Engineering Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/133/02/38/6357733/me-2011-feb5.pdf by guest on 02 October 2021 Close study of a ubiquitous musical

he classical acoustic guitar is, in some ways, a perfect musi- cal instrument. It is light- weight and self-contained, needing neither power source nor amplifier. Its voice can be altered to represent a nearly Tinfinite 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 suf- fer from poor acoustic reproduction of sound over the entire frequency range of the strings, including at least the lower harmonics. In addition to electronic ampli- fication, 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

Richard Schile is a retired mechanical engineer. Readers can e-mail him at [email protected].

38 MECHANICAL ENGINEERING | January 2011 a Better Guitar Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/133/02/38/6357733/me-2011-feb5.pdf by guest on 02 October 2021 instrument reveals potential means of improvement. By Richard Schile

intriguing question is: Can the acoustic vidual notes is critical to the overall instrument having high damping may power and fidelity of the classic guitar sound power. A standard measure of charitably be referred to as being “mel- be improved by redesigning the instru- the energy loss rate is the decrement or low” which simply means that the high ment based on the application of the the decrease in amplitude of vibration frequency overtones are lacking. principles of mechanics? If one identi- of a particular cycle of motion relative fies all the sources of energy dissipation to the previous cycle. When a luthier or in the existing structure and works to guitar maker refers to the rate of decay Mechanically, guitars are objects of reduce or eliminate such losses through of a particular note, he uses the term wood and glue. The variety of wood redesigning the guitar or substituting “sustain” which is the absence of decay. for each component is chosen by the different materials, could one build a In general, “sustain” is a desirable luthier. For instance, the soundboard, better, louder acoustic guitar? quality except in some quick passages the major sound-producing element, I recently built two guitars according when the performer may be called is usually made from a type of spruce, to engineering principles to find out. upon to damp certain notes with his which is lightweight yet strong and Modern classical guitar construction playing hand. Damping in the classic stiff, while the body materials are often is largely based on the original designs guitar manifests itself as a reduction in selected based on cosmetic appeal. of Antonio de Torres Jurado in the intensity of the higher frequencies. An The wood and adhesives have nonlin- 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 Guitar interior: Acoustic guitars feature elaborate bracing under the soundboard than bowed, the rate of decay of indi- to reduce distortion and improve the sound volume.

February 2011 | MECHANICAL ENGINEERING 39 sated for by an additional underside brace.) The braces act as constrained layer dampers, which are flat, struc- tural 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 Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/133/02/38/6357733/me-2011-feb5.pdf by guest on 02 October 2021 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 struc- ture with kerfed lining attached is so First prototype: This guitar features a brace under the bridge and a series of flexible that it cannot adequately sup- diagonal braces, similar to but simpler than the Torres design. port the soundboard without causing high local stresses. ear stress-strain curves and time- 120 pounds. This force creates a com- dependent mechanical properties. bination of compressive and tensile After close analysis, I thought I This means that creep and relaxation loads on the soundboard. could apply engineering principles can occur under static stress and that In Torres’s original design, a num- to build a superior guitar. I have the behavior under vibratory stress ber of braces were glued to the under- completed two prototype instru- is different when there is a superim- side of the soundboard, both above ments, the first in 2007 and the second posed static stress. Pre-existing static and below the bridge. These braces in 2008. If you examine the underside stress, due to either string loads or reduce the distortion of the sound- of the soundboard of each instrument, residual stresses, causes a hysteresis board in the vicinity of the bridge you will see some marked differences loop to form which dissipates energy and also improve the sound volume from conventional designs. to a degree depending on the intensity and tone. (The bridge itself acts as an In the first prototype, the transverse of the static stress. Therefore, one asymmetric transverse brace causing under-brace, located directly opposite approach to reducing energy dissipa- high local stresses unless compen- the bridge, is proportioned so that tion 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 Second prototype: A second set of diagonal braces between the bridge and the bot- applied to the bridge is approximately tom of the body may have reduced the sound volume of this guitar.

