A practical algorithm for the computation of tree felling times

Damien Scott Holloway

Abstract


The time taken for a tree to fall when felled can be expressed in closed form in terms of elliptic integrals. However, this form of the solution is of limited practical use to the non-mathematician. A straightforward numerical method is presented that can be programmed into a spreadsheet in a few lines without requiring any high level programming or mathematical skills. Good accuracy for practical purposes is obtained without any iteration, but accuracy is further improved with two or three iterations, each involving only one or two extra cells in the spreadsheet. Results are compared with the analytic solution. This article demonstrates how a challenging real problem is accurately solved numerically with basic office tools and limited mathematics.

References
  • Milton Abramowitz and Irene A Stegun. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, volume 55 of Applied Mathematics. National Bureau of Standards, 1964.
  • J.L. Meriam and L.G. Kraige. Engineering Mechanics Volume 2 Dynamics. 2nd edition, 1998.

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DOI: http://dx.doi.org/10.21914/anziamj.v49i0.368



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.