Some Fun Crunching Bow Numbers

[TradBowyer]

Recently, I’ve noticed a lot of debate ranging about what draw weight is sufficient to hunt with. These threads always pop up in the summer right before season especially elk season. Reading those threads is always enlightening as there is always a wide range of opinions from rookies to veterans to someone who knows someone who knows someone else…One thing I noticed in these threads is that some say any bow (longbow, recurve, hybrid) in the 60lb range is sufficient but there a lot of people who say to stay away from the sub 55# bows. I don’t think anyone would argue that the bows of today are more efficient than the bows of yesteryear and therefore enable us to shoot lower poundage with no decrease in performance. A statement I read often is “Fred Bear said you can shoot any animal in North America with a #55 bow” and most seem to agree with this. So, I decided to have a little fun and see what poundage a modern, top performing bow would need to match a bear #55 recurve. First thing I had to do was determine an average performance value of a #55 bear recurve. I was able to borrow a couple bear bows off a friend and tested them per Blackys setup in the TBM magazines. It is documented that Fred used 9-10gpp arrows which fit in nicely with my testing as Blacky uses 9 gpp. I did not use fast flight on these bows so I added 10 fps to the numbers to make up the difference (my experience of B50 vs fast flight). The bows averaged 170 fps. I then went back through my TBM magazines and gathered info from Blackys bow tests. The fastest bow I found that he tested (with the magazines I have) shot a 9gpp arrow 192 fps (16 strand fast flight drawn 28”) with fingers so we will use this as a basis.

At this point we have an old standard #55 Bear recurve shooting a 495 grain arrow 170 fps. Running the numbers for a momentum value (thank you Dr. Ashby) we get: (495* 170)/225218 = .37

So, using this standard, we can calculate backwards to find the arrow weight needed of a modern high performance (@ 192fps instead of the 170 fps) recurve that will give us the same .37 value:

(.37*225218)/192= 438 grains.

Since we are testing at 9gpp, (438/9) = #49

So, a modern #49 bow shooting a 438 grain arrow will perform as equally as an older #55 bear recurve shooting a 495 grain arrow.

The thing that was interesting to me is that there is only a 6# difference in bow weight needed to get these bows to the same performance levels. Or to put it in money terms, new bow: $1200, old bear recurve: $130….only 6 lbs difference…so ($1200-$130)/6 = $178/lb LOL.

For the low poundage guys, here’s another tidbit I calculated. A lot of veteran elk hunters say to use a minimum of 600 grains for elk. So recalculating this for a modern recurve using the same .37 value:

(.37*225218)/600grains = 139 fps needed…(we need to shoot a 600 grain arrow 139 fps to match Fred Bears statement)

I didn’t have a bow with a low enough draw weight to get this but I did have a 55# hybrid longbow here that shot a 800 grain arrow around 140 so this would equate to a 14.5 gpp arrow (800 grains/55 #). So, using this,  600 grains/ 14.5 gpp = 41 #

So, a #41 bow shooting a 600 grain arrow @ 139 fps will match the #55 bear recurve shooting a 9 gpp arrow.

I would love to find some hard in field testing to back this up. I had a #55 bow longbow last fall in the Rockies and was worried that I didn't have enough LOL

Crunching numbers is dangerous  

[Guru]

Whoa, Way to much for to think about!!  

[maineac]

The number crunching is interesting.  It would be nice, as you said, if people with similar setups described in your calculations could comment on experiences in the field.

[wingnut]

DAng could have saved you a lot of math.

The program I wrote a few year back does that calculation.

But lets do it this way.

Take your arrow  495 gr
and your speed   170 fps

As the standard.

The Bear did it at 55#

The 192 fps @ 9gpp bow does it at 43#

an average bow 180 fps @ 9 gpp does it at 49#

A top end bow 198 fps @ 9 gpp does it at 40#

So the same arrow that Fred Bear shot can be shot today with the same lethal force at not 6# lighter but 15# lighter.

I did this for a customer last summer.  On TradGang a fellow was talking about his 60# selfbow shooting a 600 gr arrow at 160 fps being the minimum for elk.  A customer stopped in that had been reading the thread.

So we took a 600 gr arrow and grabbed a bow off the rack.  Put it on the shooting machine and shot it at 160 fps.

