Thinned or thick-wall heads more prone to cracking?

[TWO TOOTS]

"It was actually (as Jem knows) because I was considering taking an unblemished 90-year-old thinned-head Rudall Carte Boehm on trial. But now a moot point re. that particular flute because I've also just been told that both head and foot have cracked sometime between Christmas and now!"

Could this be the answer to your original question ? If the flute has a thinned head and standard thickness walled foot and both crack during the same period due to external conditions - presumably humidity/temperature, and not being damaged by accident ?

[Peter Duggan]

Not maybe the definitive answer, but certainly plausible circumstantial evidence!

[jemtheflute]

Just a thought raised by Dave Copley's excellent contribution - when considering the resistance of a metal liner inside a wooden tube, the physical form is I think likely to be a relevant consideration in trying to work out the balance of forces. The liner is not solid metal, but a cylindrical tube. Such a tube is, so far as I understand these things, a strong shape, quite resistant to lateral forces, especially to all-round compression such as one would assume a shrinking outer wooden tube to exert. The metal may be relatively soft and malleable and easily squashed or dented or bent outside the wooden cladding, but inside it its tubular form is very strong, more than adequately resistant to compression by timber shrinking around it.

Not that that really helps answer Peter's question, but since we've got onto the underlying processes.........

[AlanG]

Like Dave I've had to dig out my old college books on stresses in compound tubes (from the 60s so probably even older than his) though they never seem to consider wood as the outer material. I agree with Dave that there are different mechanisms at play here.

I did some calcs based on thermal expansion of the inner metal tube and, with the assumptions below, conclude that the stresses induced in the wood are so low that cracking should not occur, even with fatigue or the wooden equivalent,due to repeated cycles. The approach I took was simplistic but to me it seems reasonable.

The free expansion of the tube with 10C temperature rise would cause 0.0038mm increase in diameter but because of the restrictive effect of the Blackwood outer this is only 0.0013mm. The resulting hoop stress in the Blackwood is 1.18MPa, it's hardly being tickled. Thinning the Blackwood wall causes the stress to rise but not substantially.

I would have to conclude that the principal mechanism for cracking is repeated unequal wetting & drying out of the wood.

I'll happily send the spreadsheet to anyone who's interested.

Assumptions :
The wood is properly seasoned & completely dry & does not experience any change in temperature.
The silver liner experiences a 10C rise.
No credit is taken from the retraining effects of the end rings.

Stresses in a Flute Headjoint
Wood properties African Blackwood
O/D 28 mm
I/D 19.92 mm
Modulus of Elasticity Ew 17950 MPa
Modulus of Rupture 213.6 MPa

Tube properties Sterling Silver
O/D 19.92 mm
I/D 19 mm
Modulus of Elasticity Et 8.30E+04 MPa
Yield strength 124 MPa
Therm expans coeff 1.9E-05 mm/mm/degC
Temperature difference 10 C

Free diam expans of tube 0.0038 mm
Assume negligible thermal expansion of wood
Assume total strain is shared between tube & wood
thk tube*Et 3.82E+04 mm*Mpa
thk wood*Ew 7.25E+04 mm*MPa
ie actual expans of tube 0.0013 mm
Hoop stress tube =єt*Et 10.33 MPa compressive
Hoop stress wood = єw*Ew 1.18 MPa tensile

[jemtheflute]

Without benefit of calculations, I was reliably informed many years ago that the only dimension of a metal tube which changes significantly even under considerably greater heating than a flute liner will experience in use is its length, and that poses little structural risk to the wooden outer. That information was given (I forget by whom) in response to my quoting what I then believed, having been taught it by Paul Davies and/or read it in old flute books (maybe Bate?), that the cause of metal lined wooden tubes' propensity to crack was the different coefficient of expansion, metal being more reactive than wood. I/we now know better. "We" have known for many years that it is the ongoing dessiccation shrinkage of even well seasoned timber which is the primary mechanism of cracking over a metal liner. Peter's question about the behaviour of different thicknesses of wood is, in terms of detailed exploration, a new one to me.

[TWO TOOTS]

"It was actually (as Jem knows) because I was considering taking an unblemished 90-year-old thinned-head Rudall Carte Boehm on trial. But now a moot point re. that particular flute because I've also just been told that both head and foot have cracked sometime between Christmas and now!"

Could this be the answer to your original question ? If the flute has a thinned head and standard thickness walled foot and both crack during the same period due to external conditions - presumably humidity/temperature, and not being damaged by accident ?

I was given to believe that the first lesson in any Scientific experiment or research is " Observation. " If those two pieces of the flute ( thinned head & standard foot ) both behaved in exactly the same way ( cracked ) under the exact same conditions ( assuming they were together ) during the exact same period of time - it would suggest to me that you have ample evidence to reach some informed conclusion. All you need to consider is getting that information to someone knowledgeable enough to supply the answers in language that most of us can understand, and no disrespect folks ( myself included ) it does not seem likely that you will find them here.

[Peter Duggan]

ample evidence

But is it ample evidence? It's just one flute, which is why I suggested 'plausible circumstantial evidence'. And is that combination (thinned head and normal foot) a properly controlled 'experiment' even if they are together? Are both sections lined? (The whole head but just the socket on the foot.) Because otherwise you could also argue the thicker foot cracked without quite the same provocation as the thinned head...

