[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