Another question...physics of arrows n bows

[ChuckC]

It is winter, I am bored.  

Can someone who KNOWS please explain to me this whole aspect of powerstroke ( no, not the engine).

In a lay persons mind (mine) there May, or may not be something to this in the pie in the sky working of things, however,

the reality is ( again, in my mind), the limbs will recover in the speed that they recover.

This will send the projectile out / away at a particular speed.  No matter how long the powerstroke is, a certain speed is developed, and that is the end result that matters.  A power stroke of one mile that develops a particular speed will not send an arrow any faster than a power stroke of 20 " if the same speed is developed.

Once the arrow is off the string there is no more added energy.  It is all it can be.

The way it appears to me, the length of time the arrow is on the string is not near as important as the recovery rate of the limbs, and that would be influenced by the geometry of the limbs and the physical make up of the limb materials.

Some limbs simply recover faster than others.  

Additionally, some limb designs might have changing limb recovery rates, depending upon their geometry, with working / nonworking recurves, single and double reflexes / deflexes, short limbs, long limbs etc etc.  The degree of angle of the limb compared to the riser or center / launch point might even impact the rate of recovery.

An analogy could be in rifles.  Different powders yield different recovery rates (speed).

So, how does this all work... I mean.. really
ChuckC

[BenBow]

Chuck rifles with longer barrels shoot faster than rifles with short barrels when they shoot the same ammunition, bows are similar. A longer power stroke allows the arrow to receive more of the speed the limbs produce. If you take two bows of the same draw weight and one is has belly mount limbs and one has back mount limbs the back mount limbed bow will be faster due to the longer power stroke. I make both and use the same limb with both. There is a significant difference in speed and energy between the two.

[moebow]

Chuck,

You are asking a VERY complicated question.  One that can really only be answered with advanced physics and mathematical descriptions.  The study of ballistics.

Simply, speed is a RESULT of a force applied to a mass for a given time period (the power stroke).  With trad bows, the force applied to the mass (arrow) decreases from the moment of release to arrow separation from the string.  How much it decreases is quite complicated and is based on many factors from bow design to draw length (power stroke again).  The force application of a compound bow is different, there, the force actually increases over the power stroke and is the main reason C bows shoot faster than trad bows.

A mass attains a given speed based on how long a force is applied to the mass.  Let's use your gun example but we have to compare apples to apples.  It is the length of the barrel for a GIVEN load that determines the speed of the bullet.  Take a  cartridge and shoot it out of a 10 inch barrel and then shoot the same cartridge out of a 20" barrel.  Which one will give the highest speed(velocity)?  In this example, barrel length is the power stroke and the longer barrel keeps the force applied to the bullet for a longer period of time -- hence a higher velocity.

Changing powders can change the velocity of the bullet but that is because the force applied to the bullet is different (changes differently over time).  AND!! Presumes the same barrel length (again, power stroke).

So it is not really the recovery rate of the limbs themselves, it is the force those limbs apply to the string and then the arrow.

Anyway, a great question but one that has no easy answer. Physics classes in "mechanics" address this but can take several semesters of study to get to the level of understanding.  We are addressing mass, inertia, energy, force, acceleration, velocity, etc., and the mathematical relations of all of them.  They all are connected.

This is also why there is so much misunderstanding out there about common concepts of kinetic energy, potential energy, momentum  and all that "stuff."

So, dig out the physics and calculus books and you won't be "bored" anymore.  :>)

Arne

[NothingHappenedToday]

The way I understand it, no matter what your limb geometry, when you release your arrow/string it gains speed until it reaches it's maximum, then loses speed after that point. Ideally, you want the arrow to leave the string at the maximum point of this speed/energy bell curve. If the arrow leaves too soon, the energy is wasted. If it leaves too late, the arrow loses speed/energy because it is still carrying the string after it reached peak speed.

Ooh, Arne, my brain is hurting now!!!

Chuck, you are bored!!!

Bisch

[moebow]

LOL Bisch!!

NothingHappenedToday,

You KIND of have it BUT...  As long as there is a positive FORCE (pushing the arrow) there will be a velocity increase.  Has nothing to do with string speed, just force on the arrow.  IF, the nock is too tight on the string, then there will be a decrease in velocity when the string stops and impedes the separation of the arrow from the string.  But that is a negative force that we try to avoid.

