## Tuesday, October 19, 2010

### Estimating Plaster For Slip Casting Molds

I'm working on the Plaster Molds For Slip Casting post in the Martha's Method thread at Woodland Earth Studio, and as I go through the process in my head, I make diagrams to illustrate the process. The diagram is Not To Scale.

Being a rather frugal molder, I like to estimate the volume of plaster that I'm going to pour. There are several things to take into consideration when making an estimate. The first thing to consider is the size of the pattern to be molded. In the above illustration, I'm making a mold of a sphere to be used as a hip joint. In this case, the sphere is 2 inches in diameter. There will also be a spare, used to pour carving wax, or slip into the mold. The spare has a cup shape, with the small end of the cup attached to the sphere, and the large end of the cup attached to the wall of the mold box, or coddle. So the first thing I need to do is some arithmetic to figure out how big these two items are. Fortunately, there are some formulas that can be used to do this that are brilliant.

In these formulas, the asterisk (*) means multiply.
The forward slash (/) means divide.
The carat (^#) means exponent. For example 2^2 means 2*2, or 2 to the power of 2.
Parenthesis (()) are used to group calculations that should be done first, before the others are done.

Formula to figure the volume of a sphere:
(4 / 3) * pi * r^3
The diameter of the sphere is 2 inches, so the radius is 1.
pi is 3.14.
The volume of the sphere is 1.33 * 3.14 * (1*1*1), which equals 4.1762 cu. in.
Jot that number down.

The spare must be large enough to pour carving wax or slip into, and after the walls of the casting are thick enough, large enough to pour the excess casting liquid out of the mold without leaving too large of a hole in the casting. For a small casting like this sphere, I think a 1/4 inch hole (.25") should be enough. I want the walls of the casting to be at least 1/8th inch thick, so, adding all that up comes to 1/2 inch. At the top, a 1 inch diameter should be large enough to pour into, and a 1 inch length should be sufficient to feed a casting that will have 1/8th inch thick walls. So the spare is a cup shape that is 1 inch in height, 1 inch diameter at the large end (.5 inch radius), and 1/2 inch diameter at the small end (.25 inch radius).

Formula to figure the volume of the spare:
((pi*h)/3)*(R^2 + R*r + r^2)
where R = radius of base circle;
r = radius of top circle;
and h = distance from base to top.
3.14 * 1 = 3.14
3.14 / 3 = 1.04666
.5 * .5 = .25
.50 * .25 = .125
.25 * .25 = .0625
.25 + .125 + .0625 = .4375
1.04666 * .4375 = .45791 cubic inch.

Since the sphere and the spare will be embedded halfway in a clay build up, to make a 2-piece plaster mold, I need to add the volumes together and divide the answer by two.

4.1762 cu.in. + .4375 cu.in. = 4.6137

4.6137 / 2 = 2.30685 cu.in.
Jot that number down.

Next, I need to figure out the volume of the first half of the plaster mold. I'll make the mold with 1 inch of space all around the sphere. The sphere is 2 inches in diameter, so 2+1+1=4. My mold box will have an area of 4 by 4 inches. Half of the sphere will be embedded in a clay build-up, so 1 inch will be sticking up. An inch thickness above the top of the sphere will be 2 inches deep. So the mold box will hold 4*4*2 cubic inches of plaster, or 32 cubic inches. Next, I'll subtract the volume of the spare and the sphere.

32 - 2.30685 = 29.69315 cubic inches of plaster is needed for each side of the mold.

How many cubic inches are in a cup?
One U.S. legal cup (240ml) is equal to 14.6456 cubic inches.
For reference:
1 milliliter (ml) = 1 cubic centimeter (cm^3)
1in = 2.54cm, so 1/2.54 gives us
1cm = 0.3937in
One 240ml cup occupies any theoretical space measuring 240cm^3.

29.69315/14.6456
2.02744

I can estimate that I'll need two cups of water to fill the volume of each mold half.
A good consistency for slip casting molds is 67 parts water to 100 parts plaster by weight.
This is a ratio of 2:3 by weight.

16 ounces of clean tap water weighs about 1 pound.
1 pound divided by two is 1/2 pound.
1/2 pound times 3 is 1-1/2 pounds.

1 pound of water to 1-1/2 pounds of plaster is a 2:3 ratio by weight.

The following diagrams show the formulas that I used in this estimate.

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

#### 3 comments:

1. wow you need a phd in mathematicks to solve that !!!!!

2. It is all arithmetic. Add, subtract, multiply, and divide.

3. I was wondering how much water ... and here it is WOW!
Thanks!!

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