This article discusses applying engineering principles to build a superior guitar. In one prototype created, the transverse underbrace, located directly opposite the bridge, is proportioned so that the neutral plane at this location lies within the soundboard. The underbrace is notched to allow the king brace, made of fir, to pass through. Four spruce diagonal braces are also present in the compression zone between the bridge and the lower edge of the sound hole. To support the soundboard, two short, stiff cantilever beams are bonded to the upper neck extension using spacer blocks to allow the beams to pass outside of the sound hole. The free ends are connected with a short bar to provide a reactive member supporting the compressive forces in the soundboard. In the first six months or so after construction, the acoustic performance of the first prototype was good but unexceptional. After a year, however, both the acoustic power and quality of sound were found to be outstanding.
The classical acoustic guitar is, in some ways, a perfect musical instrument. It is lightweight and self-contained, needing neither power source nor amplifier. Its voice can be altered to represent a nearly infinite range of mood and shading. And while the guitar is simple enough for a novice to pick up and strum, its full potential can be unlocked by a master.
But the classical guitar itself is far from perfected. The instrument, essentially a mechanical amplifier of the energy produced by the strings, has always been limited by low sound power output. This is fine for small halls and intimate gatherings, but performers need a microphone or electric pick-up to project sound into large areas. Classical guitars also suffer from poor acoustic reproduction of sound over the entire frequency range of the strings, including at least the lower harmonics.
In addition to electronic amplification, luthiers have employed the use of metal strings and materials other than wood for the body to try to produce a louder sound from their guitars. Some have even designed guitars with larger bodies. But these have been largely trial-and-error methods. The intriguing question is: Can the acoustic power and fidelity of the classic guitar be improved by redesigning the instrument based on the application of the principles of mechanics? If one identifies all the sources of energy dissipation in the existing structure and works to reduce or eliminate such losses through redesigning the guitar or substituting different materials, could one build a better, louder acoustic guitar?
I recently built two guitars according to engineering principles to find out.
Modern classical guitar construction is largely based on the original designs of Antonio de Torres Jurado in the mid-nineteenth century. The iconic hourglass shape of the body and the use of braces selectively applied to portions of the underside of the soundboard are characteristic of the original designs. Modern variations of these original designs are very prevalent, but all feature a hollow body most often made of wood with a soundboard, generally having a single sound hole, an attached fingerboard and a bridge attached more or less centrally to the soundboard to which the strings are tied. (Torres's original design used catgut strings; these have for the most part been replaced by nylon.)
From an engineering perspective, the hollow body and sound hole constitute a Helmholtz resonator that is tuned to the lower frequency range of the instrument.
Because the guitar is plucked rather than bowed, the rate of decay of individual notes is critical to the overall sound power. A standard measure of the energy loss rate is the decrement or the decrease in amplitude of vibration of a particular cycle of motion relative to the previous cycle. When a luthier or guitar maker refers to the rate of decay of a particular note, he uses the term “sustain” which is the absence of decay. In general, “sustain” is a desirable quality except in some quick passages when the performer may be called upon to damp certain notes with his playing hand. Damping in the classic guitar manifests itself as a reduction in intensity of the higher frequencies. An instrument having high damping may charitably be referred to as being “mellow” which simply means that the high frequency overtones are lacking.
Mechanically, guitars are objects of wood and glue. The variety of wood for each component is chosen by the luthier. For instance, the soundboard, the major sound-producing element, is usually made from a type of spruce, which is lightweight yet strong and stiff, while the body materials are often selected based on cosmetic appeal.
The wood and adhesives have nonlinear stress-strain curves and timedependent mechanical properties. This means that creep and relaxation can occur under static stress and that the behavior under vibratory stress is different when there is a superimposed static stress. Pre-existing static stress, due to either string loads or residual stresses, causes a hysteresis loop to form which dissipates energy to a degree depending on the intensity of the static stress. Therefore, one approach to reducing energy dissipation is to reduce or redistribute static stresses within the structure.
When luthiers bend and fit various parts, with or without heating, and clamp them into place until the glue has set, they induce static residual stresses within the guitar structure. Until these stresses relax, which can take up to a year after construction, the voice of the instrument is weak and tonally inferior. New guitars, it is said, have to be “played in” before the instruments “find their voices.”
The soundboard is supported by the sides of the body at the edges and by a transverse brace below the sound hole. The bridge, which holds the strings in place on the body, transfers the vibratory forces of the strings to the soundboard. At concert pitch, the sum total of the string tensile forces applied to the bridge is approximately 120 pounds. This force creates a combination of compressive and tensile loads on the soundboard.
