Response of Coniferous Trees to Wind Loading

John Moore

Introduction

Effects of wind on trees and stands– seed and pollen dispersal

– influence on mass exchange (i.e., CO2 and water vapor)

– stem form and growth patterns– damaging effects

• uprooting, stem breakage• loss of foliage

Damaging Effects of Wind

Uprooting and breakage of trees are important stand replacing disturbances.

In managed forests they are generally viewed in a negative light.

In many areas of the world, wind is a major constraint on forestry

Modeling Wind Damage

Empirical approaches– analysis of sample plot data– retrospective studies

Mechanistic approaches– static– dynamic

Dynamic Response

Trees are dynamic structures which respond to the fluctuating wind forces acting on them

Two approaches to modeling dynamic response of trees to wind:

• mechanical transfer function• dynamic structural model of tree

1. Mechanical Transfer Function

Measure both wind speed and tree response

Transfer function

Wind speed Tree movement

u(t) y(t)

)()()( HUY )(

)()(

U

YH

Example in Douglas-fir

2. Dynamic Structural Model

Predict response of trees to an applied wind force

Dynamic motion of tree described by the following equation:

)()()()( tFtkytyctym

2

)()(

2 ACtutF d

Model Requirements

• Need information on the following:• Natural frequency of tree• Damping ratio• Applied bending moment

• These can be predicted from a knowledge of the within-stand wind speed profile and tree size

Natural Frequency & Damping

Relationship to Tree Size

Applied Bending Moment

h

Wind

Center of mass

d

Factors Affecting Applied Bending Moment

• Within-stand wind speed

• Crown size and shape

• Foliage drag coefficient

• Stem stiffness

• Height to center of mass

• Presence of snow or ice

Crown Size and Shape

• Drag force acting on crown is a function of crown frontal area

• Damping is also a function of crown mass and its distribution

Crown Shape Models

• Engineering theory in mechanistic models is quite advanced

• Mensurational information is quite primitive!

Crown Shape Assumptions

CW

GC

L

Conclusions

• Mechanistic models can provide useful information on the risk of wind damage

• Present models may suffer because the mensurational information they use does not match their level of engineering sophistication

Acknowledgements

Starker ForestsMark Gourley

OSUDr Doug MaguireTim Vredenburg

Andrew BrickmanMilo Clauson