deflex and reflex theory

[sleek]

I think Steve is right on the money, I think the designs claim to fame is the superior string angle you could certainly build a reflex bow of the same length & draw that would have much greater early draw weight but would have less performance then the D/R of the same length/draw & mass !

I agree with Steve too, I'm pretty sure. (Steve please correct me if I'm wrong about that and we disagree)

Common D/R bow designs definitely have great geometry for efficiency, and offer great string angles. And yeah I agree, it's easy to make a D/R bow that outperforms a reflexed bow of the same length and draw. Some of that is because of limitations of wood, but a lot of it is also those geometric benefits.

My one quibble with what you said is about mass. Assuming the same material, same length, and same draw, I think you'd have a hard time getting a D/R bow's limbs to be the same mass as a reflexed bow's limbs. Not without going with pretty unideal limb dimensions.

Deflex also forces more thickness to be in a limb because it offers a leverage benefit over a straight or reflex limb. As a result, the limb has to be thicker to accomodate a reduced bending radius.

Exactly. And the deflex further reduces the bending radius, requiring a yet more stout limb to get up to draw weight.

I think with mass, a R/D gives you less mass. We all know the rule where a bow twice as thick is 8X stringer than one twice as wide. The side affect is that a bow twice as wide is almost twice as heavy ( EXTREEM GENERALIZATION to carry the point ). So when you deflex, you allow the reflex limbs to not need to be so wide, which drops the mass even though you are thicker in the limb to accommodate the reduced bend radius the deflex allows for.

[Halfbow]

I think with mass, a R/D gives you less mass. We all know the rule where a bow twice as thick is 8X stringer than one twice as wide. The side affect is that a bow twice as wide is almost twice as heavy ( EXTREEM GENERALIZATION to carry the point ). So when you deflex, you allow the reflex limbs to not need to be so wide, which drops the mass even though you are thicker in the limb to accommodate the reduced bend radius the deflex allows for.

I get what you're saying, but I don't think so. Imagine an R/D bow. Deflex in the handle. Cut it in half and splice it back together so the limbs are straight. Now it's a reflexed bow. Now the draw weight is higher. It probably won't even pull back to full draw anymore without breaking. Scrape some wood off the belly to get it bending more. Make those limbs thinner. Scrape till you get the draw weight down to what it was. Now you have a reflexed bow that's the same draw as the original, but with lighter limbs.

[Rākau]

but to prevent the limbs from taking massive set from the increased reflex they would need to be wider and therefore heavier would they not?

[Halfbow]

I mean potentially. But potentially not. We would need to pin down more details to have a better idea. How wide are the limbs? How deflexed is the handle? How high is the draw weight? How long is it?

To say that we would absolutely need to widen the limbs is to say our hypothetical project here is doomed from the start. But I've seen this sort of thing actually done. Cutting an old bow in half, re-splicing at a more aggressive angle, and re-tillering. It worked well. No more wood was necessary on the sides. Keep in mind that by scraping the belly, we are making the limb thinner, and thus more safe and less likely to take set.

But if you imagine a narrow limbed D/R bow that is extremely deflexed at the handle (so we have to change the angle drastically to make it straight at the handle), yeah it probably won't work. But it's just as easy to imagine subtly deflexed and wide enough D/R designs for which it will work. But all that points out is that reflexed bows are less forgiving to make. Which is definitely true. Either way, my point stands.

[Del the cat]

I think there are 2 ways to look at it.
1. The geometry and physics behind the D/R design is probably beyond most of us (it's certainly beyond me)!
2.To explain/understand it, I look at it this way:-
The reflex adds early draw weight and improves the string angle approaching full draw. However wood can't take the strain resulting from a big reflex and that's where the deflex comes in, enough deflex is added to nullify the excess strain whilst still maintaining the advantages of the reflex.
Dunno if this explanation really holds water, but it seems intuitively sensible.
Del

[sleek]

I'm going to hold fast. With the addition of deflex, you drop your bend radius and need to keep the limb thicker to accommodate that. You certainly CAN make it wider instead, but width adds mass, 8x faster than adding thickness. So the results you can get will depend on your built technique.

[Beba]

Interesting conversation. I almost never post but I can’t resist this one. It seams to me that with any reflex your increasing the forces of compression and tension. Most woods are stronger in tension so the belly is at risk of being crushed. The greater of those forces are on the surface area, lessening towards the center. I would believe more mass in width is needed, giving the needed material to resist those forces without  crystalling/checking. I suspect It could also  minimize the mass in the  neutral section of the limb. These are not so much my thoughts as they are my understanding / experience with Steve’s  mass principal. I’d love to hear any expansion on this  principal in how it pertains to the D/R limbs.

[Halfbow]

I'm going to hold fast. With the addition of deflex, you drop your bend radius and need to keep the limb thicker to accommodate that. You certainly CAN make it wider instead, but width adds mass, 8x faster than adding thickness. So the results you can get will depend on your built technique.

