Blowing in the Wind-Continued By making some assumptions about the density of crown's

Chapter 3, Problem 10

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Blowing in the Wind-Continued By making some assumptions about the density of crown's foliage, the total force F on the tree can be calculated using a formula from physics: F = pAv2/6 wherepf:::j 1.225 kg/m3 is the density of air, v is the wind speed in mis, andA is the cross-sectional area of the tree's crown. If we assume that the crown in roughly cylindrical, then its cross section is a rectangle of area A = (2R)(L/2) = RL, where R is the average radius of the cylinder. Then the total force per unit length is then Wo = Fl(U2) = 0.408Rv 2 The cross-sectional moment of inertia for a uniform cylindrical beam is l = i1Tr4, where r is the radius of the cylinder (tree trunk).