Arboriculture & Urban Forestry 35(2): March 2009 to track trajectories of pieces removed with rigging, but only measured a few pieces and the single tree (actually a section of trunk removed from a tree) was not tested in situ. Blair (1989) discussed the advantages and disadvantages of various removal techniques, stating his preference for taking single large pieces to reduce the likelihood of accidents during cutting. While noble, this approach was not based on empirical data, nor did it ad- dress the issue of overloading the tree during rigging operations. From theoretical considerations, the tension (t) in the rope during rigging operations can be calculated by (Pavier 1998): [1] t = mg* 1+ 1+ 2kF mg , where m is the mass of the falling object (kg), g is the accel- eration due to gravity (m*s-2), F is the fall factor (dimensionless), the ratio between the distance the object falls and the length of rope in the system, and k is a measure of the rope’s elasticity (N): [2] k = P *(L/x), where P is the force that extends the rope (N), x is the rope’s extension (m), and L is the initial length of rope (m) (McLaren 2006). Equation 1 is derived from equating the loss of potential energy of a falling mass and the gain in strain energy of the rope as it extends. However, the equation is less applicable as the rope’s elasticity decreases with time and so must be considered only an estimate. The tension in the rope must be doubled to estimate the force in the block and sling, which is transferred to the tree at the rigging point. The force at the block would be somewhat less than twice the tension in the rope because friction in the block would reduce the tension in the rope between the block and the friction device that anchors the rope at the base of the tree (Donzelli 1999). For a 227 kg (500 lb) mass, Donzelli (1999) determined that the reduction in rope tension between the block and the friction de- vice ranged from 4%–30%, depending on the type of block used. The objectives of the present study were to determine the forces generated during rigging operations and to investigate how these forces affect rigging gear and tree stability. In par- ticular, it was desired to determine 1) the best physical and ar- boricultural predictors of tension in the rope and force at block, and 2) how force at the block translated into stress in the trunk, including a trunk with decay. Answers to these questions were expected to inform the broader question of how massive a piece can be without risking failure of the rigging gear or the tree. METHODS AND MATERIALS Thirteen red pines (Pinus resinosa Ait.) growing in a plantation in Amherst, MA, USA were selected according to their physical similarity, proximity to an access road, lack of structural defects, and distance from other trees. The trees averaged 30.6 cm (1 ft) dbh [4.57 cm (1.8 in) standard deviation] and 21.6 m (70.87 ft) tall [1.64 m (5.38 ft) standard deviation]. Each was rigged for removal in accordance with conventional arboricultural practice. In particular, lateral branches were removed until a top remained that was small enough to remove without risking failure of the rigging gear or tree. A block [ISC Ltd., Glasgow, Scotland, 2000 kg (440.92 lb) working load limit, 20 mm (0.79 in) maximum 69 rope diameter] was attached with a 12.7 mm (0.5 in) Amsteel® (Samson Rope Technologies Inc., Ferndale, WA) sling approx- imately 7-10 cm (2.76-3.94 in) below where the cut would be made to remove the top from the trunk. A notch was made in the intended felling direction and the lowering rope [12.7 mm (0.5 in) diameter Stable Braid (Samson Rope Technologies Inc., Fern- dale, WA)] was run through the block and tied off to the top with a marl and a running bowline. The felling cut was made opposite the notch and the top was pulled by hand, as necessary, with a tag line to ensure that it fell in the appropriate direction. The lowering rope was secured to the base of the tree by a steel Port-A-Wrap (Buckingham Mfg., Binghamton, NY), which was also attached to the tree by a 12.7 mm diameter Amsteel sling. Securing the rope in this fashion caused the top to stop abruptly, generating the intended large forces. Removal of tops and pieces was videotaped with a digital video camcorder (Canon GL2, Jamesburg, NJ). After the top was removed, its length, mass, and center of gravity were determined. The trunk diameter at the base of the top was measured both parallel and normal to the direction of fall. Four additional pieces were removed from each tree, ex- cept for two trees, for which three and five additional pieces were removed, respectively. Not including the top, pieces were 1.83 m (6 ft) long, and were removed in the same fashion as the top. The mass, diameters (at the top and bottom of the piece), and center of gravity were also determined for each piece. Forces at the block and Port-A-Wrap were measured with dyna- mometers [Dillon EDxtreme, 44 kN (10,000 lbf) and 22 kN (5,000 lbf) capacity, respectively, accurate to 0.1% of capacity]. The peak load was recorded by each dynamometer, sampling at 60 Hz. The amount of rope in the rigging system and distance of fall were measured for the top and each piece so that the fall factor (see equation 1) could be calculated. Assuming minimal slack in the lowering rope, the distance of fall is twice the distance from the pin at the center of the sheave of the block to the center of gravity of the piece. Placement of a dynamometer between the sling and the block increased the fall distance compared to a work situation. The length of rope in the system is the distance from the Port-A-Wrap to the marl tied to the piece. The value for k for the lowering rope was determined using Equation 2, and the following values: P = 4.6 kN (1,034 lbf), which is 10% of the average tensile strength as provided by the manufacturer (Samson 2008), and L/x = 90.9 [rope extension at 10% of average tensile strength is 1.1% (Samson 2008)]. The value of k, how- ever, must be considered an estimate because it is inherently dif- ficult to calculate this property for ropes (McKenna et al. 2004). At approximately 1 m (3.28 ft) above ground, strains in the trunk parallel and normal to the direction of fall of the piece were measured as described by James et al. (2006). To convert strain to stress, a normalized measure, it was necessary to calibrate trees be- fore removing any pieces. Calibration involved pulling trees with a winch, which applied a bending moment to the tree, and record- ing the strain. Bending moment (M) was converted to stress (σ) by: [3] σ = 32M / (πab2 ), where a and b are, respectively, the trunk diameters nor- mal and parallel to the direction of the applied bending mo- ment. As values of a and b in equation 3 diverge, stress calcu- lations that assume a circular cross-section are increasingly erroneous (Kane 2007). As the tree was pulled with a winch, ©2009 International Society of Arboriculture
March 2009
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