Math Help Calculating h

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OiAcoustics
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Math Help Calculating h

Post by OiAcoustics » Sat Oct 23, 2021 11:47 am

Hi Math Heads

I'm building an Excel sheet to start measuring a bunch of tops I have and calculate the target thickness h. Computer and tapping are all ready to go.

I'm using all of TG's values from Table 4.5-3, and won't repeat them here. I'm good all the way through the first 12 columns (although honestly I don't understand the gigapascal GPa value well and only get o the Young's Modulus values by dividing by a lot of zeros)

On to Equ. 4.5-7 to calculate h:

The numerator (top value), rounded off as I don't need exact here, just to get the formula working):

.96 x 75 (his f stiffness value) x 490 (his plate length a) squared (call it 240,000) x the square root of 396 (his density p) (~ 19.9) = a huge # ~ 340,000,000.

The denominator is the square root of:

11.84 (his El) + 2.49 (his a/b ratio of 1.256 to the 4th power)*.82 (his Ec) + 1.58 (his a/b ratio of 1.256 squared) * (.03 (his value)*11.84 (El again) + 1.12*.91 (his Glc) = <16. The square root of all that is <4.

Divide the top by the bottom to get h and.... I'm crazy out of this world off! Even if if were a matter of decimals (i.e. mm to m, or converting GPa) it's not even close to TG's first number value of 2.72mm.

I presume some of you have built spreadsheets, can anyone spot my error or misinterpretation to be so wrong?

thanks in advance.

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kiwigeo
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Re: Math Help Calculating h

Post by kiwigeo » Sat Oct 23, 2021 3:34 pm

Usually the problem boils down to keeping track of the zeros and the units. I haven't looked closely at your coding but I think your units for plate dimension should be in metres (SI unit) not mm for the calculation. Dont quote me on this but I have a vague recollection of this being one source of error when I coded up my spreadsheet.

Trevor will no doubt pick your coding apart and find the problem(s)
Martin

OiAcoustics
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Re: Math Help Calculating h

Post by OiAcoustics » Sun Oct 24, 2021 12:39 am

Hi

Thanks for your reply. If it were a matter of decimal places (m to mm), it would be easy enough to spot, but it's off by a bizarre factor, so it seems like it would be a metric to "standard" (we're stuck up here with that nonsense so I don't think naturally in metric) or other conversion issue. Or just bad formula work, although I get the same answer manually on a calculator.

It doesn't look like I can attach an Excel file here, so I sent it to Trevor directly, hoping for help as otherwise I'm all dressed up and ready to go!

cheers

Kevin

seeaxe
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Re: Math Help Calculating h

Post by seeaxe » Sun Oct 24, 2021 12:13 pm

Hi Kevin

IF you don't hear from Trevor, I'm happy to send you mine, seems to work (as in reproduces Trevors numbers from the book). You can look through and see where the differences are?

You would need to pm me your email address

Cheers
Richard
Richard

OiAcoustics
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Re: Math Help Calculating h

Post by OiAcoustics » Mon Oct 25, 2021 12:18 am

HI Richard

thanks so much! I'm sure Trevor's a busy guy, to say the least, so having a working Excel sheet would expedite the process and I should be able to spot my error.

oi@kgillies.com

I REALLY appreciate it as I'm doing FRCs on some guitars I'm not sweet on which I will convert to falcate/live backs. I'm planning on zipping (not live) backs off this week and it would be great to start the process by nailing down the live backs first, which will be an easy conversion if I know the targeted thickness.

Thanks again!

GregHolmberg
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Re: Math Help Calculating h

Post by GregHolmberg » Mon Oct 25, 2021 5:43 am

Yes, you need to use values in the formula in Pascals and meters. The values in the table are mm and GigaPascals. So divide the mm values by 1000 and multiply the GPa values by 10^9. I.e 11.84E09.

Greg

OiAcoustics
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Re: Math Help Calculating h

Post by OiAcoustics » Mon Oct 25, 2021 7:14 am

Yep, I did figure that out after some trial and error, but I've got an odd factor in there that's still throwing it off. I look forward to seeing Richard's which will clue me in.

Thanks!

OiAcoustics
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Re: Math Help Calculating h

Post by OiAcoustics » Wed Oct 27, 2021 8:58 am

A big shout-out to seeaxe for helping me out. All good now!

WilliamDavidReynolds
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Re: Math Help Calculating h

Post by WilliamDavidReynolds » Thu Dec 08, 2022 3:02 pm

GregHolmberg wrote:
Mon Oct 25, 2021 5:43 am
Yes, you need to use values in the formula in Pascals and meters. The values in the table are mm and GigaPascals. So divide the mm values by 1000 and multiply the GPa values by 10^9. I.e 11.84E09.

Greg
So I’m getting 1.1842E+10 for 4.5-2, which is what you refer to above, how do I get it to 11.84?
I’m banging my head on the floor here, I’m having same decimal issue with correct digits for 4.5-3 and 4.5-4

WilliamDavidReynolds
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Re: Math Help Calculating h

Post by WilliamDavidReynolds » Thu Dec 08, 2022 3:08 pm

GregHolmberg wrote:
Mon Oct 25, 2021 5:43 am
Yes, you need to use values in the formula in Pascals and meters. The values in the table are mm and GigaPascals. So divide the mm values by 1000 and multiply the GPa values by 10^9. I.e 11.84E09.

Greg
So I multiplied my 1.184 by .000000001
And got 11.84,
Is this what you meant by 10^9

WilliamDavidReynolds
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Re: Math Help Calculating h

Post by WilliamDavidReynolds » Thu Dec 08, 2022 3:10 pm

GregHolmberg wrote:
Mon Oct 25, 2021 5:43 am
Yes, you need to use values in the formula in Pascals and meters. The values in the table are mm and GigaPascals. So divide the mm values by 1000 and multiply the GPa values by 10^9. I.e 11.84E09.

Greg
But I just divided my number by 10^9 and it gave me the 11.84, not sure what the protocol is here
Thanks!

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