Exactly the same as the 60# bow.  Then I asked the customer to read the weight on the bow.  42# @ 28"  

BTW he bought the bow.  LOL

Mike

[tawmio]

This does sound dangerous! interesting though enjoyed your research.

[Dave Bulla]

The question I'd have is what weight modern bow would it take to shoot an arrow that is the SAME weight as the arrow from 55# bear at the same speed?  

That comparison keeps both trajectory and impact performance equal where as the lighter bow with the heavy arrow comparison drastically changes trajectory and how you would have to hunt and how close you would have to get.

Another interesting question... in the interest of saving money like you mentioned above, how hard would it be to put your own tip overlays on an old vintage bow and allow it to shoot fast flight strings?  I'm betting there wouldn't be a whole lot of difference between the average vintage bow and the average modern bow if that was done.  ***notice I said average***

Cool thread though.

Edit**

Mike, looks like we were typing at the same time.  Your numbers are exactly what I was talking about.  But honestly, I didn't expect THAT much difference!

[mmgrode]

Thanks for crunching these numbers, Tim. You make a very important point in your experimentation; efficiency comes from proper bow design, not neccessarily bow draw weight.  That efficiency can lead to equal performance(ie. arrow momentum) from a lower weight bow using the same gpp. The more efficient the energy transfer of a particular bow design the lower the bow poundage required.  Good stuff and something to remember when discussing "How much is enough?"

Matt

[TradBowyer]

Mike,
I was comparing penetration capabilities (momentum factor) not speed. Bears setup produces a momentum factor of .37...your 40# bow analogy produces .32 not .37..using your 198 fps with 9gpp bow, you would need an arrow weighing 425 grain which means your bow weight would have to be 47# to shoot this arrow at 198 fps to match Bears .37 momentum factor.


Dave,
i have a longbow that is #55 and shoots a 700 grain arrow about 170 so using that, the arrow comes out to 12.7 gpp. So using Bears setup with a 495 grain arrow, 495/12.7 = 39#...so another longbow of this design and a draw weight of 39# would shoot the same arrow roughly the same speed. 55-39 = 16 lbs difference. Right on with what mike has found.

As far as adding modern overlay materials to the classics...I feel that is on par with sanding and refurnishing antique furniture..there's just something wrong with that LOL

I'm a numbers cruncher i admit....but its interesting to put math behind some of the thoughts out there for bow weight and performance.

[RM81]

interesting read.  makes me wanna go out and chrono my arrows to see what's what.  thanks for posting the info.

[Ragnarok Forge]

Great post, I am a number cruncher too.  

Lots of opinions in the world are not based on fact.  Most of them are based on personal experience and feelings.  Both of which can be rather innacurate.  

The good news is that once you have run the tests and know the facts you can help clear up the debate.

[NDTerminator]

Not to throw my oar in & roil already muddy waters, but these calculations don't & seemingly can't take into account broadhead sharpness & design on penetration.  Come to think about it, how about range to the critter?...

Young guys, bear in mind back in the 60's & well into the 70's, very few hunted with bows greater than 50# @ 28", most I knew used 40 or 45.

This is why I don't get hung up on arrow weight, massive FOC, and to a lesser extent, broadhead (as long as it's good & sharp).

[Jerry Wald]

So I want to shoot a 750+- grain arrow with an ACS CX longbow at about 180-185fps - what draw weight do I need for a 28" draw then.

this should be good

Jer Bear

[Doug Treat]

This is exactly the stuff I need this year, you see, I plan on hunting elk with my little kids weight bow (about 45# @ 29" but it's a new bow shooting fastflight).  I have shot all the way through elk with my old 54# Shakespeare recurve (alum. arrows with Zwickey 2 blade heads).  I chronoed it shooting a 590 gr. arrow @ 155 fps.  I haven't chronoed my lighter bow yet but it seems to shoot a heavier arrow (620 gr.) maybe just a bit slower.  I'm betting on the newer bow and heavier arrow having the same or better penetration while protecting my bad shoulder.  We'll see!

[wingnut]

You adjusting the weight of the arrow and screwing with the momentum.

Leave the arrow and speed alone and calculate the weight of the bow to do it.

The elk can't read the number on the bow.  If the 495 gr. arrow is traveling at 170 fps then the momentum and KE are identical.

Try doing your math the other way.

Your 55# longbow shooting 700 at 170 is a 202 fps at 9 gpp bow.  Dang that's faster then an ACX and a Black Swan.
 

