Drag coefficient and frontal area of a solitary mature tree

Ebba Dellwik,Nikolas Angelou,Casper C.A Bekkers

doi:10.1016/j.jweia.2021.104854

Ebba Dellwik, Nikolas Angelou + Show 1 more

Open Access

https://doi.org/10.1016/j.jweia.2021.104854

Copy DOI

Abstract

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.

Highlights

The aerodynamic characteristics of trees define their wind induced drag (Gosselin, 2019)
Whereas the majority of previous works on wind–tree interaction concern young flexible trees in wind tunnels, this study investigates the parameterization of the drag force for a mature and stiff open-grown tree in nature, which, with a few exceptions (Roodbaraky et al, 1994; Koizumi et al, 2010), has so-far received limited attention
To exclude the effect of frontal area change due to the tree being in a natural transition to more or fewer leaves, we first selected a long period ranging from May 1st 2019 until July 31th 2019

Summary

Introduction

The aerodynamic characteristics of trees define their wind induced drag (Gosselin, 2019). The drag force parameterization is of great importance for aggregating the effect of trees in heterogeneous landscapes to accurately represent the land surface friction in larger scale models (De Jong et al, 1999; Hasager et al, 2003). For all these applications, the drag force of the tree needs to be specified. The wind-induced drag D on a rigid object is expressed as a function of its size and its aerodynamic characteristics through the following expression: Whereas the majority of previous works on wind–tree interaction concern young flexible trees in wind tunnels, this study investigates the parameterization of the drag force for a mature and stiff open-grown tree in nature, which, with a few exceptions (Roodbaraky et al, 1994; Koizumi et al, 2010), has so-far received limited attention.

Objectives

Methods

Results

Discussion

Conclusion