## Friday, October 29, 2010

### Lower Leg Mold Estimation

This is an example of estimating a plaster mold for the lower leg. The lower leg in the diagram is 7 inches long. The diameter of the knee is 1.5 inches. The diameter of the ankle is 0.875 inches. I can draw the frustum of a cone around the leg that has those dimensions.

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.

I can estimate how much volume that leg has using the following formula:

V = ((pi*h)/3)*(R^2 + R*r + r^2)

R = Radius of large end (the radius is one half the diameter, so 1.5 / 2 = .75, or 3/4")
r = radius of small end (.875 / 2 = 0.4375, or 7/16")
h = height of leg = 7"
pi = 3.14

V = ((3.14 * 7) / 3) * ((.75*.75) + (.75*.4375) + (.4375 * .4375))
V = ((21.98) / 3) * ((0.56) + (0.33) + (0.19))
V = ((7.33) * (1.08))
V = 7.9 cubic inches
I can just round the volume off to 8 cubic inches.

The coddles will be a rectangular volume. I want about an inch of plaster all around the leg, and about an inch of plaster over the top of the leg. The leg is embedded about halfway in the clay build-up. So the rectangular volume will be 9.5 inches long, 3.5 inches wide, and 1.75 inches in height.

V = L*W*H

V = 9.5 * 3.5 * 1.75
V = 58.1875 cubic inches
I can round that volume off to 58 cu.in.

Finally, there is the volume of the spare. The spare is where the slip or wax is poured into the mold. I'll use the same formula that I used for the leg, but I'll change the length to 1.5 inches.

V=((3.14 * 1.5) / 3) * ((.75*.75) + (.75*.4375) + (.4375 * .4375))
V = 1.6 cu.in.
I can round that off to 1.5 cu.in.

Now all I have to do is add, subtract, and divide.
I add the volume of the leg and spare together: 8 + 1.5 = 9.5 cu.in
Since the leg is halfway in the clay build-up, I can divide that by 2: 9.5 / 2 = 4.75 cu.in.
The volume of the mold box is 58 cu. in.
58 - 4.75 = 53.25 cu.in.

The volume of a cup of water is 14.6 cu.in.

53.25 / 14.6 = 3.6 cups of water.
I can round that off to 3.5 cups of water.
This is an estimate, after all.

A good consistency for plaster is 67 parts of water to 100 parts of plaster.
That is a ratio of 2:3.
3.5 / 2 = 1.75 (1.75 is one part)
3.5 + 1.75 = 5.25

The ratio of water to plaster will be 3.5 to 5.25.
So first I weigh 3.5 cups of water on the scale.
I take that weight, divide it by 2, and add the result to the weight of the water.
That is the weight of the plaster to add to the water.

I'll have to test this method to make sure I've got it right.