Draw length/ penetration/ energy

[elk ninja]

Alright, could someone break this one down shotgun (or three piece bow) style for me....
I have a short draw length, 25.5".  If I shoot a 60# bow, the next fella has a 28" draw length, and also shoots a 60# bow, our arrows weight the same, will we get the same penetration?  Speed?  other indicators?...
I have heard it both ways and since physics is not my strong suit, thought I'd ask....
Mike

[vermonster13]

The 28" draw will get about 10% more out of their bow than the 25.5". So his will be a bit faster, carry more momentum/KE, etc etc.

[BobW]

Think of the amount of additional time the arrow is on the string (a little more is really a lot), and thus more energy per unit of time from the limbs is being transfered to the arrow.  Power stroke!  Okay, I got too far into the physics end of it didn't I?  Damn education....

[dead-eye]

The person with the longer draw will be shooting the same arrow faster, and all else equal, it will penetrate further because it has more KE (and momentum).     The reason is because the fellow with the longer draw is storing more energy at full draw than you are.  This is assuming that the two bows are very similar in design.  I know you said physics wasn't your strong suit, but think about like this.  Lets say you had two 60 lbs weights, one sitting about 4" of the ground, the other sitting about 4 feet off the ground.  If  you had to pick one to stick your foot under and let it fall on you, what one would it be?  Hopefully you would say the one at 4".  Why, because at 4" it doesn't have near as much potential or stored energy as the one at 4 feet.  Same thing goes for bows.  If you have a 60 lb bow, and pull it to  25.5",  the amount of stored energy is determined by basically those two factors (and of course limb design).  I did a rough calculation, and the guy with the longer draw is storing around 10-12% more energy than you.  For you to have the same amount of stored energy, you would need to shoot a bow around 66 –68 lbs at your draw length.  Although I may catch some guff for mentioning this, that is why cross bows have such high draw weights.  Cross bows have very short "draw lengths".  To up the amount of stored energy, they need to increase the draw weight.

[Dr. Ed Ashby]

Bob and Dave both have it. It all does boil down to the TIME factor. Just as with arrow penetration into tissues, it's the IMPULSE OF FORCE that determines how much of the bow's stored energy is transferred to the arrow.

The "impulse of force" is the TOTAL FORCE applied MULTIPLIED by the TIME that force is applied. A longer draw length gives a greater (longer) power stroke. That means the string is in contact with the arrow for a longer period of time during launch. The bow's stored energy acts upon the longer arrow for a greater period of time. Even when the AMOUNT of force applied is the same the total energy transferred from bow to arrow is greater, because the force has ACTED for a longer period of TIME. This increases bow efficiency.

Similarly, at any given draw length a heavier arrow slows the speed of the bow's limb movement. This also increases the TIME factor of the bow's impulse of force, increasing bow efficiency. This results in a net gain in both arrow ENERGY and arrow FORCE (momentum).

After launch, how the energy and momentum the arrow has derived from the bow is used depends totally upon arrow design; how efficiently the arrow uses whatever force and energy it carries.

At shorter draw lengths, it's highly beneficial to use as much arrow mass (weight) as you possibly can (while still meeting your trajectory requirements). This will increase your bow's efficiency and result in a marked increase in net arrow FORCE.

It's hard to simplify the explanation.

"Oversimplification of what is extrinsically complex merely results in something that means nothing to anyone." - Dr. Canterbury, Project Trinity

Ed
TGMM Family of the Bow

[Arwin]

I'm glad this was posted as I had a similar question in the shooters forum.

[pseman]

Great explanations. On a similar note, approximately how much increase in fps would you see with each inch of draw length? Would fps also inrease by 10-12%? My instinct tells me no, but I don't know, therefore I ask.

[Dr. Ed Ashby]

I should clarify that Brendan is also correct. He was posting at the same time I was.

With bows of equal peak draw weight, the longer draw bow also stores more energy, because of the greater draw force curve. However, even when the total stored bow force is equal, the longer draw length will still impart more energy and force to the arrow, because of the greater time of impulse.

Ed
TGMM Family of the Bow

[vermonster13]

Usually it is 3-4fps per extra inch of draw on average.

[Dr. Ed Ashby]

Mark, that depends a lot on the individual bow. When we were chronographing some A&H ACS-CX bows at the factory, using the same arrow (approximately 780 grain; can't recall exact weight at the moment), a 48#@30" gave the exact same velocity as I was getting from a matching bow of 65#@27". No doubt that my poor release, compared to the other shooter's, had some marked effect too. However, that's a BIG difference, percentage wise, for 3" of draw length and a very heavy arrow - approximately a 27% total increase; or 9% gain per inch.

Ed
TGMM Family of the Bow

[vermonster13]

I am speaking of two bows of same make and same weight at different draws, IE 50@25.5 and 50@28

[killinstuff]

But in reality, 10% differance in penatration is meaningless on a typical deer size animal.

[vermonster13]

Depends on where you hit now doesn't it?

[O.L. Adcock]

Pseman, "Great explanations. On a similar note, approximately how much increase in fps would you see with each inch of draw length? Would fps also inrease by 10-12%? My instinct tells me no, but I don't know, therefore I ask."

Vermontster is correct...The equates to 3-4% more horsepower for every inch up or down IF you keep the gr/lb the same. No, fps and horsepower (KE) velocity is squared, at the same gr/lb, 1 fps = 1% (aprox) of the total KE. FPS is like RPM to an engine, it's not in direct proportion. If you double your arrow weight you lose 25% of your FPS and vice versa.......O.L.

[SlowBowinMO]

My time spent with a chrono one day indicated adding an inch of draw length yielded about 8-10 fps of speed increase.  That was on a 51# bow drawn 28" and 29" respectively, with a 12 gpp arrow.

Makes you kinda jealous of the guys with a true 30" draw doesn't it?

[Arwin]

So would 46#@28 be better than pulling 50#@27?
I have to ask while you scientist type are around.  :D   O.L. good to see you in here!  

[vermonster13]

Depends on the bows, but odds are no because the lower draw bow in this case is almost 10% heavier. You need to compare apples to apples though. Same make/design/material bows of same weights at different draws. A bow that is 50@27 will most likely be around 53@28 so you are gaining more draw weight and the inch so it will be more than a 4% increase.

[O.L. Adcock]

SBM, with the "same" arrow those sound reasonable but not if you keep the same gr/lb, IOW, a 612gr arrow at 28" for 12gpp and 648 gr at 29" for 12 gpp, assuming a 3# increase in draw weight.

Keep in mind these numbers are for any one given bow, you can find examples of bows that shoot as hard at 24-25" as others do at 28"+....O.L.

[BobW]

Originally posted by SlowBowinMO:
Makes you kinda jealous of the guys with a true 30" draw doesn't it?

Like my 32+?  

[pseman]

Thanks again for the explanations. SlowBowinMO and I had the same comparison in mind. I have increased my draw length by roughly 1 1/2" in the last year by working on my form and was wondering approximately how much that would add(in fps) to my setups. I am still shooting the same arrow and tip weight so therefore my gpp has decreased(still between 8.5 - 9.5gpp dependeing on the particular setup).

BobW, 32"+! Wow do your knuckles drag when you walk?LOL