Observation about Brace Height

Something I have been wondering recently

There is a long discussion about crossbow efficiency on myArmory.com

http://www.myarmoury.com/talk/viewtopic.php?t=19926&postdays=0&postorder=asc&start=280

So Ralph Payne-Galway supposedly shot an antique cranequin spanned crossbow 490 yards back in 1903 or whenever it was.

Do any modern replicas approach this kind of range?

This got me thinking -


_{http://www.historyandcivilization.com/Battle_of_Crecy.jpg}
In period illustrations crossbows are generally shown braced very high. About halfway of bolt-track.
Modern "traditional" crossbows are typically braced lower.


I did some testing with a hack-saw blade

Different brace height, same power-stroke
Notice difference in limb movement to power stroke ratio




String of high braced bow moves about four times the distance of bow tip.
Whereas low braced bow draws only twice the tip movement for same absolute string movement.
High braced bow also has shorter, thus lighter string.

Assuming same recovery rate of bow limbs, a high braced can safely cast a bolt twice as fast as bow with more
common longbow style low braceheight.

Now, weather recently has been too bad for much field testing,
but anyway an I have an old x-bow with high braced stickbow prod wich I loded with
"unhealthtly" light bolt. The cast for a few unmeasured test shots appeared very compound bow-like. Also efficiency seemed reasonable.

Test bow is pulling 57kg/135mm (125#/5,5")
Test bolt was 4grams. 7x5mm wide point ( thin nail bent to horseshoe shape around 5mm dowel )made 1cm deep hole into pine board. Suggesting maybe 15-20J kinetic energy( = ~50% efficiency).
Shooting from 20m distance did not show any observable curve in trajectory, nor much observable flight time.


So my bit unscientific preliminary testing was promising.
It seems it might be possible to build plain old-school stick bows that can rival with modern compounds.

Just something for our public to try out themselves .

If I remember it correctly(I used to own his book)Sir Ralph said he shot a crossbow bolt across the Menai strait,over 800yds.For the non-brits in the forum,the Menai strait is the channel between the coast of north Wales,and the island of Anglesey,fabled home of the ancient Druids,until they seriously P.O'd the Romans,who invaded and wiped them out...........

Seemingly contradictory, from the crossbow wiki:

Bowstring/brace height: Bowstring should be as low as possible to reduce wasted energy (Baker 2000d: 48). With a crossbow the margins are smaller than with the handbow, so making a string that's just right takes a little experimenting, especially if the bowstring stretches. So, make the bowstring as long as possible without making it slack.




http://crossbow.wikia.com/wiki/Bow_design

your testing is very interesting Nerd,if you have access to a shooting chronograph,that would confirm your experiment I think,as the chrono would give you arrow speed.It seems perfectly logical to me,if you think of a bow as a spring,the amount of compression of the spring dictates the amount of power available on release.Your experiment shows that brace height and draw control the amount of compression of the spring,more compression has to result in more power on release,no?

I think it depends on the stacking of the bow. In a bow with less of a tension wall, draw length would be more important than brace height. If the bow was more efficient drawn further or increased in draw weight it would be important to get the bow drawn to that range.

with a saw blade it seems like you'd have little stacking effect.

In the first pic if you used the same power stroke (lock position) you would have twice as much limb movement which is twice the stored power. The dryfire speed may be slower but the imparted energy to a projectile of appropriate mass would be more efficient.

This is why, on a given bow, a lower brace height would be beneficial. 

I realize that this is not the point of your experiment but it's interesting enough to point out.

Here ends my contribution,as I don't have enough knowledge of theoretical physics...........

Interesting illlustration of how deflex can be used to increase energy storage.

I think in Middleton's book it is explained that higher brace gives more deflex which increases dry-fire speed.  I believe this is because the limbs are closer to parallel.  Also the F/D curve is flatter with high brace, basically starting and ending with stack.

For a given bow more energy is available with lower brace like Actionbow wrote, but lucky for us, Nerd Flintstone is not confined to a given bow!  I've been pondering lately how fast my main xbow would shoot a light arrow with lots of brace...

actionbow wrote:In the first pic if you used the same power stroke (lock position) you would have twice as much limb movement which is twice the stored power. The dryfire speed may be slower but the imparted energy to a projectile of appropriate mass would be more efficient.

