Equ 4.5-5

[jeffhigh]

That's a horror story on the car Trevor.
I just retired my '95 Commodore last week and replaced it with a low mileage 2006 Commodore.
Wealthy luthiers and their flash cars eh?

[jeffhigh]

That some seriously lightweight Englemann Martin, should make a great classical

[jeffhigh]

That some seriously lightweight Englemann Martin, should make a great classical

[kiwigeo]

Graham Hein's Englemann is amazing stuff...light and stiff and it rings like a bell.

[jeffhigh]

Yes it's what I've used on my last 3

[charangohabsburg]

Tap testing results for the falcate classical:

Plate Thickness Calculator.pdf

I know, I know, it's been an year now... but may I ask you "how vertical" the grain was (is) in that top?
I have never worked with Engelmann spruce, and the data Elong / Ecross = 21.71 really makes me wonder if this is typical for this species or if it is due to grain orientation (somewhat off perfectly quartered). I just measured several spruce tops (Picea abies) with Elong / Ecross around 8.5 to 9.9, and a red cedar top with Elong / Ecross = 13.87.

[dsgoen]

I know that this has already been discussed ad nauseam, but I have been spectacularly unable to make Excel 2010 come up with the expected numbers. I running on Windows 8.1.

In a fit of determination I spent about six hours straight trying to get the expected value of Elong at 11.90GPa and the thickness at 2.71mm as Trevor mentions in his post of Wed Jun 20, 2012 7:04 pm. By coding the same calculations in every possible way I got answers of anywhere from an 88mm thickness to 2.66mm (my final attempt).

I did get exactly the right answers by doing the equations by hand and also with a program left over from my daughter's high school days called Microsoft Mathematics.

So, my question is: how far off on Excel is still close enough? My answer of 2.66mm is only 0.05mm off, which is beyond my woodworking skill anyway. The programmer in me wants to have exactly the right answers, which we know is not always possible using Excel due to ill conditioning, but the obsessive compulsive in me wants exactly the same answers that other people have been able to achieve. I've noticed that my answers vary in accuracy for different species, some being off much more than the 0.05mm I got in test 1 for Engelmann Spruce.Should I just give it a rest and use what I have?

Also, I cannot duplicate by any method the Density figures listed in Table 4.5-3 on page 4-63 for Port Orford Cedar. I get 417.058 for the first and 412.424 instead of 417.8 and 412.8 in the table. Not a big difference, but I can't determine why such a relatively simple calculation would lead to us have any deviation between what I got and what the book lists.

Thanks
David

[charangohabsburg]

In a fit of determination I spent about six hours straight trying to get the expected value of Elong at 11.90GPa and the thickness at 2.71mm as Trevor mentions in his post of Wed Jun 20, 2012 7:04 pm. By coding the same calculations in every possible way I got answers of anywhere from an 88mm thickness to 2.66mm (my final attempt).

Six hours is quite a lot of time for a relatively simple spreadsheet with less than a dozen mathematical formulas - and still not getting it right. I suggest you to split up the calculation in smaller formulas (for each parenthesis, root operation numerator, denominator etc. one formula in one cell, and then use these cells as variables for the next higher level and so on. This may take a bit longer in the beginning but takes you pretty much straight forward to a correctly working spreadsheet, and if you get something wrong it is much easier to track down the mistake.

I did get exactly the right answers by doing the equations by hand and also with a program left over from my daughter's high school days called Microsoft Mathematics.

So why not just use this one iof you are not familiar enough with Excel?

So, my question is: how far off on Excel is still close enough? My answer of 2.66mm is only 0.05mm off, which is beyond my woodworking skill anyway.

I'd say you already gave the answer!

The programmer in me wants to have exactly the right answers, which we know is not always possible using Excel due to ill conditioning, [...]

Excel can be a nightmare in many ways, but here you can't blame its mathematical functions. I recommend you to do things step by step as I explained above, or use your daughter's program you mentioned and which you seem to handle better.

Also, I cannot duplicate by any method the Density figures listed in Table 4.5-3 on page 4-63 for Port Orford Cedar. I get 417.058 for the first and 412.424 instead of 417.8 and 412.8 in the table. Not a big difference, but I can't determine why such a relatively simple calculation would lead to us have any deviation between what I got and what the book lists.

A typo I guess. So what?

[dsgoen]

Six hours is quite a lot of time for a relatively simple spreadsheet with less than a dozen mathematical formulas - and still not getting it right. I suggest you to split up the calculation in smaller formulas (for each parenthesis, root operation numerator, denominator etc. one formula in one cell, and then use these cells as variables for the next higher level and so on. This may take a bit longer in the beginning but takes you pretty much straight forward to a correctly working spreadsheet, and if you get something wrong it is much easier to track down the mistake

I couldn't agree with you more. You start playing around with parentheses, however, and it goes to quite a lot more than a dozen variations. Maddeningly, many of the parenthesis changes also changed the results, even though the parentheses didn't technically change the mathematical order of evaluation. I've never run across that before in programming. It just became a big puzzle for me that I stubbornly wanted to solve.

So why not just use this one iof you are not familiar enough with Excel?

I would prefer Excel because it also stores formulas and constants and I can then save off a page for posterity. Doing it by hand or with MS Mathematics is a manual procedure. It's just easier if I can punch things in a spreadsheet (assuming I ever got one to work). Besides, I got stubborn. I don't think at this point it's not being familiar enough with Excel, as so many others, including Trevor, have also encountered Excel weirdness.

