Equation 4.5-7

[ScottC.]

Hello to all, I am new here. I got the Trevor's books a few weeks ago and have been studing them intensely. I really suck at math , but I was able to figure out equations 4.5-2 -4.5-4 using table 4.5-3 numbers and checking the results with the table's results, in the "Design" book. The problem is when I get to equation 4.5-7 I just can't get it even close. I have been calculating it with a calculator with repeatable wrong results, I do have Excel but don't know how to use it for something like this.
My questions are;
1.Can someone send me the formulae in a file I can load into Excel.
2.Would someone be willing to look at/check the numbers I have been using for all the variables?
Thanks much

[Trevor Gore]

Hi Scott,

There's no doubt that Eqn. 4.5-7 is correct, so that only really leaves how you "read" the equation if you are getting consistently wrong results. If it were "fingering" problems, your results would be somewhat more random.

The most frequent source of errors is getting the zero count wrong. e.g GPa = 10^9 Pascals, millimetres = 10^-3 metres. The units need to be consistent SI units.

The second most frequent source of errors is Excel incorrectly computing a technically correctly entered formula. This is a result of a computing phenomenon known as ill-conditioning and tends to happen when very large numbers (e.g. 10^9 Pascals) are mixed with very small ones e.g. 10^-3 metres. The way around this is to cancel as many zeros as you can before you enter the formulae into Excel so that Excel has more significant figures to deal with. Excel works to 15 significant figures, normally enough unless you happen to kick off with 9 zeros. As you're not using Excel (yet!) this is obviously not your problem (yet!)

After that, I'm left to guessing at your interpretation of the formulae. Even with my trusty old reverse polish HP calculator (and a lot of experience with it) I don't know that I'd trust myself to get Equ. 4.5-7 right, given that it is not particularly calculator friendly. Hence the use of spreadsheets. If you can use a calculator and a computer (both of which you've already demonstrated a competence with) you will be able to use a spreadsheet. With regard to Equ 4.5-7, make sure you observe the brackets and how they work. So, for example, to compute (a/b) to the power of 4, [(a/b)^4], first work out a/b then raise that to the power 4. (i.e. if a/b=c, then c^4 is the same as [(a*a*a*a)/(b*b*b*b)]. Also, x^0.5 is the same as the square root of x.
The format I've used here for writing out the formulae is the same as the syntax you use in a spreadsheet.

For example, to add two numbers in a spreadsheet e.g. 3+2, the formula in the cell of the spreadsheet would be =3+2. The = sign tells Excel you are writing a formula. The power comes when to add the contents of two cells together you enter in your cell =A1+A2, where A1 refers to a particular cell just like you look up a reference in a street directory. The contents of cell A1 gets added to the contents of cell A2 and the answer will be in cell A3 if that's where you wrote the formula.

It's a lot easier to just just open a spreadsheet and try things out. That's how the rest of us started! The Help menus are pretty good in Excel. There may even be some tutorials.

[Dominic]

Scott, if you can't use excel having the formula won't help. Do a bit of an online course in how to use excel first then you will have much better luck stepping through the equation.
Cheers
Dom

[ScottC.]

Thanks, I already see where I have made an error. I thought the "0.5" was a multiplication process like "0.5 times x" I know I am mathematically challanged !
To make sure I understand another part of the formulae, on the top line "fa2" = vibrational stiffness value multiplied by LL (long grain direction) squared?
I have a book on Excel I'll be starting today to figure out how to enter the formulae.
Thanks again for your help.

[Trevor Gore]

f is the vibrational stiffness parameter

a (as in a^2, or a squared) is the long grain length of the guitar body you're about to build

LL (L subscript L) is the long grain length of the of the wood sample you're testing (which is normally a little longer than a).

It's good to hear you're making progress. Good effort!

[kiwigeo]

My brother is a maths teacher........I studied Geology. Geology is a much more sensible subject..even Arts students can do it.

[ScottC.]

I was a music major.

[ScottC.]

I have to tell everyone, when I came across this equation I almost threw in the towel thinking I could never do this much math as it's like an alien language to me. But with Dr. Gore's help I was actually able to enter the equation into Excel and enter the correct variables and after a few tries, it worked! Dr. Gore didn't have to help me just because I bought his books, but he did and did so timely and with language even I could understand.
I can't wait to try his ideas in building my own guitars.
Thanks again Dr. Gore!!!!!!!

[ScottC.]

I forgot to mention, YES kids you will use this @#$% math someday!!!

[Trevor Gore]

I'm pleased to see another success!

(Oh, and there's no need to call me Doc, unless you really want me to pull the rubber gloves on...)

[ScottC.]

[kiwigeo]

I'm pleased to see another success!

(Oh, and there's no need to call me Doc, unless you really want me to pull the rubber gloves on...)

That's more "OH DOC!!"

