, Volume 18, Issue 2, pp 195–203 | Cite as

Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies

  • John R. MooreEmail author
  • Douglas A. Maguire


Previous studies that measured the natural frequencies and damping ratios of conifer trees were reviewed and results synthesized. Analysis of natural frequency measurements from 602 trees, belonging to eight different species, showed that natural frequency was strongly and linearly related to the ratio of diameter at breast height to total tree height squared (i.e., DBH/H 2). After accounting for their size, pines (Pinus spp.) were found to have a significantly lower natural frequency than both spruce (Picea spp.) and Douglas-fir (Pseudotsuga spp.). Natural sway frequencies of de-branched trees were significantly higher than those of the same trees with the branches intact, and the difference increased with an increasing ratio of DBH/H 2. Damping mechanisms were discussed and methods for measuring damping ratio were presented. Analysis of available data suggested that internal damping ratios were typically less than 0.05 and were not related to tree diameter. External damping was mainly due to aerodynamic drag on the foliage and contact between the crowns of adjacent trees. Analysis of data from previous wind-tunnel studies indicated that damping due to aerodynamic drag is a nonlinear function of velocity. Damping due to crown contact has been suggested by a previous author to be a function of both the distance to and the size of adjacent trees. Therefore, in uniformly spaced stands it may be possible to model crown contact damping as a function of stand density index (SDI), a common forestry measure which incorporates both of these variables.


Wind damage Tree mechanics Natural frequency Damping ratio 



This review was made possible through funding from the Department of Forest Resources at Oregon State University and the New Zealand Forest Research Institute Ltd. The authors would also like to thank Mr. Martin Sugden for allowing his data to be used, and Mr. Bruce Nicoll for his assistance in obtaining the data from the British Forestry Commission’s tree pulling program. Drs. Daniel Edge, Barry Gardiner, David Hann, Michael Unsworth, Solomon Yim and two anonymous reviewers provided useful comments on an earlier version of this paper.


