Primitive Archer
Main Discussion Area => Bows => Topic started by: Eric Garza on September 17, 2013, 09:21:37 am
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There are a lot of things that influence a bow's performance, including tip mass, string mass, arrow mass, and bow layout relative to the type of wood used, among others. I've been pondering whether there's a relationship between arrow velocity and the ratio of draw length to bow length (DL/BL), and whether moderating this ratio can help maximize arrow velocity. I started a thread on PaleoPlanet (http://paleoplanet69529.yuku.com/topic/56854/Role-of-draw-length-in-optimizing-arrow-speed#.UjhDH-CthjE) to this effect, but it hasn't gotten much attention so I thought I'd start one here too. Where the PP thread left off was with the following graph of arrow speed versus DL/BL, which was based on data provided by Woodbear:
(http://www.aisthetica.com/wp-content/uploads/2013/09/Idea.jpg)
The data shows that arrow speed peaks at DL/TL ratios around 40%. This leaves me with a question: Could the shorter bows (54 and 48 inches) have delivered similar arrow velocities to the longer bows (60 - 84 inches) if their draw lengths had been kept to around 40 % of their total length rather than allowing their draw lengths to rise above this mark?
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Interesting and I'm sure a fella called Steve Gardner could tell ya.As for me all I know is the longer you leave that arrow on the string the faster it will go and that your masses have a whole lot to do with it.
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Just an after thought and you may have researched it already but the book put out by Adam Karpowicz on turkish bows might help ya.Most extensive research I've ever read for sure.
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Eric, it is a good question. I just typed out 4 paragraphs and when I realized I still had a ways to go I decided to delete the post. I am not really sure how much you know or don't know at this point but I would recomend doing some google searches on things like force draw curves, virtual mass,bow efficiency, material properties etc.
I wish I were better at condensing answers because I just don't see a good short answer here beyond the fact that the geometry of the bow determines how much energy you store and the longer bows will store more energy than shorter bows because of lower string angles. You measure stored energy at each 1 inch of draw. Longer bows start off higher and build slower than shorter bows. Recurves and bows with syhas can negate a lot of that string angle advantage and be built at shorter length still storing the same energy.
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It would be most interesting to see this chart RE-run to breakout numbers for various bow design styles. (i.e. - Lever bows, recurves, long bows. and etc.)
OneBow
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That is interesting. I too would like to see a comparison of materials and designs.
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I think Badger nails it. There are too many variables to draw much of a conclusion unless you limit yourself to a specific bow style.
Even then your conclusion that 'it peaks at about 40% ' is rather stretchin it. The graph is pretty flat from about 33 - 42 I'd say a more accurate desripion would be to say it sarts dropping off over 45%, which to be be honest we all knew anyway as anything aproaching a draw of half the bow length is pushing it. If I had to say wher it peaks I'd say nearer 35 than 40%... but it's like arguing how many angels can dance on the head of a pin.
Again Bow length is to some extent meningless, does it mean working limb length? Even with identical working limbs the grip length will vary the geometry. Hence the enless boring Qs on the target archery sites about which riser I should use with my wizz bang X9000 23 pound limbs to give me good sight marks at 70 yards (yawn).
So... make to my original comment, too many variables to draw a useful conclusion IMO.
Del
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Badger, I'm not sure how much I know about bows either. I'd long held the assumption that shorter bows will simply shoot slower, but after seeing Dave's data (he posted a table on the original PaleoPlanet post that I did not reproduce here, but the graph is based on it) and looking at the graph it just got me wondering. While I'm sure we know a lot about bows and their physics, I'm open to the idea that there are new nuggets of wisdom left to be discovered.
Thanks for the comments.
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How about looking at it from another angle.
Any bow will give you it's fastest arrow just before the wood starts 'breaking down' or taking set. The real skill in tillering is keeping the wood fresh if you ask me. Getting the correct tiller is easy compared to getting correct tiller AND retaining fresh wood.
I've gradually honed my feeling to where this point is and my bows speeds have gradually crept up with it.
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How about looking at it from another angle.
Any bow will give you it's fastest arrow just before the wood starts 'breaking down' or taking set. The real skill in tillering is keeping the wood fresh if you ask me. Getting the correct tiller is easy compared to getting correct tiller AND retaining fresh wood.
I've gradually honed my feeling to where this point is and my bows speeds have gradually crept up with it.
Well said.
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I agree with the well articulated points above (about tillering), but I think we're straying a bit from the original question which is about the ratio of bow length to draw length with respect to arrow speed.
It appears to be complicated. But we can break it down a bit, right?
For example, the longer the draw -- the longer the power stroke. E.g. the longer the draw, the more time an arrow is in contact with the string and accelerating, which allows the bow to impart more stored energy into the arrow. So longer draw (in a vacuum) is a plus. BUT, if that longer draw is gained by stressing the wood, and increasing set, well than you may have negated its benefits by reducing stored energy and increasing hysteresis.
So, one way to talk about design is to say...the longest draw you can get without increasing set or stressing/breaking down the wood is a tillering goal when making wooden bows that you want to shoot fast. Usually though draw length is about the person shooting the bow, not necessarily how fast you can make an arrow go...
