Estimation of Hankinson’s formula coefficient for elastic wave transmission velocity of red pine by the indirect method

Abstract

This study determined the Hankinson’s formula coefficient n for red pine (Pinus densiflora) using the indirect elastic wave transmission test under varying moisture contents (12%, 15%, and 18%). Hankinson’s formula is a mathematical relationship used to predict the mechanical properties of wood at any angle relative to the grain. With information on the elastic wave transmission speed parallel (P, 0°) and perpendicular (Q, 90°) to the fiber direction, the wave transmission speed at intermediate angles can be predicted using Hankinson’s formula. A visually defect-free 81- to 90-year red pine board (400 × 400 × 50 mm) was selected as the test specimen. The moisture content of specimens was adjusted to 12%, 15%, and 18%. Coefficient n of Hankinson’s formula, was calculated by taking measurements were taken at grain angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90° using both ultrasonic and stress waves by the indirect transmission method.
The coefficients (n) obtained from ultrasonic wave measurements were 2.0, 1.9, and 1.9 at 12%, 15%, and 18% moisture contents, respectively. The values determined from stress wave measurements were 1.7, 1.7, and 1.6 at the same moisture contents, respectively. These results indicate that the transmission path of elastic waves in red pine can be effectively modeled using the coefficient n from Hankinson’s formula, which varies with moisture content. This suggests the potential applicability of the formula in evaluating internal defects or decay in wood through quantitative wave-based analysis.