This is why, on a given bow, a lower brace height would be beneficial. 

No. Now you think like a longbowman.
With half the limb stroke, the bow can be twice as thick. Meaning it can have eight times the stifness of low braced bow. Given the difference in leverage this means twice the draw weight for same power stroke and string length.
More than twice actually - given that deflexed bow is also longer for given string legth. Resulting in considerably more powerful and compact energy storage system.
Or to put it other way around - a low braced bow can only have half the limb thickness of high braced bow in order to survive the same power stroke.

Obviously a high braced bow should be built to permanent deflex. Or elastic materials, such as organic composites, that benefit from high pre-tension should be used.


-
The other longbowman-mistake that modern crossbow builders constantly make is to assume that crossbow has draw length. Draw length is the distance from palm of archers bowhand to his anchor point.
Crossow - unlike longbow- has powerstroke independent of brace height. So crossow with high brace height is not "wasting draw length" , it simply has longer bolt track.
And some extra length of bolt track in front of string is a desirable feature. It improves accuracy by keeping gravity from pulling bolt downwards during acceleration.

In the case of crossbows, longbows have a lot to teach us. It only takes a little research to realize that the xbows with the highest arrow velocities are the ones with the longest power strokes. Your sawblade example is a poor experiment because the tension in full draw is so disparate between the two examples. The point of the experiment is to prove that higher brace is better than lower brace if I am not mistaken, but all it shows is that higher tension is better than lower tension.

the longer the draw or power stroke (which I use interchangeably) the more power can be imparted on the projectile. This is why a recurve xbow and handbow of similar initial velocities and projectile weight have very different flight characteristics to the target. The handbow having a much flatter trajectory.

If, in your experiment, both versions had the same string tension, at brace or final draw, the one with the longer stroke would be able to accelerate its projectile more efficiently. Whether stringing the same bow to a higher brace and tension would propel a projectile faster depends on the mass of the projectile itself, the relative tension differential and  the power strokes being tested.

actionbow wrote:Your sawblade example is a poor experiment because the tension in full draw is so disparate between the two examples. The point of the experiment is to prove that higher brace is better than lower brace if I am not mistaken, but all it shows is that higher tension is better than lower tension.

Well, no offence, but you are mistaken.
The point of this example was to demonstrate difference in VIRTUAL MASS of two different brace heights.

A low braced bow needs a bolt of about 1/10-1/20th of prod mass to be efficient. The practical speed of this kind of bow is 40-70 m/s

A high braced bow with short power stroke can safely launch bolts as low as 1/40-1/100! of prod mass. With initial velocities of 80-150m/s .
Yes, that is up to and even over 400fps with plain old-school prod. And this is how it was apparently done in the Middle Ages. Something that modern arbalists with their "improved" crossbows have forgotten.

As a BONUS here comes the possibility of installing a much more powerful bow in given space.

actionbow wrote:
If, in your experiment, both versions had the same string tension, at brace or final draw, the one with the longer stroke would be able to accelerate its projectile more efficiently

Both bows have the SAME power stroke. But a high braced bow has shorter limb stroke. So for given bolt speed the limb is moving half the speed of low braced bow, wasting only a quarter of energy. Thus throwing heavier bolt with same speed or optionally a considerably lighter bolt with considerably faster speed.
So in effect bracing a bow high has similar effect as pulley compound system. Meaning that high braced bow in fact has LONGER POWER STROKE for given limb movement.

I am sorry but if you are trying to say bracing a bow higher puts a compoumd type lump in the f/d curve I will respectfully disagree.

As I have stated before some of your claims/findings seem exaggerated. I would love you to show us some chrony results to prove what you are saying.

I hate to get in the middle of this,but I cannot for the life of me see that lower bracing a bow can give more power to it.With a crossbow,the draw,or power stroke is fixed.Therefore,in order to achieve the same power from a low braced bow,the draw,or power stroke must be increased.As our power stroke is fixed...........One last point,my knowledge of physics is rudimentary,but I cant see how 2 objects(a bolt and an arrow)of the same mass and aerodynamic shape,being discharged with equal force,and being subject to the same forces(gravity friction and wind)are going to adopt different trajectories.As I have'nt been around forever,and have'nt yet discovered everything,I don't mind being proved wrong...........
                              Hermit.

