Arrow Weight & Paradox?

[Bruce Smithhammer]

#3743

This question came up recently elsewhere, and I was intrigued by some of the responses, so I thought I’d post the question here – with all else being equal in an arrow’s construction, does weight affect recovery from paradox? In other words, would a heavier, or lighter, arrow recover from paradox more quickly? Or does weight have no affect on paradox recovery at all?

(note – this isn’t really a thread about FOC, just a question of weight in general).

[grumpy]

#22912

Wondering the same, thinking of making heavier arrows, but if I make them thicker I change the spine, different wood same problem…. Since I’m shooting a 24″ arrow, its god awful stiff anyway.

[Bruce Smithhammer]

#22966

Here’s my thinking (from very much a layman’s perspective):

Additional mass would absorb oscillations more quickly, therefore, the heavier arrow would recover from paradox sooner than a lighter arrow (all else being equal).

I have no idea if that has any basis in fact, but it’s my working theory to stoke the conversation…

[Doc Nock]

#22976

What medium is the shaft, Bruce?

From my reading and correspondence with Doc Ed, high modulus graphite oscillates like ONCE and quit…(Gold Tip had that in their early days on HS video on their website, even had a VHS video of it..) where Aluminum shafts oscillated the whole way down range… then danged near folded up when they hit the target, giving rise to the notion that a carbon arrow RETAINS more of it’s stored energy by NOT wasting it oscillating down range the whole way…

I think your logic-modle makes some intuitive sense, but it doesn’t seem to follow the concept of materials that come off finger release, wrapping around a riser, will oscillate some… and varied material will do so far more than others…

What affect weight has, diameter has, aside from the stress of wrapping around the riser window (dependent also on the amount of center shot on a given bow)… I think you’ve stepped in it here, brother…

Also depends, not only on the TYPE of ahaft material, amount of center shot, and consistency of finger release off a string, but where the “weight” of the arrow lies.

This would be one for Doc Ed given all the field research he’s done…

[Bruce Smithhammer]

#22988

Doc – you wasted no time in hitting on one of my immediate follow-up thoughts as I pondered this question more, which is the varying characteristics of different shaft materials. I’m bet that, for example, wood shafts and carbon shafts are going to exhibit fairly different behaviors in this exercise.

But for simplicity’s sake – let’s keep apples to apples and just say that aside from a difference in weight, we are talking about the exact same shaft material, same shelf cut, shaft length, etc.

With all else being exactly the same, are a 450gr. arrow and a 600gr. arrow going to sustain the same amount of paradox, for the same amount of flight time?

Or, from a pure physics POV, does an object with additional mass absorb oscillations more quickly than the otherwise exact same object with lighter mass?

I realize I might be simplifying this to the point of making an answer impossible, but I’m also trying to keep from entering too many other variables into it and making it an overly complex question.

Just something fun to ponder as I sip my first pint of the evening and prepare for my Better Half to kick my @$$ in cribbage yet again…

[Patrick]

#23019

8) I love thought experiments. I’m thinking that weight is either a non-factor or has very little to do with it. Otherwise, a similar spined wood shaft would oscillate much less than a carbon shaft.

[Ralph]

#23040

With the same static spine, I’m thinking wood, I wonder if the dynamic spine is different between a lighter and heavier shaft with the same amount of force applied? That might effect oscillation???

Patrick, wood oscillate less than carbon? I thought you had to put more weight up front on carbon to make it wiggle enough.??

[Doc Nock]

#23066

You boys like to push the cranial envelope, dontcha?!

If alum and wood have static spine and carbon dynamic spine… and I cannot remember the Gold Tip video if Wood was included in the slalom effect that the arrow took… but being a “live” fiber, I’d be surprised if it behaved like carbon, or carbon would never have caught on as it did.

Carbon is purported to have ‘Dynamic’ spine. I’ve read where engineer types described the difference…all that I can retain or wrap my brain around is that dynamic spine responds to implied force very differently.

The retained energy, with carbon, and how it blew thru stuff (increased penetration,} was “blamed” on the early polturded skinny shafts, but the GT, being only .001 thinner than a 2018 alum shaft… disproved that.

It wasn’t the thinness, but the retained energy due to not continuing in paradox like “traditional” shafting (whether that included live fiber wood AND alum, but I clearly can see the high speed video in slow motion of the alum)…

Since dynamic spine of a carbon shaft retains energy due to limited paradox (oscillations), and you want to know if the heavier shaft will stop oscillating faster than a lighter shaft of the same (carbon?) material???

Since it only oscillates (paradoxes) ONE time coming off the bow, (vis a vis the GT videos) then, how can you improve on ONCE??? I’ve shot thru obstacles with my carbons at varied ranges and read as much of Dr. Ed’s stuff as my brain will absorb, and if properly tuned, the shaft comes out of paradox (carbon) instantly… one flip and back on track… retaines it energy.

I almost would doubt that with the fast recovery of carbon (if tuned) that even HIGH EFOC would make a difference in have fast it recovers.

Retained energy is one reason I became a carbon fan…(and economics of having to buy a pot full of raw shafts, spine and weight them all to get a few good ones left me chilled!)

So lets forget the Carbon. Will a wood or alum shaft of heavier weight stop oscillating faster?

HOw do you make an alum or a wood arrow heavier, but by adding point or tail weight?

I’m having a tough time isolating the intervening variables to see where this is going?

