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For about ten years now, I've been thinking
about and trying various ideas as to why acoustic guitars are so limited in their sound production capabilities. As
an engineer, I've been studying many of the previous methods addressing this problem and would like to present my conclusions
as to why the industry has been seemingly stuck with the same paradigms for so long. I also would
like to present a new build method which I believe can overcome the acoustic limitations of the existing approaches.
BACKGROUND
Most investigations always seem to lead back to some basic physics
and a little thing called energy! In mechanical terms, there are two types: Potential and Kinetic. Potential is
that which is not yet manifested in motion, but could be. Kinetic is that same energy now translated into motion.
As
related to music, everyone recognizes the power of a grand piano, the heavy strings drawn taut to store enormous amounts of
potential energy. Once struck in motion, these strings impact a heavy harp within a heavy sound box with
the obvious result, a far reaching powerful sound wave.
So
is the limitation of less massive instruments a relative lack of potential energy? It would seem so! It was at
least one of the rationales for creation of the steel string guitar with its higher string tensions. In practice, however,
a fine classical guitar can also be heard in a moderate sized theater nearly as well. Moreover, how does
one explain the enigmatic performance of another stringed instrument, the violin? It has diminutive proportions, low
mass and contains little by way of potential energy. Its strings are not steel and its box size is puny, yet
this little instrument can project sound farther than the grand piano. So what gives? The only possibility is
that the pure amount of stored energy, cannot fully account for the result. More importantly, the fact suggests
that there's a much more sound to be realized from small acoustic box sizes.
Recognizing
this, most luthiers and designers believe guitars are not lacking in potential energy, but are relatively inefficient
in the conversion into kinetic energy. As such, they focus most of their attention on optimizing sound board bracing,
materials selection and making the fingerboard and neck as immobile as possible to minimize string energy loss. These are
good things, but by focusing solely on those aspects they are overlooking another opportunity to boost efficiency.
There is something engineers call a form factor. In short, it is the way in which the makeup
of any material form defines all the dynamic boundaries of its possible modes of vibration. The makeup
is a compendium of materials used, the basic geometry, the damping and other limitations on the movement of a body.
The form factor for acoustic guitars has not changed much since it evolved from its predecessors in the middle ages!
Seems it works pretty well, but that of course is not the issue!
PROJECT
WORK – AN EXAMINATION OF STRING LOADINGS
“We can't solve problems by using
the same kind of thinking we used when we created them” – Albert Einstein
If
you consider the static loadings of a typical guitar, in its simplest form it can be viewed as an eccentrically loaded column.
The string tension causes the column to deflect in an arc. The makeup of the column is in two basic
sections, the body and the neck, the former being dense with small cross section and the latter being a larger thin walled
hollow chamber. At some point, there is a wedge inserted which forces the strings away from the column
(a bridge) which exerts an equal force upon the body. It is this deflection point which serves as both
the focal point of sound propagation as well as the origin for many structural failures.
The
stresses applied at the three points of string contact must be counteracted by structures designed to sustain the forces involved.
The structures consist of three types: fixed anchoring points, movable anchoring points and brace works.
Some guitars have two fixed anchoring points (e.g. the arch top guitar) and some
have only one (Flat top and Classical). The common fixed anchoring point for both types is provided by the tuning pegs.
In the case of the arch top, the solid end block of the lower bout provides the opposing anchorage and is relatively
immovable. Note: this is the same system employed by the entire family of viola like instruments as well.
Flat tops and classical guitars use a solid body moving anchorage point which also serves double duty as the string
deflection bridge. It is this aspect of the design which both provides both the sound propagation power
as well as some structural limitations.
When struck
into motion, the strings impart movement to the body which functions an amplifier to concurrently move the air and create
sound, even music. How the body moves depends upon its form factor and the characteristic pattern
of movement, uniquely fingerprinted and with native limitations. The most obvious moving part is the soundboard,
here examined in this figure:
There
are two key motion limitations in guitars of the second modal type:
1) the mass
of the bridge itself which must also move as the soundboard moves and 2) the necessity for structural bracing and its additional
mass required to offset the concentration of point loadings.
Greater
mass contributes to sound dampening, so in that regard represents the key impediment to sound board motion.
You
will note that archtop guitars use a thicker sound board and arch geometry to offset the loadings but this still represents
the same structural limitation. Arch tops also have only one type of board motion and do not have
a natural node at the center of the instrument as do the flat tops.
AN
OBSERVATION ABOUT AIR MOVEMENT
It’s
been said that the sound box cavity acts as a bellows during sound production, moving air in and out as the strings traverse.
If this common assertion were true, then how is it manifested in the two systems above?
