Drag coefficient and frontal area of a solitary mature tree

Trees are important natural wind engineering elements in both the urban and the agricultural contexts, but their aerodynamic description has been limited by its focus on young, flexible trees. Here, we provide a reformulation of the classical drag equation, which is also suitable for mature and wind-adapted trees. The new formulation is based on results from a full-scale experiment with focus on a solitary oak tree, for which we determined all terms in the drag equation experimentally. We also present a new photographical method for the accurate quantification of the tree's frontal area under highly variable outdoor lighting conditions. We used a database of images from a surveillance camera, from which a high-quality subset was automatically selected with machine learning algorithms. Compared to previous work on younger and smaller trees, the mature tree has a lower absolute value of the Vogel exponent, which indicates a relatively low degree of reconfiguration. The presented results underline the high efficiency of mature trees in reducing the momentum of the wind. The results can be used to quantify the effect of similar trees in wind simulations, and the new method for determining the frontal area can be applied in other tree measurement campaigns.

Automated summary

Trees are crucial wind engineering elements in urban and agricultural settings. However, the understanding of their aerodynamics has been mainly focused on young and flexible trees. In this study, a new formulation of the classical drag equation is proposed to describe the aerodynamics of mature and wind-adapted trees. A full-scale experiment on an oak tree is conducted to determine the drag equation terms, and a novel photographic method is developed to accurately measure the frontal area of the tree. The results demonstrate the high efficiency of mature trees in reducing wind momentum, which can be useful in wind simulations and other tree measurement campaigns.