Hand Tools Archive

Subject:
Re: How to measure density of ARK stones

Chuck Bjorgen
I don’t recall exactly where I was able to copy and save the following post but I know it came from one of my favorite woodworking forums. I found this information useful after I had purchased a supposedly translucent Arkansas stone that defied the usual characteristics. The stone was sold as”Sapphire Blue Translusent” and I used the following information to confirm that it did indeed show the specific gravity of a translucent stone. I only saved the author’s first name, Bryan, but this info was useful to me. A postage scale was used to take the stone’s weight. Hope this helps.
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Calculating Oil Stone Density
>I was asked to show how to calculate the specific gravity of a oil stone to aid in identification. To do this, you need to be able to accurately measure the dimensions of the stone, and the weight of the stone. I am an engineer, but for simplicity, I'm ignoring significant digits and I am rounding numbers with a bit of liberty. So be forewarned if you get hung up on such notions. I've tried to make this as simple and self explanatory as possible, for people not used to doing much math.
Specific gravity (SG) is simply the density of the stone divided by the density of water. Density (D) is simply the weight or mass of the stone (M) divided by the volume (V). Volume is simply the length (L) multiplied by width (W) multiplied by thickness (T).
So...
SG = D (stone) / D (water) 
D (stone) = M / V 
V = L x W x T
The only trick is making sure that your units of measurement are all consistent, but I’ll take care of that for you.
I found the specific gravity information for Arkansas stones on Dan's Whetstones website @ www.danswhetstone.com/stone_grades_101.htm
The specific gravities are as follows: 
Washita: < 2.25 
Soft Arkansas: 2.20 - 2.30 
Hard Arkansas: 2.30 - 2.50 
Translucent/Black: >2.50
To calculate specific gravity, first measure the length, width, and thickness of the stone, in inches. You have to be pretty precise, so measure to the nearest 1/16"l of the inch or better. Now weigh the stone.
Next, multiply L x W x T, This gives you V in cubic inches. Now divide V by 1,728. This converts the volume into cubic feet. It should be a small decimal. Second, take the weight or mass (M) of the stone in grams and divide this number by 454. This converts the mass into pounds (lbs). Third, take the mass divided by volume to get density . Forth, divide this density by the density of water (62.4 lbs/ft3). The resulting value is the specific gravity of the stone.
For example, I had a stone measuring 1" x 1-15/16" x 5-15/16". It was in perfect shape and very symmetrical. It weighed 494 grams. So my stone had the following measurments: 
. L = 5.938"
. W = 1.938"
. T = 1" 
. M = 494 grams
Now to calculate SG, do the following...
1) Calculate Volume 
. V = L x W x T 
. V = 1 x 1.938 x 5.938 
. V = 11.508 cubic inches
2) Now divide this by 1,728 
. V = 11.508 / 1,728 
. V = 0.00666 ft3
3) Divide mass (M) by 454 
. M = 494 / 454 
. M = 1.088 lbs.
4) Calculate density: 
. D = M / V 
. D = 1.088 lbs / 0.00666 ft3 
. D = 163.36 lbs/ft3
5) Calcualte specific gravity 
. SG = D / 62.4 
. SG = 163.36 / 62.4 
. SG = 2.62
So, the SG of this stone is 2.62. Comparing it to the information from the web-site, this confirmed what I already knew. It's a translucent Arkansas Stone.
Good Luck
-Bryan

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