Model-based estimation of tree centroids and required felling forces using terrestrial laser scanning data

• TLS-derived QSMs used to precisely determine trees’ centres of gravity (CoG) • Monte Carlo simulations (n = 1,000) quantify uncertainty in CoG positions • Directional felling forces computed from probabilistic mass distributions • Integrated geometric-mechanical framework for CoG and felling forces • Approach improves safety and decision-making in forestry operations Timber harvesting involves significant safety risks, often due to misjudgements of tree inclination and felling direction. This study presents a data-driven approach (N = 54 trees) to precisely determine a tree’s centre of gravity (CoG) using quantitative structure models (QSMs) derived from terrestrial laser scanning (TLS). The term “resultant” in this context refers to the total gravitational force acting on a tree, derived from the vector sum of individual cylinder weight forces. The spatial location of this resultant vector defines the tree’s CoG. Employing the TreeQSM algorithm, three-dimensional tree models were reconstructed into cylindrical segments, allowing for accurate calculation of volume, mass, and the CoG. To account for variability in trunk and branch densities, water content, and measurement errors, the model was subjected to Monte Carlo simulations (n = 1,000). These simulations enable the analysis and visualisation of the statistical distribution of CoG positions. The simulation results provided prediction intervals around the CoG and revealed how internal variability affects tree balance. Systematic variation of felling directions enabled the calculation of directional felling forces, highlighting how the required effort changes based on mass distribution and gravitational alignment. Graphical outputs, including two-dimensional visualisations of CoG positions and force curves, support intuitive interpretation and practical application. The combination of TLS-derived QSMs with probabilistic modelling provides a robust framework for understanding tree mechanics, improves the accuracy of CoG determination, and enhances the safety of forestry operations by enabling more informed and controlled felling decisions.