A number of lutherie references opine that quartersawn or vertical grain wood is traditionally used in some lutherie applications because wood is stiffer when the load on it is applied in this direction. There is not much information on this subject but what there is indicates that the opposite may be true, at least along the grain. But there is so much variation in stiffness from board to board, even those cut from the same tree that for all practical purposes grain orientation of beams makes no difference. Things are quite different for plates (like instrument tops) though. Here cross grain stiffness is a factor, and quartersawn wood is typically much stiffer cross grain than is flatsawn wood.
Last updated: January 22, 2019
You'd think that, with humans building things out of wood for thousands of years, there would be a lot of data available on which grain orientation results in a stronger or stiffer beam. But there appears to be little available reliable data on this topic. First, let me explain that for lutherie applications we probably only really care about stiffness. Strength, which refers to how much stress can be endured before absolute failure, is of little relevance in most lutherie applications. The reason this is so is because a wood component that is stiff enough for the lutherie application is pretty much guaranteed to be strong enough for that application, too.
Stiffness of a material is expressed numerically as its modulus of elasticity (MOE), also called Young's modulus. Although it may be counter intuitive given the name modulus of elasticity, the bigger the number the stiffer the material is. Since wood is anisotropic (it is structurally and therefore mechanically different in all three dimensions) it has three different MOEs, one for each dimension. Testing to determine MOE is relatively simple, but the fact that there is so little uniformity among wood samples (even samples taken from the same tree) makes it time consuming and therefore costly to collect comprehensive data. The US forest service has collected limited data from a limited number of species. Their data1, expressed as ratios of MOEs, indicates that for the most part wood is stiffer when flatsawn, that is, when the load is applied perpendicular to the growth rings. Since this reference is the single most comprehensive work on the properties of wood as an engineering material, this should be enough right there to dispel the myth that quartersawn wood is stiffer than flatsawn. But the authors of this book caution the reader in no uncertain terms that the data collected to derive these results was not extensive. Further, stiffness values differ so much from tree to tree of the same species and even from board to board cut from the same tree that the stiffness data provided can only be used as the most general indication of the average for each species for which data are available. They also provide some data on Poisson's ratios but pretty much tell you that these are "imprecisely determined" for those data that could inform us any on stiffness characteristics in quarter sawn or slab sawn wood.
A note to non-technical readers: Although the above cited reference is pretty much the last word on the subject, at least as far as boards cut to dimensions used in construction go, the relevant section is particularly difficult to penetrate. The problem is that the data is presented as ratios of stiffness perpendicular to the growth rings over stiffness along the grain, and of stiffness tangential to the growth rings over stiffness along the grain. It is very likely the data was collected as ratios to deal with the fact that samples vary so much. But in addition to dividing out the ratios to get at the stiffness data relevant here, you've also got to translate the descriptions of where the load is applied relative to the growth rings to the terms used to describe the way lumber is sawn. To offer a little help, a flatsawn beam would have the load applied perpendicular (radial) to the growth rings, and a quartersawn beam would have the load applied tangential (parallel, more or less) to the growth rings.
There are a handful of analyses of MOE done in the context of lutherie that I know of, but for the most part the methodologies employed in the testing were not rigorous enough to warrant making conclusions from them. The only works on this subject that I think are worthwhile were done by David Hurd and James Blilie. Hurd's is a small but well done study2, and it indicates that, within statistical limits, there is no difference in stiffness along the grain between quartersawn and flatsawn wood for the samples he examined. Blilie's study3 is far more extensive in size and indicates that spruce selected for lutherie use typically is stiffer when quartersawn. Confused yet?
So why are there so many parts of musical instruments where traditional construction makes use of quartersawn wood? There are a number of reasons. It is likely that appearance has a lot to do with it, just as it does in other areas of woodworking. And the expansion and contraction of wood is different depending on grain orientation, which may be a factor. With the possible exception of mahogany, wood expands and contracts more along the grain lines than across them. For example ebony shrinks a lot, and so a quartersawn ebony fingerboard would be most dimensionally stable, shrinking much more in thickness (which causes few problems) than it would in width or length (which could cause many problems). Braces are almost always made of quartered spruce. Even though this grain orientation might not make for a stiffer brace in general it does make it easier to plane the brace tops in a well-controlled fashion. And differential shrinkage would not tend to make the brace locations appear through the top, as it would if the braces were flatsawn. There are probably many other examples of reasons for the choice of a specific grain orientation for the wood used to fashion components of musical instruments.
Note that the entire discussion above is about beams and beam-like components (braces, necks, etc.). Things are quite different when we deal with panels such as instrument tops, because here cross grain stiffness is also significant. Quartersawn wood is generally much stiffer across the grain than flatsawn wood, and for instrument tops this may be advantageous.
USDA Forest Service, Wood Handbook - Wood as an Engineering Material, Table 5-1. Also see the text in the sections in chapter 5 labeled Modulus of Elasticity and Poisson's Ratio, as this contains caveats as to the reliability of the data presented. This book is available online here.
Hurd, D. "Testing Wood for Go-Bar Use", Left-Brain Lutherie
Blilie, J. "A Large New Set of Stiffness Data for Lutherie Woods and a Proposed Standard Test Method", American Lutherie #128, Winter 2016