A Dynamic Model of the Behaviour of Sitka Spruce in High Winds

This paper describes the development, verification and use of a mathematical model to describe the dynamic behaviour of typical forest trees in high winds. The model assumes (a) that the trunk can be represented by a vertical tapered cantilever with specified stiffness and mass distributions; (b) that the canopy can be represented by a cylindrical body of a different density at the top of the trunk; (c) that the wind loading can be represented by a spatially constant wind distribution applied to the upper part of the canopy, that is varying in time with realistic spectral properties; (d) that the damping of the oscillations of the tree is caused solely by aerodynamic damping. sulting complex, fourth-order differential equations are solved using numerical methods. This model is used to predict the transfer functions relating tree displacement spectra to wind spectra, and it is shown that the model is able to represent experimental spectra well, particularly with regard to the prediction of the primary natural frequency. Wind speeds for tree failure by both trunk snapping and uprooting are then pictured, and reasonably realistic values obtained. The need for a better understanding of the relationship between extreme and mean wind gusts is apparent. Through a discussion of the sensitivity of the results to variations in the different model parameters some general conclusions are drawn about the effects of the different parameters on tree stability.