Hermit wrote:I cannot for the life of me see that lower bracing a bow can give more power to it.
                              

I believe the lower brace allows the limbs to travel farther, imparting more of their stored energy to the projectile.  If you brace a given prod at 4" the limbs will be stopped by the string 1" before they would be were the prod braced at 3", thus giving the limbs less travel.  In other words, the draw weight will be the same at full draw regardless of brace height, so the lower brace, since it allows the limbs to drive the projectile farther, should give a bit of an increase in velocity.  Think of raising your brace height by 1" as losing 1" of power stroke.  I'm not sure it actually works out that neatly, of course, but I still think the idea is basically correct.

Edit: Actually, scratch that.  It just occurred to me that since the string would be shorter at a higher brace, the limbs would be pulled back farther at full draw, slightly increasing draw weight.  Oh, well.  Back to square one, I guess. 

Back in the 1940s, a guy named Klopsteg did exhaustive studies of bow-mechanics.  From what I've read and my own experience making lots of crossbows, changing your string-length to adjust brace height has little effect on actual power.  A longer string may give the bow a bit more time to accelerate, but a shorter-string will pull the bow further, giving greater draw-weight... at correspondingly shorter power-stroke.  In practice, I haven't found it makes a bean of difference.
Having said that, I suppose it's possible a very heavy/inefficient bow-material, like steel would benefit from moving a shorter distance, so limiting the energy loss from moving the heavy limbs. How much difference will it make?  I think it will be precious little, and energy will still be proportionate to length of draw X weight of draw X efficiency of the prod.  
    Then again, I was wrong about Richard Nixon.  I could be wrong about this...
Geezer, my two cents.

I did some experimenting with different string length on my first bow.  For what it is worth, I got the highest velocity with the longest string that would still stay on the bow.   (If the string is too long, the bow will un-string itself.  This is prejudicial to the bow and unnerving to the guys at the range.)

At the end of the day, I ended up using a slightly shorter string than what I found to be optimal.  The low brace did not look "medieval" and I did not like being that close to the point where it would un-string itself. 

Mac

http://crossbow.wikia.com/wiki/Bow_design

Scroll down to "adding deflex" someone already did the math for us

actionbow wrote:I am sorry but if you are trying to say bracing a bow higher puts a compoumd type lump in the f/d curve I will respectfully disagree.

F/D curve ?
I said pulleys not cams.
You do understand the concept of mass efficiency?

actionbow wrote:
As I have stated before some of your claims/findings seem exaggerated. I would love you to show us some chrony results to prove what you are saying.

Why don't you do it! Why take my word for any chrony results. You now have the recipe. You seem to be a decent bowyer. Why not give it a try!

mac wrote:I did some experimenting with different string length on my first bow.  For what it is worth, I got the highest velocity with the longest string that would still stay on the bow.  

Mac, did you cut bolt mass down to one quarter of usual when trying high braced bow ?
Also you shoud make a new tiller for each brace height, as the idea was to keep the same power stroke.
Otherwise, you kind of missed the point.

And to make full use of this approach you will also need a stiffer permanently deflexed bow.




Oh yeah , and a someone who already did the math for us was me. The graphs in my initial post is the math.
If you people fail to get it it is your loss.
I am getting tired of repeating myself.

Oh-kay, now we're getting somewhere.  If you're assuming that working from a larger brace height, with the Same length of power-stroke will produce higher velocities, I agree with you.  By bracing the bow higher, you're pre-stressing the prod, which will result in a slightly higher force per inch of draw... that's covered in Klopsteg's formulations from 60 years ago.  If on the other hand, you were saying a higher brace versus a lower one on a given stock will produce better velocities, a lot of experience suggests that's wrong.. in fact, the lower brace and longer draw will produce slightly better results, but from my observation, not very much. 
Anyhow, taking prod X and drawing it 10 inches from a 5 inch brace will produce more power than the same prod drawn 10 inches from a 3 inch brace.  It will also stress the prod more, taking it closer to the stacking/yield point.  Geezer.

