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I have Trevor's books with his instructions, which I understand. These require the tidous epoxing of carbon fiber on the bottom and top of the laminated braces. I know that the top and bottom surhaces of the brace carry most of the load within the brace, so this location for the carbon makes sense. The carbon also helps keep the brace from deforming over time.

However, I saw that Portland Guitars (https://portlandguitar.com/blogs/featur ... ng-science) put the carbon fiber in the laminate between the wood laminates of the bracing. This would be a much faster and cleaner construction method. But obviously, this reduces the amount of carbon fiber at the critical top and bottom surfaces of the brace (but does add carbon fiber in the center of the brace where none previously existed.) I wonder how much stiffness and deformation resistent is lost with Portland's approach?

What are your thoughts and/or experience regarding the location of carbon fiber location for falcate bracing?

Do you have any experience with leaving the carbon out altogether and making the braces higher? How much higher?

Do you have any other thoughts or ideas to simplify the messy carbon fiber gluing for Trevor's original instructions?

Stress is at its maximum in a brace at the point farthest from the soundboard, i.e. the top of the brace. This is where the CF makes the biggest difference. CF vertically within the layers of the brace wouldn't help, I think. In fact, on page 4-46, it says this is exactly how not to do it.

I'm not sure what the purpose of the CF on the bottom of the brace is. In the book, Trevor says that the main benefit of CF is not strength or stiffness, but rather to prevent cold creep. Maybe that's the purpose of the CF on the bottom. Not sure.

The book lists stiffness (elastic modulus) for wood+CF braces in table 4.4-1. Unfortunately, the book doesn't show how to use this information to size braces. It just shows how to measure top stiffness and bridge rotation after you build it, and so implies a trial&error approach. In the brace stress section 4.4.7, is says to consult an engineering textbook.

I didn't want to build a dozen guitars in order to figure out brace sizing, so I consulted a textbook and calculated brace stress, EI, and sound board deflection from material properties and brace dimensions. You can find these calculations in my spreadsheets.

For a steel-string guitar with rectangular braces of King Billy Pine+CF and a target top frequency of 170 Hz, I calculated minor falcate braces of 5x4.70 mm and major braces of 5x8.15. So fairly close to what the book says (Build page 11-52). EI=44 N·m².

For triangular braces (height 2.4 times width) of Yellow Poplar (no CF), I calculated 3.86x9.26 and 5.79x13.90. EI=51 N·m².

In the spreadsheet, you can try other shapes and wood species to get appropriate dimensions. I used species averages, but wood is a highly variable material, and you should measure the individual pieces you have, using either frequency or deflection, as shown in section 4.4.4.

Take these numbers as a starting point--I have not actually built a guitar with braces in these dimensions.

So it appears that a guitar without CF can also produce a high monopole mobility and SPL, although the CF braces were a little lighter, and so produce a little better MM. And SPL is 1.2 dB higher.

Hope this helps,

Greg

A student and I did a few experiments with vertical CF lamination in braces many years ago. We decided that they really don't do much for you. The stiffness was not all that much greater than plain spruce bracing, and there was, at least, no saving of weight.

My construction sequence involves 'free' plate tuning, using Chladni patterns, of the top and back plates before they're glued to the rim. This is accomplished mostly by shaving down the height of the braces after they're glued to the plate, with shapes of the patterns indicating where to remove material. This would be much more difficult with the vertical CF laminations. I have no idea how on would do it with CF 'flanges'. At any rate, the whole exercise is based on optimizing the brace stiffness to work with the stiffness and mass distribution of the particular plate, which can't be determined precisely in advance, so you can't 'design' the braces in detail.

All of the bracing on a typical guitar top amounts to about 25%-30% of the total weight of the top. Much of that is in the upper transverse brace, which is structurally necessary, and has relatively little effect on the sound. The place to save weight is in the top plate itself, rather than the bracing. Gore's 'Falcate' system, as far as I can see, in effect mimics the structure and stiffness of an archtop, extending the vibrating area of the 'main top' resonance upward a bit to increase the A/m ratio.

I did put CF 'caps' on the bracing of a couple of archtop guitars, just on the 'inward' facing sides, as insurance against creep under the sustained down load of the bridge. It didn't seem to make much difference either structually or acoustically, and I stopped doing it when I started using 'curtate cycloid' cross arches, which seem to work better than the scheme (or lack thereof) I was using before.

Just had to look it up.
https://www.liutaiomottola.com/formulae/curtate.htm

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

The hazards of having two engineers (one an aeronautical sort) as mentors for the past 15 years is that I half-understand these sorts of questions and quarter-understand the responses. Yes - a CF flange on the beam does create greater stiffness for a given brace (web) height versus plain spruce - but the increased mass of the CF itself and adhesive used must be considered as well as whether a slightly taller brace might not be an equally efficient option to provide the same stiffness.

