On Moments of Inertia for Logs and Tree Segments
Abstract: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.
Document Type: Research Article
Publication date: 2012-08-02
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