In Torres's original design, a number of braces were glued to the underside of the soundboard, both above and below the bridge. These braces reduce the distortion of the soundboard in the vicinity of the bridge and also improve the sound volume and tone. (The bridge itself acts as an asymmetric transverse brace causing high local stresses unless compensated for by an additional underside brace.) The braces act as constrained layer dampers, which are flat, structural elements adhered to a vibrating structure with a viscoelastic adhesive for the purpose of noise reduction. The engineering principle behind the bracing was not known to Torres or to most contemporary luthiers, and the advantages and limitations have been intuited rather than analyzed.
There are some other, quirky aspects to the classical guitar design. The interior lining of the body to which the soundboard is glued is kerfed in order to follow the guitar's curves. Unfortunately, a side structure with kerfed lining attached is so flexible that it cannot adequately support the soundboard without causing high local stresses.
After close analysis, I thought I could apply engineering principles to build a superior guitar. I have completed two prototype instruments, the first in 2007 and the second in 2008. If you examine the underside of the soundboard of each instrument, you will see some marked differences from conventional designs.
In the first prototype, the transverse under-brace, located directly opposite the bridge, is proportioned so that the neutral plane at this location lies within the soundboard. The under-brace is notched to allow the king brace, made of fir, to pass through. Four spruce diagonal braces are also present in the compression zone between the bridge and the lower edge of the sound hole.
To support the soundboard, two short, stiff cantilever beams are bonded to the upper neck extension using spacer blocks to allow the beams to pass outside of the sound hole. The free ends are connected with a short bar to provide a reactive member supporting the compressive forces in the soundboard. The lower neck extension is fastened securely to one of the back braces. Because this connection bonds end grain to flat grain, the joint is reinforced with two nails. And instead of a kerfed lining, a much stiffer continuous laminated lining is used for bonding to the edge of the soundboard.
I made some additional changes in the second prototype. For instance, the soundboard has a second set of diagonal braces in the tension zone of the soundboard between the bridge and the bottom of the body. The body structure possesses two additional struts connecting the edge of the lower body directly to the neck, effectively immobilizing the lower edge of the soundboard. A 3/8-inch clearance was provided between the upper edges of the struts and the underside of the soundboard. The net result is that the forces in the soundboard resulting from the string loads are about 60 pounds compression above the bridge and 60 pounds tension below the bridge—far less than on a conventional guitar.
The value of any instrument comes only when it is played, and for the first six months or so after construction, the acoustic performance of the first prototype was good but unexceptional. After a year, however, both the acoustic power and quality of sound were outstanding. By comparison, even after a year to find its voice, the performance of the second prototype is very good, but not as good as the first. The second instrument is not as powerful as the first and the tone is not as full. The mid-range seems deficient in fullness of tone.
It appears that the second instrument is over-braced. Adding tensile stress to a flexural member tends to decrease the vibration amplitude. Adding bracing only compounds the problem. Also, the balance between the level of compression in the soundboard above the bridge and tension below the bridge seems to be about right in the first instrument, while there is too much shift from compression to tension in the second instrument.
Further examination confirms some of the design choices. A laminated lining, for instance, is far superior to a kerfed lining; it is much stiffer and reduces the high compressive stress in the soundboard due to the string loads. In addition, the robust support structure at the top of the body, which provides for the direct transfer of the string loads into the neck, provides a structure with very low damping.
As a result, the guitars—especially the first prototype—have very high sustain. In fact, notes played on these guitars may carry on longer than planned, and the instrument actually may be too loud when played with normal force. Incidental clicks and squeaks that go unnoticed in a normal instrument are amplified along with the high overtones.
Indeed, while these guitars, built with the application of engineering principles, are exceptional at producing clear, loud sound, they are somewhat unforgiving. A performer must play these guitars with extreme discipline because the smallest mistakes can be heard.
In engineering a better guitar, it is possible to make the instrument too good.
Resetting the Hourglass
Modern guitar builders seem to have taken the Torres-inspired hourglass shape as a universal constraint for an acoustic guitar body. But that design leads to the presence of the sound hole at the end of the fret board, which puts limits on the size of the soundboard.
In fact, the sound hole is not required to be in any particular position. Relocating the sound hole to a new position alongside the fret board and increasing the width of the body by eliminating the waist can increase the area of the soundboard by about 40 percent. A soundboard that large should result in a considerable increase in sound power.
I have designed a new instrument to test this idea, and a prototype is nearing completion. The partially completed instrument has the same body size as a standard classical guitar but a considerably larger soundboard. The internal bracing is essentially the same as the first prototype except for some modifications to account for the larger soundboard area.
I’ll begin testing the new instrument soon, though it may take a year to get the full measure of its potential.