Years ago, Mr. Mario Proulx was asked why he used vertical CF laminates on his main braces given his acknowledgement of the design's inherent lack of structural efficiency and greater total brace mass for given stiffness (note: not necessarily the case for a flange laminate in plane with the soundboard). As an engineer, Mr. Proulx knew that for braces without a constrained height dimension, a slightly taller brace could generate the additional stiffness desired without additional labor, chemical exposure, and cost of tow and resin. But Mr. Proulx also understood what experienced repair people see on a routine basis: wood placed under long-term static loading will eventually permanently change shape under that load. Mr. Proulx's answer to reducing that deformation over time was his vertically laminated X and - IIRC - a few other major braces.

Woodie,
Thanks much for your response. I find it very interesting.

If Trevor's reasoning for the horizontal CF (on top of braces) was mainly to stop creep as noted by some in this thread, then vertically laminated CF inside the brace would also aid creep prevention as you noted. I had thought of this aid when originally writing the post and wondered if anyone would call it out.

A slightly taller brace with laminated vertical CF, but also trianglated from top to bottom to eliminate some added weight, would be another option bracing option to ease construction mess and time (Trevor's braces are not in triangle shape to, I assume, provide space on top for the horizontal CF, which would not be needed for vertical laminated CF)

CF doesn’t like to stretch, at all. The purpose of the GG method is to create what is functionally an Ibeam. Unless the CF in the laminated version has a continuous unbroken strand both top and bottom I feel it would be functionally irrelevant. But I ain’t no engineer.

It would be pretty easy to test with a few layups.

I did some deflection testing and found that adding a strand of 3000tow top and bottom gave a 30% stiffness increase with no real perceptible increase in mass. There are ways to add the CF very cleanly.

Rye Bear put out a masterclass on building a falcate top that you might find instructive…

I have built a bunch of falcate braced guitars with CF on top and under the brace. I found that using CF for a relevant percentage of a brace's stiffness gives me better consistency. This consistency helps me hit target resonances for a top by design. That is I can pick a desired resonance and size the brace to hit that resonance.

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http://www.Harvestmoonguitars.com

Where can I find the instruction?

A few days ago I did some deflection testing of braces and what I found was that a laminated brace, if sawn into three pieces and then glued together (with epoxy) is actually weaker than a solid brace of the same size. I also discovered that adding a 3K CF Tow to both the top and bottom of the braces add no additional stiffness than only using CF on either the top or the bottom. All braces were of identical length, width and height. Brace deflection was measured before gluing the tow(s) to it. Epoxy used was West System with fast hardener.

Powlonia sample #1 Deflection
Bare sample .080"
CF 3K tow, on top .070"
CF 3K tow, on top & bottom .070"

Powlonia sample #2
3 ply Laminated brace .105"
Single unlaminated brace .080"

Powlonia sample #3
Bare sample .070"
CF 3K Tow on top .060"
CF 3K tow, top & bottom .060"

Sitka:
Bare sample .040"
CF 3K tow, on top .035"
CF 3K tow, on top & bottom .035"

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tim...
http://www.mcknightguitars.com

Take these numbers as a starting point--I have not actually built a guitar with braces in these dimensions.

Greg, thanks for the spreadsheet. I am curious if you have made a falcate guitar, and if so, if you left off the carbon fiber in any application. I’m curious your thought process on that if you have, or how you came to those calculations

If CF was left off, but the braces were made in those bigger dimensions, would the braces resist creep enough or avoid other problems the CF is trying to solve?

Kyle, I have not built a guitar with falcate braces without CF. The formulas for soundboard stiffness and frequency are based on equations for beams of multiple materials (as suggested in the book, page 4-49). However, a soundboard is not exactly a beam, with distance between the braces and the sides attached. So a soundboard with braces built to these dimensions will actually be stiffer/higher-frequency than the formulas predict. I guess that's good, because then you could shave them down to the right frequency. So these dimensions are really just a starting point.

What I need to do now is build a guitar and then make some adjustments to the parameters to fit the real guitar. For example, I would probably adjust the length of the "beam", which right now is the distance from the tail block to the major transverse brace minus 25 mm ("l_active" in the spreadsheet). I would change it until the predicted stiffness ("Kt_actual") matched the guitar.

One check on the sanity of these calculations is the value for rigidity 50 mm forward of the saddle, EI, which does not depend on l_active. Trevor suggests using the EI value as the target on page 4-40. He suggests a target for steel-string guitars of 45 to 50 N·m². In the calcs for brace dimensions using Yellow Poplar (bendable) and no CF, I got an EI of 51. So I think those brace dimensions are close. Approximately 4x9 mm triangles for the minor ones, and 6x14 mm triangles for the major ones.

But we won't know until someone actually builds it.

As for creep without CF, not sure. I'm going to guess it would be about the same as any flat-top guitar built without CF. I'm not sure what the creep qualities of Yellow Poplar are. Some people have been able to bend Sitka or Paulownia, so maybe they creep less? Not sure. Acoustic performance (top mass and monopole mobility) with Yellow Poplar appears to be about the same as when using KBP+CF.

