The kinematics of wheat struck by a wind gust

A nonlinear model of the kinematics of a wheat stalk struck by a wind gust is developed. Individual stalks were excited from each of many directions and observed by videophotography The underdamped flexural response involved anisotropic circling motion that can be reproduced by a nonlinear system of ODEs. In the model, the horizontal path traveled by the grain mass is described in principal coordinates X-I and X-II. The four required constants are stiffnesses k(I)<k(II) in these directions, linear viscous damping <zeta>. and coupling strength beta related to a torque imposed by wind drag. This stem torque can cause nonlinear coupling if both XI and XII are excited and if k(i) not equal k(II), such that damping can vary by 30 percent over each cycle. The directionality of the single stalk may promote interplant collision, which could have important integrated effects on crop behavior at larger size scales.