Help on Energy in Arrows

LaCroix · Post by **LaCroix** » 2006-01-31 06:25am

I am in a discussion about arrow design, and I need a quick confirmation or utter destruction of my math...

Statement1:
A flying arrow is a carrying dyn. Energy. That energy is stared in all parts of the arrow, correlating to their share of mass.

If the feathers weight 1%, the head 20%, and the shaft 79% of the total weight, then 79% of the total energy are stored in the shaft.

Statement2:
Fact Info: An arrow is bent by the acceleration when released. This is intensified by the great muss of the head, causing the arrow to bend even more until the heads "resting mass"? is also accelerated. It swings in flight until arodynamic drag (Barrowmans equation on stability) and the dampening of the shaft itself dampens the oszillation to zero (or close to that).

Thus, a heavier head is decreasing energy transfer eficience, since a bigger part of energy is wasted in bending the shaft, and some energy is wased when that "spring" releases it again. Also, the shaft is still bent and swinging while in flight, causing a part of energy to be worked away in the process.

Conclusion:
A lighter head on a similar weight arrow would cause the whole arrow to store more energy in the process of being accelerated by the bow string..

Post by **Darth Wong** » 2006-01-31 09:29am

If the spring deformation is in the elastic range, one would expect that the difference is functionally negligible.

LaCroix · Post by **LaCroix** » 2006-01-31 12:42pm

Since arrows can be reused a hundreds of times, I expect the spring deformation to be not overly stressing. Normally not over 2cm on a 28" arrow.

Its just a nitpick thingy, the effect would be quite neglectable, it's just a "am I theoretically right"-question.

Post by **Darth Wong** » 2006-01-31 12:45pm

If the shaft is only deformed in the elastic range, the only energy "wasted" in deforming the shaft would be heat dissipation, which is negligible in the elastic range anyway. You only get real energy loss to deformation when the deformation is permanent. Otherwise it's pretty close to a reversible thermodynamic process.

LaCroix · Post by **LaCroix** » 2006-01-31 01:15pm

Ok, thank you!

Cykeisme · Post by **Cykeisme** » 2006-01-31 08:20pm

Eh, silly question.. if the elastic limit is surpassed and deformation is permanent, where has the energy gone? Into breaking inter-molecular bonds...?

Post by **Surlethe** » 2006-01-31 08:26pm

Cykeisme wrote:Eh, silly question.. if the elastic limit is surpassed and deformation is permanent, where has the energy gone? Into breaking inter-molecular bonds...?

Heat, I do believe. This is why steel comes out of a rolling press hot, IIRC.

tharkûn · Post by **tharkûn** » 2006-01-31 10:10pm

Eh, silly question.. if the elastic limit is surpassed and deformation is permanent, where has the energy gone? Into breaking inter-molecular bonds...?

Yes. You when you bend a lump of iron you are moving around atoms which are metallicly bonded. When you irreversably stretch polymers you are changing their packing arrangment. These bonds may be hydrogen bonding, Van der Waals, ionic, steric interlock, etc. rather than the traditional ones you first heard about. Also it is quite common to break one (or more) bond and make another bond (or more) that has different enthalpy. For istance when you crack a network solid, you expend energy cracking the bonds between the two new surfaces, some of the energy is regained by the atoms undergoing surface rearrangement.

drachefly · Post by **drachefly** » 2006-02-01 12:52pm

Overall, I'd expect the difference in dissipation over the course of flight to be much greater, and that would favor a heavier arrow with its lower velocity.

Also, in case you're firing on well-armored targets (which you're probably not), then you may be in the semi-elastic regime. In that case (and more so the closer you get to the fully elastic regime) a heavier arrow transfers energy to the target more efficiently because it carries more momentum.

The Dude · Post by **The Dude** » 2006-02-01 02:18pm

Cykeisme wrote:Eh, silly question.. if the elastic limit is surpassed and deformation is permanent, where has the energy gone? Into breaking inter-molecular bonds...?

Almost all of the energy ends up as heat. In metals, the remainder is mostly stored as dislocations* (or, more properly, the stress fields associated with dislocations). Bonds are not really "broken" in metals; although in fracture there is an energy requirement for generating two (or more) new surfaces. In general, the energy required to break bonds is very, very tiny compared to the energy stored in dislocations, which is in turn much smaller than the heat generated in plastic deformation.

In ceramics, there is no plastic deformation, so it goes straight from elastic to fracture.

Polymers are more complicated, but since they at most partially crystalline, they store less energy; more ends up as heat.

*dislocations are discontinuities in a crystal structure

The Dude · Post by **The Dude** » 2006-02-01 02:22pm

LaCroix wrote:Thus, a heavier head is decreasing energy transfer eficience, since a bigger part of energy is wasted in bending the shaft, and some energy is wased when that "spring" releases it again. Also, the shaft is still bent and swinging while in flight, causing a part of energy to be worked away in the process.

The energy lost to heat in bending will be insignificant compared to the energy lost to drag due to the less aerodynamic profile of a bent arrow.

hawkwind · Post by **hawkwind** » 2006-02-01 02:51pm

Which straightens after few times flexing oscilating with smaller amplitude each time.
No arrow flies bent, unles made not straight and that is bad arrow.

This problematic has been treated by people like Klopsteg who first came up with concepts of spine (relation of stiffnes of the shaft to its dynamic properties)

To setting up the experiment shoot an arrow and take a serie of short exposition photos from up.
Then you can analyze whats happening.

Word from bowmaker.

The Dude · Post by **The Dude** » 2006-02-01 03:24pm

hawkwind wrote:Which straightens after few times flexing oscilating with smaller amplitude each time.
No arrow flies bent, unles made not straight and that is bad arrow.

