Bow Performance 55 @ 28 vs 55 @ 30

[John Havard]

Chuck,
My answers are based on testing the same bows at 26", 28", and 30" - all at 9 grains per pound of draw at each draw length.  There's NO way to compare different bows without having to test each bow individually.  I'll refer you to this website.  Of particular applicability is example #4 in the attached link (toward the very end).  It gives a real-world example of what can be accomplished with the same arrow and with draw weight changes.

 http://dryadbows.com/Defining%20Bow%20Performance%20Dryad.pdf

[Orion]

A lot of the responses deal with the increased speed/performance  attained by the same bow as it's drawn farther.  It gains speed/performance because it gains draw weight as the draw is increased from 28 to 30 inches.  But that's not the question asked.

The question asked is, is a bow drawn to 50#@30 inches faster than a bow drawn to 50#@28 inches, all other things being equal, and by how much?  Most assume that the longer power stroke of the 30-inch draw would yield a faster arrow, but so far, no one has provided proof, an example of that being so. I don't have proof of it either, but that's the way to bet.    

[John Havard]

The examples I have offered are based on ceteris paribus - all things being equal.  If a bow is drawn to 28" and a 9 grain per pound arrow is shot from it, and the same bow is drawn to 30" and a 9 grain per pound arrow is shot from it (ALL things being equal including brace height and string weight), the 30" 9gpp arrow will be 10 fps (within 1-2 fps) faster than the 9 gpp arrow shot with a 28" draw length.  Several examples are offered with explanations in the Dryad website that explain how/why that is.

[Friend]

John - Other information posted from the wheelie world relayed the same ~10 fps gain, though these tests were completed maintaining the same arrow wt, draw wt and merely altering the power stroke.

[Ragnarok Forge]

The original post was about differing draw lengths for the same exact bow design at 55lbs of draw weight.

So what I am getting from the discussion and based on tests that have been run is that there is approximately 5 fps gained for every inch of increased draw length in this situation.  

This brings on the next question.  What difference in speed can you expect to gain or will any speed be gained for two bows of identical design shooting a 10 gpp arrow at 50 and 60 lbs.  Theoretically if the energy curves are the same and the arrows gpp at that draw weight are the same, I would think you would be shooting the arrow at the same speed out of the two bows.

[Sixby]

My recurves gain a bit more than 2 lb per inch. Longbows a bit more. 'With the numbers John gives that would be about 4.8 fps gain per lb.  That would be one efficient bow.

God bless you all, Steve

[John Havard]

Lowell,

A 50# @ 28" bow shooting a 500 grain arrow (10 gpp) will shoot "X" fps.  The same exact bow design that's 60# @ 28" will shoot a 600 grain arrow (same 10 gpp) at the same "X" fps.  There will be NO difference in arrow speed at the same draw length and at the same grains per pound.  

Another way to say the same thing is that any bow of a particular design will shoot the same gpp at any draw length the same speed.

[Orion]

Oops, I didn't see that you were keeping gpp constant in your first post, John.  As you point out, another way of measuring the same thing.  

[Ragnarok Forge]

John,

I want to say thanks for posting the answers you have based on testing.  I am overly curious about technical details and would have eventually let it drive me to testing all these things myself.  Your experience and results are greatly appreciated.

While I have your attention I would like to ask one more question.  Have you done the testing to know what equivalent draw weight of the same design bow you would need to match a 55 lb bow drawn to 30 inches?  I have read and understand that adding 10 fps due to 2 extra inches of draw is giving you the equivalent fps of a heavier bow at a shorter draw length. I suppose you could calculate it if you knew a set increase in fps per lb of draw weight.

[Sixby]

OOPs, Sorry there, I misread. John's right on. Should have known that. Its a gain of about 1 fps per lb. That jives. LOL lots of oops ssss there


God bless you all, Steve

[Ragnarok Forge]

John,

I want to say thanks for posting the answers you have that are based in actual testing.  I am overly curious about technical details and would have eventually let it drive me to testing all these things myself.  Your experience and results are greatly appreciated.