Note, that you shouldn't use the dimensions calculated here, even if you use Yellow Poplar. The values I used for density and flexural modulus are just averages for the species. Wood has a huge range of variability within a species, and even within a tree. So you would need to measure the pieces you have, for example using beam frequency as described on page 4-39.

By the way, I'm working on moving all these calculations into code (Python) and combining it with a CAD package to get accurate areas and volumes for the 4DOF model. And then building a user-interface for it.

If anyone has skills with FreeCAD, I could use some help.

Greg

Thanks Greg and thanks of course Trevor for the original work!

I had very similar results when I got into deflection testing with CF. It wasn’t obvious that it changed the strength of the brace, I put this to Trevor and he assured me that the purpose of the CF is to prevent cold creep first and furnish.

It was interesting that your brace once laminated was less strong. I wouldn’t imagine it to be one tiny bit stronger, but significantly less was interesting. Making falcate braces always involves laminates I tend to use spruce with a cedar sandwich filling, it looks quite pretty! My rationale is not to make a stronger brace but to make one that has significant less chance of twisting over time. In planning for this a do like to turn the spruce laminate around so they are not glued together in the same orientation as they grew.

I’ve never bothered with the CF, far too messy and icky for me, and I don’t really have an idea of the time frame that cold creep takes to set in.

I think it's important to separate the concepts of "strength" and "stiffness" of a material.

Strength determines the amount of force it takes to break a piece. For example, a beam supported on both ends with a force in the middle, is called the flexural strength. This is usually measured with the modulus of rupture, which is the force per square area (lbf/in² or Pascals), and sometimes designated with an 'F'. With this number and the dimensions of the piece, you can calculate the force at which the piece will break.

Stiffness determines how much a piece will deflect under a force. With a similar test (force in the middle) we can measure the flexural modulus, also called the modulus of elasticity or Young's modulus, which is again force per square area, and usually designated with an 'E'. With this number and the dimensions of the piece you can calculate the deflection for a given force, called the rigidity of the piece. The rigidity of the completed soundboard (force per deflection) determines the natural frequency of the top, which is an important part of the overall sound of a guitar, so it's important to get the rigidity of the braces right.

You can find average values for E and F for a species on the wood database or the USDA Wood Handbook.

In table 4.4-1, Trevor shows his results for measuring stiffness E for five species of wood vs. adding one or two strands of CF to them. For example, for King Billy Pine and two strands (row 21), mass increased 17% while stiffness more than doubled (5.80 vs. 12.44 GPa), meaning deflection would be less than half with CF.

Regarding strength, breaking occurs at the point of highest stress, which is the top of the brace, where the CF is. The F for CF is very high, and I calculated that in a steel-string guitar, stress would only be at 2% of CF's maximum. Versus about 45% for Yellow Poplar (6x14 mm triangles). So strength is never a problem with CF.

I used E=12.44 GPa to calculate brace dimensions for KBP+CF and got about 5x8 mm rectangular for a coupled top frequency of 170 Hz. This is pretty close to the book (5x7).

If you changed to a different species with CF, you would need to measure E for those braces and recalculate the dimensions. You can see what Trevor got in the table for Sitka, Balsa, WRC, KBP, and Australian Silver Ash.

It's important to do this because with CF on top you can't shave the braces later. You have to get it right from the start.

Wood is a highly variable material within a species, and even within a tree. For example, E in wood has a co-efficient of variation of 22%, which means that 68% of samples (a standard deviation) would fall between +- 22% of the average. For Sitka (E=11.03), 68% of samples would range from E=8.6 to 13.5. That's huge. And why you should measure the E of the actual pieces of wood you have on your workbench if you want to calculate their proper dimensions for your guitar.

So one of the main benefits of using CF is that the E for the brace comes out pretty much the same regardless of the piece of wood that you used (assuming same species). And after you measure it for one brace with CF, you don't ever have to do it again. Nor do you need to shave the braces.

Greg

Modulus of elasticity is a measure of how much force it takes to stretch/compress a piece of a certain size by a certain amount. For a beam in bending stretching and compression at the surfaces provides most of the restoring force, so a simplified model that doesn't take other forces, such as shear, into account is generally 'close enough'.

Wood 'cold creeps' when there are shearing forces involved. The cellulose fibers which take up tension loads are glued together with lignin, a phenolic resin 'glue' with a 'filler' of hemicellulose. Lignin is a thermoplastic, it softens when heated up, which is why we can bend sides. Most thermoplastics will 'flow' to a certain extent, even under small loads, at well below their nominal softening temperature. This allows the cellulose fibers to slide past each other in shear, and the brace, or top, 'takes a set' over time in the direction of the bend. Over time, as the bend becomes tighter, the shearing loads are transferred to tension and compression at the surfaces, and the creep slows to the point where it's effectively stopped. From what I've read it seems that with wood the deflection under a sustained load tends to stop when it reaches about three times the initial short-term deflection.

As I understand it, this can also happen with CF composites, depending on the resin used to bind the fibers together. The deflection limit is much less than it is with wood for a number of reasons: small, but non-zero, mostly because of the extremely high Young's modulus of the carbon fibers.