[PSUBS-MAILIST] K3000 spherical shell calculations

[Personal Submersibles General Discussion]

I just wanted to add that the form is similar for elliptical shells, only you must take into consideration that, for example, a 2:1 semi-elliptical head only has true 2:1 shape on one side of the shell (typically the inside), since you are adding constant thickness to that shape in all directions, as opposed to a concentric ellipsoid. Thus, for major inner radius r, the volume of such a head would be:

V = {4/3 × π × [(r+t)(r+t)((r/2)+t)-(r)(r)(r/2)]}/2

Sean


On April 16, 2014 11:28:11 PM MDT, Personal Submersibles General Discussion <personal_submersibles at psubs.org> wrote:
>Calculating volume using surface area multiplied by thickness is not
>accurate unless you use calculus and integrate between the radius
>limits. Fortunately, this is how we derive the rule-of-thumb formulas
>for volume, which are simpler and easier to use.  For a spherical
>shell, 
>
>V = (4/3) × π × (ro^3 - ri^3)
>
>For a cylindrical shell, 
>
>V = π × (ro^2 - ri^2) × L
>
>Once you have your material volume, multiply by its density to get the
>mass.
>
>Sean