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On Moments of Inertia for Logs and Tree Segments

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The theory of moments of inertia is used to derive an equation for the mass moment of inertia of logs and segments of tree stems. This formula is valid for logs shaped as frusta of cones, neiloids, paraboloids, and many intermediate shapes generated by a simple power function solid of revolution. The equation assumes constant density within the log. Application of the equation indicated that moments of inertia for a typical log were similar among shape assumptions for large log small-end/large-end diameter ratios (e.g., larger than 0.8). However, variation in the shape parameter can make a substantial difference when the log end-diameter ratio is small. The largest values for moment of inertia were obtained for paraboloid frusta, with frusta of the paracone, cone, and neiloid being successively smaller. Log moment of inertia may be useful for designing and testing log handling equipment, because it can be used to help compute rotational forces relating to log handling.

Keywords: forest engineering; forest harvesting

Document Type: Research Article

DOI: http://dx.doi.org/10.5849/forsci.11-079

Publication date: August 2, 2012

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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