Thank Geezer, for at last clearing the matter !!

Nerd Flintstone wrote:

mac wrote:I did some experimenting with different string length on my first bow.  For what it is worth, I got the highest velocity with the longest string that would still stay on the bow.  

Mac, did you cut bolt mass down to one quarter of usual when trying high braced bow ?
Also you shoud make  a new tiller for each brace height, as the idea was to keep the same power stroke.
Otherwise, you kind of missed the point.

Nerd F,

Yes, I think I did miss it.  I should have read your post more carefully.

Thank you.

Mac

I have followed this discussion with interest,and as my experience is mostly in practical engineering,and the theory involved,here is my take on this discussion. 
                                                          A bow is a spring.A spring is a device that,among other uses,is used to store energy.When a spring is at rest,it has no energy.When 'pre-load' is applied to a spring,it is storing energy.When a bow is strung it is said to be pre.loaded.When a spring has a further load applied to it,and is then released,the total energy released,will be that of the draw(additional load) PLUS the pre-load.It goes without saying,that a high strung bow has more pre-load than a low strung bow,and is storing more energy,therefore,upon release,the high strung bow must release more energy for the same power stroke,than the low strung bow,I believe Nerd's experiment shows this.As I am enjoying this discussion,I look forward to reading posts from anyone who can pick holes in my logic.One last word to Nerd.........If you are considering a career in the diplomatic service................reconsider.............lol

Here are my little opinions to this discussion.


A bow should/must be "loaded" to a defined amount of its specific allowed material tension (mostly talking about steel, but should be transfered to every kind of stuff) to get out the maximum possible speed and power.

This should be calculated down to a certain tip movement (or applied force).
In either way of low or high brace the tip movement (or applied force) mustn´t be exeeded or bow breakage will be provoked.


So a high braced and a low braced bow store in its (different, otherwise breaking) maximum draw the same amount of energy.
With a shorter string the prestress of the bow increases resulting in a shorter possible power draw since tip movement must stay the same.


So stressing a bow to a longer draw than calculated by its producer can be considered dangerous.
When making my own bows I usually calculate with a reserve to prevent accidents caused by stupid behavior.
In this case a small amount of exeed can increase power and speed due to more power,tension and alternated angle.
But just in case the builder did not calculate a reserve be prepared for some nasty shrapnels flying around.


Needless to say, a bow with very low brace will suffer when bending in opposite direction and material is vibrating.
But the more prestress when strung the highter the energy flowing back unused (compareable to dryfire).


**Edited due to reconsideration**
Concerns about explanation difficulties. Just don´t want to state sth. I am not completely satisfied with.
Does not take effect on tension difficultiesmentioned above.



Rizzar

I just came here for some advice on a different project but this is a brilliant discussion.

IMPULSE, is the word (Grease isn't).  Think of Impulse as the twin of momentum. It's the amount of force imparted over a period of time.

Spring rate is the force (assuming a linear rate)  and draw length is the time (this is sketchy explaining, I'll admit.

The two need to be in balance. Brace and Draw Length.  It's fine to have a longer acceleration period (longbows) but not if you sacrifice the prod energy.

Reducio ad Absurdum.

Imagine a Longbow with a 200lb draw. If you can pull it too your cheek, then it's completely slack at rest. This is where the angle of the string comes in as a factor of spring rate. There is a point of diminishing returns in both directions.

You want to accelerate the bolt as long as possible, but you also want as high a spring rate as possible to be focused..

The same thing is seen in firearms barrel lengths (though not as much as I would have thought. If the energy of a cartridge has more barrel to accelerate the slug it will go faster (using the same round) out of the muzzle. But, if you make the barrel too long the peak energy is expended before the bullet exists.  Too short and the bullet isn't accelerated to it's full potential. 

There is no right answer unless you specify the prods, their material and the draw length. All of which are dependant on each other for an ideal energy transfer.

Using natural materials we don't get linear spring rates often.

THAT IS WHY THIS IS AN ARTFORM.  If you could grab a physics book and plug in numbers it would be a craft or science. Trial and Error elevates this to an art form, there is not correct answer. At best you get correct for these variables.