Actually, I think you're both saying generally the same thing. Roger's D is a density unit to be determined later. Anthony's is sites/area.
However, I'm confused. Anthony-- where is 2pi coming from? Area is pi*r^2, so shouldn't your first equation be: #sites = pi*r^2 * D-- no integral required? Then this gets stuck in the energy integral depending on how the units are designated. If you have the quick explanation, I'm listening. Otherwise I'm going to have to sit down with pen and paper and figure out specificities of your x and y units, too, see if it all works out. -vk -vk -------------- Original message -------------- From: Anthony Jackson <[EMAIL PROTECTED]> > Roger Burton West wrote: > > If anyone else would like to check my maths, please feel free! > > I think I would set up the math slightly differently, but I get similar > results. Mostly, I would measure D in sites per unit area, and thus I > wind up with a factor of 2pi in the equations. > > Let's assume D is the total sites per unit area, x is the production per > site, y is the cost per unit distance, and r is distance from the center. > > The total from any given site is equal to x-ry. > > Now, if you look at all sites within a given radius R, the formula for > the total number of sites is equal to 2pi * D * integral (0-R) r, or pi > * D * R^2. The formula for the total energy, however, is equal to 2pi * > D * integral(0-R) (rx - r^2y) = 2pi * D * (1/2R^2x - 1/3R^3y). > _______________________________________________ > GurpsNet-L mailing list > http://mail.sjgames.com/mailman/listinfo/gurpsnet-l _______________________________________________ GurpsNet-L mailing list <[email protected]> http://mail.sjgames.com/mailman/listinfo/gurpsnet-l
