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Author Topic: Math Formula  (Read 916 times)

Gemini

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Math Formula
« on: January 15, 2019, 11:12:45 AM »
Hi,
Does anyone know how to reverse the formula for volume of the finishes stone given on designs?
Thanks

Rusted

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Re: Math Formula
« Reply #1 on: January 15, 2019, 11:20:22 AM »
Are you talking faceting designs?
What do you mean reverse the formula?
What is it you are attempting to achieve?

MakkyBrown

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Re: Math Formula
« Reply #2 on: January 15, 2019, 05:04:03 PM »
You could probably work it out using the gemcad data. Pavilion is easy, crown you'd need to use the T/W aswell as the C/W, and also make an assumption of % girdle width. But as Rusted says why?

Gemini

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Re: Math Formula
« Reply #3 on: January 16, 2019, 08:06:33 AM »
Good morning,
Each faceting design has a formula that (I presume) tells you the weight/volume of a given stone cut from this design. The formula is expressed as: Vol./W3=0.223 (for example) with Vol. and W being unknown.
What I would like to do is to take the known value, namely the 0.223-factor, combine it with an estimated with, to work out in advance the weight of stone cut from a given design.
I presume this must be possible - but I am no mathematician and can't figure out how.
Appreciate your help.

Ghost

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Re: Math Formula
« Reply #4 on: January 16, 2019, 08:46:49 AM »
As I read Gemcad instructions, I think the Vol./W3 refers to the volume of the finished stone as related to the Width Cubed (W3).
If so, you can use this to calculate that the weight of a finished stone, assuming that you started with a cubic piece of rough equal to the width.   Eg; Vol./W3 = .223 would mean that 77.7 percent of the original weight is ground away.
NOTE:   My interpretation may be wrong.
Regards,   Ghost.
« Last Edit: January 16, 2019, 09:27:13 AM by Ghost »

Rusted

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Re: Math Formula
« Reply #5 on: January 16, 2019, 09:52:22 AM »
I think you can do this fairly easily in Gemcut studio. It's not something I have explored but I have noticed it is there.
It appears he used a formula or program from this site
https://www.facetlab.xyz/search

MakkyBrown

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Re: Math Formula
« Reply #6 on: January 16, 2019, 10:10:40 AM »
I'm thinking it is probably as simple as 

Stone weight in ct =V/W3 *5 * SG *(Width Cubed in millimeters/1000)

V/W3 from diagram
SG = specific gravity
« Last Edit: January 16, 2019, 10:28:45 AM by MakkyBrown »

Bucket

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Re: Math Formula
« Reply #7 on: January 16, 2019, 11:02:06 AM »
Not really sure why you want to reverse the formula, a specific design doesn't limit you to a specific sized finished stone. While the formula may give you the volume of the finished stone, each stone could be a different size anyway.
Common sense isn't exactly common

Gemini

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Re: Math Formula
« Reply #8 on: January 16, 2019, 01:59:08 PM »
Thanks everybody. The reason I want to do this is so that I can choose the design that will yield the biggest (in weight) cut stone from any given rough. Sometimes a piece of rough has got limited depth but plenty of width etc. - or vise versa.
By measuring the rough you can pretty accurately estimate the width of your finished stone, which means that you know two of the values from the formula, namely W and the volume-factor. Surely it must be possible to reverse the formula to arrive at a finished weight for a stone of a given width?

MakkyBrown

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Re: Math Formula
« Reply #9 on: January 16, 2019, 08:11:40 PM »
Thanks everybody. The reason I want to do this is so that I can choose the design that will yield the biggest (in weight) cut stone from any given rough. Sometimes a piece of rough has got limited depth but plenty of width etc. - or vise versa.
By measuring the rough you can pretty accurately estimate the width of your finished stone, which means that you know two of the values from the formula, namely W and the volume-factor. Surely it must be possible to reverse the formula to arrive at a finished weight for a stone of a given width?
That is what the formula I posted below should do, give you the finished weight in ct.  I'm pretty sure it's right :)

Gemini

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Re: Math Formula
« Reply #10 on: January 19, 2019, 11:33:14 AM »
I am sure you are right, MakkyBrown, but with my limited understanding of math and how I interpret your formula, I can't make it work.
Your formula:

Stone weight in ct =V/W3 *5 * SG *(Width Cubed in millimeters/1000)

V/W3 from diagram
SG = specific gravity

My interpretation (example: 6mm sapphire, design vol-factor 0.223): 0.223 divided by 1296 multiplied by 5 multiplied by 4

I am unsure about where the '5' comes from and also, I don't know whether there is a third multiplication.

The above stone should come out pretty close to a carat but no matter which way I calculate it, I can't get anywhere near that.
Please excuse my ignorance, I had no idea it would be this complex, just thought there was an easy way to reverse the calculation.
Appreciate everybody's input. Thank you.

MakkyBrown

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Re: Math Formula
« Reply #11 on: January 19, 2019, 01:44:00 PM »
I am sure you are right, MakkyBrown, but with my limited understanding of math and how I interpret your formula, I can't make it work.
Your formula:

Stone weight in ct =V/W3 *5 * SG *(Width Cubed in millimeters/1000)

V/W3 from diagram
SG = specific gravity

My interpretation (example: 6mm sapphire, design vol-factor 0.223): 0.223 divided by 1296 multiplied by 5 multiplied by 4

I am unsure about where the '5' comes from and also, I don't know whether there is a third multiplication.

The above stone should come out pretty close to a carat but no matter which way I calculate it, I can't get anywhere near that.
Please excuse my ignorance, I had no idea it would be this complex, just thought there was an easy way to reverse the calculation.
Appreciate everybody's input. Thank you.
Ok
the 5 is from 5ct in 1gram

V/W3 = 0.223
SG = 4 for sapphire
https://www.gemselect.com/gem-info/specific-gravity.php

Stone width 6mm
Stone weight in ct =V/W3 *5 * SG *(Width Cubed in millimeters/1000)
don't need the brackets
ct = 0.223 *5*4 *6*6*6/1000 = 0.96
   
 :)
« Last Edit: January 19, 2019, 02:12:29 PM by MakkyBrown »

MakkyBrown

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Re: Math Formula
« Reply #12 on: January 19, 2019, 09:21:13 PM »
You'll get variation in finished stones due to girdle thickness.

Gemini

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Re: Math Formula
« Reply #13 on: January 20, 2019, 07:34:45 AM »
Awesome! Thank you very much.

MakkyBrown

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Re: Math Formula
« Reply #14 on: January 20, 2019, 08:12:12 PM »
Thanks for asking the question, I've now got a formula I'll probably use myself.
  beers
« Last Edit: January 21, 2019, 12:37:09 PM by MakkyBrown »

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