Lam stack thickness/weight ?

[scars]

If someone made a hill style bow and missed the weight they could pike it to gain a few extra pounds. So many pounds per inch. But if you had a bow at say 68" and you liked it. But you wanted to make another bow with the same weight at say 64" could you measure 2 inches away from the fades towards the tips, get the stack thickness there to make a bow 4 inches shorter and retain the same weight? Sorta like piking the bow in the middle of the bow before glue up.

[canopyboy]

Deflection at the end of a cantilevered beam is a function of length cubed over cross sectional moment of inertia (which is a function of thickness cubed.)

I'll now skip the steps that will bore you as no one seems to find them that cool.  But the math cancels out to the following:

For the same draw weight and length (ignoring slight differences in string/limb angles from the change), your stack thickness should vary as a ratio of the working limb length.  So if you have a 68" bow you like with a 16" riser, you have a 26" working limb nominally.  If you want to go to 64" with the same riser, you have a 24" working limb.  To maintain the same weight, drop the stack thickness to 24/26 or 92.3% of the original. This assumes your materials are all the same, etc.

Measuring the thickness 2" out won't help you.  Some people use very little thickness taper in their limbs and so you would not see a significant reduction in stack dimensions.  Even with 0.006 taper, you will be in the area of 97-98% 2" farther out.

[LittleBen]

If you don;t know the taper and want to find it, measure two points on the limb betweent eh fades and any tip wedges, and make the measurements at 20" apart ... then you can get the taper, and you can backtrack to get the stack butt thickness.

[Pheonixarcher]

Wow! That's some good info right there.

[scars]

Canopyboy, thanks I like that, a simple division to get %'s. I wonder if as long as the SG and the MOE are the same the wood used can be changed?

Little Ben, You are saying that the total thickness of the stack once known can be divided by the number of lams, even number is same taper, odd would be different size taper?

Pheonixarcher, that why I like asking here at tradgang.

Thanks  all

Joe

[canopyboy]

Do you mean SG = specific gravity and MOE is modulus of elasticity?  If so than I would agree, especially with the modulus of elasticity (Young's Modulus - E).  I think specific gravity will only affect the mass of your limbs, not the stiffness -- which will affect the limb dynamics but not the static draw weight. The problem though is that E changes with woods, even the same species lam to lam somewhat.  Luckily your glass is the most important player being at the outer fiber and having the highest value of E.  And glass tends to be more consistent.  But as I realized with my yew bow, the core can make a difference as the limb gets thicker as on a Hill bow, or if you change glass thickness.

Ben's method above gives you total stack taper.  If you measure a 0.100" difference in thickness over a 20" span, you have 0.005/in total taper.  You can do it with several parallels and one 0.005 taper lam, or (5) 0.001 taper lams, or (2) 0.002 and (1) 0.001 taper lams, etc.

As for the math with my first paragraph in case you are really interested in the details:  deflection of cantilivered beam is proportional to (force*length^3)/(moment of inertia*Young's modulus) or WL^3/IE.  If draw weight (W) at a given deflection stays the same, you're left with L cubed over EI.  I is width * height^3/12.

[scars]

canopyboy,

Geez, I only have ten fingers...    
Just had to do that.
I mentioned the SG in regards to limb mass.
MOE and your cantilevered beam deflection I am familiar with from the TBB series and Adams K book.

Bens method of 20" in midlimb is interesting because if the total number of lams does not add up then it means that there are parallels in it. If I am seeing it correctly.

I have been making my lams with a power hand planer. Dean T style, for backed bows and tri lams. But I don't think that is going to work with a glass bow. So I am doing some research looking for the easy way.

Thanks for your knowledge and experience.

[canopyboy]

Yep, I think more common to find a bow with at least one parallel lam than all tapered lams.

You really can't beat the price/service/quality of one of the sponsors like Kenny, Troy, Kurt, etc here on TG for lams for a glass bow.  Heck, Kenny has even ground wood that I harvested and seasoned and sent to him.  I thought about trying to set myself up several different ways.  In fact, I almost bought the baby griz drum sander last month.  But have come to the conclusion I would have to be cranking out a lot of bows to make it worth the expense and hassle.  And nobody I've talked to seems to find it much fun.  Just my two cents.  It's tempting until you really think it all through.