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For those left brain luthiers in the group - I hope you can educate me about some of the properties of tonewoods.

I've found lots of data online regarding "Janka" measrements for various hardwoods, but nothing similar for "Q" rating.

My understanding of Janka is that it is purely a measurment of hardness, and does not have much to do with the appropriateness of wood for musical instruments. e.g. wood could be very hard, yet also extremely massive and a poor conduit for soundwaves. If one is generally looking for wood that is very stiff relative to it's weight, hard but heavy woods might not work well.

Also, I've come across some woods that are extremely hard, yet not very stiff at the thicknesses we tend to use for backs and sides (e.g. Dogwood - the stuff is like iron to saw, plane, sand, but once I got some sides down to 80 thou, it was like a noodle - curious.)

Thanks

Generally speaking, it seems to be a good idea to make the top of the guitar as light as you can while still having enough stiffness to keep it from folding up. As it turns out, softwoods are generally better for this then hardwoods, mosly because they have good stiffness along the grain for their density.

Stiffness, the ability to resist deflection under load, will be proportional to the Young's modulus in the direction of bending, and the cube of the thickness. Young's modulus (E) is a measure of how much force it takes to stretch or compress a given size piece of material by a certain amount, and it's the stretching of the 'outside' surface and the compression of the'inside' one that resist the bending. As the piece gets thicker, and those surfaces get further apart, they become more effective at resisting bending, so the stiffness rises very quickly; hence the cubic term.

There are lots of ways to measure the E value of wood. One I use is to vibrate top or back halves, and find the pitch of the lowest resonant modes for bending along and across the grain. If you know the mode ferequency, and the length, width, thickness, and mass, of the piece, you can calculate the Young's modulus. It will be:
E= (0.946 * d * F^2 * L^4) / H^2
where:
d= density, in kilograms per cubic meter
F= the resonant frequency in Hz
L= length, in meters, and
H= the height (thickness) in meters.
"^" means 'to the power of', so H^2 is the thickness squared

The results of this are in units of 'Pascals', and the E values for most woods run in the billions of Pascals, so at some point you're going to want to divide by a thousand or so to keep the numbers in bounds. Also, remember, your results can't be any better than your least accurate measurement: if all you can do is measure to tenths of a millimeter (three significant digits) then everything past the first three numbers in the result is a suggestion.

It also happens that this equation, as imprssive as it looks, is not the last word: you really have to go to higher order partial differentials to get truly accurate results. I'm told this is good to within 10% or so, but since you probably don't work your wood thickness much more accurately than +/- 3% (.003" in .1") that's a wash: 1.03^3=1.093 or so.

If you plot out the E values for bending along the grain against the density of the wood, you'll see that most of the points on the graph fall pretty close to the same line _for_all_of_the_usual_softwoods_. Western Red cedar is usually less dense than Red spruce, and most WRC samples will be somewhere down in one corner of the chart, while the Red spruce ones will be up in the other corner, but there will be some of both closer to the middle if you test enough pieces. I have a WRC top and a Red Spruce top that test out exactly the same, except for the damping factor.

One advantage of the vibration test is that you can check for the damping factor at the same time as you figure out the E value. Once you find the resonant pitch, turn the frelquency knob down until the amplitude is just 70.7% of what it was at the peak, without any change in the input power. Note that frequency and call it 'Flo'. Do the same on the high side of the peak to find 'Fhi'. These are the points where the energy in the system is one half what it is at the maximum, so the difference between Fhi and Flo is the 'half power bandwidth'. If you take the peak frequency and dicvide by the bandwidth (Fp/(Fhi-Flo)) you get the 'Q value', or 'Quality factor'. It's a measure of the amount of energy that is dissipated as the piece vibrates: if the Q=100, then 1/100th of the energy is 'lost' for every cycle of vibration. The higher the Q, the longer the thing rings whe it's tapped. That WRC top has the same density, and stiffness along and across the grain as the Red spruce one, but it has a much higher Q value. It will be interesting to make a 'matched pair' and see how the sound differs.

