over centre, and same brace?
or can speed and tune be two separate features, and there for BH can be different? based on the bendability of the arrow and bow?


----------



## Borderbows (Apr 4, 2009)

i would propose that BH can be tuned to give nodal alingment through the use of centreshot, and arrow spine. as per all bows including Flatbows, ELB's etc.


----------



## Vittorio (Jul 17, 2003)

Sorry to say, but I don't see any relationship between torsional (static) stability of limbs and energy transmission to the arrow. 
Torsional stability and vertical stability are related to the possibility to "forgive" a bad release, only. Nothing more The power stroke to the arrow is related to limbs elasticity and curve shape only, plus full travel lenght of the string from hold to zero (shorter the distance to the riser at 0, i.e shorter is the BH, longer is the power stroke).
Then, not all manufacturers are considering torsional stability related to the curve zone of the limbs, only... 
Torsional stability should be considered at full draw, only, that is were the release happens. And a limb very rigid on the tip area may be very week torsionally at ful draw in the middle area, so becoming more sensitive to bad releases. For instance, FX limbs were torsionally very bad at static level in tip area, but quite good at ful draw, and it seems to me that new F7 (and F4 and F3 before too) are in same situation. 
There are no more secrets about what happens during and after release,since the Casio F1 has been made available to all of us, but of course if you cointinue to consider all items in the system a part of the tuning process at the same time, you may end up not understanding what Hi speed movies are telling you. 

John, if you can EXACTLY tune EXACTLY the same arrow with limbs different 1.5# each other, I still really doubt that the output measured speed in hte two condition can be really different. 
But considering the poundage factor, only, several archers will prefer the high poundage to the low poundage solution, as despite the lack of efficiency, the set up will be by definition more forgiving. For instance, my son is considering 50# as ythe poundage he wants, plus or minus 1/2#, and if limbs are too fast for his arrow (yes, as usual, arrow is a constant) he will slow down them by addding limbs savers and using an heavier string with longer serving and so on, inordert to get them tuning at the poundage he needs. 
Well, of course 55# are better than 50# in terms of forgiveness, but then the durability of the human parts managing the system have to be taken into account. At 20 years in Atlanta Michele was shooting 53# and Magnus Petterson, same age, 55#. But that kind of level can't be handled for too many years without severe risk of damages. And 16 years have passed already... Younger archers can do it with limited risk, if they are phisically very strong and in good shape. Elder archers have to be very careful while staying close to the 50# level, as a minimum mistake can sort aout very bad injuries. 
John, go for the heavier poundage if you can manage it SAFELY only!


----------



## gig'em 99 (Feb 1, 2008)

Borderbows said:


> i would propose that BH can be tuned to give nodal alingment through the use of centreshot, and arrow spine. as per all bows including Flatbows, ELB's etc.


I'm surprised that it took so long for center shot come up. The use of Border limbs is the only reason that I ever even considered bucking the standard CS offsets that are simply accepted as a necessity due to "paradox.". But findings are somewhat different than what has been eluded to here. In my experience, I'm able to shoot my recurve with no CS offset (point to left of string). I use the exact arrow I had when I was shooting my n-apecs limbs, same draw weight too. Lower than recommended BH. It lead me to believe that I have a far greater range of tunable arrows. I have a high speed camera too. No clearance issues, and no problems shooting my BS at 70m. No left/right anomalies between distances either. Limb performance can absolutely be very different, when various relationships to the kit are tweaked or adjusted.


----------



## cc46 (Jan 22, 2005)

Excellent thread guys!!

I will read this again in a few days.....thanks


----------



## limbwalker (Sep 26, 2003)

> John, if you can EXACTLY tune EXACTLY the same arrow with limbs different 1.5# each other, I still really doubt that the output measured speed in hte two condition can be really different.


Vittorio, I wouldn't have believed it either, but that's where it led me. At least 7 fps. difference, if you're willing to draw the additional 1.5#. 

What perplexes me is the question of whether it would be better to shoot a stiffer, heavier, or lower FOC arrow at a lower speed with that extra 1.5# on another limb?

Basically, what it amounts to is that at the same draw weight on the fingers, I can either shoot a 370 grain arrow at 13% FOC 211 fps., or a 390 grain arrow at 12% FOC at 202 fps.



> Younger archers can do it with limited risk, if they are phisically very strong and in good shape. Elder archers have to be very careful while staying close to the 50# level, as a minimum mistake can sort aout very bad injuries.
> John, go for the heavier poundage if you can manage it SAFELY only!


What exactly are you trying to say? ha, ha...  
I've now had one significant archery-related injury that caused me to miss the 2008 Olympic trials, and I have no desire to repeat that. These days, 47# at 32.5" sounds really good to me 

I would agree that - at least for me - anything below 46# begins to present a problem for achieving a clean release.

