Time-of-flight modeling of transversal ultrasonic scan of wood

Time-of-flight is a time for an ultrasonic pulse to cross a sample. It contains valuable information about the mechanical properties of a material. For the ultrasonic pulse propagating in wood perpendicular to the grain the relation between the time-of-flight and the elastic constants is rather complex due to the strong anisotropicity of wood. With the help of some assumptions this relation can be established from the elastic theory. The analytical calculation results in a function which represents a change of time-of-flight when the direction of propagation shifts from the radial to the tangential direction while scanning a board crosswise. The function takes into account the location of the pith and the geometry of the growth rings. The measurement performed on a sample of European spruce confirms the theoretical prediction.