Lower Basal Wedge Equation - Super Simplified Version 3

General discussions of measurement techniques and the results of testing of techniques and equipment.

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#1)  Lower Basal Wedge Equation - Super Simplified Version 3

Postby M.W.Taylor » Sat Sep 23, 2017 6:00 pm

Bob Leverett took a look at this equation, waved his magic wand, and was able to greatly simplify it.  The attached is the latest and greatest. The final equation for volume is now simple. You can use this formula without needing to use a scientific calculator. There is beauty in simplicity !
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slanted frustum-V3.jpg
the simplified version is easy to use with a regular calculator
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#2)  Re: Lower Basal Wedge Equation - Super Simplified Version 3

Postby MarkGraham » Sat Sep 23, 2017 11:35 pm

Thanks, good approach.  Tried it out for a couple hypothetical trees, very reasonable results.  And not too hard to put into Excel, only gave me a slight headache.
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#3)  Re: Lower Basal Wedge Equation - Super Simplified Version 3

Postby dbhguru » Thu Sep 28, 2017 8:39 pm

Mark, et. al.,

   Michael has led the way in exploring and developing methods for measuring the basal area of tree trunks. A lot of progress has been made.

   Below is a formula I recently derived for measuring the frustum of a slanted elliptical cone. If the ellipses are changed to circles, we get the standard formula for the frustum of a cone. The derivation is available for any one who wants to see it. Note that this formula does not need the height of the complete cone, only the frustum. You can find other formulas for the frustum of an elliptical cone, but they usually include the cone's total height.

               
                       
SlantedEllipticalConicalFrustum.png
                                       
               


Bob
Robert T. Leverett
Co-founder and Executive Director
Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
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