Just a few thoughts. I'm open to changing them if somebody can convince me otherwise.
Gabe
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I agree with the well articulated points above (about tillering), but I think we're straying a bit from the original question which is about the ratio of bow length to draw length with respect to arrow speed.
It appears to be complicated. But we can break it down a bit, right?
For example, the longer the draw -- the longer the power stroke. E.g. the longer the draw, the more time an arrow is in contact with the string and accelerating, which allows the bow to impart more stored energy into the arrow. So longer draw (in a vacuum) is a plus. BUT, if that longer draw is gained by stressing the wood, and increasing set, well than you may have negated its benefits by reducing stored energy and increasing hysteresis.
So, one way to talk about design is to say...the longest draw you can get without increasing set or stressing/breaking down the wood is a tillering goal when making wooden bows that you want to shoot fast. Usually though draw length is about the person shooting the bow, not necessarily how fast you can make an arrow go...
Just a few thoughts. I'm open to changing them if somebody can convince me otherwise.
Gabe
All good points. Practical example: my 90#@30" maple backed yew warbow will regularly outshoot my 100#@32" tri-lam warbow. Why? Because the 100# warbow has 3"+ set and the yew bow has 1/2" of set. A good lighter draw weight bow will out shoot a poor heavier draw weight bow in my experience.
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It really is not the lenght of the draw as much as it is the power curve under the draw. A longer bow will have lower string angles and start off at a higher draw weight and build slower as you draw, allowing for a lot more stored energy than a shorter bow pulling the same distance and the same draw weight. A shorter bow will start off lower and build more rapidly at the end of the draw storing a lot less energy than the loner bow. The shorter bow may have some advantage in efficiency than a very long bow so usually find the least of the evils or the best compromise which usually results in ratios between 35% and 45%.
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Eric, in Dave's data the shortest bow was the slowest. 66" for a 28" draw seemed to be the best fit for efficiency and arrow speed.
The longer the bow the better but his data also shows a point of diminishing returns where increased draw did not result in more speed or efficiency.
That seems to be a the case with a lot of things archery.
Jawge
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The title of the thread is confusing. It asks about draw length and then talks about drawlength/bowlength!
Draw length has a great increase in stored energy which is especially usefull in overcomming the inertia of heavy arrows, hence the proportions of a warbow.
50# @32" stores about 20% more energy than 50# @ 28"
Del
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Eric, in Dave's data the shortest bow was the slowest...
Yes, I'm not claiming otherwise.
The model he used to generate the data assumed an identical draw length for all bows, regardless of length. The result is that when you divide draw length by bow length and plot it against the resulting arrow speed, you get the graph I showed at the start of the thread. It's clear that there are diminishing returns as you increase the ratio of draw length to bow length beyond 45%, and it also appears that diminishing returns are just starting as you decrease the ratio of draw length to bow length below 35%.
The question I'm asking is, if you shortened the draw length of the shorter bows so that their draw length to bow length ratio stayed in the 35-45% range, would their arrow speed stay up at the top of the curve? It seems the balance of opinion is that it would not, but at any rate that's the question I'm asking.
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I would think not because the longer power stroke of the longer draw would make the difference. Jawge
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Eric, the above example by Woodbear just illustrates an example of the best tradeoff for stored energy and efficiency. Longer draw bows will always have an advantage at 10 grain per pound arrow weights. As the arrow weights lower the edge leans more toward efficiency rather than stored energy but the slope is very gradual.
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Great topic ;) I have often wondered if the longer bows storing more energy would be cancelled out by the increased mass vs the shorter Bows with less mass and stored energy when it translates to Arrows speed...
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Eric, in Dave's data the shortest bow was the slowest...
Yes, I'm not claiming otherwise.
The model he used to generate the data assumed an identical draw length for all bows, regardless of length. The result is that when you divide draw length by bow length and plot it against the resulting arrow speed, you get the graph I showed at the start of the thread. It's clear that there are diminishing returns as you increase the ratio of draw length to bow length beyond 45%, and it also appears that diminishing returns are just starting as you decrease the ratio of draw length to bow length below 35%.
The question I'm asking is, if you shortened the draw length of the shorter bows so that their draw length to bow length ratio stayed in the 35-45% range, would their arrow speed stay up at the top of the curve? It seems the balance of opinion is that it would not, but at any rate that's the question I'm asking.
Are you saying the graph is based on a mathematical model and not real data????!!!
If it's based on a mathematical model, then all bets are off. There is no point discussing the graph, we may as well just pore over the equations used in the model or apply some maths to find the optimum FOR THAT MODEL.
Maths and physics are just tools, approximations to help us predict and explain the natuaral world. In some areas they can be incredibly accurate. But I wouldn't trust a computer model of a self bow further than I could fling Bill Gates.
It's like discussing the tiller of a bow created in Photoshop ::)
Del
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Are you saying the graph is based on a mathematical model and not real data?!!!