While I have your attention I would like to ask a couple more questions.  Have you done the testing to know what equivalent draw weight at 28 inches in the same design bow you would need to match a 55 lb bow drawn to 30 inches?

Is there a rough constant of increased fps at a set gpp of arrow weight per lb of draw weight?

[swampthing]

Easy one.... approx 5 fps per Inch of draw, sooooo.
  55# @ 30 and a 65#@28, should, be about the same speed with the same weight tuned arrow.
  But. and this is a big one......
 One major oversight by a lot of peeps is the diference will be offset by the additional 2" of arrow length. Take a wood arrow of 55-60# and then one for 65-70# you would need for the 30" draw with a 125g point, if one used a heavier 160g point they would need probably 70-75#. These 2 different spine shafts will weigh "a bit different" you could say. Or for tech comparo, about 50-75g more. With carbon you would find that the difference would be a bit less, to the tune of 25g or so.
        I find that for my Hill style bows, they typically and linear- ally drop 1fps for every 10g arrow weight. So in this instance the 30" draw would loose 5fps and 2.5fps, anyway, over what the math says the difference would be between the 2 different draw lengths.
     Using the average of:
                                     A 30" draw is 10fps faster than a 28" draw with same bow, that can handle a 30" draw. Take away 5 fps for the heavier arrow needed for the longer draw, so we are now at 5fps faster with the 30" draw and longer arrow. Pretty close already, just remember though upping draw weight will require stiffer/possibly heavier arrows so we will need to take that into consideration. So about 5#+/- a pound or 2 more for a 28" draw should get you right in there with the speed of the 30" draw.  
         Please remember that my model was a Hill Style bow, not affected "as much" to arrow weight through my chronograph. It consistently shows that for every 10g arrow weight will affect speed by 1fps. Some of the newer bows, D/R bows and recurves, do not exhibit the same change in speed in regards to the same difference in arrow weight, usually the are bogged down a little more per 10g of arrow weight then a Hill.

[John Havard]

Hi Lowell,

I haven't done that exact testing but the results are fairly easy to calculate given enough background data.

First of all, you need to know SE/PDF28 and SE/PDF30 for the bow in question.  Let's say that SE/PDF 28 is 0.900 and SE/PDF30 is 1.000.  That means that the 55# @ 30" bow stores 55 ft-lbs of energy.

Second, we need to know what the DE (dynamic efficiency) of the bow design being tested is.  My testing results suggest that there's very little (so small it's hard to measure) difference in DE at varying draw lengths (within reason GIVEN CONSTANT GRAINS PER POUND ARROW WEIGHT).  

But, given that DE varies with grains per pound, let's assume in this example that the 55# @ 30" bow is shooting a 10 gpp arrow, or 550 grains.  Further, let's assume that in this example we want to know what draw weight in the same design bow is needed to shoot THE SAME 550-GRAIN ARROW THE SAME SPEED.

Now we calculate:  the 55# @ 30" bow stores 55 ft-lbs of energy and the arrow shot from that bow (because of the DE of 85% - a very high number FWIW) contains 55 ft-lbs*0.85=46.75 ft-lbs of energy.  Knowing the equation for kinetic energy, we can calculate the speed of the arrow being shot from this particular 55# @ 30" bow.  An arrow weighing 550 grains (10 gpp) with 46.75 ft-lbs of energy is traveling at 195.6 fps.  

To quote from one of my college differential equations books "therefore it should be obvious to the most casual observer that....." the same bow design being drawn to 28" and shooting the same 550-grain arrow the same speed will also have to deliver 46.75 ft-lbs of energy to the arrow.  The DE for the 28" example will be lower because in order to shoot the same arrow the same speed (and therefore have the same total ft-lbs of energy), the bow being drawn to 28" will have to have a higher draw weight at 28" than 55#.  Iteration here is necessary to fine-tune the answer but I'll cut to the chase with a simplifying assumption:  With the higher draw weight at 28" let's assume DE drops from .85 to .835 when shooting the same 550 grain arrow at the same speed of 195.6 fps.  

