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Avoiding Dendrometry Bias When Trees Lean or Taper

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Tree taper, lean, instrument crosslevel tilt, and inclination of line-of-sight (LOS) all interact rather obscurely to affect dendrometer estimates of tree diameter, hypsometer estimates of tree height, and estimates of slant range by any device. Most dendrometry formulae heretofore have assumed zero value for taper, lean, and hypsometer tilt--some have even implicitly assumed zero inclination of LOS in making diameter estimates. Violation of these assumptions has resulted in biases of unknown magnitude. This paper develops a slant-plane geometry appropriate to gravity-activated hypsometers and to all 3 types of dendrometer (optical calipers, optical forks, optical rangefinders). From this, some new trigonometric formulae are derived that give unbiased estimates of diameter, slant range, and height above a doubly tilted reference plane. One part of tree lean occurs in the plane of observer and tree axis, the remainder (crosslevel) occurs in a plane normal to the first plane. These formulae make possible for the first time the calculation and comparison of biases implicit in less exact dendrometry formulae used previously. Forest Sci. 26:203-215.

Keywords: Hypsometer tilt; conic sections; crosslevel

Document Type: Journal Article

Affiliations: Forestry Consultant, P.O. Box 13106, Gainesville, FL 32604

Publication date: June 1, 1980

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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