Brian, great post. I'm impressed. And I'm heading in that direction, only just now discovering some of the things you've most likely already figured out with a similar combination of equipment.

John


----------



## limbwalker (Sep 26, 2003)

Vittorio, I have another arrow/FOC question, but I'll start another thread for that one.


----------



## Hank D Thoreau (Dec 9, 2008)

limbwalker said:


> That's so easy Sid, I'll give you two:
> 
> http://www.w4wc.org/bill_stewart/home.htm
> 
> ...


I would like to see a draw force curve (and smoothness curve) on the Bill Stewart limbs to how he substantiates his cam-less cam action claim. They are more funky than the Greenhorn Ellipse.


----------



## Borderbows (Apr 4, 2009)

gig'em 99 said:


> I'm surprised that it took so long for center shot come up. The use of Border limbs is the only reason that I ever even considered bucking the standard CS offsets that are simply accepted as a necessity due to "paradox.". But findings are somewhat different than what has been eluded to here. In my experience, I'm able to shoot my recurve with no CS offset (point to left of string). I use the exact arrow I had when I was shooting my n-apecs limbs, same draw weight too. Lower than recommended BH. It lead me to believe that I have a far greater range of tunable arrows. I have a high speed camera too. No clearance issues, and no problems shooting my BS at 70m. No left/right anomalies between distances either. Limb performance can absolutely be very different, when various relationships to the kit are tweaked or adjusted.



one advanatage in a true centreshot is the ability to change brace heights and the only impact would be NP.

For example string your bow up with a 10" brace hight and watch your NP change position.
but do this with conventional CS settings and measure point over centre. then reduce BH to say 6" and remeasure centreshot and NP heights.


t


----------



## Borderbows (Apr 4, 2009)

Hank D Thoreau said:


> I would like to see a draw force curve (and smoothness curve) on the Bill Stewart limbs to how he substantiates his cam-less cam action claim. They are more funky than the Greenhorn Ellipse.



We have a DFC of a green horn limb and we are of the impression that the least mass is the straightest line. if energy is equal.
if the cam is the same size and profile, and nominal limb angles are the same, the DFC should be the same.

If that makes any sense to you... 
You have seen a few DFC's so hope that makes sence
Black swans Wavy longbow limb here:
http://www.tradtalk.com/forums/archive/index.php/t-21355.html


----------



## John_K (Oct 30, 2011)

Can I just say, this thread reminds me of some of the better discussions on the old Sagi board - conflicting opinions, but civilised debate inspired by genuine interest in learning. 

Regarding the effects of torsional and vertical stability: I'm no physicist or engineer by any means, but might it not be the case that reducing the amount a string deflects in any plane results in more energy going into the arrow? It may not be a great deal, but string movement must represent an expenditure of energy, and if it can be made to move less, then that energy has to go somewhere.

Just a thought. Happy to be corrected


----------



## Borderbows (Apr 4, 2009)

Brian, your post was nearly 2 years ago when you notice some of these observations.


CJSdrftFLAT said:


> from the above link
> 
> Border Hex5-H Review
> « on: March 08, 2010, 01:59:12 PM »
> ...


----------



## gig'em 99 (Feb 1, 2008)

Sid,

Wow, surprised you found that, but yes. It didn't take me long to get to my conclusions with a little testing. I had tons of time then. Not so much these days. Once I transitioned to carbon arrows, under the same true CS conditions, I was able to tune two x10 spines. Eventually settling on 500s vs one spine weaker. For me, I wanted the heavier arrow for outdoor use.

The speed difference with carbons vs my conventional limbs was very similar to John's. 7-8 fps faster, but that was at the exact same weight on the fingers.

All this being said, the PSE handles have a lot of offset in the window. I never tested the limbs with a different handle, but feel like I may not have been able to get clearance with my large vane indoor arrows, and possibly even blazer style vanes on carbons without that PSE. I was getting clear but, spin wings I felt were a must. This last paragraph is all theory on my part though. I didn't test every thing.


----------



## Borderbows (Apr 4, 2009)

gig'em 99 said:


> Sid,
> 
> Wow, surprised you found that, but yes. It didn't take me long to get to my conclusions with a little testing. I had tons of time then. Not so much these days. Once I transitioned to carbon arrows, under the same true CS conditions, I was able to tune two x10 spines. Eventually settling on 500s vs one spine weaker. For me, I wanted the heavier arrow for outdoor use.
> 
> ...


That is fantastic info. Not many people give us this kind of feedback.

We agree... on our trad side we went from 3/16 past centre to 5/16 for a wooden risers to help cover this concept.
We think it might/could/possibly be a area of further investigation, but that said, parradox can skip a longbow. and surely there is no clearance allowed on a bow like that. So we dont know the answer here either. but we know that it might be worth looking into, but we think we need an open mind.