Yes. David (Woodbear) has a good understanding of the physics of bows, hence I value his model and the data that comes from it. If you feel otherwise, feel free to drop out of the discussion.
Badger, do you have any sense for how light an arrow must be for shorter bows with more efficient limbs to gain an advantage over longer bows with less efficient limbs?
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Are you saying the graph is based on a mathematical model and not real data?!!!
Yes. David (Woodbear) has a good understanding of the physics of bows, hence I value his model and the data that comes from it. If you feel otherwise, feel free to drop out of the discussion.
Badger, do you have any sense for how light an arrow must be for shorter bows with more efficient limbs to gain an advantage over longer bows with less efficient limbs?
Yup, I'm out, but I gotta say I think the graph was posted under false pretences... this is 'Primitive Archer' not a mathematicam modelling forum.
Original post says...
" which was based on data provided by Woodbear:" It says 'data'.. not 'data produced by a mathematical model'
Del
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Eric, this is where it starts to get a bit complicated as design issues with each bow will affect the outcome. In recent years both modern and primitive bows have become a lot more efficient, due in large part to better string materials and pushing the limits on low mass tips. Better reflex deflex profiles have also contributed. As efficiency increases the length of the most effective bows with very light arrows gets longer than it might have been say 50 years ago. I would suspect it might go something like this. shooting 10 grains per pound maybe 67" proves to be optimum, at 8 grains it might drop to 63" at 6 grains 58", at 4 grains 54" at 3 grains maybe 50" or something close to this.
With a few measurements you can actually work this out using the virtual mass of a bow. Say you shoot a 50# bow with a 500 grain arrow at 170 fps. The bow stores 48ft#'s of Ke and the arrow is only taking 32ft#'s of ke. To find the virtual mass you simply extrapolate to find out how much arrow eight it could shoot at 170 fps if it were 100% efficient. In this case it would be 750 grains. So your bow would have a virtual mass of 250 grains that would remain fairly constant regardless of arrow weight. At a glance you can see that if you were now shooting a 250 grain arrow the efficiency would drop to 50% from where it is with 500 grains at about 66%. As the bows get shorter the stored energy goes down but the efficiency should start to rise. At some point of arrow weight they cross, I really can't say exactly where.
I am actually working on next years flight bows right now, I will let you know what I come up with. I plan on shooting arrows around 220 grains.
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This thread just became a LOT less interesting knowing that the curve represented is just mathmatical ponderings and not actual measured observations made with REAL BOWS. No wonder there's no break out for the type of bows!
Does it even belong in this section? I'd nominate it for the campfire...
OneBow
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I'm still just a bystander here but read this thread with interest,and this is flying over my head a bit,and do understand it mostly.The thing that sticks in my mind is the fact that longer bows start out storing more energy earlier than shorter bows but end up at full draw the same.Except in the case of a short horn bow with set back siyahs that unfolds as the draw gets longer to smooth it out.
Now is it best for a bow to have nice even gaining draw weight gain or stored energy from a bow every two inches right from the brace?Say bows that are 60" to 64" long?Being tillered properly so that set is minimal and future set does'nt occur with use.
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For maximum effiency I mean.
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Onebow, Woodbear is usually pretty accurate when he puts something into print. He has tested plenty of bows. My guess would be they are real life numbers as they seem to coincide with my own findings even though I dodn't write things down and track them the way he does.
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In trying to fully understand this and I don't care if I sound stupid bows made 60" to 70" long with a 28" draw fall into this 40% to 45 % efficiency catagory.That is'nt taking in the fact of design here though of having less imb length working say for mollys.Maybe I'm offttrack here.It's been my experience if I can get a shorter working section on a bow that keeps from taking set, that it shoots my arrows faster.Maximizing the work done on a shorter working length limb.I'll stand off to the side now.Lots of variables with this stuff.
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Yes, there are absolutely lots of variables. When I started the thread with the title "Role of draw length in maximizing arrow speed", it definitely wasn't my intention to imply that draw length (relative to bow length) was the only thing that played a role in maximizing arrow speed. It just seemed from Dave's data that it did play a role, among other things, and I hadn't seen that role explored explicitly before.
Thanks for your description Badger, and for your estimates of ideal arrow mass relative to bow length. Dave's model assumed a constant arrow mass for all bows (as well as constant draw weight, and constant draw length), so it doesn't take changing arrow mass into consideration. What you've offered gives me more food for thought...
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Cool
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Very interesting topic!
It looks like the arrow velocity drops quite quickly, when the bow is a certain amount shorter then the ideal length. It doesn´t drop as fast when the bow is the same amount longer! In addition, a bow with long limbs is very durable and it is also more precise!
When I read this topic, I imediatelly thought at the warbows found on the Mary Rose! I´ve so often heard that these bows were only made so long in order not to not break and that they could be much faster if they were shorter. Of cause they could be more efficient, but they would be slower.
The average draw length is 30,5-31 inches and the average bow length is almost 78". So the draw length is almost 40% of the bow length, which shows that the length was also optimized in performance! In addition to that, warbows of a certain length and drawweight have less mass then other bows.