Carbon fiber and neck stiffness

[Michael Thames]

Here are the results of Jim Martin's neck reinforcement models, I think the numbers speak for themselves no need to go to far into this. As everyone knows there was a heated debate about this prior to these results, so here they are!

There seems to be a big misunderstanding between the two sides who have presented data and a hypothesis of the data, namely Trevor Gore and yours truly. My initial motivation to present new data was to correct a very serious misconception concerning the use of FC truss rods for neck reinforcement. While perhaps not a burning issue for those who build steel string guitars using an adjustable truss rod, it is of paramount importance to classical guitar makers due to the fact that adjustable truss rods are not traditional and classical makers usually opt for non adjustable CF rods, or ebony strips etc.

The information published by Trevor Gore in the Guild of American Luthiers stated CF neck reinforcement was unnecessary and added no benefit over "reasonable wood". Trevor, based his conclusions on Hurd's program which had the worse possible placement for the CF rod, as well as a modulus of almost half of that of present day industry standards.

Using this data it's not hard to understand why Trevor arrived at the conclusions he did about CF neck reinforcements, and published his findings. However, I and a lot of luthiers didn't buy it. So, we took some time studied the issues and instead of using wrong data, and the worse possible placement of the truss rod, we decided to use the latest correct data for CF, and place the truss rod where it would be of optimal benefit...... namely off the neutral plane, buried deep into the neck. It is with this motivation that Jim Martin ran the numbers with the correct data and CF placement. He got a 92% increase in stiffness while Trevor Gore got a 9% increase. Jim's finding are extremely significant for those who are, or are considering CF reinforcements.

So without further ado, I proudly present Jim Martin's models on CF reinforcements. We hope you find these useful in you guitar making, we certainly have.


To investigate the issue of neck reinforcement I modeled a guitar neck using the structural mechanics capability of COMSOL™ Multiphysics Engineering Simulation Software. This is a finite element code that is very accurate and is widely licensed to academic institutions and industry. Those interested in this code can visit their website.

Neck stiffness is strongly dependent on neck geometry. I used a 6 mm thick fingerboard, a total neck thickness of 22.5 mm, a 0.250”x0.500” rectangular carbon fiber rod placed 2.3 mm below the fingerboard and radiused the neck back to 48.625 mm. The neck is thus comprised of the 6 mm fingerboard, a 7mm rectangular section of cedro or mahogany, a semicircular section of cedro, and the embedded cf rod. The neck width was 57 mm. These dimensions are a good approximation to the necks I am interested in, but may differ from other designs.
The material parameters are also critical and I could not determine the basis for some of the parameters used by Gordis in his informative article on neck reinforcement.

http://www.ukuleles.com/Technology/neck.html

In particular, I noticed that the specific gravity of ebony is given as 0.65, but it is actually listed as 1.1-1.2 in engineering texts and all of the ebony I have tested does indeed sink in water. Likewise, the specific gravity of carbon fiber composite is listed as ~0.9, but in engineering tables is given as 1.6. The carbon fiber composites I’ve tested also sink in water. Although these discrepancies do not affect stiffness calculations, they led me to investigate the basis for the various Young’s moduli. In particular, the Young’s modulus of carbon fiber composite is given as 10.0 Mpsi and the source of this value is given as Moses, Inc. This value is much lower than the published value of unidirectional carbon fiber pultrusions and would lead to a significant underestimate of neck reinforcement. For example, the table at

http://www.performance-composites.com/c ... ties_2.asp

gives the modulus as 135 GPa (19.6 Mpsi). However, 10.0 Mpsi is extremely close to the accepted value for woven fabric (70 GPa, 10.1 Mpsi), so perhaps woven fabric is the source of this value. However, I am interested in reinforcement with unidirectional pultrusions so I contacted Moses, Inc. who directed me to DragonPlate, and there I talked with design engineer Joe Kummer, who was extremely helpful and knowledgeable. Joe informed me that a modulus of roughly 125-135 GPa is reasonable for unidirectional pultrusions, and I used 135 GPa. However, it would always be optimal to test the materials you plan to use to obtain their particular properties. For high modulus carbon fiber unidirectional pultrusions I used the value 170 GPa (24.6 Mpsi), which is published on the website listed above. For both materials I used a Poisson’s ratio of 0.30, also taken from this site.