[Dominic]

It really is worth just pluggin away at this and working it out. As frustrating as it can seem you will become more familiar with the equations and how the variables relate etc. And the variables are number generated by your guitar afterall, and they all fit together somehow.
In excel, the first thing to do is to make a list of all the variables in the equation. Once you have that a good way is to step through it in bits. For instance, a part of an equation like (x+1/y)sq+(a+b)^2.5 can be broken up and calculate each part seperatly before adding them. Trying to get some of those very long equations into excel with lots of brackets can be tough and you can have a one bracket in the wrong place and it won't work. Just be patient and stay at it.
And as Scott has found you'll be well chuffed when you get it.
Cheers
Dom

[weslewis]

anyone using open office calc??? I am not very proficient but can be very persistent??!!

[Dominic]

=0.95977*D9*D20^2*D3^0.5/(D13+D22^4*D14+D22^2*(0.02857*D13+1.12*D16))^0.5*1000

Here is how to set out the equation in excel. Read through the equation and link up your variables to the correct cell reference (all the D?). Use exactly this arrangement of brackets and you should get it easy. Using the numbers from Trevors table you should get 2.73mm for Eng 1 and 2.70mm for Eng 2.
Put everything in m and kms first.
Good luck
Cheers
Dom

[Trevor Gore]

Wes, I've just had a quick look at Open Office Calc and to a first approximation it seems to work in a very similar way to Excel. So for the more straight forward spreadsheets I would expect the coding etc. to be pretty much 1:1 compatible.

[Barry Daniels]

Would it be possible to upload an Excel spreadsheet with this already setup?

[Trevor Gore]

Would it be possible to upload an Excel spreadsheet with this already setup?

Writing your own spreadsheets is part of the process of understanding what you're doing. I encourage everyone to do that so that they understand both the benefits and the limitations.

[weslewis]

I am using open office calc...my spread sheet comes out to 2.99 for the sample used in table 4.5-3 instead of 2.73 ..close but for some of the formula's I have simply divided by 1000 i.e El and Ec to get the decimal point in the correct place, and why do I have to enter the panel length and width as a decimal but the thickness as a whole number to get the correct answer??????

Am I off base

[Trevor Gore]

Am I off base

Likely!

I suspect that the 2.99 you got is just chance. You should be closer than that. The things that usually go awry are conversions in and out of imperial units and keeping track of the zero count. For example, GPa is 10^9 Pascals, millimetres is 10^-3 metres. Make sure you keep track of all those zeros. If you run into trouble you can't handle, send me a message via my website.

[weslewis]

I managed to get everything under control...with the same results in open office calc, so I acquired excel 2010 and now my answers are in line with yours...

[Trevor Gore]

Well done, Wes!

[Craig Bumgarner]

I understand section 4.5.2 and it seems great to have a way to quantify top wood, but how is this used by a limited production luthier in the real world? More specifically, how does one use it to obtain top wood capable of "world class guitars". I can't quite picture asking my supplier to run top sets through the 4.5.2 routine until we find ones I like. So how do I use this other than buy a lot of wood, keeping only the best and throwing the rest?

Or is the idea that supplier's grading systems are sufficient to get in the ball park and then use the 4.5.2 routine to optimize top thickness? I guess I don't see much evidence that suppliers actually use any kind of empirical test for stiffness to weight ratios, so I wonder how the grading standards for this are established and maintained.

[jeffhigh]

Well Craig you are right, there are no suppliers doing testing.

If you are lucky, the wood is being processed to avoid runout, otherwise the grading is on how well quartered it is, grain count and uniformity, colour, figure.
Quartering does have an effect on crossgrain stiffness, the other factors are mostly cosmetic

Since you are focussed on selmacs, equation 4.5-7 with its suggested vibrational stiffness values may not be directly usable.
The use of a pliage and the ladder bracing, and tailpiece means you can utilize much thinner plates.

But if you test wood and build with it and assess your results you may be able to develop your own guidelines
It is not about using the "Best Wood" but more about allowing you to make sensible decisions on plate thickness with what you have. It may however lead you to rejecting particularly low stiffness or high density pieces.

[Trevor Gore]

Section 4.5.2 is about making the best of the wood you have, rather than the wood you wish you had, as per the intro to Section 4.5.

Assuming you have "reasonable wood" (lets call it a top), if you follow the procedures, the difference between two tops will be a slight difference in mass and hence monopole mobility. One guitar will not be quite as loud as the other, though you might struggle to tell the difference, because as, it happens, stiffer wood is generally also denser. On the other hand, if you take the route of thicknessing to a dimension, all the modal frequencies are likely to be different between two guitars and the guitars will sound quite different. The determinant of a "world class" guitar is 90% in the design and build and 10% in the materials. For example, it's pretty difficult to tell that this was recorded using this guitar.

Regarding suppliers' grading systems, they are almost purely cosmetic, although some cosmetic features do correlate to some mechanical properties (e.g. medulary ray to cross grain stiffness). Given the way that the wood suppliers have corrupted the cosmetic grading system, could they ever be trusted not to corrupt a mechanical properties grading system?

I like to tap test my wood before purchase, listening primarily to the damping, but I rarely get that luxury. So ultimately one has to build a relationship with a supplier who will supply what you want, pretty much like any other business.