Role of draw length in maximizing arrow speed?

[Eric Garza]

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.

[George Tsoukalas]

I would think not because the longer power stroke of the longer draw would make the difference. Jawge

[Badger]

       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.

[soy]

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...

[Del the cat]

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

[Eric Garza]

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?

[Del the cat]

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

[Badger]

  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.

[Onebowonder]

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

[BowEd]

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.

[BowEd]

For maximum effiency I mean.

[Badger]

  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.

[BowEd]

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.

[Eric Garza]

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...

[Joec123able]

Cool