62"

 

I would think the 62" may be fastest if shot with fingers, because it will make for a smoother release due to string angle. From a machine, I would guess the shortest will be fastest.

 

60"

 

"I would guess the shortest will be fastest."
I'm curious Raisins, I know there are variables, but what science/math supports that impression?

 

Well, with all else being equal (that's the key that I don't know about), the shorter limb will be lighter and therefore resist its own movement less (see rusty below). An interesting question though about a system more complex than it seems on its face. One thing harder to wrap my head around, at each instantaneous 'snap shot' as the string is moving from draw to brace, there is likely an optimal angle between string and limb for creating arrow speed. I have no idea what that is or which limb is more likely to achieve it more during the power stroke.

 

Still too many questions and variables to make any kind of accurate guess. Obviously the shooting will be done with a machine? Once the fdc has been done I think I would be able to tell you. Are all bows braced the same?
My guess out of a blue sky is shortest to longest. Fastest to slowest. But very little difference.
John

 

All limbs will be braced the same to get the same power stroke and shot from a machine.

Blacky

 

As the SA riser is shorter than the MA I'll go with the 58" limb set up.
If I guess right do I get the limbs?

 

My guess would be shortest to longest also. No experience to base that on, I'm looking to learn something here.

 

In a test of just one set of limbs of each length the result could be any of them. If you were to test a hundred of each length(all on the same riser) in past testing done by some serious hot rod bowyers, the fastest has been from longest to shortest(up to a point and 62" is well within that zone). My answer is based on the results of these various previous tests.

 

shortest limbs should have the least mass. shortest limbs should have less string weight. if the shortest limbs are not overdrawn they would be the fastest all other things equal.

I don't know this bow very well but I'll guess that the 56" may be short for max speed at 29" draw. I'll go with the 58" bow.

rusty

 

I'll go with the shortest limbs also??

 

This'll be a very interesting test to see.

If the limbs were synthetic I'd say shortest to longest would be fastest to slowest---everything else being equal. And my guess is that thats probably what will show here--at least one of the two shorter ones will prove fastest.
However given that the limbs are natural materials that can throw a set of random variables into the mix, I'd not be willing to make any substantial bets on the outcome.
I suspect that the action-boo and action-maple cores may go a long way in homogenizing natural fibre inconsistencies as compared to flat ground core lams.

Will you also compare the KE for the set?
And maybe throw in a heavy/light arrow variable?

Someday I'd like to see arrow trajectories plotted--say out to 40 yards for hunting bows and farther for target ones with a midrange trajectory rating like they do for rifle ammo

 

I am going to guess the fastest bow will be the shortest and the slowest the longest with the other two sets following the same pattern. When i was doing business with Groves archery, Jim Elrod, their bowyer told me the shorter bows "get the most out of the limbs". So that's my prediction....fastest will be shortest to longest.

 

Yep, too many variables to hazard anything but a guess. I guessed 60" because those Widow limbs that I have and have seen can get pretty narrow.Most shorter limbs I've seen by them are wider. My PSX vs. the TFX might be shading my impressions a bit. My experience has been that wider is slower.

I'm dropping by to see 'em next week so I could cheat a bit....

 

Weight difference isn't enough to matter in the small difference in limb lengths. The tips on the shorter limbs have to travel farther than the longer limbs. The string angles that raisins mentioned are what make the difference. A&H has done a lot of testing(longbow of course) and the longer limbs are faster than the shorter, the new short limbs they make are 4-5 fps slower.

 

Weight difference isn't enough to matter in the small difference in limb lengths.

Really? A shorter thing is stiffer for the same thickness, so the short limbs will also be thinner, I would reckon.

 

I know it's apples and oranges but the 65# 48" Bear I used to shoot underperformed the 55# Kodiak hunter in speed.

 

Seems there will be a 'happy medium' here. I bet a 10 foot bow would be slow as well, because limb weight becomes an issue. I guess it is balancing a few things and finding the right compromise. I have a 52" bear that I used to shoot. When I moved from this to a warf with carbon limbs, my arrows hit over a foot higher.

 

It will be interesting to see the performance from the draw force curve of each set of limbs and their corresponding speed factor.

 

I'm a bit geometrically challenged I guess. I'm having s hard time envisioning the limb tip motion
Anyone have a tillering board laid out with squares on the backing board?
I'd love to see photos of any given riser with a set of longs/mediums/shorts all pulled to say--28 amo so we could get an idea of the actual limb position at full draw.

