Plate target thickness of non rectangular plates using deflection testing

 Blackwood
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Plate target thickness of non rectangular plates using deflection testing
I am starting a new flamenco blanca guitar with spanish cypress back and sides. The Gore plate thicknessing method using tap tones as described The Book requires evenly thicknessed rectangular plates. Often times with nice back and side sets the plates are non rectangular taking advantage of the fact that the upper bout is narrower than the lower bout. My spanish cypress set for a new flamenco guitar has trapezoidal plates that were too small to square up. So I went ahead and did the work required to allow me to get my thickness targets using deflection measurements. I thought some might find some value seeing how I did it. Also if I mucked anything up I will be sure to get corrections.
For this process I needed two good representative rectangular samples of the back plates for a long grain stiffness value and a cross grain stiffness measurement. As you could see in the first photo. I was able to create a square section on one of the plates. Also after taking a long grain deflection I will have enough length to cut off a rectangular section of the same plate.
Previously I have built a deflection jig that allows me to take deflection measurements on a variety of span lengths. So first off I measured the long grain deflection under a measured load.
Next I cut off a 50 mm or so rectangular section off of the plate, set up the deflection jig and measured the cross grain deflection
The last additional bit of information I needed was the density of the wood. To determine the density of the wood I needed the mass of the cross grain sample.
The last step was to modify my previously spreadsheet for calculating target thickness using tap frequencies to use deflection based young's modulus calculations. Luckily I had a handy spreadsheet from the Modal Tuning with Trevor Gore class I took at Robbie's place to calculate the long and cross grain young's modulus for the plate. The book also has the information needed to make these calculations. I substituted the deflection based El and Ec calculations for the frequency calculations in my original spreadsheet and set the Elc to an average value. This term has little effect in the overall calculation. With all the required inputs I got what looks like a good thickness target for the plate. This target is very close to my frequency based target from my first flamenco guitar using spanish cypress. So it seems like the method worked well.
Just for reference here is the spreadsheet for my tap baised thickness calculation for the top plates on this guitar.
For this process I needed two good representative rectangular samples of the back plates for a long grain stiffness value and a cross grain stiffness measurement. As you could see in the first photo. I was able to create a square section on one of the plates. Also after taking a long grain deflection I will have enough length to cut off a rectangular section of the same plate.
Previously I have built a deflection jig that allows me to take deflection measurements on a variety of span lengths. So first off I measured the long grain deflection under a measured load.
Next I cut off a 50 mm or so rectangular section off of the plate, set up the deflection jig and measured the cross grain deflection
The last additional bit of information I needed was the density of the wood. To determine the density of the wood I needed the mass of the cross grain sample.
The last step was to modify my previously spreadsheet for calculating target thickness using tap frequencies to use deflection based young's modulus calculations. Luckily I had a handy spreadsheet from the Modal Tuning with Trevor Gore class I took at Robbie's place to calculate the long and cross grain young's modulus for the plate. The book also has the information needed to make these calculations. I substituted the deflection based El and Ec calculations for the frequency calculations in my original spreadsheet and set the Elc to an average value. This term has little effect in the overall calculation. With all the required inputs I got what looks like a good thickness target for the plate. This target is very close to my frequency based target from my first flamenco guitar using spanish cypress. So it seems like the method worked well.
Just for reference here is the spreadsheet for my tap baised thickness calculation for the top plates on this guitar.
Re: Plate target thickness of non rectangular plates using deflection testing
Nice one John. That is going to be a pretty thin top...