The whole exercise did get me wondering how much a deviation is acceptable. I don' think my small error is worth worry about, but where is the line? 5%? 10% When dealing with fractions of a millimeter I became curious at what point a change in thickness becomes significant.

My best results were from breaking up the final equation into chunks and specifically spelling things out for the spreadsheet (such as repeated multiplications instead of using exponents, using SQRT instead of the exponent 0.5, etc.).

A typo I guess. So what?

If it is a typo, then you're right, so what? As I stated in another post, the book seems remarkably free of errors, but I have never encountered a work of this size that didn't have some errors, so a few things wrong here or there seems expected. If it is a table generated from Excel then it's another mystery. I've done a lot of programming and when I see unexplained errors it peaks my interest and makes me wonder about the source of the error. Not that I consider setting up an Excel spreadsheet to be programming. It's more like voodoo!

[charangohabsburg]

Six hours is quite a lot of time for a relatively simple spreadsheet with less than a dozen mathematical formulas - and still not getting it right. I suggest you to split up the calculation in smaller formulas (for each parenthesis, root operation numerator, denominator etc. one formula in one cell, and then use these cells as variables for the next higher level and so on. This may take a bit longer in the beginning but takes you pretty much straight forward to a correctly working spreadsheet, and if you get something wrong it is much easier to track down the mistake

I couldn't agree with you more. You start playing around with parentheses, however, and it goes to quite a lot more than a dozen variations. Maddeningly, many of the parenthesis changes also changed the results, even though the parentheses didn't technically change the mathematical order of evaluation. I've never run across that before in programming. It just became a big puzzle for me that I stubbornly wanted to solve.

Programming languages and spreadsheets (including Excel) never failed me on parenthesis, it was always me (I do programming since more than 25 years, most of them on a professional basis). Excel is extremely awkward to read and edit though, which is why I suggest to dismantle large formulas, at least one cell for each parenthesis, otherwise tracking down an error can take forever. It helps to first write down the formula on a sheet of paper (not too small), then mark and number the elements you want to treat separately with differently coloured crayons (may look childish but saves a lot of time and sweat). On a second sheet of paper you re-write each element and mark them with the correct colour and number, and only afterwards you switch on your computer.

Only like this you can see if and where the program does something different than what you expected, and normally you will say "oh no, why did I not see that before!"

In the case of Equ. 4.5-7 it anyway does not make much sense to mash everything in one cell because you will (should) be interested in a few intermediate results like density, EL, EC and GLC.

If you still believe Excel is the culprit but want to use it, you can install OpenOffice (its free and does and looks pretty much the same s Excel does, and also reads all and writes most Excel versions formats). Then look if it does something different. Open Office is what I work with since a few years now.

[Trevor Gore]

So, my question is: how far off on Excel is still close enough?

Until you've had enough of it!

I can understand wanting to replicate the results exactly, but I guess that's not always going to be the case. I think all the known problems have been discussed already. The numbers printed in the book are rounded and truncated, so will not be the 15 significant figures that Excel works with. My spreadsheets are linked all through, so from the input data onwards I keep all significant figures. If you do that and correct for the issues discussed earlier in the thread I think you'll be as close as you're likely to get. The rest is down to the idiosyncratics of Excel. Personally, I think you're close enough already to make no difference.

Also, I cannot duplicate by any method the Density figures listed in Table 4.5-3 on page 4-63 for Port Orford Cedar.

Rounding, methinks. Going back to my original data I have the width in there as 282.5mm, which to three figures Excel rounds to 283mm, which is what got printed. That fixes things.

[Jim Kirby]

I admit to somewhat of a lack of experience, as excel scared me off early on, but, today, I would never let a student do what needed to be a serious computation using it, and I would not attempt it myself. The discussions in this subforum alone are enough to point out why. You would need to go to pretty great lengths to convince me it is even a vaguely, minimally serious programming tool. To me, it is a tool for building tables and lists, and I don't even like to use it for that.

Diatribe ended

[GregHolmberg]

Here's the Hearmon paper, in case any one wants it.

The Fundamental Frequency of Vibration of Rectangular Wood and Plywood Plates
R. F. S. Hearmon, 1946 Proc. Phys. Soc. 58 78

One thing I learned from this paper is that the constants shown in the book, Equ. 4.5-6 (126 and 4/7=0.5714) are for a clamped plate (no rotation, no displacement at the edges). In the paper, they clamped (vertically) the wood between two steel frames.

Hearmon also produces constants for the case of a plate that is "supported". In this case, they created a frame with a horizontal "V" slot around the inside edge, and then tightened the frame horizontally. The constants were then 756/31=24.387 and 867/434=1.998. This gives very different results, of course.

Which case a glued panel is most similar to, I don't know.

Here's my spreadsheet (Google Docs--online) implementing the thickness calculation and using average values for density and Elong for many common species used for tops and backs. There are of course exceptional pieces for any species, but the species making the lightest top panels on average are (in order):

• Balsa
• Paulownia
• Sugi
• Engelmann Spruce
• Western Red Cedar
• Black Cottonwood
• Noble Fir
• Northern White Cedar
• Norway (European/German/Italian/etc.) Spruce
• White Fir
• Eastern White Pine
• Sitka Spruce
• Basswood
• Obeche
• Sugar Pine
• Red Spruce
• California Red Fir
• Coast Redwood
• Western White Pine
• White Spruce
• Yellow Poplar
• Okoumé
• Port Orford Cedar

The list continues in the spreadsheet. Also for species used in backs.

It's surprising how far you have go down the list to find the standard top species, Sitka Spruce. Many of these species have never been used in a guitar, to my knowledge. Maybe it's time to give them a try?


Greg