Obtaining modulus values for wood is a second issue with its own problems. Everyone who works with wood is painfully aware of the significant variations of its modulus and I can think of no material more problematic in its behavior. Not only do significant modulus and density variations occur, but the material is viscoelastic and can exhibit significant creep, the rate of which is strongly temperature dependent. Creep helps archers straighten arrows and helps luthiers bend sides, but it drives the bow maker crazy because he has to wait roughly a decade for yew wood to age sufficiently that a bow can be made that does not too seriously ‘follow the string’ and can lead to increasing deformation of a guitar neck under the persistent tension of strings (especially one left inside a hot car). So it must be appreciated that the moduli tables listed for wood are for experiments that are of short duration, on the order of minutes or seconds. If the duration of the experiment is very long (months or years) the observed moduli can relax to significantly lower values. The kinetics of this relaxation will be markedly influenced by temperature and humidity. It is easy enough to find tables of moduli for a variety of woods, but these are only the moduli one would use to compute the immediate stiffness of a neck, and do not pertain to its deformation over long time periods (stability). The proper way to think of wood is that when a load is applied the strain will generally increase with time, due to the relaxation of the initial modulus relative to that load. If an additional load is applied the initial modulus must then be used to compute the additional immediate strain, and then this modulus also relaxes with time. The proper computation of strain for a viscoelastic material subjected to a variable load history is treated in any standard text on viscoelasticity and is a simple integral involving the load history and the time-dependent modulus. The point here is that wood modulus values from published tables pertain only to the initial neck deformation and cannot be used to compute neck stability. None of this discussion should be misinterpreted to mean that the physical properties of the wood are changing with time: this might occur, but aging is an additional consideration.

To obtain some idea of the increase in long-term neck stability due to CF rod reinforcement one can recompute the neck stiffness assuming a lower modulus for the various wood components. Ideally, one would collect these time-dependent moduli data from experiments of long duration or would conduct experiments of shorter duration and use ‘time-temperature superposition’ to compute the relaxation behavior of the material at lower temperatures, which is the standard experimental method for viscoelastic materials, especially those with a glassy transition temperature far above the application temperature.

After some investigations into the literature I used the following values for the various initial Young’s moduli of the neck woods, typically measured at 12% moisture content. To determine the actual values for the wood you are using each piece must be tested using a 3-point bend or other convenient method.

2.0 Mpsi – ebony
1.80 Mpsi – royal mahogany (Honduras mahogany is ~1.5 Mpsi)
1.00 Mpsi – cedro (This is an estimate based on its density. Does anyone have data?)

Ebony appears to be remarkably compliant for a wood of such high density. I would appreciate hearing of any measurements of its initial modulus. Poisson’s ratios were taken as 0.35, typical for wood in this geometry. The neck bending stiffnesses were then computed and their relative values are:

1. cedro/ebony - 1
2. cedro/ebony/carbon - 1.92 (92% increase)
3. cedro/ebony/HM carbon - 2.09 (109% increase)
4. r. mahog/ebony - 1.40
5. r. mahog/ebony/carbon - 2.14 (53% increase)
6. r. mahog/ebony/HM carbon - 2.30 (64% increase)

We see that the DragonPlate CF pultrusions significantly increase neck stiffness in the specified geometry. Some of you might have other moduli you would like to see run, and I could accommodate a few requests, but the effects are fairly clear, and the moduli of royal mahogany and cedro probably bracket that of any neck wood one would use. For example, for unreinforced H. mahogany one would expect the relative neck bending stiffness to be roughly 1+0.4x0.5/0.8=1.25. If reinforced, the neck bending stiffness is roughly 1.92+0.22x0.5/0.8=2.058. The stiffness increase is then roughly 65%.

