Testing Mandolin Top Wood Billets

[Neil Miller]

In the past, I’ve had trouble comparing stiffness calculations derived from physical deflection to those calculated from frequency testing, but I haven’t had this range of material. With a multi-species data set, I found a clear correlation between the longitudinal stiffness of the two methods, though deflection produced E long values 1.5-2 Gpa lower than frequency. Within individual species, however, the comparison broke down, presumably because one or more of the methods wasn’t precise enough to parse the smaller within-species differences.

Plotting stiffness against density I think I found the source of the inconsistency. The relationship with frequency-based stiffness was close and linear across and within species, with the exception of the redwood. Deflection-based stiffness had much more scatter, and no apparent relationship within samples of the same species. This observation didn’t surprise me. When measuring deflection, I had to recalibrate the apparatus for each sample, and even then I often wasn’t happy with the consistency of measurement.

Conclusion: Frequency and deflection produced similar results, but frequency-based stiffness measurements were more precise and therefore preferable for comparing samples. Furthermore, with frequency analysis, I could measure cross-grain stiffness, which varied 90-180% within species versus just 9-14% for longitudinal stiffness. Finally, frequency analysis was much quicker and didn’t make my back hurt as much as repeatedly lifting a 50 lb. weight onto a spruce blank!

[Neil Miller]

Testing rough-sawn samples is attractive since it allows me to visit a supplier and sort through multiple samples in order to select the best candidates. I tested 7 Englemann samples before and after planning and sanding them smooth. Density calculations increased 1% and stiffness calculations increased 3-4% after cleaning them up, probably because the rough-sawn surfaces led to over-estimated thickness measurements. One summary measure of wood quality, the Sound Radiation Coefficient, has longitudinal stiffness in the numerator and density (cubed) in the denominator, so the final quality statistic for the before and after measurements was virtually identical.

One drawback to measuring samples in the rough was that the cross-grain stiffness was much more difficult to measure. While longitudinal and twisting peaks were readily apparent in the rough-sawn frequency analysis, it was often unclear which peak represented the main cross-grain frequency. Once the samples were planed and smoothed, the cross-grain mode showed up much more clearly and consistently.

Conclusion: Rough-sawn samples produced data which were very useful in initial triage, though for a fuller assessment of wood quality, samples should be rechecked after planning them to a consistent thickness and smooth surface.

I hope these observations are useful. I’m eager for feedback, and happy to share more detail on my methods and data.

[martino quintavalla]

Hello Neil,

I also measure wood properties when I build mandolins and what you did is very similar to what I have tried, so I’d like to share some thoughts and comments.
From my engineer point of view, I see some critical points in your measurements I have also gone through when attempting to do the exact same thing.

1) Measuring the stiffness via deflection requires a strictly line like load, mid length. Applying the load to a larger area would make your billet apparently much stiffer than it is, thus overestimating the elastic modulus. From the picture, I can’t see exactly how the load is applied and this may largely impact the results. Moreover, a 20 mm thick billet is very rigid and requires measuring the deflection quite accurately.
In this case I usually use a digital gauge with resolution 1/1000 mm and apply a preload to minimize mechanical play, before applying the real load.

2) Using the acoustical method (which I personally prefer for the exact same reasons: quicker and more accurate) is ok for thin boards but, again, there are limitations. The formula reported by Giuliano and Trevor, originally by Graham Caldersmith for boards and by many others (quite old physics 😊 ) is correct for thin beams (say thickness/Length ratio less than 0.01). In the case of your billets this ratio is larger, and the elastic modulus can be underestimated.

This problem is typical of carved top/back instruments where wood is in form of billets or wedges. I am currently making some research to retrieve the stiffness from thick samples and wedges but it will require some time before being published.

Another way you can measure the longitudinal elastic modulus is by tapping the sample at the extremities to excite a longitudinal vibration mode. This should give you a frequency around 6 KHz (for a 400 mm long spruce billet) and you can retrieve the elastic modulus as

E = 4*f^2*rho*L^2

The problem here is that the measurement occurs at a higher frequency than the other acoustic method. Since wood is viscoelastic (the stiffness depends on frequency) you will likely obtain a lager value with respect to the other techniques, which is correct anyway, only related to a different frequency range.

So, it is very difficult and sometimes frustrating to take good measurements, but it’s good to share experience and ideas, therefore I hope these comments can be helpful!

On the 11^th of December, Geoff (iii mandolins) and I will have a talk on the Looth group about these things. I hope you can participate and share your thoughts!

Cheers,
Martino

[Neil Miller]

Thanks for this great feedback! Your observations push me further in the direction of thinking deflection measurements just aren’t practical for my needs.

With regard to frequency testing, if the stiffness measurements are over-estimated, can I assume that this is consistent from sample to sample? My main objective is to compare samples, so if they’re consistently off, I can still achieve what I need.

Do you feel the alternative method you propose is more appropriate for thicker billets than the method in Nicoletti’s book? If so, is there somewhere I could get more detailed methods? I assume when you say to strike the “extremity” you mean striking the end of the beam with a blow parallel to the long axis, correct?

I’m VERY eager to see what you develop for thicker beams. If you have pre-publication information, that is welcome as well. I’ll do all I can to attend the December meeting.

Neil

[Geoff Burghardt iii mandolin]

Interesting stuff here. I’m interested to see what follows from this. I use deflection and resonance but only once I’ve got my plate in the carving state. What is the ultimate goal of getting this information in the billet stage? Do you anticipate being able to pre-determine arch height/graduations/thicknesses based on properties of the wood in billet form?

[Neil Miller]

My initial interest in testing billets was to identify the wood with the highest stiffness to density ratio. I find there is a wide variation even within the same species and supplier. So being able to test in the billet stage gives me the ability to pick out the wood that will produce plates with adequate stiffness but the least mass. A significant issue I still struggle with is the fact that transverse stiffness varies much more widely from billet to billet than does longitudinal thickness, and in an instrument without any transverse bracing it seems like that should be a critical factor to consider. Yet the sound radiation coefficient used by Gore and Nicoletti for guitars doesn’t incorporate it.

Having these data also helps me adjust initial targets for carving thickness, but final my thicknessing happens with measuring deflection and listening to tone in the white.

That said, as noted in my original post, I’m still trying to figure out the best methodology from both a standpoint of practicality and accuracy and I’m eager for feedback and ideas. I was glad to hear Martino confirm in the recent webinar that while my frequency testing methods may not be completely appropriate for thicker billets, they should at least be consistently off from billet to billet, so as long as I stick to the same methodology, I should still be able to measure relative properties between billets.