I understand that it's oscillating with declining amplitude; nonetheless, for the duration of these cycles the arrow is indeed flying bent.

Post by **Darth Wong** » 2006-02-01 05:09pm

The aerodynamic penalty associated with the arrow not being perfectly straight during the initial flight phase is probably negligible. Unless the thing is flopping around like a noodle, a slight short-term column-buckling effect just isn't going to make a big difference to its aerodynamic profile.

As for the eventual destination of the energy lost in non-elastic deformation, go look at a steel rolling mill sometime. After a few compression passes it's red-hot. Try passing a single strip of aluminum through a rolling mill just once and you'll feel how warm it is, even with minimal compression.

hawkwind · Post by **hawkwind** » 2006-02-01 11:08pm

Actually the aerodynamic drag together with other factors is one of things which damp the oscillation, the other is hysteresis.

Arrow dynamics is interesting topic to do practically, e.g. to make lots of arrows (different) ,measure the deflection, shoot them into distance, measure it, compare the data.
Take a look on yahoo flightshooting group if you are interested.

LaCroix · Post by **LaCroix** » 2006-02-02 04:49am

drachefly wrote:Overall, I'd expect the difference in dissipation over the course of flight to be much greater, and that would favor a heavier arrow with its lower velocity.

Also, in case you're firing on well-armored targets (which you're probably not), then you may be in the semi-elastic regime. In that case (and more so the closer you get to the fully elastic regime) a heavier arrow transfers energy to the target more efficiently because it carries more momentum.

Of course it is, I questioned about energy transfer from bow to arrow, eg. total stored energy.

Also, I created a case where total weight of arrow was the same, but one having a heavier shaft, the other one a heavy head. The energy transfer to the target would be the same.

But, since the one arrow has the heavy head, it would bend more than the one with its weight equal distributed. (Of course, it would hit more left of the traget because of being stiffer)

But the idea is, would a stiff arrow of the same weigth than a more bending arrow store more energy in the process of being shot and oszillating to straightness.

A stiff arrow bends less, thus more energy would be used for propelling it, instead of oszillating it.

hawkwind · Post by **hawkwind** » 2006-02-02 08:17am

Likelly, but overstiff arrow whacks the bow and does other mischievous things, the reason modern bows utilise dampening arrowrest.

Very good target archers use bit stiffer arow (say 5#) stiffer and correlate or cant the bow. (In english archery).

What I find interesting is that primitive archery often uses very long arrows which stick in front of the bow. This helps for aiming, BUT I think that main reason is to rest arrow against the bow at the place of front node of oscilation, which causes clean relase, because node doesnt oscilate....

drachefly · Post by **drachefly** » 2006-02-02 02:11pm

So, an arrow which is exactly twice as long as the distance from the arrow-rest to the extent of the drawn bow would be their choice?

hawkwind · Post by **hawkwind** » 2006-02-02 10:00pm

It must not necessary be that long, but rather longer than with modern equipment. You are assuming that the diameter of arrow is all the way constant, but thats not the case when you are making it from a young tree shot.

Do some search for aboriginal archery, tak a look for andaman bows (which are interesting in cultural crossrefference sense)

http://198.66.52.119/images/b_sprfsh.JPG

http://198.66.52.119/images/image_misc_04.JPG

Thats not that they understand (abo people) such concepts, but they empirically arrived to a setup where stiffness of arrow doesnt count as variable, hence producing smallest margin of error in equipment.

(Assuming that used arrows varry in stiffnes)

hawkwind · Post by **hawkwind** » 2006-02-02 10:10pm

Now it strikes me - twice as long is necessary for an arrow without an arrowhead. Nonetheless shaft in praxis will be fitted..

LaCroix · Post by **LaCroix** » 2006-02-03 05:31am

Of course the stiffer arrow would not allow a clean release, as I said, it was a theoretical question.

Btw, I am a primitive archer...

I make and use selfbows ("bending sticks"

, no modern materials, no arrow rests, they are shot over the hand) and I can tell you that most "primitive" archers dont use overly long arrows. A normal arrow for a selfbow is about 29" for an 28" draw. I also make my own arrows out of split wood, so I can tell you that there is no need for longer arrows, exept wanting them.

The longer arrows used by "aboriginals" where due to try/error for getting the correct spine - a modification of diameter to get correct spine (bending value) is hard work, modifying the lenght is easy.

Also for having more arrow mass, thus increasing penetration.
A light arrow as for FITA is only wanted to ease targeting at bigger ranges, but not for impact. I once compared a Fita bow with my bow, and the penetration at 20m (hunting distance) was about 2 times bigger, although the fita-arrow had 50% more speed. My arrow had nearly triple weight.
Momentum kills.

As bonus, a longer arrow can be more easyly repaired when broken, you can use "foreshafts" easyer to change arroheads when needed, etc.
A very complex question.

hawkwind · Post by **hawkwind** » 2006-02-03 05:47am

I m professional bowmaker and I make wooden equipment only. Assume I know what I m talking about.

Read again what I wrote about overlenght arrows and relation of such setup to spine variable.

Most todays "primitive" archers spines their arrows or at least understand the concept. Nothing abo here.
They dont need long arrows as they understand the spine.

Im not interested in FITA, its after all organisation of French origin. In english target archery the praxis is to set up for slightly stiffer arrows.

For heavy hunting arrows - nothing new here, empirically proven and scientifically treated by dr. Ashby from Australian bowhunter assoc.

Mind you - I m shooting 1300 grain english war shafts using 100# + bow. Guess I know what heavy arrow does better than most bowhunters.

If you are interested in these topics go to Paleoplanet and look for related threads about bow and arrow setup, particulary for Rod Parsons advices, he is one of people with best understanding of related problematic and brilliant logic.

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Help on Energy in Arrows

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