40 MECHANICAL ENGINEERING | February 2011 the neutral plane at this location lies as powerful as the first and the tone transfer of the string loads into the within the soundboard. The under- is not as full. The mid-range seems neck, provides a structure with very brace is notched to allow the king deficient in fullness of tone. low damping. brace, made of fir, to pass through. It appears that the second instru- As a result, the guitars—especially Four spruce diagonal braces are also ment is over-braced. Adding tensile the first prototype—have very high present in the compression zone stress to a flexural member tends to sustain. In fact, notes played on these between the bridge and the lower decrease the vibration amplitude. Add- guitars may carry on longer than edge of the sound hole. ing bracing only compounds the prob- planned, and the instrument actually To support the soundboard, two lem. Also, the balance between the may be too loud when played with short, stiff cantilever beams are level of compression in the soundboard normal force. Incidental clicks and bonded to the upper neck exten- above the bridge and tension below squeaks that go unnoticed in a normal sion using spacer blocks to allow the the bridge seems to be about right in instrument are amplified along with Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/133/02/38/6357733/me-2011-feb5.pdf by guest on 02 October 2021 beams to pass outside of the sound the first instrument, while there is too the high overtones. hole. The free ends are connected much shift from compression to ten- Indeed, while these guitars, built with a short bar to provide a reactive sion in the second instrument. with the application of engineering member supporting the compressive Further examination confirms principles, are exceptional at pro- forces in the soundboard. The lower some of the design choices. A laminat- ducing clear, loud sound, they are neck extension is fastened securely to ed lining, for instance, is far superior somewhat unforgiving. A performer one of the back braces. Because this to a kerfed lining; it is much stiffer must play these guitars with extreme connection bonds end grain to flat and reduces the high compressive discipline because the smallest mis- grain, the joint is reinforced with two stress in the soundboard due to the takes can be heard. nails. And instead of a kerfed lining, string loads. In addition, the robust In engineering a better guitar, it a much stiffer continuous laminated support structure at the top of the is possible to make the instrument lining is used for bonding to the edge body, which provides for the direct too good. Q of the soundboard. I made some additional changes in the second prototype. For instance, the soundboard has a second set of Resetting the Hourglass diagonal braces in the tension zone of the soundboard between the bridge Modern guitar builders seem to have taken the and the bottom of the body. The body Torres-inspired hourglass shape as a universal structure possesses two additional constraint for an acoustic guitar body. But that design struts connecting the edge of the leads to the presence of the sound hole at the end lower body directly to the neck, effec- of the fret board, which puts limits on the size of the tively immobilizing the lower edge of soundboard. the soundboard. A 3/8-inch clearance In fact, the sound hole is not required to be in any was provided between the upper particular position. Relocating the sound hole to a edges of the struts and the underside new position alongside the fret board and increas- of the soundboard. The net result ing the width of the body by eliminating the waist is that the forces in the soundboard can increase the area of the soundboard by about 40 resulting from the string loads are percent. A soundboard that large should result in a about 60 pounds compression above considerable increase in sound power. the bridge and 60 pounds tension I have designed a new instrument to test this below the bridge—far less than on a idea, and a prototype is nearing completion. conventional guitar. The partially completed instrument has the The value of any instrument comes same body size as a standard classical only when it is played, and for the first guitar but a considerably larger sound- six months or so after construction, board. The internal bracing is essentially the acoustic performance of the first the same as the first prototype except prototype was good but unexcep- for some modifications to account for tional. After a year, however, both the the larger soundboard area. acoustic power and quality of sound I’ll begin testing the new instrument were outstanding. By comparison, soon, though it may take a year to get even after a year to find its voice, the the full measure of its potential. performance of the second prototype is very good, but not as good as the first. The second instrument is not

February 2011 | MECHANICAL ENGINEERING 41