Dense woods and width/torsional stiffness

[DC]

That's what I thought your original question was.  I think the rotational stiffness will be close. 
The mass may be a little more in the higher SG, but not enough to make much of a noticeable speed difference.  This is just a guess.
As Steve's mass principle implies, SG and strength go hand and hand.  It would make sense that torsional stiffness would also be proportional to the SG.

Yes I knew you were following me but I thought some others were getting off track. After thinking about my imaginary idea I'm not so sure that the mass/stiffness thing is linear. Trouble with this stuff is running into a wall like this and just not knowing. I'm thinking how much stiffer a floor joist gets when you increase it's depth. Makes me wonder if dimensions might have a bigger say in things.
 Now I'm starting to wonder if stiffness is directly tied to density. I know that Ocean Spray SG 1.2 is incredibly stiff. Is there such a thing as a dense limber wood?

[Bayou Ben]

Yes I agree that dimensions are very important in making it stable.  But what I'm saying is once you find that cross section that makes the reflex stable you can shrink them down proportionately to account for the increased torsional rigidity of the higher SG wood, and the end result will be close in mass.
I've seen your bows.  You know how to make a bow stable 

[Halfbow]

Hmm I worry we are seeing disagreements where there are none.

I don't think anyone was arguing that denser woods wouldn't be rotationally stiffer. Of course they are. There is some variation of course, like I think osage is unusually limber for its density. But for the most part, stiffness is surprisingly predicable from density, and vice versa. And I'd expect rotational stiffness to track closely with overall stiffness, as it's all operating on the same compression/tension forces.

But, as we all know, dimensions also matter greatly to the stiffness of piece of wood. You can make a heavy draw weight bow from a light wood or a dense wood.

So DC, when you ask:

I agree but do the dimensions trump the density?

Most of us have given you the same answer in various different words. A "yes". Dimensions trump density. This is not a rule of physics, but rather comes from the fact that in bow making, we specifically tune the dimensions to trump density. This is how we get to our desired stiffness (our desired draw weight) with various woods.

This is not saying that dense woods aren't rotationally stiffer. Of course they are. But a bow made of dense wood will use less wood. You don't need much to hit your draw weight. So the question we are answering is: is this smaller piece of wood rotationally stiffer than a bigger lighter one. I think the answer is no (as long as the ratio of width to thickness stays the same) and I think that's the most relevant answer to bow making.

Maybe an imaginary way of looking at it is if you take a piece of wood with a .5 SG and magically compress it in width and thickness until it has an SG of 1 will it still have the same rotational stiffness? Hmmmm, I'm starting to think no.

If I read you right, this is basically the exact situation I laid out earlier, your SG numbers are even pretty close to erc and ipe. But yes, so long as the ratio of width to thickness stays the same, and the overall stiffness of the board stays the same, I would expect the rotational stiffness to also stay the same.

For your Ocean Spray bow, how you handle it will depend largely on the design of the bow. I agree with what Pat B was saying about that. I recommend following the standard knowledge. For example, I don't think the high density will help you get away with a narrow thick bow with big hooks on the end.

[bradsmith2010]

That makes sense,..I think I can follow that