A comparison between the various values also shows that neck stability is also significantly increased. For example, suppose that one builds a neck of mahogany/ebony and the modulus of the mahogany to the initial string load relaxes to that of cedro over some extended period of time. The relative stiffness to that load thus relaxes from 1.40 to 1.0, a 28.6% reduction. If the neck is reinforced with standard CF the neck stiffness to the initial load relaxes from 2.14 to 1.92, a reduction of only 10.3%. [I became curious enough about this linear interpolation approximation to actually run H. mahogany. For an unreinforced neck the relative stiffness is 1.265 (vs. 1.25 estimated) and for the reinforced neck I obtained 2.062 (vs 2.058 estimated). The stiffness increase is thus 63% (vs 65% estimated).]

If more modest levels of neck reinforcement are desired, perhaps to achieve the optimal string relief, then smaller carbon fiber materials can be placed just under the fingerboard. For example, if a woven CF fabric of cross section 0.125”x0.375” and modulus 10.0 Mpsi is used to reinforce an H. Mahogany neck of the dimensions we initially specified, the stiffness increase is only 3.7%. If a unidirectional pultrusion of dimensions 0.125”x0.500” and modulus 19.6 Mpsi is used, then the stiffness increase is 22%. Clearly CF materials enable a luthier to judiciously control neck stiffness over a wide range.

In modern recurve bow limbs a thin cross woven carbon fiber fabric is sometimes laminated in the neutral plane of the limb. This vastly increases torsional stiffness, and thus limb stability, without greatly increasing the bending stiffness of the limb. This approach could also be applied to guitar necks in combination with the CF rods. One simple approach is to laminate this material to the bottom of the fingerboard.

Finally, Joe Kummer of DragonPlate pointed out the new “D” section CF neck reinforcements, which look pretty interesting. These also increase the torsional rigidity of the neck, thus reducing warpage. I would be very interested in hearing from anyone who has tried this product.

James E. Martin
Tijeras, New Mexico

[Dekka]

Phew! Thanks for that, Michael. I couldn't have coped with another sleepless night worrying if I was achieving maximum stiffness.

Rigid regards, Derek

[Michael Thames]

Phew! Thanks for that, Michael. I couldn't have coped with another sleepless night worrying if I was achieving maximum stiffness.

Rigid regards, Derek

Dear Rigid, there are an entirely different set of models for that kind of calculation, first I would avoid alcohol altogether, hang out with beautiful women as much as possible, in fact, buy them alcohol instead. If you marry, marry a young girl, not one your age, if ur not married, then keep an assorted collection of lovely ladies around, nothing like variety for maximum stiffness. Don't over eat, and get fat. Last but not least, don't read any high tech books on this subject, I've just given you all the information you need.

Good luck and I hope things improve for you.

[Trevor Gore]

Not again, Michael. I am getting heartily sick of your putting words into my mouth, just so you can argue about them.

Let’s just get the record straight about what I have and have not published.

The information published by Trevor Gore in the Guild of American Luthiers stated CF neck reinforcement was unnecessary and added no benefit over "reasonable wood".

This is a complete fabrication on your behalf.

What I wrote in American Lutherie #111 when invited as a “subject matter expert” (their words) by GAL in response to a reader enquiry was this:

“Finally, the neck can be made stiffer. One way of achieving this is by adding carbon fibre rods to the neck shaft. However, using the types of rods that are typically available and placing them in the neck wood beneath the fretboard achieves a stiffness increase of ~9%. A similar increase in stiffness can be achieved by making the neck ~1mm thicker.”

The full document, for context, is here,

Response to GAL.pdf

(41.38 KiB) Downloaded 675 times

or check it in AL #111.

CF rod is available from both LMII and Stewmac and these suppliers are typically where guitar makers would source their supplies. Both organisations recommend installing the CF immediately beneath the fretboard. Stewmac have the recommendation on their website, LMII have it in their printed handbook-catalogue. Rightly or wrongly, this is how the vast majority of builders install the CF and is why I mentioned that configuration in AL #111. Taking the range of available Stewmac rods and using Hurd’s program, a typical classical guitar neck/fretboard configuration and a modulus for the CF of 20Mpsi the range of increase in stiffness is from ~6.5% to ~16%. I have no reason to doubt the efficacy of Hurd’s program as a recent independent finite element analysis by Jim Watts has produced essentially the same answer (15%) for this configuration using similar input data. Anyone using this technique in an attempt to solve a stability problem will still have at least 84% of the problem remaining.

