TY - JOUR T1 - The Accuracy Of Formulas Used To Assess Strength Loss Due To Decay In Trees JF - Arboriculture & Urban Forestry (AUF) JO - JOA SP - 347 LP - 356 DO - 10.48044/jauf.2004.042 VL - 30 IS - 6 AU - Brian C.P. Kane AU - H. Dennis P. Ryan III Y1 - 2004/11/01 UR - http://auf.isa-arbor.com/content/30/6/347.abstract N2 - There are four formulas that arborists in the United States often use to assess the probability of tree failure. Although they are commonly referred to as “strength loss formulas,” three of the formulas (Wagener 1963; Coder 1989; Smiley and Fraedrich 1992) actually estimate the loss in stem moment of inertia (ISTEM) to evaluate the probability of failure. The formulas estimate the loss in ISTEM by modeling the stem and decay cross-sectional areas as concentric circles. For many trees with decay, however, neither the stem nor the decay cross-sectional areas resemble concentric circles, which may limit the formulas’ accuracy. The fourth formula (Mattheck and Breloer 1998) is based on the buckling strength of a cylinder; it also offers a measure of the probability of stem failure. To test how well the formulas estimate the loss in ISTEM, we compared each formula’s estimates for loss in ISTEM to the actual loss in ISTEM that we calculated using the parallel axis theorem, an engineering technique. Although the parallel axis theorem provides the actual loss in ISTEM, it cannot be used in practice because an image of the tree’s cross-section is needed to apply it. Significant differences existed between two formulas’ (Wagener 1963; Coder 1989) estimates of loss in ISTEM and the actual value. Each of the formulas misclassified some trees as to whether they exceeded the formula’s action threshold. When we calculated the actual loss in ISTEM for those trees, however, it was less than 33%. We present representative stem cross-sections for which the formulas did not accurately represent loss in ISTEM. ER -