Neoloid form Uncloaked Bob Leverett Dec. 12, 2007

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TOPIC: Neiloid form uncloaked
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== 1 of 1 ==
Date: Wed, Dec 12 2007 6:13 pm
From: dbhguru

ENTS,

Gary Beluzo and I are close to completing the article for the next Bulletin on tree modeling. Will has supplied ample data for the article and we thank him very much. The article will contain most of the formulas we have developed to date as part of our continuing development of the art and science of dendromorphometry, although more formulas and processes are in the pipeline. One form that I've had little to say about is the neiloid form and I gave it next to no space in the article, until Ed pointed out the need to say more about it. One reason I had avoided the neiloid was that I hadn't had the basic two-dimensional curve form that gives rise to the volume formula when rotated around the X or Y axis. So, after Ed's encouragement, I set about deriving a curve(taper) formula that produces the volume formula V= (1/4)*pi*r^2. The following summary shows the curve forms that generate the volume formulas. I should mentione that there are other neiloid curve formulas. I shoot f
or the most basic. The trees don't know that their supposed to shape themselves along the line of some exotic taper formula. Much of the analysis I've seen on the subject, I regard as more academic than real.

 Let: R = radius of base of solid H = height of solid r = radius at point h from vertex of solid h = height at point of r as measured from vertex V = volume of solid pi = 3.141593 Solid Curve Formula Volume Formula Cone r = R*(h/H) V = (1/3)*(pi)*r2 Paraboloid r = R*SQRT(h/H) V=(1/2)*(pi)*r2 Neiloid r = R*(h/H)3/2 V=(1/4)*(pi)*r2

The attachment shows the derivation of the volume formula from the curve formula for the neiloid. I will include all derivations as attachments in future e-mails.

Bob