The development of a theoretical model for the windthrow of plants

This paper describes the development of a theoretical model for the windthrow of plants, from cereals to forest trees. The model predicts natural frequencies for cereals and trees that are in accord with full-scale measurements. The model is first used to investigate the behaviour of isolated trees in high winds, by calculating base bending moment spectra and then calculating the extreme values of that parameter that would be expected to occur. These extreme values are then used in simple stem base and root failure criteria to obtain estimates of failure wind speeds. The model is then applied to the cases of cereal and forest canopies, where the wind loading has been shown by previous investigators to be intermittent and thus not amenable to spectral analysis. A step wind input is assumed which causes the plants to undergo damped harmonic oscillations. The maximum values of base bending moment are then found, and these are again used in simple failure criteria to predict failure wind speeds. In all applications of the model, broad quantitative agreement is found between predicted and measured values of spectra and extreme displacements/bending moments, but the available experimental data is sparse.