Dave
Dave

 Blackwood
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Re: Plate target thickness of non rectangular plates using deflection testing
I am trying to match my results from my first Flamenco. It is an amazing sounding instrument. All of the flamenco players that have tried it have been shock at its sound. I watched them go from skeptical to slightly interested when they felt how light the guitar was, to very engaged when they started playing and spending a lot of time with the instrument. My thought at the time was to go very light on the top and make up the stiffness with the braces. It sounds like a flamenco and not a classical.
The resonances are 95 Hz 198.5 Hz and 157 Hz. The bridge rotates 1° and monopole mobility is 30.47
The resonances are 95 Hz 198.5 Hz and 157 Hz. The bridge rotates 1° and monopole mobility is 30.47
Re: Plate target thickness of non rectangular plates using deflection testing
Great topic. Does the weight you use to deflect the board matter or is it predetermined?
Zef guerra
Zef guerra
Re: Plate target thickness of non rectangular plates using deflection testing
It's maybe easier for himself to use the same weight every time, but a heavier weight gives more deflection  and the equations takes care of everything, including the distance between the two supporting bars underneath the top.
So you are free to use any weight, I would however not use any extremely light or extremely heavy ones.
So you are free to use any weight, I would however not use any extremely light or extremely heavy ones.
Re: Plate target thickness of non rectangular plates using deflection testing
Hi, I wasn´t sure if I should start a new thread or not but the topic is exactly the same: I aquired a nice Padouk set from madinter and just realized later that the plates were cut as a trapezoid without leaving much flesh.
Probably I can determine E for the longitudinal by taking an average width an using a deflection jig similar to what John used. But the cross grain value I can´t get on this way. The plate size is even not enough to get a decent sized cut for the cross grain measurement. If I´m lucky I can cut a 3cm wide piece. I´m not sure that´s enough for the deflection test.
To give you an impression of the shape: Here´s a picture of the back plates including my OOO template The influence of Glc on the thickness calculation is smaller than E (cross grain) so probably I could use an average value for that as John did. The thing is, this is the first time I use Padouk for a back so I don´t know ...
I could try to use the method for determining Glc woodsy proposed in this thread: viewtopic.php?f=33&t=7239&hilit=non+rectangular. But as far as I understand it is based on the assumption that the plate is rectangular. I´m not sure if it´s possible to assume again an average width for this method especially because off the strange shape of the plates.
Does anyone have an idea on how to get at least an idea of the right plate thickness?
Juergen
Probably I can determine E for the longitudinal by taking an average width an using a deflection jig similar to what John used. But the cross grain value I can´t get on this way. The plate size is even not enough to get a decent sized cut for the cross grain measurement. If I´m lucky I can cut a 3cm wide piece. I´m not sure that´s enough for the deflection test.
To give you an impression of the shape: Here´s a picture of the back plates including my OOO template The influence of Glc on the thickness calculation is smaller than E (cross grain) so probably I could use an average value for that as John did. The thing is, this is the first time I use Padouk for a back so I don´t know ...
I could try to use the method for determining Glc woodsy proposed in this thread: viewtopic.php?f=33&t=7239&hilit=non+rectangular. But as far as I understand it is based on the assumption that the plate is rectangular. I´m not sure if it´s possible to assume again an average width for this method especially because off the strange shape of the plates.
Does anyone have an idea on how to get at least an idea of the right plate thickness?
Juergen

 Blackwood
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Re: Plate target thickness of non rectangular plates using deflection testing
I would square up the upper bout and do a deflection test on the squared portion for the long grain. It seems like a deflection tests on a rectangular 3 cm strip should work. Use less mass for the deflection test. Or if you have sides from the same wood take a strip off one end of the sides.
Re: Plate target thickness of non rectangular plates using deflection testing
Thanks for the fast reply John.
Does that mean you did those measurement on pieces with less than 5cm width at some point? I assumed that 5cm is the lower limit for reliable numbers. Didn´t find a posting here on the forum with less than 5cm (but probably that´s because Trevor recommended it?).
I think I will try that on the Top as well just to get a feeling how the deflection measurements deviate from the frequency method.
If anyone ist interested I will post the results here
Does that mean you did those measurement on pieces with less than 5cm width at some point? I assumed that 5cm is the lower limit for reliable numbers. Didn´t find a posting here on the forum with less than 5cm (but probably that´s because Trevor recommended it?).
I think I will try that on the Top as well just to get a feeling how the deflection measurements deviate from the frequency method.
If anyone ist interested I will post the results here