Jerry,

Somewhere about 72#s or so.  It depends on which length limb and what vintage of ACX.  But if it's the one that tested at 199 fps @ 9gpp this should be close.


Mike

[TradBowyer]

Mike, I think we are both right we are just working it differnt ways. THere are many ways to get the same performance levels and we are just going about it different ways. You are finding the bow poundage that will shoot the same arrow the same speed. I'm going the other way...starting with the momemtum factor and finding the setup that will give me the same number. My arrow weight will differ from yours but both setups will give the same number. you proved that a bow 15# lighter will shoot the same arrow the same speed. I showed that a bow 6# lighter will shoot a slighter lighter arrow and get the same. both are right its just what setup you want to use.

[Jerry Wald]

So I just got off the A&H website and this example is for a 700 grain arrow at around 181fps - perfect - now this is a comparison from a modern RECURVE @ 28" and an ACS @ 26" so with my 28" draw it shoudl be even better, but I am adding about 50 grains ok...

Example # 5
One archer draws only 26” and his hunting buddy draws 28”.   The archer with the short draw wants the same amount of energy for elk hunting as his partner.  His partner is using a top-of-the-line recurve that pulls 60# @ 28” and is shooting a 700 grain arrow (11.7 gr/#).  Because of the heavier arrow the recurve has a DE of around 78% and therefore puts 42.6 ft-lbs into the 700 grain arrow (compared with 40.95 for the 540 grain arrow).  This means that he shoots the 700 grain arrow at 181 fps.  The archer with the shorter draw length wants his ACS longbow to have the same amount of energy as his friend’s recurve and shoot the same weight arrow at the same speed.  What should his draw weight be at 26” with an ACS longbow in order to deliver the same amount of kinetic energy into his arrow as his friend’s bow?

Answer:  From the above discussion the top-of-the-line recurve that draws 60# @ 28” will deliver 42.6 ft-lbs into an arrow weighing almost 12 grains per pound.  An ACS longbow has a dynamic efficiency of .84 at 9 grains per pound, or about .87 at about 12 grains per pound.  The ACS has a SE/PDF at 26” of  .88.  Solving for the necessary ACS draw weight at 26” yields:  42.6/.87 = 49.0 ft-lbs of stored energy.  And given a SE/PDF of .88 we can calculate that the 26” draw ACS would need to pull 49.0/.88 = 55.7# @ 26” in order to equal his friend’s top-of-the-line recurve drawing 60# @ 28”.  So an ACS drawing 56# @ 26” is equivalent to a top-of-the-line recurve drawing 60# @ 28”.  Talk about leveling the playing field!  That’s what better performance is all about.

cooooooooooool jer bear

That's why I bought and ACS CX in the first place - I just want shorter limbs so she's for sale, but she's a performer

[don kauss]

my brain hurts...

[Guru]

Originally posted by Ragnarok Forge:
 Most of them are based on personal experience and feelings.  Both of which can be rather innacurate.  

The good news is that once you have run the tests and know the facts you can help clear up the debate.

I don't know Clay, I'd rather take "real world" personal experience" from a reputable bowhunter that's "been there,done that". Over numbers crunched by a computer....just my opinion and "experience"...

These threads are pretty cool and interesting though

[bearsfeet]

great post thatnks for the info

[Doug Treat]

Here's another way to look at this:  Let's say you're like me who wants good performance for reliable penetration on big game from a low poundage bow (for shoulder pain), but doesn't want to spend the money to buy a top performance bow.  The question is: not what weight bow you need, but what weight arrow you need.  For example, a fast bow today will shoot 9/gpp @ about 192 fps. so for this example a 55# bow will shoot a 495 gr. arrow @ 192 fps which equates to a momentum of 13.58.  If you take a slow 45# bow, you can get the same momentum just by increasing your arrow weight.  Let's say that you go to a 650 gr. arrow and your 45# bow will shoot this heavy arrow @ only 147 fps- that's about 23% slower, but slightly more momentum than the super fast bow shot the lighter arrow.  Now the question becomes, can I deal with the trajectory that the heavy, slow arrow gives me, or can I restrict myself to closer shots?  Using the same argument, one could shoot a selfbow with even less bow performance but end up with the same "arrow performance" with an even heavier arrow.  Hope this didn't hijack your original thought (which I agree with)but might be something else for folks to consider when crunching numbers.