If
you graph the sound wave produced by single tone, it is your well known sinusoidal wave. It has a
direct relationship to the string motion producing it, which also happens to be a sinusoidal wave of the same frequency.
Examining a graph of string tension and velocity versus air movement, we see that a string which was initially deflected
will start at zero velocity and accelerate to a maximum, just as string tension drops to its minimum. Tidal
air velocity peaks and returns to zero twice in every string cycle, half the time spent inflowing and half spent out flowing.
Where that happens (ebb and flow), is something we’ll return to examine shortly.
Once
the string velocity has slowed to zero, the string is again at its maximum tension while tidal air has ceased to flow and
the cycle is poised to start again. This system does indeed act as a bellows on a very microscopic scale.
Not much air is moving, but it is doing so very rapidly.
Looking first at the simpler arch top system, you’d think that
air would be exiting the box when the string’s inertia and velocity were on the rise, but you’d be wrong.
In fact, tidal air previously expelled from the box during maximum string deflection is re-entering as the string accelerates,
first inflowing until the string hits its peak velocity, then out flowing while the string slows down to zero. As the string is hitting its peak velocity, the box volume also maxes out
and air expulsion begins. The system is shown in the following graph:
This
expulsion occurs throughout the time the string is slowing down and continues until the tidal air is fully expelled (exhale
completed). Meanwhile, potential energy has peaked and string motion has ceased.
Conceptually,
the box is only pushing air out of its sound holes during the interval when the string speed is declining and the tension
is rebuilding. The box distortion acts as a spring counterbalance to the system, first powering the inhale as the string accelerates
to the max (highest kinetic energy), then slowing the exhale as the string slows to zero (highest potential energy), always
trying to reassume its original box volume in the process.
As dynamic systems
go, there’s nothing “wrong” with the resulting harmonic motion. But it seems like a better system of power
projection would have its springs loaded up (when Potential energy and tension are highest) to deliver an expulsion of air
rather than a powerful inhale. I know of no natural example of any animal that growls, barks or shouts
by inhaling. An example of this more natural system is seen in the following graph.
What
about flat top systems? Which model do they follow?
Flat
tops do both deflect in and out at the same time by virtue of their nodal aspect. But the basic geometry
of their design places the node at a point midway between two cavities (the upper bout and the lower bout) at a point near
the box’s area centroid. Though the lower bout is the dominant volume and pulls air in during maximum
string deflection, the upper bout is simultaneously doing the reverse. It is difficult to say for sure which of the two opposing
effects holds sway. The actual answer might be that it depends upon the bracing systems employed. And that
answer just might explain why lighter bracing systems seem to sound better.
Scalloping
braces might allow the differential to favor lower bout dominance during periods of maximum string deflection. If
so, it would better match the inhale on deflect system! Could this actually be the true reason why
scalloped braces work? The traditional view explains the benefit mostly in terms of greater vibratory top
movement. But if the real reason has more to do with the breathing system of the box, then amplifying
this effect should be possible and a project worthy of some attention! As it stands, however, scalloping
and light weight brace designs alone can only take you so far given the structural limitations!
A
NEW DESIGN APPROACH
“Paradigm shifts can only occur following
the demise of preconceived notions”. –Thomas Kuhn
Though
neither existing system is specifically designed to expel air during maximum string deflection, flat tops may do so as a net
sum accident (serendipity!). What if this could happen as a result of intentional
design? Such a design would need to change the basic form factor of the acoustic
guitar in a way which allows some new body dynamics.
Look again
at Figure 1 and note the following:
Arch tops offer no means whatsoever for doing other than compressing
the cavity. The bridge is held in place by string tension and nothing else is available to increase box
volume. But arch tops do afford us one clue that might help in a design sense.
Namely, they impart a constant downward pressure on the sound board. This is the opposite
of flat tops which always exert a net upward pull on the board. This spells OPPORTUNITY to an engineer
as a means of cancelling out some stresses!
--------------------------------
THE DUAL
BRIDGE SYSTEM TM HYBRID FLAT TOP GUITAR Patent Pending
Project Statement of Objectives:
I’ve
had it in mind for some time to build a guitar with a string tethering system that spreads out or reduces the point loading
stresses at the bridge. As I see it, this is the key to allowing a lighter braced top to function
with less concern for structural failure.
In the previous analysis, I contend that an inhale on string
deflection system would be a key asset in the quest for greater sound output. One objective is to clearly demonstrate
the advantage and value of this claim.
I would also like to produce a design that allows more active
sound production to occur in the upper bout, an area notably under exploited by virtue of its geometry and traditional
function as real estate for the sound hole and counteractive superstructure for the neck mount.
I would also
like to create better ergonomic access to the upper registers, without necessarily resorting to a cut away design.
