Cross-grain stiffness of spruce: Importance and correlation to long-grain stiffness.

[Michael Szyper]

I‘ve had an interesting chat at Oberlin this year about the relationship of stiffness along and across the grain. I was told, that really high radiation ratio wood has very likely a low crossgrain stiffness and therefore not ideal acoustical properties.

Honestly i measure RR on a regular basis and have plenty of data, but never recorded cross-grain stiffness. Therefore i can‘t judge the claim.

Do you have any knowledge about this?

 

[David Burgess]

1 hour ago, Michael Szyper said:

Do you have any knowledge about this?

Not a lot.
We had one guy at Oberlin who experimented with severely reducing cross-grain stiffness by carving grooves between the grains on the inside of the fiddle, which made very little difference in longitudinal stiffness. I tried one violin which he had done that way, and thought it sounded pretty good.

I also made one viola which happened to have unusually high cross-grain stiffness (due to the wood used), and never managed to get it sounding the way I liked.

[Wood Butcher]

What way(s) are the best to measure the cross-grain stiffness?

[Don Noon]

2 hours ago, Wood Butcher said:

What way(s) are the best to measure the cross-grain stiffness?

Lucchi meter.  Far less convenient: cut samples

I borrowed a Lucchi meter and measured a bunch of my spruce.  Interesting that the trendline is dead-flat with a zero R^2 value.  There could be a hidden slight correlation with density; it is my feeling that very low density with high longitudinal speed would have crossgrain speed on the low side.  I'm not going to dig thru the data to see, though. 

As for the effect on an instrument, a viola I made with high longitudinal and low crossgrain stiffness managed to get a certificate for tone at VSA.  I don't have any clear examples, but it seems to me that low crossgrain stiffness on a violin loses some punch and snap... which is OK for a viola.  David:  did your not-so-hot viola with high crossgrain stiffness sound too harsh?

This is all torrefied wood:

 

[Andreas Preuss]

10 hours ago, Michael Szyper said:

Honestly i measure RR on a regular basis and have plenty of data, but never recorded cross-grain stiffness.

I think that the entire stiffness of the sound box in the direction across the grain (east-west) is very important. However this must not necessarily come from the top. Somehow this helps to get a soprano quality and therefore is important on violins. For violas things are quite different.

[HoGo]

I once made a mandolin out of Engelmann spruce that was exremely light and had definately low crossgrain stiffness When I glued the wedges I could bend it across like a wet noodle. With a pencil under centerline I could bend both "wings" down to bench with no effort (the wedges were 7mm/1/4" thick at the edges). Felt like balsa. After some thinking I decided not to do standard parallel tonebars but crossed the bars 3" above bridge and leave it considerably thicker.

The mandolin worked nicely and was very responsive and balanced. Had more velvety character to tone instead of more aggressive punch, but that is often associated with crossbars.

[David Burgess]

11 hours ago, Don Noon said:

David:  did your not-so-hot viola with high crossgrain stiffness sound too harsh?

Yes. Tight, harsh, lacking in depth.

[Don Noon]

Looks like there might be a subjective trend here:  low crossgrain stiffness = pleasant and mellow, high crossgrain stiffness = balance shifted to higher frequencies.  Theoretically, it makes some sense to me, as the antinode area of the higher frequencies would increase and become more efficient, as well as the "ring mode" effect shifting to higher frequencies.  Maybe.

[Marty Kasprzyk]

19 hours ago, Michael Szyper said:

I‘ve had an interesting chat at Oberlin this year about the relationship of stiffness along and across the grain. I was told, that really high radiation ratio wood has very likely a low crossgrain stiffness and therefore not ideal acoustical properties.

Honestly i measure RR on a regular basis and have plenty of data, but never recorded cross-grain stiffness. Therefore i can‘t judge the claim.

Do you have any knowledge about this?

 

Quite often people only measure the wood's speed of sound Cx in the longitudinal direction but it is also important in the cross grain direction Cy because both of them determine the various mode frequencies fN of a plate.  This is seen in the attached  equation 11.24 taken from Cremer's 1981 book "The Physics of the Violin" for a simple flat rectanular plate.

nx is the mode number in the longitudinal direction and ny is the mode number in the cross grain direction.  Lx is the length of the plate and Ly is the width of the plate, and h is th plate thickness.

The longitudinal speed of sound Cx is roughly three or four times greater than the cross grain speed of sound Cy so it is often thought to be more important.  However notice in Cremer's equation that the plate's length Lx  and width Ly are squared.  Since the violin's width is roughly half the length it gives four times the effect.

Thus the cross grain speed of sound has about the same importance as the longitudinal speed of sound for determining the mode frequencies.  So a spruce wood with a higher cross grain speed of sound will have higher mode frequencies which will make the instrument sound brighter if the thickness h stays the same.  If this brightness is undesirable the plate should be simply made thinner.  If a deep sounding instrument is desired picking a wood with a low cross grain stiffness would be helpful.