  1. Baker CJ (1995) The development of a theoretical model for the windthrow of plants. J Theor Biol 175:355–375CrossRefGoogle Scholar
  2. Baker CJ (1997) Measurement of the natural frequencies of trees. J Exp Bot 48:1125–1132Google Scholar
  3. Blackburn P, Miller KF, Petty JA (1988) An assessment of the static and dynamic factors involved in windthrow. Forestry 61:29–43Google Scholar
  4. Clough RW, Penzien J (1993) Dynamics of structures. McGraw Hill, New YorkGoogle Scholar
  5. Everham EM (1995) A comparison of methods for quantifying catastrophic wind damage to forests. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, Cambridge, pp 340–357Google Scholar
  6. Flesch TK, Wilson JD (1999) Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics. Agric For Meteorol 93:243–258CrossRefGoogle Scholar
  7. Forest Products Laboratory (1999) Wood handbook—wood as an engineering material. Gen Tech Rep FPL-GTR-113, U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, Wis.Google Scholar
  8. Furnival GM (1961) An index for comparing equations used in constructing volume tables. For Sci 7:337–341Google Scholar
  9. Gardiner BA (1992). Mathematical modelling of the static and dynamic characteristics of plantation trees. In: Franke J, Roeder A (eds) Mathematical modelling of forest ecosystems. Sauerländer, Frankfurt/Main, pp 40–61Google Scholar
  10. Gardiner BA, Stacey GR, Belcher RE, Wood CJ (1997) Field and wind tunnel assessments and the implications of respacing and thinning for tree stability. Forestry 70:233–252Google Scholar
  11. Hassinen A, Lemettinen M, Peltola H, Kellomaki S, Gardiner B (1998) A prism-based system for monitoring the swaying of trees under wind loading. Agric For Meteorol 90:187–194CrossRefGoogle Scholar
  12. Hoag DL, Fridley RB, Hutchinson JR (1971) Experimental measurement of internal and external damping properties of tree limbs. Trans ASAE 14:20–28Google Scholar
  13. Holbo HR, Corbett TC, Horton PJ (1980) Aeromechanical behaviour of selected Douglas-fir. Agric Meteorol 21:81–91CrossRefGoogle Scholar
  14. Kerzenmacher T, Gardiner BA (1998) A mathematical model to describe the dynamic response of a spruce tree to the wind. Trees 12:385–394CrossRefGoogle Scholar
  15. Larsen DR, Hann DW (1987) Height diameter equations for seventeen tree species in southwest Oregon. Research Paper 49. Oregon Forest Research Laboratory, Oregon State University, Corvallis, Ore.Google Scholar
  16. Loo SP (1975) Aerodynamic characteristics of a flexible structure (tree). ME Thesis, University of Canterbury, ChristchurchGoogle Scholar
  17. Mayer H (1987) Wind-induced tree sways. Trees 1:195–206Google Scholar
  18. Mayhead GJ (1973a) Sway periods of forest trees. Scot For 27:19–23Google Scholar
  19. Mayhead GJ (1973b) Some drag coefficients for British forest trees derived from wind tunnel studies. Agric Meteorol 12:123–130CrossRefGoogle Scholar
  20. Mayhead GJ, Gardiner JBH, Durrant DW (1975) A report on the physical properties of conifers in relation to plantation stability, Unpublished report of the Forestry Commission Research and Development Branch, EdinburghGoogle Scholar
  21. Means JE, Hansen HA, Koerper GJ, Alaback PB, Klopsh MW (1994) Software for computing plant biomass—BIOPAK users guide. Gen Tech Rep PNW-GTR-340. U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, Ore.Google Scholar
  22. Milne R (1991) Dynamics of swaying Picea sitchensis . Tree Physiol 9:383–399Google Scholar
  23. Niklas KJ (1992) Plant biomechanics: an engineering approach to plant form and function. The University of Chicago Press, ChicagoGoogle Scholar
  24. Nowacki GJ, Kramer MG (1998) The effect of wind disturbance on temperate rain forest structure and dynamics of southeast Alaska. Gen Tech Rep PNW-GTR-421. U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, Ore.Google Scholar
  25. O’Sullivan MF, Ritchie RM (1992) An apparatus to apply dynamic loads to forest trees. J Agric Eng Res 51:153–156Google Scholar
  26. Papesch AJG (1984) Wind effects on (Canterbury) forests. Ph.D Thesis, University of Canterbury, ChristchurchGoogle Scholar
  27. Peltola H, Kellomaki S, Hassinen A, Lemittinen M, Aho J (1993) Swaying of trees as caused by wind: analysis of field measurements. Silva Fenn 27: 113-126Google Scholar
  28. Quine CP (1995) Assessing the risk of wind damage to forests: practices and pitfalls. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, Cambridge, pp 379–403Google Scholar
  29. Quine CP, Gardiner BA (1991) Storm damage to forests: a major abiotic threat with global occurrence. Proceedings of the Tenth World Forestry Conference, Paris, September, 1991, Paris, pp 339–345Google Scholar
  30. Raymer WG (1962) Wind resistance of conifers. Report 1008. National Physical Laboratory, Aerodynamics Division, TeddingtonGoogle Scholar
  31. Reineke JL (1933) Perfecting a stand density index for even-aged forests. J Agric Res 46:627–638Google Scholar
  32. Rodgers M, Casey A, McMenamin C, Hendrick E (1995) An experimental investigation of the effects of dynamic loading on coniferous trees planted on wet mineral soils. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, Cambridge, pp 204–219Google Scholar
  33. Roodbaraky HJ, Baker CJ, Dawson AR, Wright CJ (1994) Experimental observations of the aerodynamic characteristics of urban trees. J Wind Eng Ind Aerodyn 52:171–184CrossRefGoogle Scholar
  34. Sugden MJ (1962) Tree sway period—a possible new parameter for crown classification and stand competition. For Chron 38:336–344Google Scholar
  35. Vogel S (1988) Life’s devices: the physical world of animals and plants. Princeton University Press, Princeton, New JerseyGoogle Scholar
  36. White RG, White MF, Mayhead GJ (1976) Measurement of the motion of trees in two dimensions. Research Report 86, University of Southampton, Institute of Sound and Vibration, SouthamptonGoogle Scholar
  37. Wood CJ (1995) Understanding wind forces on trees. In: Coutts MP, Grace J (eds), Wind and trees. Cambridge University Press, Cambridge, pp 133–164Google Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Forest ResourcesOregon State UniversityCorvallisUSA
  2. 2.Department of Forest ScienceOregon State UniversityCorvallisUSA
  3. 3.Forest ResearchChristchurchNew Zealand

Personalised recommendations