Arboriculture & Urban Forestry 35(2): March 2009 a significant predictor of tension in the rope for pieces (and margin- ally significant for tops), the relationship was, paradoxically, inversely proportional. Intuitively, one expects that a deeper notch would cause the piece to release from the trunk sooner, which would increase the time it fell, and thus its velocity, before the rope stops it. It is unclear why this occurred, but careful investigation of the extent to which the depth and angle of the notch influence the length of time before the piece releases from the trunk should lend insight into this phenomenon. Detter (2008) observed possible differ- ences in rotation of the cut piece depending on the type of notch (conventional or Humboldt), but there were too few observa- tions and no statistical analyses to draw meaningful conclusions. Notch depth and angle, as well as fall distance, are theoreti- cally less important than mass, since velocity is proportional to the square root of the fall distance, while acceleration required to stop the piece is directly proportional to mass. The poor pre- diction of normalized force at the block and tension in the rope by any of the variables in those models supports the idea that mass was far more influential than either fall distance or depth and angle of the notch. Assuming that the intuitive expectation that the depth and angle of the notch influence the force required to stop a falling piece, it is unclear that their influence would supersede the influence of fall distance, because taking a longer piece increases fall distance linearly. Practically speaking, climb- ers are advised to 1) take a less massive piece, 2) take a shorter piece, 3) keep the block close to the cut, and 4) avoid slack in the lowering rope, since these factors will have a greater impact on stopping force than notch depth and angle. In many situations, however, any one of these recommendations may not apply or, worse, may cause a greater risk to the climber. For example, situ- ations often arise in rigging when the climber intentionally adds slack to the rigging to avoid a cut piece from swinging back into the climber. Thus, the recommendations should not supersede a climber’s good judgment when deciding on how to set the rig- ging, but rather help guide a climber’s decisions with respect to safety. It is also important to exercise caution when extrapolating from the results of our small sample of trees. Species, tree struc- ture, and alternate rigging practices may all affect our findings. Some of the results agreed nicely with theoretical predictions, as shown by intercepts statistically similar to zero in the multiple regression models. Also expected from theory was the finding that force at the block was more than double tension in the rope. Since rope tension was measured in such a way that friction of the block was not accounted for, doubling rope tension would under- estimate force at the block. The effect of friction added 20% to twice the tension in the rope to predict force at the block, within the range reported by Donzelli (1999), but more than the value assumed by Detter (2008). The finding that tension in the rope was only 17% of predicted tension from equation 1 was likely due to the impact effects of loading. Because the lowering rope was relatively inelastic, the impact force would not have been attenuated as much as by a rope that would have stretched more, thereby reducing the impact force, as predicted from equation 1. Other factors that may have been relevant include inherent im- precision in assigning a value for k (McKenna et al. 2004) for Stable Braid, and the inapplicability of fall distance from equa- tion 1. Pieces and tops did not free fall the entire fall distance, but rather, rotated on the hinge after the back cut was made. We did not quantify the rotation, but Detter’s (2008) observations 73 indicate that the angle of rotation is similar to the angle of the felling notch, which, in the present study, did not exceed 75º. Measured fall distance, then, would not have been more than twice the actual fall distance. Halving the fall distance used in equation 1, however, only improved prediction to 26% for pieces and 17% for tops, so this explanation is insufficient. When we re-analyzed the data including only pieces removed with bypass cuts, which would be expected to cause pieces to free fall for the distance closest to the measured fall distance, the prediction of rope tension was similar to pieces removed with notches (19%). Since equation 1 does not adequately describe rigging-induced forces, a new model that accounts for 1) the rotation (as opposed to free fall) of pieces (and how this affects fall distance), and 2) the comparative inelastic nature of lowering ropes is necessary. Blair (1995) suggested that tension (t) in the rope could be estimated from the mass (m) of the piece using: [6] t = m * d + m, where d is the distance of fall. This guideline overestimat- ed rope tension by 82% for tops but only 18% for pieces, which underscored the previously-described difference be- tween tops and pieces with respect to the forces generated. A final practical application of the findings was to estimate the allowable amount of decay in the trunk before risking tree failure during rigging. For concentric decay columns, tree failure would have occurred when the cross-section was 60% hollow; for decay columns offset to the periphery of the cross-section, tree failure would have occurred when the cross-section was only 45% hollow. These values must be taken with extreme cau- tion, since stress was only measured at the base of the tree and the values presented are likely smaller than actual stress since we used the static elastic modulus in equations 4 and 5. The impact of the piece being removed on the trunk below the rig- ging point might cause failure at a different location than where stress was measured. A climber’s experience may still be more valuable in determining whether a tree is safe to climb, but the hollow cross-sections estimated above can provide some guidance in assessing the safety of rigging a particular tree. CONCLUSION We have demonstrated the importance of mass in predicting rig- ging-induced forces, as well as interesting differences between tops and pieces with respect to force and stress. We have also shown that predicting force from the theoretical analysis derived for falling rock climbers is less applicable in rigging trees. Such disparities highlight the need for additional studies to assess the forces and stresses generated during rigging. Future areas of in- vestigation include exploring differences between tops and piec- es, measuring deflection at the rigging point, comparing pieces of similar mass while varying fall distance, and more precisely mea- suring the effect of notches and hinges on movement of the piece after cutting. Finally, a more robust analysis with respect to the dynamic response of trees during rigging would be most helpful. Acknowledgments. The authors gratefully acknowledge the assistance of Ed Carpenter, Melissa Duffy, Mollie Freilicher, Marcy Gladdys, Dan Goodman, and Noel Watkins, as well as two anonymous reviewers for helpful comments on earlier versions of the manuscript. ©2009 International Society of Arboriculture
March 2009
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