The importance of the wood's cross grain speed of sound has been known for a long time and Haine's 1980 CAS article is attached which discusses various wood properties.  More recent 2015 finite element analysis (see attachment) by Gough of violin shaped arched plates have also shown how the mode frequencies are dependent upon the anisotropic ratio of longitudinal elastic modulus El to cross grain elastic modulus where C=(E/p)^.5  therefore E= pC^2  A ratio of 1 would be for plywood and typical spruce would be around 15.

So finally getting back to the radiation ratio RR calculation of RR=C/p.  A plate made from wood with a high RR can be made lighter than a plate with a low RR at the same mode frequencies which will therefore increase its sound output. Haines thought the RR for both the longitudinal and cross grain directions were important for selecting wood not just the longitudial one.

 

 

RR is often calculated for just the longitudinal direction.  

Haines, pdf.pdf

[LCF]

As a total simplification, if the elastic constants were the same in each direction the ideal sound board shape might be circular. That suggests for woods with a higher cross grain strength the model should be wider.  There's a rough equality of travel time from centre to edge in each direction. 

How does the arching interact with that? Cross arches look a bit 'floppier' than lengthways arches. But ...?

[Marty Kasprzyk]

1 hour ago, LCF said:

As a total simplification, if the elastic constants were the same in each direction the ideal sound board shape might be circular. That suggests for woods with a higher cross grain strength the model should be wider.  There's a rough equality of travel time from centre to edge in each direction. 

How does the arching interact with that? Cross arches look a bit 'floppier' than lengthways arches. But ...?

I think so too.  Maybe one reason why plywood instruments often don't sound very good is that they are not wide enough for their nearly equal longitudinal and cross grain stiffnesses. 

Many early flat topped instruments might have had their oval shapes because of their highly anisotropic wood used. A newer desire for bowing of individual strings with an arched bridge led to the C bout being cut out of the oval to give better bow clearance.

A higher bridge also helped give more bow clearance but this also created greater downward string tension load so the tops were then made with stiffer arched shapes to better resist this increased string load. 

The arching makes the equation I posted earlier a real big mess with different radius of curvatures Ra in the long direction and Rb in the cross direction. These affect the mode frequencies proportional to their reciprocals squared: (1/Ra)^2 and (1/Rb)^2.  The arch height in both directions is the same so the radius of curvature Ra in the violin's long length in the  longitudinal direction is real large so its reciprocal squared is therefore small and it has only a small affect on the mode frequencies.

On the other hand the radius of curvature Rb in the cross direction is small so its reciprocal is large and it gives a much larger increase on the mode frequencies.  

So the arch height and the wood's cross grain stiffness both have a large affect on the various mode frequencies. 

Cremer's analytical equations are much too messy to show this stuff and it's much easier to grasp with Colin Gough's FEA color illustrations and graphs and his entire paper is attached.

Violin Plate Modes JASA, Nov 9, 2015.pdf

[LCF]

Interesting paper, thanks! It will take me a while to work through that interesting section on rib constraint. 

[Michael Szyper]

Quite a lot of smart input. @Don Noon since you used a lucchi for the cross grain stiffness I assume that your smacking method does not work for cross grain measurements?

[HoGo]

7 hours ago, Marty Kasprzyk said:

Many early flat topped instruments might have had their oval shapes because of their highly anisotropic wood used. A newer desire for bowing of individual strings with an arched bridge led to the C bout being cut out of the oval to give better bow clearance.

Could be also because trees grow in kinda longish trunk shape so it's easier to extract long and less wide pieces of wood

Thanks for the papers.

 

[David DEROY]

4 hours ago, Michael Szyper said:

Quite a lot of smart input. @Don Noon since you used a lucchi for the cross grain stiffness I assume that your smacking method does not work for cross grain measurements?

Hello Michael , i have come across this method , but never tried it yet : https://www.hisviolins.com/post/note-measuring-the-sound-speed-inwood-without-a-lucchi-meter

[Don Noon]

6 hours ago, Michael Szyper said:

@Don Noon since you used a lucchi for the cross grain stiffness I assume that your smacking method does not work for cross grain measurements?

It only works for uniform cross-sections (crossgrain for a wedge is thin at one side and wide at the other), and where the the wave has to travel a long-ish distance compared to the "width" (in this case, the "width" is the longitudinal dimension).

So, no.

Either a Lucchi meter, or cut samples to get the crossgrain reading.

[Anders Buen]

To get low crossgrain stiffness in relation to along grain stiffness, simply cut the wood off 90degrees with the grainlines. The wood quickly weakens sideways then the grainlines come at an angle <= 90 degrees to the rib plane, I think it may halve by about 90-30 degrees = 60 degrees. 
In many older insturments they apparaently did not care as much on this. 

[Marty Kasprzyk]

2 hours ago, Anders Buen said:

To get low crossgrain stiffness in relation to along grain stiffness, simply cut the wood off 90degrees with the grainlines. The wood quickly weakens sideways then the grainlines come at an angle <= 90 degrees to the rib plane, I think it may halve by about 90-30 degrees = 60 degrees. 
In many older insturments they apparaently did not care as much on this. 