If the reader enquiry had been “how can I make a really stiff neck”, I would have given a different answer, probably along the lines of “make your necks like Ken Parker does”. Ken laminates the CF around the whole of the outside of the neck and fretboard.

In a paper I was invited to write by the Acoustical Society of America, I said this:

“A stable neck can be manufactured from a wide range of woods. Further, if reasonable
wood is chosen, the author’s experience has been that it is unnecessary to complicate the
manufacture of the neck by using multiple laminates of either wood or composites to add
stiffness and stability to the neck. Adding carbon fibre to the neck does not seem to
produce any audible advantage whilst adding significantly to the build complexity”.

The first sentence is clearly true. The second sentence is also true, in my experience. The vast majority of guitar necks are not multiple laminates and do not contain CF composites and survive just fine and have done for decades if not hundreds of years. Let’s look at the third sentence. I can’t hear any difference due to CF in guitar necks. I’ve never heard of anyone who can pick where a guitar neck has CF in it just by listening to it. Let’s face it, most people can’t pick with any great certainty a guitar with CF in its soundboard. So we’re left with arguing about build complexity. If you put CF right though the neck, like a multi-lam neck, you have serious problems shaping the neck. The CF will chip out tungsten carbide tooling. I know, I’ve tried it. If you bury the CF deep in the neck, broadside across, so it’s of most benefit, you have to cut a deep, wide, channel in the neck shaft leaving ~2mm of wood at the bottom, lay in the CF rod, then fill the channel. I wouldn’t be jumping to do that operation with a router, rather a table saw and dado blade. But a table saw is otherwise unnecessary for building guitars. So that seems to add quite a bit of complexity. Or you can do it like Stewmac and LMII recommend, which is simpler but is of little benefit.

So there’s not much to argue about in that quotation. It’s only when you selectively and maliciously mix portions of the two quotes out of context that you have anything to argue about.

Further, let’s look at some other things I’ve written:

Here, here, here, and here, a total of 4 times just recently, I’ve said words to the effect that if you better position the CF in the neck you’ll get a greater increase in stiffness.

My initial motivation to present new data was to correct a very serious misconception concerning the use of FC truss rods for neck reinforcement.

I assure you, whereas others might have misconceptions about how to use CF, I haven’t.

I’m pleased that you have become interested in the engineering side of guitar design but how about you just stick to the facts and give the fabricated “quotes” a rest.

[Michael Thames]

Trevor, I acknowledge all your calculations are correct except the correct modulus for CF. I said that in my opening post. I also said you didn't do the calculations for optimal CF placement, or did I miss something? Jim Martin's idea was to show the optimum results instead of the lowball ones you gave, regardless of your motivation, and justifications. End of story!

Oh BTW, Jim Watts agrees with Jim Martin, I'm sure you already are aware of that right?

Look up the definition of the word "quote" as opposed to a "paraphrase". I told you in another post I was tired of supplying endless quotes so I restored to paraphrasing, so shoot me!

Bottom line is you argued endlessly with me sticking to your guns not budging an inch over your 9% stiffness increase, through 15 F&%king pages on delcamp. If people don't believe me they can look it up at delcamp scroll back to page 34 you can find it there, get out the popcorn sit back and watch the train wreck.

I'm now done with you, I did what I said I would do (supply optimal models via Jim Martin) and mission accomplished.

Now I leave you all with my heartfelt wish.........may everyone's rod attain a higher stiffness than Trevoe Gore's.......... good day!

[ozwood]

Hi Trevor,

This nugget is for you, I was one locked in a debate that was going nowhere, a lot like this one , not because my logic was flawed, but because because the person I was arguing with had little interest in the facts, anyone elses point of veiw or anything other than there own agenda, it was for that individual, about being right at any cost .

My Boss, at the time pulled me aside and said, " if you ague with an idiot for too long, after a while it becomes unclear which one is the idiot".

