A method for measuring the forces acting on a tree trunk using strain gauges

Abstract

The wind force acted on a tree constantly changes in magnitude, direction, and distribution. We developed a method to measure simultaneously the amount of force (F), centroid of the distributed force (C), and direction of force (D) on a tree trunk using four strain gauges. F and C were estimated from the difference in the bending moments at two different positions along the long axis of the stem. D was estimated using the difference in the sensor outputs at two different radial positions at the same height. In principle, the two strain gauges should be oriented precisely 90o apart; however, this is unrealistic on an actual tree trunk. To calculate D, we developed a new method to detect the radial position and modulus of elasticity of each strain gauge after attaching it. We conducted three types of experiment. First, we loaded a wood pole with weights arranged in 11 patterns to test the accuracies of F and C for a distributed load. Next, we applied tensile forces to the wood pole and an evergreen conifer sapling from eight directions to test the accuracy of D, F, and C. On average, estimation errors were < 2% for both the distributed load and circumferential tensile load. Our method can estimate F, C, and D precisely, even if the wood is uneven and the strain gauges are not aligned. This is a great advantage for field wind force measurements.