I think you'd have to sacrifice a truckload of flutes in order to come to any reliable conclusions.

Perhaps someone could just turn a whole load of cylinder offcuts of varying thickness, slot them onto a metal tube/rod and leave them out to dry?

[TWO TOOTS]

There seems to be a certain sense of Dejas Vu with this topic with many well worn if not conclusive theories. As was mentioned earlier, unless someone takes the time, trouble and expense to conduct multiple controlled trials, then we are no wiser as to a definitive answer. In the absence of this knowledge, Care must be the watchword.

[Peter Duggan]

There seems to be a certain sense of Dejas Vu with this topic with many well worn if not conclusive theories.

Well, I asked the question, am seeing a certain amount of interest in attempting to answer it rather than any strong sense of déjà vu re. flute cracks in general and am certainly not bored of it yet. Not expecting definitive conclusions, but might struggle to reconcile having (your words) 'ample evidence to reach some informed conclusion' with being 'no wiser as to a definitive answer'.

[dcopley]

when considering the resistance of a metal liner inside a wooden tube, the physical form is I think likely to be a relevant consideration in trying to work out the balance of forces. The liner is not solid metal, but a cylindrical tube. Such a tube is, so far as I understand these things, a strong shape, quite resistant to lateral forces, especially to all-round compression such as one would assume a shrinking outer wooden tube to exert. The metal may be relatively soft and malleable and easily squashed or dented or bent outside the wooden cladding, but inside it its tubular form is very strong, more than adequately resistant to compression by timber shrinking around it.

Totally in agreement there Jem, and that was an assumption I did not spell out. Everything I wrote assumes that the metal is not stressed beyond its elastic limit, and does not get permanently deformed. And yes, the tube on its own could be more easily bent as you described. I would assume that any flute maker would use tubing in a hardened condition to minimize this sort of damage on any exposed metal.

[AlanG]

Do most flute makers actually go to the trouble of heat treating their metal tubing ? And is it actually desireable ? I'd have thought it better to have the metal section inside the headjoint as soft and malleable as possible to reduce resistance against shrinkage of the wood. Plastic deformation inside the headjoint would be small & wouldn't affect anything. The tubing needs to be just strong enough for the section outside the headjoint to withstand the rigours of handling & assembly.

I quite like Peter's suggestion about the offcuts. It would be interesting to know how flute dimensions vary with changes in humidity throughout the year. If anyone has an old section of flute they don't want, maybe a maker with one that went wrong, plus a micrometer, hygrometer and a nerdish curiosity maybe they could make regular measurements.

[Peter Duggan]

In the absence of this knowledge, Care must be the watchword.

I don't get this bit. What care? Care in interpreting theories without hard evidence, or care of the flute? Of course care is required in either case but, if the latter, the presence/absence of said knowledge makes no difference because you're not going to start treating your flute carelessly after discovering that whichever you have (thick or thin) has a slightly reduced risk!

[Nanohedron]

I think you'd have to sacrifice a truckload of flutes in order to come to any reliable conclusions.

Perhaps someone could just turn a whole load of cylinder offcuts of varying thickness, slot them onto a metal tube/rod and leave them out to dry?

Ah, but imagine the hordes of fluters beating their breasts and rending their garments at the unlucky spectacle of a hundred whole flutes abandoned en masse to the elements. That's entertainment.

[TWO TOOTS]

I think you'd have to sacrifice a truckload of flutes in order to come to any reliable conclusions.

Ah, but imagine the hordes of fluters beating their breasts and rending their garments at the unlucky spectacle of a hundred whole flutes abandoned en masse to the elements. That's entertainment.

Sounds like a cracking idea!!

[dcopley]

I did some calcs based on thermal expansion of the inner metal tube and, with the assumptions below, conclude that the stresses induced in the wood are so low that cracking should not occur, even with fatigue or the wooden equivalent,due to repeated cycles. The approach I took was simplistic but to me it seems reasonable.

The free expansion of the tube with 10C temperature rise would cause 0.0038mm increase in diameter but because of the restrictive effect of the Blackwood outer this is only 0.0013mm. The resulting hoop stress in the Blackwood is 1.18MPa, it's hardly being tickled. Thinning the Blackwood wall causes the stress to rise but not substantially.

I would have to conclude that the principal mechanism for cracking is repeated unequal wetting & drying out of the wood.

Looks like you did what I was too lazy to do ! Quite a few years ago I reached the same conclusion with a very quick and dirty experiment, reported somewhere in the Chiff and Fipple archives. There had been some discussion as to whether head joint cracking was caused by thermal expansion of the metal liner. I took a lined blackwood headjoint, sealed up the embouchure hole, and poured boiling water into it. No cracks. The same boiling water technique also works well to free a stuck tuning slide.

The only thing I would question in your calculation is the modulus of elasticity for the blackwood. Most data sources only give the modulus in the direction parallel to the grain, and the modulus in the radial and tangential directions is from 10 to 20 times lower than that along the grain.