Now I am not suggesting for one second your an idiot, but clearly your locked in a debate with one, in actual fact most of us don't give a shit what this blow in has to say, I hope Bob deletes the whole sorry affair, which is clearly just an attempt by a nasty and somewhat obsessed individual to discredit you on your home forum, having dressed it up as trying to serve the greater good.

Sometimes the best thing to do with an attention seeker is just to ignore them !.

I suggest WE ALL do just that , I'm taking Bobs advice heading up the shed to make some sawdust.

Cheers,

[Michael Thames]

Ozwood, I see you are doing your best to incite another riot here, ha ha! I'm not going there mate.

I've given the numbers, so I can't be accused of waving numbers around anymore. Trevor's highest number for stiffness reached 16% Jim Martin's 92%....... Jim gives specific tolerances for inlaying the rod, Trevor never did, I suggest everyone view this as an addendum to Trevor's exhaustive research. Trevor is free to debate Jim Martin over the results, so far I see he hasn't. Wise decision on Trevor's part.

Sorry, I wasn't aware this was Trevor Gore's forum.

[Michael Thames]

Hi Trevor,

This nugget is for you, I was one locked in a debate that was going nowhere, a lot like this one , not because my logic was flawed, but because because the person I was arguing with had little interest in the facts, anyone elses point of veiw or anything other than there own agenda, it was for that individual, about being right at any cost .

My Boss, at the time pulled me aside and said, " if you ague with an idiot for too long, after a while it becomes unclear which one is the idiot".

Now I am not suggesting for one second your an idiot, but clearly your locked in a debate with one, in actual fact most of us don't give a shit what this blow in has to say, I hope Bob deletes the whole sorry affair, which is clearly just an attempt by a nasty and somewhat obsessed individual to discredit you on your home forum, having dressed it up as trying to serve the greater good.

Sometimes the best thing to do with an attention seeker is just to ignore them !.

I suggest WE ALL do just that , I'm taking Bobs advice heading up the shed to make some sawdust.



Cheers,

[kiwigeo]

Sorry, I wasn't aware this was Trevor Gore's forum.

No it's not Trevor's forum but Trevor's been around this forum alot longer than you have. He also understands that the respect that he gets in this forum is mainly because he exhibits good manners and treats other members with respect.

[nnickusa]

+1.

It's Martin's forum, it's my forum, it's Paul's forum, it's Allen's, Alan's, Trevor's, Kim's, etc, etc, but Mr Thames. It clearly is NOT YOUR FORUM. I'm with Paul. Oh, as an aside, if in future you have the temerity to offer ANY opinion on me, my behaviour, and my sobriety, you better have a bigger set of balls than you came here with this time, Mate. How dare you? You've made whatever point you wanted to when you tracked Trevor to his "home" forum, now fuck off....

[Dekka]

You've made whatever point you wanted to when you tracked Trevor to his "home" forum, now fuck off....

All those in favour say aye.......AYE! AYE! AYE! AYE! AYE! AYE!

[ozwood]

Aye aye aye


If we get enough votes , maybe one of the Mods will roll out the old ,

Clown-Mushroom-Cloud.jpg (93.72 KiB) Viewed 15499 times

not used since ....erm ... well since Jobobkidding .... and now all of a sudden he/she did not seem so bad , actually this bloke makes Kim Il seem like a reasonable chap.

[jeffhigh]

Thus saith the LORD of hosts, the God of Israel, Behold, I will bring upon this city and upon all her towns all the evil that I have pronounced against it; because they have made their neck stiff, that they might not hear my words.

Actually I think it's Bob's forum I'll leave it to him to deal with since he is God here

[Kim]

Michael Thames account has now been deleted.

He was warned this :am but clearly he only ever signed up to the ANZLF to pursue baggage he was carrying from another internet guitar forum at which he had an exchange with one of the ANZLF's respected members....it's a tragedy to see a grown man making such a fool of himself so publicly but I will not delete his post..(except for his last offensive rant). Rather they can live on forever in the cloud along with other sage advise such as not running with scissors so that all can see what can become of a man should he eat meat after 8pm and get behind the wheel of a keyboard.

Carry on

Cheers

Kim

[ozziebluesman]

I wasn't going to comment but I am glad to hear the last of him!

Thanks Kim

Alan