Top density

[Christ Kacoyannakis]

Hi all! I have two spruce tops given to me by a friend to make some tops for him. When I took a look at the tops, they appeared to be from very close together on the same log (the color is almost identical, and there appear to be some markings and knots that are very similarly located). However, one is a lot heavier than the other. When I picked it up, I was really shocked and looked at is closely to make sure it was spruce. That is when I noticed the similar markings. The are both almost perfectly quartered. The heavier piece is much stiffer. I thickness sanded them with exactly the same settings on my thickness sander, one right after the other, jointed the center seam, and glued them together. They are almost the same size, but the heavier one weighs 541 grams (even though slightly narrower), and the lighter 488 grams. The heavier one has extremely close grain pattern towards the center, with incredible medullary rays, while the lighter one has wider grain and hardly noticeable rays. I calculated the density of both, and the heavier one comes out to .526 (10 to the 3 kg/m3) and the lighter one .488). The tap tone on the heavier one is much higher and clearer. I am wondering, all things being equal, which is the more desirable piece of wood to use for a top (notice, I did not ask which would make the better top!). Obviously, I plan to make the heavier, stiffer one thinner. However, I just always thought that lower weight to stiffness was better, so I am curious about your thoughts. Thanks!

[Trevor Gore]

To a reasonable extent, stiffness (as in Young's modulus) tracks density for the spruces. The flexural rigidity of a panel is directly proportional to Young's modulus and to its thickness cubed. So the stiffness increases very rapidly with thickness, which means that in most cases the low density, low Young's modulus wood will turn out to be of lower panel mass at the same flexural rigidity, even though it will be thicker. More importantly, perhaps, is that it will also be of lower panel mass at the same vibrational frequency. A low mass top is easier to accelerate under the string drive forces, therefore should be louder for the same pluck displacement.

[Alan Carruth]

What Trevor said.

It does seem to me that denser wood tends to make a to with more 'headroom'. It may not have quite as much power when you push it hard, but there's less of a tendency for the sound to 'break up'. Both of those are pretty dense, so there's not really much to choose there.

[Christ Kacoyannakis]

I got around to sanding these two tops to thickness today. I made an Ervin Smogyi type deflection tester with a 1 kg weight and a digital depth gauge. I sanded the more flexible top to 3/32, and tested the deflection. Then I sanded the stiffer top down to where it had the same deflection. It was only a tiny bit thinner for the same deflection, along the grain. But, here is the really surprising thing. The stiffer top, with the really pronounced medullary rays was way stiffer across the grain! When I put both on the deflection tester, the more flexible top bottomed out the gauge, i.e., the weight pushed the top down until the gauge bottomed out. On the stiffer top, across grain deflection was almost the same (just a bit more) than along the grain. As I said at the start, they appear to be from the same tree, because the color, grain, and a few knots all seem to match, but I don't know how one could have such pronounced medullary rays, and the other does not.

[Alan Carruth]

"But, here is the really surprising thing. The stiffer top, with the really pronounced medullary rays was way stiffer across the grain!"

Not surprising at all, really. We usually talk about stiffness ratio; how much stiffer the wood is along the grain than across. Good softwood that's perfectly quartered might have a stiffness ratio of 10:1 or even a shade lower: it's ten times as stiff along the grain as across it. Perfectly flat cut might be more like 12:1: the stiffness along the grain is the same, but it's a bit less stiff across the grain. Softwood that's cut 'skew', with the ring lines at 45 degrees to the surface, has very low cross grain stiffness; often the ratio runs around 60:1, and can go as low as 100:1. I've seen a few tops like that; you can almost wrap them around a soda can.

All of this is related to the structure of the wood. If you look at the end grain of a softwood the cell walls look like rectangular boxes. One set of walls runs along the radius of the tree, and the other is parallel to the surface of the trunk (they're so small that the radial walls are essentially parallel). The medullary rays are small bundles of cells that run in between the radial walls. When you bend a quartered piece of wood you have to stretch the radial walls of the cells and also the medullary ray cells. On a flat cut piece you're stretching the tangential walls, but the medullary rays run through the thickness, so you don't have to stretch those, whicg is why flat cut wood is a little less stiff across the grain. With skew cut wood the cells at the surface make a diamond pattern, and all you need to do is deform those a little to stretch the surface, which is easy. That's why skew cut wood lacks cross grain stiffness.

I doesn't take much of an angle off quarter to reduce the cross grain stiffness noticeably. Last year I cut a couple of tops 'in flitch' from a split wedge of Western Red cedar. One has a stiffness ratio of 11.4:1. and the other 14:1. The first is more or less perfectly quartered, and the second no more than 3 degrees off, but there's a noticeable difference.

[Christ Kacoyannakis]

I checked, and the more flexible top has about a 30 degree angle to the grain, while the stiffer top is perfectly quartered.

[Bryan Bear]

Alan, thank you. That is the clearest explanation of why cross grain stiffness changes with the cut I have ever read!

[Alan Carruth]

Thanks Bryan. I meant to add that one reason hardwoods don't show as much difference in stiffness ratio with the ring angle is that they tend to have cells that are more round than rectangular.