I can't decide if the tips on the long or the short actually travel in a longer arc.

It also seems to me that stiffer limbs that move on release from full draw to rest with minimal bouncing would be more efficient--though maybe a bit "shockier".

So much wonderful mystery still left in the sport!!!
I'd absolutely love to win a lottery ticket and set up a little lab with some quality equipment, shooting machine, hi-speed cameras, acoustic meters, etc etc to figure some of this stuff out.

 

It's harder to think in curved surfaces or do math with them (unless it is a well-understood curve like the side of circle). I think you can see this thinking in straight lines. Imagine that the string at the center has to go from brace height to draw length, let's say from 7" to 27". So, 27 - 7 = 20". Imagine a right triangle now with this 20" length as its base. The hypotenuse is 1/2 the string length. Let's say our string is 60", so the hypotenuse of our right triangle is 30". This right triangle is looking at the top half of the bow at full draw. The side of this triangle we don't know is from the center to the limb tip. Using the pythagorean theorem, that length is the square root of (30 squared minus 20 squared), which is 22.4. Before drawing, the limb tip was 30" from center (half the string) and so during draw the limb tip moved downward 30 - 22.4 = 7.6". Of course, it also moved back too, which complicates the calculation enough that I won't give it here, but you'll get the point. Now, try the same process with the same draw length and brace height, but this time with a 50" bow, which will have a half-string length of 25".

This is...

25 - square root of (25 squared minus 20 squared) = 10"

So, with the 50" string (shorter limbs) you get 10-7.6 = 2.4" more downward movement.

R.

 

Well I am just going by a couple fellows I know, one with the most efficient bow Blacky ever tested and one with the fastest. Like you said raisins it's more complicated than folks think. Also goes to how much of the limb is actually working limb.

 

I'm not absolutely sure about this, but it seems to me that comparing the way a longbow functions on release to the way a recurve does is probably a bit of apples/oranges too. that extra curve flexing has to create differences. you basically have a leaf spring with one bend compared to a leaf spring with two bends.
It might be too that the amount of recurve in a recurve limb might make a significant difference. Bill Stewart was sure convinced and his multicurved limbs were the fastest Norb Mullany tested for a long time, and might still be for a pure wood/glas limb.

 

Another thing...we are looking at two things changing simultaneously limb length and total length/string length (and probably brace height too). Would be interesting to see a shorter limb on longer riser to maintain same total length, etc. As riser length decreases, any limb is moving more, hence stacking.

 

It has worked for recurves also. Only so much of the limb does any actual work.

 

Ok guys and gals,

with this test I don't want to do something too sientific. The reason I'm doing this is to get a feel of what the limb length will do to the bow's speed. A lot of times, customers opt for the shorter limbs, because they'll think that they'll get more speed. And I'm speaking of mostly target archers, that think a few more fps will do wonders, if they misjudge the distance to the target.

If you look at the guesses on this thread, they vary quite a bit. And to be honest, I also don't have clue what to expect.

But I have a gut feeling, that the differences in speed will not be much. At least not enough to worry about and to make compromises, when choosing the right limb length.

After reading the replies to my thread I'll Choose the following set-up for my testing:

I create f-d curves of all four sets of limbs and calculate the stored energy. Then I'll shoot each set at 26", 27", 28", 29" and 30" with an arrow of 9 grains/pound. I'll measure the different speeds and will calculate the dynamic efficiencies. This will give you guys and gals some numbers on what to expect, when you would shoot the different PSA riser/limb combos.

Like I said, nothing scientific, since I'm only using one set of limbs per length. And the results would also only be for that specific model from Black Widow.

I'll plan to do that on different bows of different manufacturers in the near future, so you could get a better feel, of what length limb would be best suited for your needs.

Blacky

 

Problem is when things like this are done, too many folks make it into more than it is on the WWW. It will be interesting and fun to see the results, but in reality it is no where near a conclusive test sample. Though you are right, the speed differences are usually very minute, though 4-5fps will make a measurable difference efficiency wise.

Well done on the math raisins, you are seeing part of the reason for my choice.

 

Also the simple fact is that most of us shooting with our fingers will probably get more shot to shot velocity variation because of release and anchor fluctuations than the various limb sets will generate.

Maybe a top rank target archer using a clicker will be more consistent but most of us shooting for fun and the freezer simply are not that well trained or motivated.