My thought experiment was exactly an example of a D/R bow having thicker limbs to accommodate the reduced bend radius. No change in width between the 2 bows. That's what you're saying, right? With no change in width, the thicker limb is heavier. And the thought experiment is realistic, I've seen it done before. Just thinning the limb can be enough to get it happily bending more.

However, adding width does not add mass 8x as fast. The stat is: doubling a bow's thickness makes it 8x as a stiff, while doubling a bows width makes it 2x as stiff. The change in stiffness is the interesting bit there, and nothing is happening at 8x the speed. The change in stiffness is exponential.

But mass gets added linearly with how much volume you add. So long as your bow limb is wider than it is thick, making it a millimeter wider will actually add less mass than making it a millimeter thicker.

So even in the cases where the deflexed bow could never be cut in half and converted in to a reflexed bow because the limbs are too narrow, if we could magically add mass to the sides, let's not get carried away with how much weight that would add. Yes, we all know that for any given stiffness a narrower thicker limb will have less mass than a wider thinner one. But we are not talking about the same stiffness here. Easier to bend limbs tend to be lighter. That's why lighter draw bows tend to have lighter limbs. If the difference in stiffness is significant, I think you'd have to have some pretty extreme paddle bow esque dimensions before the easier to bend limb actually became heavier. And we know that good reflex bows are possible without looking like extreme paddle bows.

[willie]

so here is a thought to consider....

if a glass bow is not subject to the same limitations as a wood bow (set), then why do so many glass bow designs incorporate the deflex along with the desirable reflex?

[Stick Bender]

Willie ask the same question that was in my mind , glass D/R bows where there's no worries about over stressing the materials, but they achieve superior performance over reflexed glass bows of identical mass why?  I think because of the superior string angle/leverage same with wood I think another real advantage of the design is you can make a shorter bow for a given draw length vs a strait reflexed bow do to the deflex ! Fred Bear spent a life time perfecting the D/R design !

[PatM]

Deflex reflex leaves less residual energy in the bow after the loose so they are more user friendly.

 Fred didn't actually devote a lifetime to that design.   Probably only 30 years if that.

[Selfbowman]

Fred new his stuff along with a few others. Yes this is all true in a glass bow . The mass ratio between glass limbs and wood are different are they not? The make up of compression strength is also different. So comparing the same design is not a good comparison in my opinion. The stable r-d bows end up with to much mass on the otter limbs imo. Causing shock and slows the bow. This is in a wood bow more than a glass bow. I have built both and prefer Longbows with only reflex plus what ever set you end up with. Again set is the enemy in any wood bow no matter the design! Arvin

[Stick Bender]

Arvin maybe the glass vs wood was not the best example ,all thought the same design principals are at play with the exception the wood being a less radical bend as a example of that the guys I know that are making some of the BBO, BBH ect are getting some pretty good numbers over a  ASL glass bow of the same length and draw/weight if you compared the BBO in the example to the glass ASL full draw profile the string angle on the D/R BBO with the mild D/R is still superior to the glass ASL even with it taking set granted the glass has a slight increase in mass, I'm not arguing that set & mass location doesn't play a roll in the design in the wood D/R ,I'm  just saying that the better the string/leverage angle in any bow regardless of material the more superior the performance & Pat is right about the design being user friendly especially with the shorter bows designed for longer then normal draws , there are guys out here playing with some more radical bent bamboo backed bows it would be interesting to see the numbers on those ! I think Steve said the same thing I did in 2 paragraphs vs my long winded version....lol

[Halfbow]

Some highly reflexed asiatic style glass bows do put up good numbers. But I agree with PatM, D/R bows are more user friendly. Easier to string, easier to tune, easier to be accurate with, less delicate etc etc. But they also perform well. It's a good choice for commercial fool proof bows.

If you accept what I've been saying about reflexed bows having higher string tension and lighter limbs for the same draw weight (as stuckinthemud said in his original post), it might seem odd that D/R bows can hold their own in performance. As many have been saying, I think it's largely due to the geometry and string angles.

Recurved tips are good, but they don't make the difference here. You can recurve the tips of both reflexed and deflexed bows. The difference maker is the deflex.

I can actually shed some light on the geometric benefits of deflex. It's not terribly mysterious. In fact, I think I can sum it up in one sentence:

A straight line is the most efficient way to cover distance, and deflexed bows are usually less bent at full draw, so the tips end up farther from the handle.

To illustrate:


These two bows have exactly the same limb length, the same brace height, and the same draw length. Yet you can see that the deflexed bow ends up with better string angles, and is acting like a longer bow at full draw. These bows start with straight limbs just to make it simpler, but for basically any limb shape, curved, recurved, whatever, the more overall reflex a bow has, the farther its limbs have to bend. The farther they bend, the more their effective length changes. So the reflexed bow will usually have lighter limbs and higher initial string tension, but the deflexed bow usually has better geometry.

[Stick Bender]

Thats a great illustration & concept I really like bow B my current test bow has the same geometry in deflex but with working reflex & is one of the best performing bows for being a short bow of 58" drawn to 31"  with the string angle of a much longer strait bow its my best performing short bow to date ! The other user friendly trate on these bows is when built right they have very little energy left over and zero detictable hand shock !