Official Luthiers Forum!

I've come a long way with yours and Gerard's books, but there's still so far to go!

One day I'm going to try falcate, when I have time.

Right. You've seen the Michael Moore bit where he tries to get anyone to explain derivitaves....

Ah, the difference between a derivation and a derivative...sometimes it's subtle. But if it's being traded, probably a derivative...

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Can we have some examples, I'm sure it would help medlingfool and me to understand as I suspect the maths is not really that hard.
I'll have a go, correct my mistakes or give me a gold star.
I'm going to make-up the numbers from the top of my head as I don't have any material at hand at it doesn't really matter anyway.
We have 2 pieces of spruce both 10mm x 20mm x 400mm that's a cubic area of 80,000mm
Piece 1 weighs 20 grams
piece 2 weighs 25 grams

If I divide weight into area that gives me (is it mass? density?):
piece 1 80,000mm3/ 20g= 4000 ?
piece 2 80,000mm3/ 25g = 3200?

I do a deflection test, deflection is
piece 1 3mm
piece 2 2mm

To get the magic number I divide deflection into density (? number)
piece 1 4000?/ 3mm =1,333.333
piece 2 3200/ 2mm= 1,600

So piece 2 has a better stiffness to weight ratio.
I wish I hadn't said the maths was easy I'm not sure I got things right.
Please help!

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We are all in the gutter but some of us are looking at guitars.

So is "E" in there somewhere? What is this E you speak of?

Danny, I hope you're not asking me. I'm waiting for Trevor or Todd post.

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We are all in the gutter but some of us are looking at guitars.

Heh, that's why I always liked classical physics better than chemistry or biology. You can derive everything from scratch on the fly. You don't have to remember anything! Taxonomy? Phooey!

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Jim Kirby
kirby@udel.edu

Joe,

Density is mass per unit volume (see above). Also best to work in metres, kgs and seconds. (SI units)

So weigh the piece, say 20 grams which is 0.02 kgs

The volume is 0.01 x 0.02 x .4 = 0.00008 m^3

Divide the mass by the volume = 0.02/0.00008 = 250kg/m^3 which is the density (spruce typically has a density of ~ 400kg/m^3) Also look up mass, weight and density in Wikipaedia so that you'll understand the difference.

To measure stiffness, you're best off using E (Young's modulus) as the measure for stiffness. There's the deflection method of measuring E (also called the static method) and there's the vibration method, also called the dynamic method as discussed above. Full instructions for both methods are in the book or Google "beam deflections" and you'll find suitable formulae in Wikipaedia or similar. The advantage of using E is that your results will then be comparable with anybody else's, whereas if you use the deflection under the weight of a heavy spanner (for example) you can only compare your results with someone who has a similar spanner.

So if you use E, the ratio E/density is the stiffness-to-density ratio.

A less satisfactory alternative is to just measure the deflection. The load needs to be a standard size, also the span and the sectional dimensions. You are then using deflection as an analogue of stiffness, and the ratio becomes deflection (measured in whatever units you like) divided by the density as discussed earlier.

For Danny, E is Young's Modulus, a measure of material stiffness. Again Google/Wikipaedia is your friend.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Trevor, as always, thanks for spending the time. I do understand now.
I got a bit confused earlier because mass was used in place of weight.

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We are all in the gutter but some of us are looking at guitars.

Trevor: Everyone has a pipe wrench like me............!!! You started my day off with a smile. Thanks.
Tom

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A person who has never made a mistake has never made anything!!!

Though I have indulged in and remain fascinated with scientific research I would think that apparatuses used here and the degree of significant in the number crunching that this data is almost meaningless except for the simple enjoyment in the exercise of data gathering.

I do such but only to measure deflection of the top before and after bracing.

Just what would be an your acceptable tolerance between similar braces to be used on the same instrument?

I’m sitting in Padma’s camp.

The knowledge and process is indeed worth knowing.

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Michael Lloyd

“I was born to ignorance, yes, and lesser poverties ...
I was born to privilege that I did not see ... I didn’t know it, but my way was paved” – John Gorka

I'm still wondering if my equations were right?

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We are all in the gutter but some of us are looking at guitars.

If that's a serious question: No. The first was inverted.
For density you had volume/mass. Should be mass/volume. Referring back:

Your second equation is also inverted compared to convention which usually looks at a stiffness to density ratio which is stiffness (however you want to measure that) divided by density.

If you lived in the southern hemisphere it would all be a lot easier.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

What?

So equations written below the equator run counter clockwise too? No wonder they make no sense to me!

No, just upside down.

Because the equations themselves are concepts rather than physical entities, they don't have mass, so they aren't subject to Coriolis effects.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

It was indeed a serious question and thanks for answering it.
This is why examples are so useful.

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We are all in the gutter but some of us are looking at guitars.