Thanks, I had forgotten how important it was to have the wood cut with the annual rings perpendicular to the surface (zerro degrees).  Attached is a graph showing the cross grain speed of sound of spruce wood cut at different angles.

A high cross grain speed of sound allows a plate to be thinner (and therefore lighter)while achieving the same mode frequencies as seen in another attached graph generated from mathematical equations.  So just a little off perpendicular cutting is harmful if you want to increase the sound output.

The usual derivation for a wood quality radiation ratio RR assumes an isotropic material with one value of the speed of sound and an example is Wegst's article "Wood for sound" (attached) which ranks various woods on the basis of their longitudinal speeds of sound . But Cremer's book "The Physics of the Violin" uses the geometric mean C of the longitudinal Cx and cross grain Cy speeds: C= (CxCy)^0.5  when he calculates his modal densities.

So maybe the geometric mean speed of sound/density  might be a better measure of wood quality than just the usual longitudinal speed of sound/density ranking.

 

Wood for Sound, Wesgt.pdf

[Anders Buen]

I think Bearclaw spruce may have somewhat higher crossgrain stiffness than plain spruce. If that shows up on ultrasonic readings or not, I do not know. 

[LCF]

14 hours ago, HoGo said:

Could be also because trees grow in kinda longish trunk shape so it's easier to extract long and less wide pieces of wood

Thanks for the papers.

 

The 'poster child' instruments for round soundboards are those with membranes. Originally skin now often plastic. Banjos inevitably spring to mind but there  are many others such as kemancheh (spike fiddles from various countries) kora, etc. However I also think of guitar as being an approximate round soundboard instrument. The aspect is much wider than violins and although spruce is the usual soundboard material there is a prevalence of cross grain bracing systems. Guitar is an intrument where the lower resonance modes make a strong and obvious contribution to the sound output and the lowest of those (1,1) is a type of ring mode which is ~circular.  Some of the newer types of guitar  body/soundboard combinations are more like membranes over an internal round-ish support. Also think about lattice bracing, that is 'homogenizing'.  Some of the best spruce for guitars has a high cross grain stiffness. (Perhaps this is why plywood guitars work so well even if they don't sound pretty?)

That is a very different situation to that for violins and it recapitulates  the different ways that string vibration is coupled to the boards. Guitar couples mostly by a pumping motion. Violin by a sideways rocking. This is pivotal ( pun intended). Even the respective  soundhole systems relate to the coupling differences. 

 

[FiddleMkr]

Is there a correlation between the speed of sound within the tone wood and the sound produced by the instrument? Or a correlation to the response (“peppiness”)? 

[LCF]

Just now, FiddleMkr said:

Is there a correlation between the speed of sound within the tone wood and the sound produced by the instrument? Or a correlation to the response (“peppiness”)? 

The big questions.

[Don Noon]

5 hours ago, Marty Kasprzyk said:

Attached is a graph showing the cross grain speed of sound of spruce wood cut at different angles.

I only measured this effect once, although on some slightly off-quarter pieces, I did see lower than usual crossgrain speed.  The one I measured is in red.  I didn't measure maple, but it almost certainly wouldn't vary as much, due to the less rectangular cell shape.

It's also interesting to note that carved arching will necessarily have stiffness variations across the width, and who knows what effect that has.  Off-quarter spruce and carved arching will have different stiffness variations, also with who-knows-what effect on tone.

[LCF]

1 minute ago, Don Noon said:

I only measured this effect once, although on some slightly off-quarter pieces, I did see lower than usual crossgrain speed.  The one I measured is in red.  I didn't measure maple, but it almost certainly wouldn't vary as much, due to the less rectangular cell shape.

It's also interesting to note that carved arching will necessarily have stiffness variations across the width, and who knows what effect that has.  Off-quarter spruce and carved arching will have different stiffness variations, also with who-knows-what effect on tone.

Don, do you have a plot of density vs cross grain speed? Apologies if you already posted and if I missed it.

[Don Noon]

2 hours ago, Anders Buen said:

I think Bearclaw spruce may have somewhat higher crossgrain stiffness than plain spruce. If that shows up on ultrasonic readings or not, I do not know. 

Bearclaw is a wave in the radial/tangential plane, so I would expect the crossgrain to be fractionally lower, if anything.  Also, the wave screws up the cell geometry pretty bad, another reason it might be lower.  It's not like maple figure, which is a wave in the longitudinal/tangential plane.

25 minutes ago, FiddleMkr said:

Is there a correlation between the speed of sound within the tone wood and the sound produced by the instrument? Or a correlation to the response (“peppiness”)? 

Most of the speed of sound is within +/- 10% of say 5500 m/s, and generally that level of difference isn't a biggie as far as perceptible sound goes.  My experiments with MDF plates and Walmart firewood seem to confirm that.  But getting stiffness too low means heavier plates, and reduced response and volume, depending on how bad it is.  Damping might also be correlated with low speed of sound, and that might be even more important... but I don't have good data on that.