Re: [PSUBS-MAILIST] Math question:

["Rob Carlson" <rob.carlson@verizon.net>]

There is an estimation formula (derived with Calculus) called the prismoidal
formula.  The fomula applies to a curve rotated about an axis and works
great for calculating volumes of the bow/dome of a sub.  It is as follows:

V = H/6 *( Ao + 4Am + A1)  where

H = length of the object
A0 = Area of the cross-section of one end
A1 = Area of cross section for the end
Am = Area of cross section for the middle.

To verify this you can use a cylinder where A0=A1=Am and you get V = H* A

The volume of a parabloid of length L and radius r is  V= 1/2 *(pi * r^2 *
L) = 1/2 A * L.

One thing to consider for the stern where it may taper to a point is to
determine the point where it tapers and use the volume formula for a
circular cone.  The curved part is then calculated using the prismoidal
formula and then added to the cone to determine the complete volume.

Hope that helps.

 -Rob

> >
> > I'd like to be able to calculate wetted surface and volume for
> > more complex shapes.  Burcher and Rydill say that the ideal shape
> > is a "parabolic stern" and an "elliptical bow."  I can't find the
> > formulae to arrive at those areas and volumes. And a proper
> > paraboloid does not have pointed a vertex.
> >
> > Suggestions are hereby solicited.
> >
> >
> > Mike Holt
> >
>