Minimum adequate structure

I recently received an interesting inquiry:
 I am a senior mechanical engineering major at The Catholic University of America in Washington D.C. Part of my group's senior project entails for us to build a carbon fiber top of a classical guitar and analyze the sound using spectrograms. I was wondering if you had any guidance as to how thick the carbon fiber top should be and why? It would be really helpful to us. I would be really grateful if you had the time to respond. One more question, do you know how to design a bracing system or pick a bracing system for the soundboard? We are struggling to find resources online.

There are almost as many schools of thought regarding bracing systems and patterns as there are luthiers. My approach is different from the great majority of builders. The more common view is that besides limiting the distortion of the tension-loaded soundboard, the particular pattern or scheme molds or “guides” the sound to some undefined ideal, and insist that the traditional “Martin” x-brace arrangement produces the iconic sound on steel string guitars and the “Torres” fan bracing system produces the iconic sound on nylon string Spanish or Classical guitars. Beyond that, most luthiers will add or subtract braces, or create braces that arch over other braces or play with the angles between them or their size and numbers in an effort to reach some sort of elusive or ill-defined sonic goal. The vast majority of builders are however, unschooled in even the most fundamental tenets of wave physics or acoustics, so they are flying blind or expecting to be winners in some sort of sonic lottery.  Others fall into the trap of chasing traditional myths, such as the belief that the soundboard produces all the sound of the instrument [it produces only a limited part] and that it can be divided into bass and treble halves, i.e. that the bass response can be manipulated by altering the braces under the bass strings and the treble response the braces under the treble strings. So the field of guitar making is largely populated by finish carpenters who think they can handily control and mold the resonances of an impossibly complex vibrating system.

My having been mentored by an acoustics scientist has freed me from much of that baggage. Accordingly, my approach has been a stark departure from the norm. My approach is to work within the traditional forms while striving to achieve what I call minimum adequate structure. What that implies is that the guitar is not the creator of the sound, that the true source of all of its musicality is the string's harmonic series. Thus Mario Macaferri's dictum, the string is the heart of the guitar. Indeed,  the guitar actually gets in the way, clouding and diminishing the string’s perfect signal—because it is essentially a cultural artifact, not an optimized energy transformer. The result of this fact is that it is a crude and inefficient energy transformer, succeeding in transforming only a small fraction of the string’s kinetic energy into acoustic energy. The major portion of the string’s kinetic energy is frittered away by the guitar as heat. So the luthier’s dilemma is how to take this fetishized cultural artifact—which due to its traditional form and structure, is inherently a poor acoustic  machine—and create out of it a usable, hopefully desirable, tool for musical expression.

The way I reconcile this dilemma is to try to get as much of the guitar out and away from the strings, that is, to make its impediment to the strings' signal as minimal as possible. I’ve reduced as much mass and structure from the traditional model as is possible, while focusing primarily on the architectural requirements imposed on the structure by string tension. This is what I call minimum adequate structure. If the structure is excessive, the beauty is muffled, limited, impaired. If the structure is inadequate, the guitar will slowly fold under tension and become unplayable.
So my guitars, then, emerge as the inevitable product of my unique approach. You’d have to hear and play them to know what that means exactly. This is admittedly a long answer to your request for bracing information. If you’re using carbon fiber instead of spruce you have to be aware of 1) the different stiffnesses/mass ratios of the two materials 2) the amount of tension stress which is being dumped onto the soundboard and 3) that little detail that luthiers usually ignore, that the distortion of a plate under load increases as a cube of its span. Obviously, the width of the soundboard plate and the actual load at the bridge are crucial factors that must be taken into account if you’re optimizing the system.