So how thick should we make the plaster? Initially, I’d guess about an inch thick as a minimum, with some internal reinforcement possibly, to prevent cave-in’s. So, just how heavy would this globe be? Let’s work out the weight…
If we want a 1-inch thick layer of plaster, the volume would be equal to a volume of a 30-inch sphere minus the volume of a 28-inch sphere. The volume for a sphere is calculated as V=(4/3) * pi * r3. Therefore, if a 30-inch sphere is 14137.166943 cubic inches and a 28-inch sphere is 11494.0403234 cubic inches, then the volume of a 1-inch thick layer of plaster would be 2643.1266196 cubic inches (14137.166943 – 11494.0403234 = 2643.1266196).
The density of plaster is equal to 0.490753134528 ounces per cubic inches, and the formula for weight is w=p*v. Given p and v, we can calculate the weight of the globe as 81.07 pounds.
A little heavy, but workable with a strong base.
How about some other thicknesses? Using the same formulas, we can work out some other weights for a 30-inch globe based on the thickness of the plaster:
|Thickness (inches)||Volume (cubic inches)||Weight (pounds)|
|0.5||14137.166943 – 12770.0505397 = 1367.1164033||41.93|
|1.0||14137.166943 – 11494.0403234 = 2643.1266196||81.07|
|1.5||14137.166943 – 10305.9947014 = 3831.1722416||117.51|
|2.0||14137.166943 – 9202.77208112 = 4934.3948618||151.35|
I think that a 1-inch layer of plaster is just about right.