Larry Stamm, Luthier

Soundboard Properties

I have long known that wood qualities vary tremendously within the same species, but assumed that much of that variation was due to mixing various age classes and log qualities of timber in the output of a typical commodity sawmill. But when I started running tests on the tonewood I was producing, that I knew came from high quality logs and was carefully quarter sawn and air dried, I discovered the same variations in quality found in commodity lumber.

There are three easily measurable properties that affect the ability of a wood plate to vibrate:

• The average density of the wood
• The stiffness of the wood, and
• The amount of vibrational damping, or losses to internal friction.

In addition because of the way wood is produced as the tree grows, with the new growth laid down just underneath the bark in alternating rings of soft early growth and hard late growth, the stiffness varies depending on the orientation with respect to the growth rings (parallel, perpendicular, or tangential). My wood test always include measurements of longitudinal stiffness (parallel to the grain) and perpendicular, or cross-grain, stiffness.

Static Longitudinal Deflection Test on a Guitar Top

Measurements are taken on wood samples that have been accurately thicknessed and trimmed. Density is determined by weighing the test sample and dividing by its volume; I have not been using the oven-dry density in my calculations because instruments are not played in an oven-dry state.
The stiffness is determined by two methods: Measuring the deflection of the plate when placed under a load of known force (usually an accurately weighed steel bar), and also by measuring the fundamental vibrational resonances of the plate. The stiffness is then determined by calculating the Modulus of Elasticity from the density, size, and deflection of the plate in the case of the static load method, or using the fundamental resonance frequency in the case of the vibrational method.

The acoustical damping is determined by measuring the "Q" factor, or half-power bandwidth of the resonance frequencies, or alternatively, measuring the rate of decrease of vibrations begun from a single impulsive force (usually a thump from a hard rubber ball).

This research is a work in progress, and only partial results will be presented here. I hope to present a fuller discussion of my findings as they occur, and I get the data into presentable shape. I should also mention that I owe a lot to discussion and data exchange with other luthiers, especially David Hurd, Brian Burns, and all the participants of the Left Brain Luthiers mailing list.

The charts shown below are all taken from static deflection tests of rectangular wooden plates, about 3.5 mm thick. The test samples were all well quarter-sawn, with minimal runout, and no knots or other obvious defects. The samples varied considerably in growth ring spacing, evenness of growth, and evenness of colour. Only averages from Engelmann spruce, western red cedar, and Douglas fir are presented for now. The averages are represented by the bars, while the standard deviations are represented by the thin vertical lines laid over the bars.

A few things stand out from these graphs:

1. Quarter-sawn soundboard wood is much stiffer in the direction of the grain lines than it is across the grain, on the order of 10 to 15 times stiffer. This is for wood that is well-quartered; if the wood is skew sawn (off-quarter) then the cross grain stiffness is even less.
2. Variations on the order of 10% to 20% in densities and Moduli of Elasticity are common, even from wood samples taken from a relatively small geographic area.

Now if we graph the average stiffnesses against the densities some more interesting details emerge (the cross-hair lines represent standard deviations):

Notice how as the density goes up, the stiffness goes up too. But this is strictly a statistical relationship, and does not mean that a light piece of wood will necessarily be less stiff than a denser piece of wood. This chart again shows how much variability is found within a single species that is not due to any defects.

Notice too, how the Engelmann spruce is above the line (which represents the best fit of the stiffness/density relationship for these three species) for the longitudinal stiffness/density ratio, but is below the line in cross grain stiffness/density. In other words, the spruce is relatively stiffer for its weight along the grain than the red cedar and the Doug fir, but is more flexible than the other two species across the grain.

Both directions of stiffness are important in a good soundboard, but the relative importance of each is still an open question. However, if we multiply the parallel Modulus of Elasticity by the perpendicular Modulus, and divide by the density (and also divide by 10**16 to get a reasonable number for presentation purposes) we get a number that gives equal weight to both directions of stiffness and the density, and hopefully allows us to better compare the absolute stiffness/density ratios of different woods in a way that is useful to judge performance as a soundboard resisting the stress of string pressure. I am not entirely convinced this is the most useful measurement but here is the chart anyways:

The numbers on the vertical axis have no real meaning other than as a numerical comparison. But this chart shows the three species as much more equal in structural effectiveness than the other charts, and also shows how the variability in individual properties is magnified when they are considered as a product of properties.

This is just a cursory presentation of some of the data I have gathered, and I hope to present a more complete report in the near future.

Other Areas of Wood Research

In addition to just measuring wood properties, I have a couple of other areas of investigation. One is an attempt to unearth some of the silvicultural factors influencing wood quality in the growing forest. Since this sort of research can get really complex, most of my efforts in this direction have gone towards encouraging graduate students to investigate some aspect of this broad area.

To date, one student has completed a study of the wood from two spruce stands growing in very different but well defined micro-climates. One stand was a small patch of spruce growing in a good level valley bottom site surrounded by cedar and hemlock, and the other stand was situated at a mid-level elevation on poor soil at about 1500 m elevation. The upshot of his findings were that the higher elevation stand produced wood that was slightly denser and stiffer on average than the low level stand, but the extreme variations found within each stand completely overshadowed the slight average difference.

Since both of these stands were of similar ages, and growing in small areas with a consistent soil type and micro-climate throughout the stand, I think this study allows one to safely discount micro-climate factors as important determinants of wood quality.

The other area I am investigating is the changes that occur as wood ages. In 2001, I set aside a few dozen samples in a stickered pile in my shop to age in that relatively controlled environment. Each year the samples are measured, and the measurements are compared with previous measurements. As of the fall of 2004, I have seen no significant changes in the wood.