As for cribbage…must be a Western States thing. When I first moved to MT, met an o lder gent school teacher who let me stay with he and his wife since his son moved to the West Coast, and he insisted in me learning to play cribbage…

I wish I could remember any of the rules or game itself! I enjoyed it… wiled away many a winter’s night by the fireplace playing that game… did ok as I remember, but then memory isn’t what it was!

[Ralph]

#23088

Ash instead of cedar for wood. Make heavier wood shaft of same static spine right?AL don’t remember for sure but I think you could get similar spine with different weigh shafting.

Doc whilst your deep thinking, http://www.ponderabout.com/archives/3225/zenos-paradox-of-the-arrow.aspx.

It’s amazing what search engines can do to get one off track using the same words.

[Doc Nock]

#23099

I’ll check out your link another day…

If I had a nickle for every bit of bogus data I got off the internet about things I knew were wrong, versus the stuff I don’t know, and have to either assume or reject, I’d be a rich man!

Alas, spine is spine… 60# spine Ash that is the same (measured) static spine as Cedar, as is 60# spine of Aluminum is still 60# spine…

Paradox is related to how hard the arrow gets kicked int he kiester by the string/limb combo, and then how much it has to wrap around the riser…and the roll of finger release of the string, cause that sideways oscillations… or paradox.

I think the only variable is shaft material and it’s recovery from paradox… is that dreaded ancient wood called CARBON…

But I’ve been wrong before. This should be sent to Doc and see what he says… :0

[Bruce Smithhammer]

#23105

Hmmm….this thread is already exceeding my expectations. 😉

Thanks for all the input folks. The idea that shaft material, and not weight, is the only variable, makes me think of new questions, but I’ll hold off on those for now. I’m looking forward to Graf weighing in on this one…

[David Coulter]

#23151

All things being equal includes length, right? dwc

[Stephen Graf]

#23625

Sometimes it helps to understand the behavior of systems by breaking those systems into their simplest parts, and looking at boundary conditions.

An arrow is a system which includes a spring and a mass. We can look at one boundary value of this system where the spring constant stays the same, but the mass goes to zero.

In this case, the spring would be stretched (as the bow is shot) and when the force was removed (arrow leaves the string) it would return to it’s rest state and stop (as there is no mass, there is no inertia to store the energy released as the spring relaxes)

Thus it can be seen (all else being equal) that the lighter the arrow, the faster it will recover from paradox.

Other factors that affect vibration damping in arrows would be internal molecular resistance to bending, and the air resistance on the feathers/shaft from moving through the air. There may be others. The internal molecular friction in the aluminum arrow is much much less than in wood or graphite (that’s why they make springs out of metal and not wood) and that’s why aluminum arrows tend to oscillate all the way to the target. Nothing to do with weight really.

Taken together, the mass and spring contained in the arrow along with the forces affecting the arrow form a system. The system can be under damped, over damped, or critically damped. Critically damped is what you want. This means that the arrow goes through the least number of oscillations and that each oscillation is much less than the last in magnitude.

Carbon has the highest molecular friction, lowest density, and highest modulus of elasticity. Thus it oscillates less than the other materials.

[Stephen Graf]

#23651

R2 wrote: …Doc whilst your deep thinking, http://www.ponderabout.com/archives/3225/zenos-paradox-of-the-arrow.aspx.

I like it! And that helps us understand when we find out that time is not continuous, but granular. And the smallest increment of time is 10^-33 second.

Reminds me of the other space-time conundrum: If a man walks across a room to leave by the door, he must first traverse half the room. And then he must again traverse half the remaining distance to the door, and so on and so forth… By this observation and reasoning, the man can never get to the door, because he must always traverse half the distance first…

Now I’m wondering what my chances are of making it to the bathroom to get rid of all this coffee 😳

[Ralph]

#23715

Maybe we need to tie a rope on the bucket and pull it towards us as we traverse towards it (the bucket) and surely we and the bucket will meet in the middle. Two halves make a whole right. 😕

Then it’s just a matter of timing. 🙄

[Patrick]

#23787

Steve Graf wrote: Thus it can be seen (all else being equal) that the lighter the arrow, the faster it will recover from paradox.

Right on Steve! This is the answer in a nut shell, and it drives me crazy to think that I didn’t think of it from this angle, even though it makes compete and simple sense. 😳

[Bruce Smithhammer]

#23813

Excellent. Thanks, all.

[Jason Wesbrock]

#24371

Very interesting discussion. I just wanted to add something about the theory that carbon arrows only flex once and then they are “out of paradox.” Yes, I am familiar with the old marketing videos done by a few manufacturers in an attempt to prove their products are best. But if you watch enough coverage of Olympic recurve archery, you’ll see a lot of slow motion scenes from behind the archer toward the target. Those arrows, both solid carbon and carbon/aluminum types, oscillate a long, long way down range — far past what most would consider normal hunting distance.

[Fallguy]

#25254

As far as I know your typical Olympic shooter is using the lightest arrow weight possible to flatten the trajectory. So are we looking at at arrow that is on the low end of the spine chart for a given draw weight?

[Jason Wesbrock]

#25261

Actually, their bows can handle a lot lighter than what they shoot. Is memory serves, they’re usually around 7 gpp. Regardless, a lighter static spine requires a lighter point, which puts you right back to the proper dynamic spine.

[Forresterwoods]

#25286

Proof is in the pudding. I hear guys with heavy bows having to go way high in spine using light soft woods like cedar… (85# spine in 23/64 for a 70# bow)…whereas I’ve used 48# 9/32 hardwood shafts on my 58# RD longbow with great results. Seems to be a combination of weight AND diameter. Smaller diameter is closer to center shot!

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