### Comparison of Three Equations for Predicting Stress Wave Velocity As A Function of Grain Angle

#### Abstract

Assessment of a nondestructive test system for detecting defects in the gluelines of edge-glued hardwood panels required development of a mathematical relationship for predicting stress wave velocity as a function of grain angle. This relationship was necessary to understand better how stress waves propagated around gaps or flaws in a glueline. In addition, the relationship was needed to assess the influence of specimen geometry upon the effectiveness of the stress wave technique.

Equations were generated by a statistical regression analysis software package and compared to Hankinson's equation. Equations were based upon measured velocity of stress waves traveling at angles between 0 and 90 degrees to the grain at 15 degree intervals in birch, black cherry, red oak, yellow-poplar, and western white pine boards. Regression analyses indicated that the best correlations were found with second order hyperbolic and parabolic equations. The two equations were compared to Hankinson's equation and to each other by using Absolute Average Error (AAE) for each equation for each species and for all species combined at each of the grain angles for which data were collected. Hankinson's equation produces the least AAE of the three equations although the hyperbolic and parabolic equations must also be considered reasonable predictors of stress wave velocity at most angles to the grain.

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