What I'm trying to say is that "speed" is a result of force whether on the string or arrow  and as long as that force (of ANY magnitude) is positive (pushing the arrow) then we have acceleration.  To be as correct as possible, force on  a mass produces acceleration.  Then at any given point (this is where calculus comes in) a velocity (speed) can be determined.

Arne

[NothingHappenedToday]

Moebow -- thanks for the clarification. makes perfect sense

[McDave]

Originally posted by ChuckC:


No matter how long the powerstroke is, a certain speed is developed, and that is the end result that matters.  A power stroke of one mile that develops a particular speed will not send an arrow any faster than a power stroke of 20 " if the same speed is developed.

  This is correct.  If you could figure out a way to achieve a certain initial velocity with only a 10" draw, the downrange trajectory would be the same as a bow with a 30" draw that achieved the same initial velocity, given the same arrow.

The way it appears to me, the length of time the arrow is on the string is not near as important as the recovery rate of the limbs, and that would be influenced by the geometry of the limbs and the physical make up of the limb materials.

Some limbs simply recover faster than others.  

  This is also mostly correct, but there is no way, given current limb materials, to achieve a fast enough recovery rate to where a bow drawn to 10" would have the same initial velocity as a bow drawn to 30", assuming the bow weight is the same for both bows at their respective draw lengths.  In order to achieve the same initial velocity, the bow with a 10" draw length would have to have a substantially higher draw weight at 10" than the 30" bow did at 30". Unless, I suppose, the 30" bow's limbs were made from some really doggy material with a recovery rate much less than any bow currently being made  

[ChuckC]

I see what is being said, but always being the devils advocate, a rifle barrel 30 feet long will not increase the speed over one, say 24" long ... will it ?  

(Unless the amount of powder used in creating the force is not fully burned and the gas is still expanding after all that volume has opened up, which is why the short barrel loses, because that all expanding gas is dumped out the barrel end before it can make the projectile reach maximum speed).  

My point is, is there a never ending, all encompassing length matters ( OMG) thing going on here ?  

Is that force ALWAYS pushing with the same... force, from release to detachment of arrow (or exit of bullet from barrel) ?

Doesn't design.. which in a bow creates that force, throw a big kicker into the play ?  As you pointed out the positive force generated by the bow pushes the arrow, but is that force ALWAYS the same from release to finish ?  Why are some bows faster than others, no matter what the power stroke is ?

ChuckC

[ChuckC]

Yes.... bored !    

ChuckC

[Bladepeek]

Chuck C, I would suggest a good game of Pick up Sticks, or maybe Euchre.

As you pointed out, maximum velocity is achieved when barrel length is matched to optimum powder charge for that cartridge. Don't hold my feet to the fire over the exact number, but I believe a .22LR reaches maximum velocity in around 16" of bbl length. Beyond that, the force of friction actually reduces velocity. Change the cartridge to .22Mag and that length changes quite a bit.

The force is not constant with either gun powder or bow limb. There will always be some form of curve if you graph  the pressure applied to the rear of the bullet or arrow. The bow's forward acceleration ends when it reaches the static braced height. The only way to increase the total force applied to the arrow for a given draw weight and limb design is to increase the rearward travel before release.

Me, I kind of like the idea of a good Euchre game when I don't want to get out in nasty weather.

[Orion]

Chuck, if you could somehow eliminate the friction, then yes, a 30 foot barrel would yield a faster bullet than a 24-inchbarrel, all other things equal.

Arne's explanation is right on.  Look at it this way, if you plot a force/draw curve, the area encompassed under the curve (the energy or force to be imparted to the arrow) will be larger with a reduced brace height because the draw becomes longer.

[Mike Mecredy]

Chuck, You're pretty much spot on with the limb recovery speed.  The faster the limbs straighten out after release the better performance. And concerning power stroke.  I have found that a bow that can be shot with a lower brace ht does have a bit of an edge on performance.

Another other thing, is that the longer the limbs the less distance the tips have to travel on release, so (to a point) longer limbs and lower  brace ht. makes it even better.  Lower brace ht, giving the arrow a bit more distance on the string before it's launched.

But...

If the limbs are too long for the size of the riser, it makes the working limb more massive and can slow things down. (when it comes to riser length:total bow length:working limbs length, there is a "sweet spot" I've found)
 

Ideally the limbs need to be as light as possible to achieve a certain draw weight to perform the best, especially at the tips.  That's why the Adcock ACS bow performed so well, the way he did things enable him to make limbs about half as thick as other bows.