This is getting long, so I'll wrap up. I measure this stuff by driving the wood with my signal generator, using a loudspeaker. I stick a little piece of 'meglass': the little silvery strips of special iron that you find in those store security bubble stick-ons, to the piece in the center of one end. A standard electric guitar pickup will get a decent signal from this if it's close enough, and you can read it on an AC millivolt meter. Some glitter helps you home in on the modes., with the piece up on foam pads, of course.

Wow. Alan - thanks for the education. And what's more, I think I understand what you've explained!
What are your thoughts on measurements of back (and sides?) Do you apply the same testing to the woods you use for those? Do the same principles apply?
Thanks!

I have been measuring the properties of my back woods, but have not yet tried to use the measurements to 'optimize' the backs. For one thing, what's 'optimimum'? The back does a different job than the top does, and it's a little harder to say what's the most important aspect of that job. Also, the back has less of an effect on the final sound of the guitar, so it's not as critical.

Daniel Haines did a lot of work on wood properties, mostly in connection with violins, but he did test some guitar wood samples, too. He published the results in several places, including, iirc, American Lutherie, so you might try looking there. The original articles were in the Catgut Acoustical Society 'Journal', and I'm not sure if al of those are up on line. Maybe a search on Haines' name and 'wood properties' will turn something up?

A great education on vibrations, waves, harmonic motion etc. is available to all for free here.

http://ocw.mit.edu/OcwWeb/Physics/8-03F ... /index.htm

Even if some of the math is heavier than you want to deal with, the demos are worth the price of admission.

And this is a great Young's modulus lecture.

http://ocw.mit.edu/OcwWeb/Physics/8-01P ... mbed26.htm

John

On Q ratings...

The data I have seen suggests that there is *Giant* order of magnitude type variation in Q ratings between boards cut from the same tree... much less from 1 species to another...

You may be able to generalize that some woods "Tend" to have Low Q values, while other woods may have "High Q" Potential...

For example...
Pernambuco is generally believed to have a High Q potential... Some boards have extremely high Q values... while others don't.

Spruce is another good example of the same thing....

On the other hand, a wood like Ebony is generally believed to have a "Low Q"...

The biggest problem is that Grain and grain runout has a *Giant* effect on Q value of wood.... so "Curly" woods tend to have lower Q values and Straight grained woods tend to have higher Q values.... Kinda.....

This means you can find a piece of Ebony that has a higher Q than a piece of spruce.....

So.. if you want to know, you have to find some way to test it out.

Not sure if this helped any.... but it is my perspective on things.

Good luck

John

Most luthiers do test the Q value of the woods they use, they just don't get a number. The longer something rings when you tap it, and the more clear the impression of pitch you get, the higher the Q value. Genrally that's all the information on that you will need.

As usual, there are times whan that doesn't work as well as you'd like, and that's where the numbers come in handy. Several years ago I got curious about balsa: some folks are using it as a core in 'sandwich' construction, and I'd always felt it had very high damping. It was hard to test pieces from the hobby shop: they are so light the speaker just blows them away. I had picked up a piece about 3x3 inches, and 42" long, several years prior, and dug that out to test. It turned out to have a Q value along the grain of about 120, better than a lot of spruce, and better even than some Indian rosewood! It occured to me that the issue with those thin sheets is that they have to move a lot of air to vibrate, and being so light themselves, the air damping is more significant than it usually is in wood testing. You can get the opposite effect with really dense woods: you have to hit them so hard to get them to ring at all that they can go on for some time.

Although the role of the Q value of the materials seems obvious, I'm not at all sure we really understand it fully yet. Cedar tends to have high Q, low damping, and that would tend to favor the high end sounds. So why do cedar topped guitars have the reputaion of being 'warm'; an attribute that is usually associated with lots of lows? Maybe it's the added power in the upper partials, that is being assigned to the fundamental by the ear, that makes them sound 'warm'? It's hard to say.

Thanks, Alan. I really appreciate your taking the time to give such a complete response.

Regards,

Ooops - thanks to you too, John!