Algebraic Analysis for Partitioning Root and Stem Lodging in Rice Plant

Lodging is classified as root lodging caused by the loss of supporting force in the root, bending caused by the deformation of the stem and breaking where the stem breaks down as loads exceeding critical elasticity were applied. This research excluded breaking which is not in a state of equilibrium and tried to partition the level of lodging using an algebraic model in root lodging and stem lodging, or bending. When a vertical load was applied, the deformation of the stem of rice plant showed the form of a quadratic equation. The trace of the panicle neck in the process of lodging was an ellipse-shape. When loading was pure root lodging, the trace of the panicle neck became a circle of which culm length is the radius. When it was a pure stem lodging, the trace of the panicle neck is an ellipse of which major axis is culm length and minor axis is 0.64*culm length. When both stem lodging and root lodging occurred in a natural setting, the partitioning of lodging can be calculated by a formula using eccentricity of an ellipse, S=e*100/0.768(S is the ratio of stem lodging in the whole lodging, e is eccentricity of the ellipse). This method is expected to be useful in simple lodging partitioning. We could also calculate the partitioning of stem lodging and root lodging as units of angles as an accuracy method, by using a straight line calculated by differentiating a quadratic equation of stem deformation at the origin of the coordinates. These two methods for dividing root and stem lodging showed different values. However, each of them showed almost same values with different lodging degree in one plant.