Now the solution is easy and simple.  The same bow design being drawn to 28" delivers 46.75 ft-lbs to the arrow.  Its DE is .835, so that means it must store 46.75/.835=56 ft-lbs of energy.  And given the fact that SE/PDF28 = 0.900 the bow being drawn to 28" must have a draw weight of 56/.900=62.2#.

The answer from this example based on reasonable numbers for a better-than-average recurve is:  Bow of "X" design and manufacture being drawn to 55# @ 30" would have to be 62.2# @ 28" in order to shoot the same 550-grain arrow the same speed.

Now, if we wanted to keep the gpp constant the DE for the 28" bow would be higher, and through iteration we could hone in on the answer.  Suffice to say that somewhere in the 60-62# range at 28" would shoot the same arrow the same speed as a bow of precisely the same design being drawn to 55# @ 30".

There are several more examples in our website that provide more background and explanation if you're interested:

  http://www.dryadbows.com/Defining%20Bow%20Performance%20Dryad.pdf

[wingnut]

Nerd ALERT!!!

Now you know why John is such a good guy to have on board when you are designing a new limb.


LOL

Mike

[John Havard]

I resemble that remark Mike.

[hybridbow hunter]

Originally posted by John Havard:
Chuck,
My answers are based on testing the same bows at 26", 28", and 30" - all at 9 grains per pound of draw at each draw length.  There's NO way to compare different bows without having to test each bow individually.  I'll refer you to this website.  Of particular applicability is example #4 in the attached link (toward the very end).  It gives a real-world example of what can be accomplished with the same arrow and with draw weight changes.

          http://dryadbows.com/Defining%20Bow%20Performance%20Dryad.pdf          

John i went on your link and found (you wrote it and i also measured 3 to 4% variation) that for 1" of draw SE/PDF is increasing with 3,5% and DE remains the same and of course arrow mass (m) is identical and V is arrow speed

here is what you wrote on Dryad link about Store energy variation according to draw length:

   
We can do the math:

Dynamic Efficiency X Store Energy = arrow Kinetic Energy= 1/2 X m X  V2  
So  V2= SE X 2DE/m and V= Square Root(SE X 2DE/m)

If you increase SE by 7 % then for 30" then speed becomes
SqR(1,07SE X 2DE/m)= SqR(1,07) X SqR(SE X 2DE/m)= SqR(1,07) X V so the factor of speed gain is SqR(1,07)=1,0344

So Arrow Speed@30" = Arrow Speed@28" X 1,0344

If You test a  Recurve bow giving 180 FPS # @ 28" then Arrow speed @ 30" is 180 X 1,0344= 186,19 fps

If you test an ACS CX @ 10 gpp and 28" you get 190 fps.
At 30"  speed will be 190 X 1,0344=196,53 fps

If you test a Howard Hill bow giving 160 fps @ 10 gpp/28" speed when drawn to 30" will be 165,5 fps

From 28" to 30", speed gain is about 6 fps...

Laurent

[Whip]

Originally posted by wingnut:
Nerd ALERT!!!

Now you know why John is such a good guy to have on board when you are designing a new limb.


LOL

Mike

     

It's good to know that you guys really understand what you're doing.    :cool:  

Speaking from the perspective of a dummy who never even took physics in high school, I think I'll just take John's word for it and be happy that I have long arms.  From John's explaination I'm pretty sure that's a good thing....

I'll try to remember this thread the next time someone asks what the minimum bow weight is to hunt elk.   It all depends ....    

[John Havard]

Merci Laurent!

[Ragnarok Forge]

John,

I understood the equations, and all our remarks.  Thanks for clearning that one up nicely.

Clay

[AWPForester]

I would say based on design it will vary but a good rule of thumb in my expierence is 5-8 fps aross all draw lengths on average.  If all things are equal it is in my opinion the variable that affects performance