Logan Oplinger on wed 14 jan 04
On Tue, 13 Jan 2004 00:37:42 -0500, Linda Pahl
wrote:
>I'm having trouble figuring out how to blend two different glaze
>recipes in a proportion of 75% of one recipe with 25% of the other in
>order to come up with a third recipe with the correct proportions and
>still adding up to 100 (including the colorants).
>
>I'd like to take 75% of this recipe: (Weathered Bronze)
>
>nepheline syenite 60.00
>ball clay 10.00
>strontium carbonate 20.00
>lithium carbonate 1.00
>flint 9.00
>Totals: 100.00 %
>
>Also add:
>titanium dioxide 5.00
>copper carbonate 5.00
>
>with 25% of this recipe: (Satin White)
>
>whiting 18.80
>zinc oxide 8.60
>feldspar 51.60
>epk 15.40
>flint 5.60
>Totals: 100.00 %
>
Hello Linda,
First, I will use your second glaze as an illustration to show how the
calculation process works. The concept, once understood, is straight
forward. Think of the percentages in the recipe as being equal to the
amount you need in grams for each material, 100% = 100g
So, 25% of 100 grams is 25 grams, or 25g.
If 18.8g of whiting is needed for a 100g recipe, then using proportioning,
you can calculate how many grams of whiting are needed for a 25g recipe:
18.8g x
---- = --- or, 18.8/100 = x/25
100g 25g
(At this point the math purists may scream!) Multiply the numbers on both
sides of the equal sign by 25 to solve for x, the value you are looking for.
On the right side of the equation (25)x divided by 25 is the same as
dividing 25 by 25, or 1, so
(25)18.8/100 = (25)x/25, (25)18.8/100 = x
then,
(25)18.8 470
-------- = --- = 4.7 = x You need only 4.7g of whiting to make 25g of
100 100 glaze.
The same process would apply for each ingredient.
Another way to do this is realize that since you need only 25% of the
glaze, you need only 25% of each ingredient:
25% of 18.8g whiting = (0.25)18.8g = 4.70g
25% of 8.6g zinc oxide = (0.25) 8.6g = 2.15g
25% of 51.6g feldspar = (0.25)51.6g = 12.90g
25% of 15.4g epk = (0.25)15.4g = 3.85g
25% of 5.6g flint = (0.25) 5.6g = 1.40g
----------------------------------------------
25% of 100.0g glaze = (0.25)100.0g = 25.0g
The last column of numbers adds up to 25g
If you wanted to make a 30% batch of glaze, or 30g, then you would use the
same process.
If you want to make 4000g of glaze, this is 40 times 100g. Multiply the
amount of each ingredient by 40 times:
18.8g(40) = 752g whiting
8.6g(40) = 344g zinc oxide
51.6g(40) = 2064g feldspar
15.4g(40) = 616g epk
5.6g(40) = 224g flint
--------------------------------
100.0g(40) = 4000g glaze
Keeping the conversion of percent to grams in mind, the first glaze total
amount of ingredients is 100% glaze base plus 10% total colorants. This
would give a dry glaze weight of 110g if the percentages were converted to
grams. At this point, since you said that you want the (new glaze) to add
up to a total of 100, I will assume you mean you want to make a (new glaze)
that is by weight 75% of (bronze), and 25% (satin). If you have the dry
materials for both glazes already weighed out and mixed, but no water has
been added, then all you need to do is take 75g of the dry (bronze) and
combine that with 25g of the dry (satin) to get 100g of dry (new glaze).
If the two glazes have water added already, then it would be necessary to
know exactly how much water each glaze contained. If each glaze contains
exactly the same proportion of water, then it is a simple mater to weigh
out and combine 75g of wet (bronze) with 25g of wet (satin).
If you want to make up the glazes fresh in the amounts necessary to create
the (new glaze) then you must proceed a little differently with the
(bronze). You must first reset the proportion values (grams) of materials
so that when added together, base materials plus the colorants add up to
100 (grams). Since the total material amounts would give you more than 100
(grams), you need less of each ingredient. The proportionate amount of
each ingredient you need can be calculated by the following:
100g = (110g)x, where x is a number that when 110g is multiplied by it will
give you 100g. Dividing both sides of the equation by 110g,
100g (110g)x 100g
---- = -------, and ---- = x, and 0.91 = x
110g 110g 110g
If you multiply 110g by 0.91 you get 100.1g because 0.91 was "rounded up"
from the actual number to the nearest 100ths. Good enough for glaze work!
(The actual number is 0.909090909.... to infinity).
Now you can calaculate how much of each material of (bronze) must be used
to make 75g:
First--
60.00g(0.91) = 54.6g nepheline syenite
10.00g(0.91) = 9.1g ball clay
20.00g(0.91) = 18.2g strontium carbonate
1.00g(0.91) = 0.9g lithium carbonate
9.00g(0.91) = 8.2g flint
5.00g(0.91) = 4.6g titanium dioxide
5.00g(0.91) = 4.6g copper carbonate
------------------------------------
100.2g (The ".2g" results again from the rounding up.)
Second, using the example from the first glaze--
54.6g(0.75) = 40.95g nepheline syenite
9.1g(0.75) = 6.83g ball clay
18.2g(0.75) = 13.65g strontium carbonate
0.9g(0.75) = 0.68g lithium carbonate
8.2g(0.75) = 6.15g flint
4.6g(0.75) = 3.45g titanium dioxide
4.6g(0.75) = 3.45g copper carbonate
------------------------------------------------
75.16g
Adding this to 25g of the (satin) will give you 100g of (new glaze),
ignoring rounding errors.
A simpler way to do this is first multiply 0.91 by 0.75 to get 0.6825, then
multiply the amount of each material by this number, for example:
60.0g(0.6825) = 40.95g nepheline syenite, etc.
Note that both glazes contain the same material, flint. It is only
necessary to weigh out 11.75g of flint once.
Having said all this, all you need by dry weight, is 75 parts of the
Weathered Bronze combined with 25 parts of Satin White (grams, ounces,
etc.), or 3 parts of (bronze) combined with 1 part of (satin).
I am hoping that someone else will have something to say about the rules
for working with rounded numbers in order to keep from introducing errors
from multiple rounding up or down. I have forgoten them precisely.
I do hope this helps.
Logan Oplinger
Another Tropical Island
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