compensation spreadsheet question

[JurgenV]

A year ago I started with my compensation spreadsheet. I stopped when the optimization seemed to work with some data I found in the forum thanks to woodsy23 (Richard).
The last few days I tried to get the complete calculation including string stiffness measurements and neck curve model running. It looks like the neck model is so far ok as I could compare it again with the neck profile used by woodsy. Just very small deviations from his model, which didn´t change anything in the optimization.
I used the 12th fret as the last fret in the calculation as I didn´t use the bolt on bolt off design for the neck.
alpha=0.5
beta=1
scale lenth 645.16mm
which give me for the 6th string the following values:

compensation_action_E.JPG (73.16 KiB) Viewed 21530 times

I hope someone can confirm that it looks ok.

With the string properties I seem to be not as lucky:
for my D´Addario EXP16
I get the following results:

I think there is something wrong with these numbers but I can´t figure out what. I would appreciate I someone could give me a complete set of numbers for a string so that I can check my spreadsheet on errors. Another thing is that I wonder how stable your frequency measurements are. When I use g-tune the frequency varies with 0.5Hz or more which according to my calculations change the intonation errors quite a lot. I use a cheap piezo pickup with preamp which delivers the signal to the notebook. Some comments on how to improve the stability would be helpful.

Ok. If I take these numbers for the optimization I get these compensations:

As long as I can´t trust the string properties I found, I don´t want to rout the saddle slot for the two guitars I´m still trying to finish. Another possibility would be to use the values from the book for steel strings to find a rough location for the slot and then use the other spreadsheet for compensation which I used to calculate the nut and saddle compensation for an existing guitar. But I´m not sure if that´s a good idea at all and in addition I don´t want to waste all the time and effort I put into the spreadsheet for full compensation
As usual: Any help on these topics would be appreciated

Jurgen

[jeffhigh]

Without getting too far into it and having to go back and check terminology etc, I suspect that your problem is that you have used the measured overall string diameter.
For string longitudinal stiffness calculations, you need to use the measured core diameter excluding the wrap. The wrap contributes mass but not stiffness since it carries no load

[JurgenV]

Thanks Jeff.

Yepp, you´re right. It had been a year ago when I put the spreadsheet together so I just mixed it up. I found one more mistake: at one point I used the wrong unit (m^2 instead of ^2).
To get more stable measurements I played a bit around with g-tune: with a higher sensitivity setting and a window concentrated on the region of interest I got a lot more stable measurements. With the exception of the high e string I have now at least more consistent results for the string properties:

The high e string I measured roughly 10 times but I always more or less the same result. To be sure that the measured frequencies ar not too far off I used two different approaches tor the mass unit length µ:
1. measuring length and mass of a string
2. via the expression in the design book using the tension and the measured frequency
Results looks quite similar: for the sixth string it´s 1.03*10^-2 kg/N and 1.02*10^-2kg/N

So now I would need a confirmation that the Youngs Modulus for steel strings can be that much higher than the textbook value. At the moment I start to trust the values and used this to calculate the nut and saddle compensation. The nut blanks are milled and I hope I can start with the saddle compensation during the week.

Jurgen

[jeffhigh]

Are you trying to determine E from you test results? I don't see how?
It should be a constant around 190GPa as it is just a material property
Do you have a jig with pulley and weight to supply tension? The contant tension provided will not give meaningful compensation results Pictures?

[JurgenV]

The jig is more or less the same as described in the book on page 4-107: plank of wood with a bolt and screw on one side to hold the string and a pulley on the other side. Distance between the locking nut and the bridge is 650mm and at middle there is a hinged fret.
For the compensation calculation you need "... the longitudinal unit string stiffness k, defined as the change in tension per change in extension per unit length, k=dT/(dL/L)..." p4-108
dT via Mersenne´s formula for fretted and unfretted string and so on. Actually following the equations 4.7-6 to 4.7-12
According to Trevor I can convert k to E (youngs modulus) by deviding by A (cross-sectional area of the string) which I did to get the value for E in the spreadsheet to compare it with the textbook value.

Then I used the textbook value of 210GPa for steel to calculate K and used this for the compensation calculation.

And as there is a big difference between the textbook value of the youngs modulus of steel (210GPa) and my values, the resulting k and therefore the compensation is quite different.
That´s why I started the thread. It would be nice to know if my values are making any sense or not. I couldn´t find examples in the forum giving the measured frequencies and diameters together with the results.

[jeffhigh]

I had my copies of Trevors books stored away. I have pulled them out now.

I'll note that the second paragraph of 4.7.3.1 indicates that the use of published values for the modus of steel are fine for steel strings, and only recommends the jig for use on Nylon or the like Classical strings

I would suspect that the greater bending stiffness of the steel strings may not be giving sufficiently accurate results on the jig for these sort of calculations

[GregHolmberg]

Jurgen--

I know it's been four years since you posted this, but did you ever figure this out?

I got the same results you did. I got a value for E that was nearly twice the usual value (411 vs. 210 GPa).

Using your numbers for the E string:

Code: Select all

T = 8.07 * 9.80665 = 79.14 N
ΔT = 79.14 * ((((135.7*325.25) / (67.1*650))^2 - 1) = 1.9036 N
ΔL = SQRT((650-325.25)^2 + 2.72^2) + SQRT(325.25^2 + 2.72^2) - 650 = 0.02276 mm
ΔT/ΔL = 1.9036 / 0.02276 = 83.62 N/mm
k = 650 * 83.62 = 54354 N
E = 54354 / (π * (0.00041/2)^2) ≈ 411 000 000 000 Pa

The only way I can think to fix this is if in Equ. 4.7-12

Code: Select all

k = L1 * ΔT/ΔL

It should be L2. That would give E = 206 GPa.

But thinking through the logic, I think L1 is correct. So I'm at a loss.

Greg

[JurgenV]

Hi Greg,
nope, I didn´t. I actually nowadays work with the textbook value to get a good start and then do the optimization (routine for an existing guitar) to get as good as possible. Not the best solution but at least it worked for my guitars.
Too bad Trevor never reacted on the question. Perhaps he would have had an idea.

If you ever find a solution: Please post it here

[Trevor Gore]

This takes me back 15 years or so when I initially wrote these equations....

I haven't found any errors in the equations and nobody has reported any, so I think they are all OK. But I also got high results for E so I always use the classical string method even for steel strings (though I started out initially by using standard values for E). The only explanation for the high values that I could come up with was that they were actually correct! We end up getting into the metallurgy of string drawing. If the string happens to be drawn from a single crystal of material (or a very low number of crystals) you can potentially get these high values. Things as large as turbine blades can be made of single crystals of material. Proving that hypothesis requires access to a lot of specialised equipment, so I couldn't determine the veracity of that hypothesis either way. That, I think, is why I left the rather enigmatic expression about determining E "should you so wish"....

Using the classical string method of determination of string stiffness will give a better result, as the method uses what actually happens on a particular string rather than some theoretical presumption.

If anyone has any better explanations, I'll be happy to hear them!

[GregHolmberg]

Unfortunately, I have no further explanations, just further information.

A little googling, and I found that steel strings on guitars are made of the same material as piano wire.

Which is spring steel.

Specifically, SAE grade 1080 (ASTM A228), which has an elastic modulus of 190 GPa. Or maybe 210.

So there's that little bit of information.

Greg