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Rather to my surprise, since it’s a pretty arcane subject, my last post on the elastic properties of spruce and how these vary according to the orientation of the growth rings attracted a lot of attention. Thanks to everyone who took the trouble to email me with their thoughts or to post comments. Stimulated by your interest, I thought that I might expand on a few things.

Because of the primitive way I carried out these experiments, there must be some questions about the validity of the measurements. One reason why I couldn’t show a difference between the stiffness of the wood in the different growth ring orientations might have been that my measurements weren’t sensitive enough. Another might have been that my preparation of the test bars of wood lacked accuracy or consistency. These possibilities seemed worth checking.

First, I re-planed the 9 test bars so that they were as square and straight and, this time, as uniform in their dimensions as I could reasonably manage.

Then I made an estimate of their stiffness, in the same way as before, by clamping them in a vice one at a time and measuring the downward deflection produced by a load of 2lbs applied 20 cms from the vice jaws. Again, every piece was measured 4 times, rotating it through 90° between measurements. For each individual bar, I calculated the mean deflection (in inches) for the 2 measurements in the different growth ring orientations. 3 days later, I measured them again without reference to the earlier readings. The results are set out in the table below, rounded to the nearest hundredth of an inch.

These results seemed encouragingly consistent. The bars that were stiffer in the first set of measurements came out stiffer in the second set too. So it doesn’t look as if the readings are being swamped by random errors introduced by deficiencies in the experimental set-up or that any differences are due to lack of precision. And the actual values in the 2 sets of measurements were quite close too, so the findings are fairly reproducible.

As you can see, there was some variation in stiffness between bars. The deflections recorded for bars 1 and 4, for example, are somewhere between 10% and 20% less than those recorded for bars 5 and 9. It occurred to me that this might have been because my planing had been inaccurate, but when I checked the dimensions with vernier calipers I didn’t find that the stiffer bars were any larger. It may be that this variation is simply a reflection of how the properties of small pieces of wood differ slightly even when cut from the same board.

Although hardly necessary, since it’s obvious from the table that there’s no consistent difference in stiffness between quarter-sawn and flat-sawn orientations for individual bars, I carried out a straightforward analysis using a paired t test, which confirmed that there was no statistically significant difference. [Difference (quarter sawn minus flat sawn) = -0.004 (95% confidence interval : -0.015 to 0.007) p=0.38 df=8]

Guitar makers often flex wood in their hands to get a feel for its stiffness and I wondered if I would be able to identify the stiffest and the least stiff of the test bars by doing just that. Not a chance! I was quite unable to distinguish differences in stiffness between these bars by feeling how much they bent in my hands. It might be worth doing some more experiments to find out what sort of differences in stiffness can be reliably identified in this way. Perhaps we’re not as good at judging stiffness as we’d like to think?

One final thing, which someone kindly emailed me to point out, is that any shrinkage or expansion across the grain because of a change in moisture content of wood tends to be less at right angles to the growth rings than in parallel with them. So, where the growth rings are orientated vertically in the strut, any change in the width of the strut at the glue line with the soundboard will be smaller than if the growth rings had been orientated horizontally. Now in a guitar it’s hard to see that this will matter much because the struts are small, not usually subject to large changes in humidity and are glued in all sorts of different relations to the direction of grain of the soundboard itself, which is also going to move in response to changes in moisture content. But where the strut lies in the same north-south axis as the grain and growth rings of the soundboard – as, for example, in the bass bars of violins or cellos – I can see that there might be an advantage in keeping the growth rings of the strut in the same orientation as the soundboard. This is the best reason I’ve yet heard for keeping growth rings in bass bars vertical, although as I mentioned in my last post, it wasn’t a rule always followed by the great luthiers of the past.

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2 Comments

  1. Hi

    I found this interesting. It confirmed what I had found with some similar tests, it can also be predicted by calculation (I’m a structural engineer). However I think your use of the terms flat sawn and quarter sawn is a bit misleading because they refer to how the log was cut whereas you are using it to describe the orientation of the growth rings. All your samples were effectively quarter sawn. These terms have precise meanings so it can be a bit confusing if they are used loosely.

    Best wishes

    John

  2. Yes, you are quite right and I’m sorry to have taken so long to say so. Where I’ve said ‘quarter- sawn’, I meant that the growth rings of the wood were orientated vertically in the same direction as the load. Where I’ve said ‘flat-sawn’ I meant that the growth rings were orientated horizontally – that is to say at right angles to the direction of the load.


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