In effect this is to build an acoustic guitar that an electric guy could come to love.
I would also
like to create a box design which could be universally applicable to an entire new family of instruments, all with
superior sound production capabilities by design, not by an accident of fortuitous tone wood combinations.
Finally,
I would have this instrument be as lightweight as any fine acoustic guitar on the market today. The bracing
system must be minimal allowing good sound board travel, musical sustain and resonance.
Resultant Design:
In earlier consideration of the vibratory modes of arch tops versus
flat top guitars, I noted an opportunity to cancel out some of the stresses imposed on the flat top guitar design.
Specifically, to convert some of the strings anchorages to the same type as utilized by arch tops in order to offset
the effect of the upward pull of a standard pinned bridge. The main impediment to doing this straightway
by tie in directly to the end block of the lower bout is that arch top geometry elevates the strings to impart some pressure
at the deflection point. The flat top has a much lower set in its string profile and the two geometries
don’t readily line up.
The solution to this dilemma has some amazing side benefits which ended up meeting
most all the objectives of the project. Stated simply, the answer was to move some optional tethering points below the
plane of the sound board into the box cavity and use a portion of the bracing system as its anchorage. To facilitate this,
some means of passage through the sound box was required. Though there are several ways to do it, the method
chosen was to use the sound hole, reversing its position with the bridge. The following figure illustrates:
Note: Only some of
the strings need be tethered to what is termed a Trapeze BridgeTM
The result is that
1/3 to 1/2 of the strings remain in their normal pinned bridge location side by side with a companion trapeze bridge tethered
string. The saddle remains in its original position on the pinned bridge and provides a typical 15 degree
string deflection regardless of the string tethering point. Conveniently, the sound hole also
provides a relatively easy insertion point for replacing selected strings. The effect on string loadings
is as shown in the next figure:
The vibratory deflections
are as indicated by the dotted lines and are the same basic nodal inflection type as a conventional flat top guitar, with
one key difference. The nodal point now resides at approximately the center of the lower bout sitting astride the sound hole.
This is where the cross sectional mass is minimal which is a good feature for an inflection point! The
net uplift effect of the strings means that increasing string tension by deflection will draw in more air (the desired inhale
on deflection system) and it happens on BOTH sides of the node.
This design is a very radical change, so its public acceptance must occur by virtue
of its performance alone. It looks very strange to our eyes and has no precedent that I could uncover!
But the choice for the hole location not only provides the necessary string path, but it also accomplishes the following:
(1)
Aforementioned ease of access for trapeze bridge string changes.
(2) The hole now sits at the circular center
of the lower bout, whose parabolic back shape focuses sound straight out rather than at the usual oblique angle.
The musician’s hand does not sit in front of the sound hole during play.
(3) the entire string
scale length effective area is now free to be shifted up given there is no hole obstructing placement of
the bridge – net effect is many more frets (16 and up) are clear of the body.
(3) The shifted hole
location frees up brace works of the upper bout for two reasons:
1. there
is no longer a sound hole there to reinforce and
2. the up shifted fingerboard
is shorter, hence requires less cantilever bracing.
With less braces, the upper bout can now resonate much more
than before and can actually contribute to the sound output, thus meeting that project objective. This can happen even in
a smaller total body package (remember the upper bout formerly contributed very little to sound production).
The
design and choice to use the trapeze bridge also has some other ancillary side benefits. The nominal
length of strings tethered there can be adjusted to be a quarter length of the scale, hence carry the same note two octaves
higher. Though you don’t strike this string, overtone harmonics of the open string when struck pass in and out of the
sound hole. This make for an interesting ring and an exceptionally long note sustain. I’m not an expert in this area…this
effect was observed in the prototype!
And yes, there is in fact a prototype DBS guitar
set up as a six string steel requinto (clear frets to 16) shown here with two trapeze tethered strings in place.
The X brace
ahead of the bridge is about half the normal mass and is designed for up to four normally anchored strings, which leaves room
for an even lighter weight model (3 string). Adding the third trapeze tethered string would serve to offload
the X brace more, but I’ve found it gets in the way of poking around in the box. The two E
strings do not inhibit access and guitar sounds fabulous with either two or three in the hole. Any
of the strings can be tethered in any location as can be seen in this photo of the Trapeze Bridge.
It is thought that a normal transverse brace would probably do
the job of the X brace equally as well. Certainly, it should be the one used for Classical versions. So there you have it!
Here’s an offering that could just be representative of the next great paradigm shift in acoustic sound
production…
shown
side by side with the old:
Somewhat odd
looking, but once you’ve played one, there’s no going back!
Copyright J.C. Steinert -
July 4, 2011.
