112 Cullen: Trees and Wind—Drag Equation Velocity Exponent to Plantation Stability. Unpublished report of the Forestry Commission Research and Development Division, Edinburgh, Scotland. Moore, J.R., and D.A. Maguire. 2002. The mechanics of trees under wind loading, pp. 39–50. In Smiley, E.T., and K.D. Coder (Eds.). Proceedings of the Tree Structure and Mechanics Conference, 14–16 Oct. 2002. Savannah, GA. International Society of Arboriculture, Champaign, IL. Niklas, K.J. 1992. Plant Biomechanics: An Engineering Approach to Plant Form and Function. University of Chicago Press, Chicago, IL. ———. 2002. Wind, size, and tree safety. J. Arboric. 28(2):84–93. ———. 2003. Personal communication, April 23. Niklas, K.J., F. Molina-Freaner, C. Tinoco-Ojanguren, and D.J. Poalillo. 2002. The biomechanics of Pachycereus pringlei root systems. Am. J. Bot. 89(1):12–21. Peltola, H., S. Kellomäki, H. Väisänen, and V.-P. Ikonen. 1999. A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce and birch. Can. J. For. Res. 29:247–661. Peltola, H., B. Gardiner. S. Kellomäki, T. Kolström, R. Lässig, J. Moore, C. Quine, and J.-C. Ruel (Eds.). 2000. Special Issue: Wind and Other Abiotic Risks to Forests. For. Ecol. Manage. 135(1–3). Pokorny, J. 2003. Urban Tree Risk Management: A Community Guide to Program Design and Implementation. NA-TP-03-03. USDA Forest Service, Northeastern Area, State and Private Forestry, St. Paul, MN. 194 pp. Raymer, W.G. 1962. Wind resistance of conifers. NPL Aero. Rept. 1008. Robertson, A. 1987. The use of trees to study wind. Arboric. J. 11:127–143. Roodbaraky, H.J., C.J. Baker, A.R. Dawson, and C.J. Wright. 1994. Experimental observations of the aerodynamic characteristics of urban trees. J. Wind Eng. Indus. Aerodyn. 52:171–184. Sauer, F.M., W.L. Fons, and K. Arnold. 1951. Experimental Investigation of Aerodynamic Drag in Tree Crowns Exposd to Steady Wind, Conifers. U.S. Department of Agriculture, Forest Service, Division of Forest Fire Research, Washington, DC. Shelley, M. 2003. Personal communication. Shi-Igai, H., and T. Maruyama. 1988. Measurement of wind drag forces on trees. J. Natural Disaster Sci. 10(2):25–33. Sinn, G., and L. Wessolly. 1989. A contribution to the proper assessment of the strength and stability of trees. Arboric. J. 13(1):45–65. Smiley, E.T. 2000. Personal communication. Smiley, E.T., A. Key, and C. Greco. 2000. Root barriers and windthrow potential. J. Arboric. 26(4):213–217. © International Society of Arboriculture Spatz, H.-C., and F. Bruechert. 2000. Basic biomechanics of self-supporting plants: Wind loads and gravitational loads on a Norway spruce tree. For. Ecol. Manage. 135(1–3):33–44. Standards Australia. 1989. AS 1170.2-1989 Minimum Design Loads on Structures and Amdt. 1-1991, Amdts. 2-3, 1993 (SAA Loading Code—Wind Loads). Standards Australia, Sydney, Australia. Steinberg, V. 2002. Hydrodynamics: Bend and survive. Nature 420:473. Tirén, L. 1926. Nágra undersokningar över stamformen (Some research on tree stem form). Skogsvárdsforeningens Tidskrift 24(1–2):23–88 [in Swedish]. ———. 1928. Einige untersuchungen uber die schaftform. Meddelanden Fran Statens Skogsforsoksanstalt, Hafte 24 5(4):81–152 [in German]. Vogel, S. 1989. Drag and reconfiguration of broad leaves in high wind. J. Exper. Bot. 40:941–948. ———. 1994. Life in Moving Fluids: The Physical Biology of Flow (2nd ed.). Princeton University Press, Princeton, NJ. ———. 1996. Blowing in the wind: Storm-resisting features of the design of trees. J. Arboric. 22(2):92–98. Wessolly, L. 1995. Fracture diagnosis of trees: Part 3— Boring is no way for reliable fracture diagnosis. Stadt und Gruen (9):635–640. Wessolly, L., and M. Erb. 1998. Handbüch der Baumstatik und Baumkontrolle. Patzer-Verlag, Berlin, Germany. Wood, C.J. 1995. Understanding wind forces on trees, pp. 133–164. in Coutts, M.P., and J. Grace (Eds.). Wind and Trees. Cambridge University Press, Cambridge, UK. Acknowledgments. I am grateful to Prof. Karl Niklas, Cornell University, for his review of a draft of the original, research- oriented paper (Cullen 2003); to Dr. John Moore, Forest Research New Zealand, for input on his review of the Mayhead and Hoag data and on the mathematics involved in deriving drag coeffi- cients; to Prof. Michael J. Shelley, The Courant Institute, New York University, for his input on Equation 8; to Mr. Ken James, Burnley College, University of Melbourne, for his review of a draft of the original paper and for input on the Australian Wind Loading Standard; to Dr. Richard Bonser, Silsoe Institute and Prof. A. Roland Ennos of the University of Manchester, for their input on drag coefficient decrease rates; and to Dr. Tom Smiley, Barttlett Tree Research Laboratories, for comment on his research findings. Two anonymous reviewers provided useful comments. I am also indebted to Prof. Steven Vogel, Duke University, for his lucid explanation of the drag equation in Life in Moving Fluids. Consulting Arborist P.O. Box 31152 Greenwich, Connecticut, 06831, U.S.
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