Arboriculture & Urban Forestry 35(2): March 2009 (Table 1). The model was also consistent with physical param- eters from equation 1 as the intercept was not significantly differ- ent from zero. For tops, mass was also the best predictor, and the model was more robust than for pieces. While fall distance was a significant predictor of force at the block for tops, it only ac- counted for 3.2% of the variance, compared with 94% for mass. It was also inversely proportional to force at the block, which was not consistent with equation 1 and the greater velocity of objects falling a greater distance in a gravitational field. The mod- els to predict normalized force at the block (i.e., force divided by mass) were much less robust (adjusted R2 < 0.25) and non- significant (P > 0.20) for pieces and tops (data not presented). Force at the block was greater for tops and piece 4 (the last piece removed), than for piece 1 (the piece just below the top), but did not differ among any other pieces (Table 2). In contrast, normalized force at the block was least for tops, and did not vary among the remaining pieces (Table 2). Tension in the Rope For tops and pieces, force at the block was slightly more than double the tension in the rope (Figure 3). For pieces, mass was the best pre- dictor of tension in the rope (Table 1). Depth of the notch was a significant, but less important predictor, and, counter-intuitively, the relationship was inversely proportional (Table 1). The regres- sion model was slightly less robust than the model predicting force at the block, and it conformed to the physical parameters from equation 1 since the intercept was not significantly differ- ent from zero (Table 1). For tops, mass was the best and only 71 significant predictor of tension in the rope, and the model was more robust than for pieces (Table 1). There was weak evidence that fall distance was inversely proportional to tension in the rope (Table 1). Predictions of normalized tension in the rope were much less robust (adjusted R2 < 0.10) and not significant (P > 0.10) for pieces and tops. Tension in the rope followed the same pattern as force at the block: force at the block was greater for tops and piece 4 than for piece 1, but did not differ among any other pieces (Table 2). Normalized tension in the rope was least for tops, as well as greater for piece 2 than piece 3 (Table 2). For Figure 3. Prediction of force at the block (FB) by tension in the rope (T). The linear prediction equation was FB = 2.02*T+1411 (r2 = 0.80, P < 0.0001), and it did not vary between tops and pieces, which have been plotted together. Table 1. Results of multiple regression analyses to predict force at the block (FB) and tension in the rope (T) for Pieces and Tops. Estimate refers to either the intercept or the regression coefficient (slope) for each parameter in the model, SE is standard error of the estimate, and contribution to model is the percentage of the overall sum of squares contributed by the parameter. Pieces FB (R2 = 0.78, P < 0.0001) Variable Intercept Mass Estimate (SE) P 4,815 (3,439) Fall distance -633 (1,029) Cut angle 84.6 (6.71) 5.53 (5.92) Rope length -33.9 (63.7) Cut depth Contribution to model 0.1684 0.0001 0.5420 0.3552 0.5969 -1,818 (1,410) 0.2038 77.6 0.2 0.3 0.1 2.1 T (R2 = 0.71, P < 0.0001) Estimate (SE) P -1,354 (1,955) 0.4922 36.8 (3.81) 758 (585) -1.24 (3.36) 6.36 (36.2) -2,006 (801) 0.0001 0.2015 0.7139 0.8612 0.0160 Contribution to model 69.3 0.9 0.1 0.0 3.3 FB (R2 Estimate (SE) 5,088 (3,681) 59.3 (4.63) -557 (199) 8.29 (20.3) -82.6 (261) -1,499 (3,410) = 0.96, P < 0.0001) P 0.2094 0.0001 0.0268 0.6949 0.7611 0.6734 Tops T (R2 Contribution to model 94.0 3.2 0.1 0.0 0.1 = 0.91, P = 0.0003) Estimate (SE) P 3,294 (2,165) 24.0 (2.73) -251 (117) -9.34 (11.9) -32.3 (154) Contribution to model 0.1720 0.0001 0.0696 0.4592 0.8394 -2,720 (2,005) 0.2171 88.6 4.3 0.5 0.0 1.1 Table 2. Means (standard deviation in parentheses) for variables of interest: force at the block (FB), tension in the rope (T), force at the block / mass of the piece or top (AccelFB), tension in the rope / mass of the piece or top (AccelT), mass, fall distance, fall factor, and stress. Read down a column, means followed by the same letter are not different (P > 0.05) by Tukey’s studentized range test. Fall Piece Top 1 2 3 4 n 13 13 13 13 12 FB (N) 8,783 (4,303) a 5,439 b (1,960) b 7,057 (1,864) abc 7,235 (2,015) abc 8,592 (2,526) ac T (N) 3,347 (1,734) a 2,152 AccelFB (m/s2 ) 58.5 (9.22) a 123 (819) b (24.0) b 2,991 (1,014) abc (15.2) b 3,401 (1,110) abc (22.5) b 2,835 126 113 115 (1,038) ac (22.4) b AccelT (m/s2 ) 22.4 (5.19) a 48.2 (8.80) bc 52.9 (17.6) b 43.2 (8.64) c 47.1 (7.40) c Mass (kg) 152 (72.7) a 45.5 (18.0) b 58.2 (21.0) b 65.6 (22.0) b 77.1 (25.3) b Distance (m) 7.40 (1.38) a 3.47 (0.14) b 3.47 (0.16) b 3.48 (0.16) b 3.46 (0.15) b Fall Ratio 0.56 (0.10) a 0.30 (0.03) b 0.36 (0.05) b 0.45 (0.07) c 0.58 (0.10) a Length of Piece (m) 6.27 (1.00) a 1.83 (0.00) b 1.83 (0.00) b 1.83 (0.00) b 1.83 (0.00) b Stressz (kPa) 9,202 (6,433) a 4,175 (2,521) b 5,388 (3,514) b 6,437 (4,010) ab 6,533 (4,231) ab Strain (mm/mm) 0.0021 (0.0012) a 0.0009 (0.0005) b 0.0011 (0.0004) b 0.0014 (0.0006) b 0.0014 (0.0006) b zBecause stress was measured both normal and parallel to the direction of fall, the sample size was 25 (23 for piece 4 since one tree only had 3 pieces after the top). ©2009 International Society of Arboriculture
March 2009
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