24 



Fishery Bulletin 104(1) 



were averaged for each experimental treatment on each 

 haul. Mean off-bottom distances for each bridle and foot- 

 rope position, except the footrope center, were grouped by 

 offset distance (i.e., long side vs. short side of an experi- 

 mental treatment) where, for example, the distance 

 measurements from the 25-m position on the starboard 

 bridle collected on a starboard treatment (long side) was 

 grouped with the measurements from the 25-m position 

 on the port bridle during a port treatment. Under these 

 groupings, we assumed equality and subsequently refer 

 to the offsets by whether they were on the long or short 

 side (e.g., long 5 m) rather than whether they were on 

 the port or starboard side (e.g., port 5 m). 



To allow interpolation between the experimental off- 

 sets, cubic spline models (Venables and Ripley, 1994) 

 were fitted to door spread, wing spread, headrope 

 height, and the off-bottom distances for each bridle and 

 footrope position as a function of offset. Bootstrapped 

 empirical 95% confidence intervals (CI; Efron and Tib- 

 shirani, 1993) were estimated for all measured catego- 

 ries as described in the following example for off-bottom 

 distance as follows: 1) assuming that mean off-bottom 

 distances within a set were correlated because of local 

 environmental conditions, we chose 1000 bootstrap rep- 

 licates by sampling entire sets of measurements with 

 replacement; 2) we fitted a cubic spline, weighted by the 

 inverse of the variance, to each bootstrap sample, and 

 then predicted the mean off-bottom distance for each 

 1 m of offset; and 3) we ranked the predicted values, 

 then chose the 25"^ highest and lowest values as the CI 

 bounds. Similarly, we estimated the empirical 95% CIs 

 about the mean off-bottom distance at zero offset in the 

 same manner except that only zero offset treatments 

 were considered. 



angle-of-attack between the bridle and the direction 

 of travel (a). For flatfish, the vertical distance of the 

 bridle from the sea floor at which a herding response is 

 initiated (reaction height) will vary with species, size, 

 viewing conditions, arousal state, and other variables, 

 but for illustrative purposes, we considered a reaction 

 height of 1 cm where video observations indicated that 

 this value is appropriate for a small flatfish, initially 

 at rest and unaware of the approaching bridle (Somer- 

 ton, unpubl. data). Thus the value of the bridle contact 

 length was determined as the distance between the 

 wing tip and the point along the bridle at which the 

 interpolated value of off-bottom distance reached the 

 reaction height. The angle-of-attack, a, was not mea- 

 sured during the experiment; however, when the trawl 

 is symmetric, a can be modeled as 



a = Sin"'(0.5(D-W)/B), 



where D = the distance between doors; 



W = the distance between wing tips; and 

 B = the distance between the wing tip and the 

 door. 



It is not clear, however, how a will differ between the 

 long and short side of the trawl when warp offsets occur. 

 For illustrative purposes, we assumed that o is sym- 

 metrical and remains constant during all experimental 

 values of warp offset. Thus, for each side of the trawl 

 and for each offset, a value of bridle contact length and 

 o were first calculated as above, then the width of the 

 herding area on each side of the trawl was computed as 

 the bridle contact length times sin (o) and the two areas 

 were summed together. 



Modeling trawl shape 



To help visualize the distortion of the trawl that occurs 

 in response to offset, we created three views of the trawl; 

 1) the shape of the lower bridle when viewed laterally, 2) 

 the shape of the headrope when viewed from above, and 

 3) the shape of the footrope when viewed from in front 

 of the trawl. In addition, we calculated the area swept 

 by the bridles (herding area) and the effective net width 

 (i.e., the greatest lateral dimension of the net). 



Bridle shape and herding area 



The shape of the lower bridle, when viewed laterally 

 (i.e., off-bottom distance as a function of position along 

 the bridles), was approximated by linear interpola- 

 tion between the mean off-bottom distances measured 

 at the wing, and the 25-, 40-, and 50-m bridle posi- 

 tions. Such shape functions were calculated for both 

 the long side and the short side of the trawl at each 

 offset increment. 



The herding area can be considered as a function 

 of the bridle contact length, that is, the length of the 

 bridle that is sufficiently close to the bottom to elicit a 

 herding response (Somerton and Munro, 2001) and the 



Headrope shape and effective net width 



The curved shape of the headrope when viewed from 

 above can be approximated as a quadratic (parabolic) 

 function when the warps are equal in length and there 

 are no external forces to distort the symmetry of the net 

 (Fridman, 1969). If the shape remains parabolic as the 

 warp offset is increased, then the headrope shape can 

 be uniquely determined with three geometric measure- 

 ments: 1) the length of the headrope; 2) the distance 

 between wing tips; and 3) the tangent to the headrope at 

 its center. The first quantity was measured at the start 

 of the experiment. The second quantity was measured 

 acoustically on all hauls, and then averaged by treatment. 

 The third quantity was calculated as the quotient of the 

 tangential water velocity (U) divided by the perpendicular 

 velocity (V) measured by the headrope speed sensor (i.e., 

 U/V). With these quantities, the headrope shape was 

 determined as described in Appendix A. 



Although the shape of the headrope determined by 

 this method is assumed to be parabolic, the headrope 

 becomes increasingly asymmetric about the direction 

 of travel as the degree of warp offset increases because 

 the wing tip on the short side of the net precedes that 

 on the long side. When this distortion occurs, the mea- 