 Blackwood
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Re: Plate target thickness of non rectangular plates using deflection testing
I did do the cross grain at exactly 5 cm but I picked 5 cm because I had that much. I was not following any guidance. We rely on the stiffness of wood at 6 mm wide when we use it for braces, so it seems like 30 mm or so should be OK.
 Trevor Gore
 Blackwood
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Re: Plate target thickness of non rectangular plates using deflection testing
It's not that hard to get the cross grain stiffness using deflection methods. The pics here are of my old deflection jig as they show the technique better. First the jig. Note that the support tubes themselves are longer than the panel is.
Here's the normal arrangement for measuring long grain Young's Modulus:
Here's the cross grain arrangement:
The requirement is only for the area between the supports (the span) to be rectangular, for both the long grain and cross grain measurements.
Here's the normal arrangement for measuring long grain Young's Modulus:
Here's the cross grain arrangement:
The requirement is only for the area between the supports (the span) to be rectangular, for both the long grain and cross grain measurements.
Fine classical and steel string guitars
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

 Blackwood
 Posts: 485
 Joined: Mon Jan 21, 2013 2:59 am
 Location: Seattle
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Re: Plate target thickness of non rectangular plates using deflection testing
Thanks Trevor, That makes the cross grain a lot easier with odd shaped plates.
Re: Plate target thickness of non rectangular plates using deflection testing
As I couldn´t find anyone posting a comparison of recommended thickness calculations for the frequency approach and the deflection approach I thought it could be interesting to to put my results here.
I tested 2 sets of backs and 2 sets of tops (will be 1 classical guitar and 1 steel string). For the deflection tests I repeated the test for each plate side (therefore plate 1a and plate 1b are the same piece of wood but once flipped). This means here I had 4 values per set.
For the frequency approach each plate was tested (obviously it didn´t make sense to flip the plate, hence just 2 values per set.
Except of the padouk set each set consisted of rectangular plates. For the padouk set I used in the calculations for the deflection test an average of the plate width ( which differed by 3cm between the upper and lower contact with the support). The calculations for the frequency approach assumed a rectangular plate with the forementioned average width and the actual plate length. (I didn´t expect to get any useful numbers because the theory is based on rectangular plates but thought I should include that as well). The following table shows the results for the thickness calculation for both approaches.
Summary:
the different methods for determining the recommended thicknesses agree quite well for cedar and spruce while there is a significant difference for the sapeli. An explanation could be that the plated had been slightly bend. Probably this changed the vibrational properties of the plates.
But I was quite surprised to see that both approaches resulted as well in almost identical average values for the recommended thickness for the padouk even with all the simplifications concerning the plate geometry.
I tested 2 sets of backs and 2 sets of tops (will be 1 classical guitar and 1 steel string). For the deflection tests I repeated the test for each plate side (therefore plate 1a and plate 1b are the same piece of wood but once flipped). This means here I had 4 values per set.
For the frequency approach each plate was tested (obviously it didn´t make sense to flip the plate, hence just 2 values per set.
Except of the padouk set each set consisted of rectangular plates. For the padouk set I used in the calculations for the deflection test an average of the plate width ( which differed by 3cm between the upper and lower contact with the support). The calculations for the frequency approach assumed a rectangular plate with the forementioned average width and the actual plate length. (I didn´t expect to get any useful numbers because the theory is based on rectangular plates but thought I should include that as well). The following table shows the results for the thickness calculation for both approaches.
Summary:
the different methods for determining the recommended thicknesses agree quite well for cedar and spruce while there is a significant difference for the sapeli. An explanation could be that the plated had been slightly bend. Probably this changed the vibrational properties of the plates.
But I was quite surprised to see that both approaches resulted as well in almost identical average values for the recommended thickness for the padouk even with all the simplifications concerning the plate geometry.
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