----------



## Sighting In (Feb 5, 2009)

Sorry if this has been brought up already (dont' have time to read all of this now), but...

I John's origional post, he suggested that a heaver arrow would be needed to keep the stiffer limbs at the same weight as the smooth limbs, in order to keep in tune. This could mean adding mass to the front, slowing it down, or using a stiffer shaft, which are also heavier in general. Either way, the arrow weighs more, making it slower.

Have you considered just cutting off a half inch in front of the shaft? I know we don't like to cut them when we don't have to, but this would achieve both a stiffer shaft, a few grains off, making it lighter, and a slightly higher FOC. So now we have a stiff limb with a stiffer, and lighter, shaft, with good FOC, that should, in theory at least, go even faster. 

I'm not a recurve shooter, but there is more than a half inch of play in the clicker to make that slightly shorter arrow work, right?


----------



## Borderbows (Apr 4, 2009)

Sighting In said:


> Sorry if this has been brought up already (dont' have time to read all of this now), but...
> 
> I John's origional post, he suggested that a heaver arrow would be needed to keep the stiffer limbs at the same weight as the smooth limbs, in order to keep in tune. This could mean adding mass to the front, slowing it down, or using a stiffer shaft, which are also heavier in general. Either way, the arrow weighs more, making it slower.
> 
> ...


Johns point if ive got him correctly, is not about tuning an arrow to the bow, but using the arrow as a guide to bow performance. so if you take the same shaft etc, you can see that some bows not only shoot faster, but also can shoot faster with the same arrow. kinda like linking bow efficency with a need to retain parradox.


----------



## limbwalker (Sep 26, 2003)

Exactly. 

As for the specific tune, I have lots of variables I could play with to achieve this, but that's not really the point of this particular question. You are absolutely correct in your assessment however.

John.


----------



## Borderbows (Apr 4, 2009)

limbwalker said:


> Exactly.
> 
> As for the specific tune, I have lots of variables I could play with to achieve this, but that's not really the point of this particular question. You are absolutely correct in your assessment however.
> 
> John.


i might have some fun for you, but can i ask, what was the choosen BH, and what limb bolt positions did you have to achieve these speeds/spine observations?

(i'll start with making a general observation now, before we head any further)
Limb bolts wound in are faster for the same weight than wound out.
so 40lbs at 28" achived when the bolts are fully in, is faster than [email protected]" when the limbs are wound out.

lower brace hieghts are faster in general than the upper end of the range.


----------



## limbwalker (Sep 26, 2003)

Sid, the limb bolts were middle range, except for the heaviest arrow (450) where they were turned fully in.

John


----------



## Joe T (Apr 5, 2003)

> John, if you can EXACTLY tune EXACTLY the same arrow with limbs different 1.5# each other, I still really doubt that the output measured speed in hte two condition can be really different.





limbwalker said:


> Vittorio, I wouldn't have believed it either, but that's where it led me. At least 7 fps. difference, if you're willing to draw the additional 1.5#.


Vittorio's limb assessments came to the conclusion that with the same arrow and equivalent limbs for a tuned system the arrow speed was always pretty much the same (hence the draw weight to produce this speed became the performance parameter) - why was this? Answer is that the overall flex rate of the arrow is the same with different limbs. For the correct arrow/bow match setup the arrow speed is determined by the flex rate of the arrow geometrically matching the bow geometry.

However if the arrow flex rate significantly varies between limbs then this correlation breaks down and this constant speed effect disappears. So what can change the flex rate of an arrow; a lot of things but only only factors inherent to the limb are relevant (so forget e.g center shot). The obvious candidate is torsional stability which by restricting the lateral movement of the nock changes both the flex amplitude and the flex frequency. An alternative possible (and less likely) candidate is variation between limbs of the nock string/force over the power stroke .


----------



## limbwalker (Sep 26, 2003)

http://www.archerytalk.com/vb/showthread.php?t=1697275

Very interesting stuff, as usual Joe. 

Out of curiosity, which of the three arrows described in my "help me choose a competition arrow" thread would you prefer?


----------



## Joe T (Apr 5, 2003)

In my view the only person who can decide which is the best arrow is the archer themselves, which is why three different archers can easily come up with three different answers. Not even sure which, if any, is the most important component - I would guess maybe the fletchings are number 1 with shaft/point secondary.

I agree to some extent with Vittorio's idea of the ideal arrow. Problem is this ideal arrow is going to vary with the environment (distance/wind) and only some archers will be physically compatible with this ideal arrow (not me for sure  ).


----------



## limbwalker (Sep 26, 2003)

Roger that. 

Many times I've gone to the range with the idea that one arrow or one bow will be my favorite, only to leave after surprising results downrange...

If you shoot enough, pretty soon you will discover what combination you can score with, and which one you can't...

John


----------

