Role of draw length in maximizing arrow speed?

[Eric Garza]

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 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:



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?

[BowEd]

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.

[BowEd]

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.

[Badger]

     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.

[Onebowonder]

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

[paoliguy]

That is interesting. I too would like to see a comparison of materials and designs.

[Del the cat]

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

[Eric Garza]

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.

[mikekeswick]

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.

[adb]

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.

[rossfactor]

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

[adb]

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.

[Badger]

   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%.

[George Tsoukalas]

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

[Del the cat]

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