The mass of the limbs as I stated, is evident when comparing self bows to laminated bows,  take one of each, 50# each 62" long and the laminated bow having less mass to the limbs will have the edge, if you get into things like carbon and foam limbs and it gets even more evident.

[**DONOTDELETE**]

"The force application of a compound bow is different, there, the force actually increases over the power stroke and is the main reason C bows shoot faster than trad bows."

Hey Arnie, That was a pretty good explanation of the power strokes effect on arrow speed in layman's terms...    

But regarding your example of the compound bow increasing in exceleration as the string moves forward, vs Traditional bows that don't.... i think you'll find that with some traditional limb designs, that the exceleration does increase in the last few inches that arrow stays on the string..... If you look closely at the pounds per inch energy storage on a DFC chart, you can see that some designs with higher preload store a lot of the limbs total energy storage in the first few inches....... These type bows have much more tension on the string at brace height which stops the forward limb motion cleaner, and transfers more of the stored energy into the shaft......

For example we could take two 55# bows. one of them is a long bow only storing 12 #'s in the first 4" of the draw cycle with a nice even 3 pounds per inch draw right from the start..... This bow is very easy to string and has very little preload.... Unfortunately you get a lot more hand shock from this design because the string isn't tight enough at brace to stop the limb travel.TA lot of stored energy is wasted and stays in the bows limbs.

The second bow is a RC design with high preload. It gains 16# in the first 4 inches of the draw cycle. These bows need a stringer to get strung up and a lot more pressure is on those limbs at brace. (Pre-load).....  Now take these 2 bows and shoot the same weight arrow from both bows at different draw lengths..... You are going to see an amazing difference on how the power stroke effects the velocity....btw.... the high preload bow transfers MUCH more energy to the arrow shaft

here's a chart you guys can look at to help understand what i'm talking about.

 

[Sixby]

If you understand the statement I am going to make the answer is so simple that I can actually answer it in one sentence.
 
At an equal power stroke distance and an equal poundage the quicker the limbs return to brace the faster the bow.


God bless, Steve

[moebow]

It is too easy to mix things up.  Yes, a gun will have a maximum "efficiency" (highest possible velocity for that particular load) IFFF the powder charge is completely burned AND the pressure of the gasses produced allow the projectile to leave the barrel while there is still a small amount of pressure behind it. That point would be where the volume of gas produced by the burning powder is just slightly greater than the volume of the barrel.  

But that is NOT the point.

The velocity of a projectile is produced simply by the amount of force applied over time. The longer that force PUSHES, the faster the item will go. To be sure, that force must be greater than any resistance force (friction, hysteresis,etc.) but as long as the "push force" is greater than the "resist force" the item will accelerate.

A short barrel will not allow the force to act for as long a time as a longer barrel will.  Not saying a 30' barrel, let's be realistic.  Force for a time is what produces velocity.  So for a given load, you will get less velocity from a 10" barrel than you will from a 20" barrel.  That is NOT necessarily the max velocity available for the load, just relative velocities in comparison to each other and using longer or shorter sections of the force curve.

So for the bow, we've all seen force draw curves for bows,  the farther you pull the string back, the LONGER it has to push the arrow.  Yes, brace height will help here too but there we are usually talking about an inch where for full draw it could be as much as 5 or 6 inches depending on your comparison points.  Longer distance to travel allows the force to act for a longer period of time hence higher velocity.

Can't explain it any better.  As long a FORCE is pushing an item and as long as that force is greater than ANY resistance force, the item will accelerate. So, if it PUSHES for a longer time you will get a higher speed at the point it quits pushing.

Arne

[moebow]

Kirkll,

I didn't say acceleration, I said force.  In general, the FORCE produced by a trad bow will decrease as the string returns to brace height.  In a C bow the force increases to a max after release to it's max.  Obviously the force curves are very different between bows.  But it's still force applied over time/distance that produces speed.

Arne

[katman]

AHH winter time discussions, a long way to spring.

As has been stated the way I understand it the longer the power stroke on the same bow ie. shorter brace height, gives more time to accelerate the arrow. According to my chrony, not much velocity gained. At my hunting distances not enough to matter.

[Mr. fingers]

I took up trad because of the simplicity and you guys are ruining it!!!    

[Mike Mecredy]

The shooting/tuning part is simple. But when it comes to design there's actually a lot to it, so much that could make two bows that look similar, shoot as different as night and day.