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In contrast to the electrodes, which have physical contact with the sea floor, tension relief cords generally do not touch the sea floor Depestele et al. Small vessels are allowed to fish for flatfish with two beam trawls of up to 4. All of the small vessels fishing with a pulse trawl use the PUL-R rigging type, mostly in combination with a beam.

About two-thirds of the large pulse trawl vessels use a wing and one-third a traditional beam to fix the horizontal net opening. Towing speed differs across gears and fleet segments Poos et al. The fishing effort of the Dutch beam trawl fleet is dominated by large vessels, which contribute to The hydrodynamic drag was estimated for the gear components that are in contact with the seafloor, or towed just above the seafloor: ground gear, tickler chains, chain mat, electrodes and tension relief cords, bottom panels of the net, shoes of the beam trawl, and the nose of the wing.

Data were compiled on the number, length, angle of attack, and frontal surface area of the various components as described in the Supplementary material SM1 and are representative for the flatfish fisheries in the period — Data on conventional tickler chain and chain mat beam trawls were available from enquiries on-board fishing vessels and with net makers and from direct measurements of chain mat beam trawls in Belgian and Dutch harbours.

The enquiry data were complemented with data obtained from the literature Fonteyne and Polet, ; de Groot and Lindeboom, ; van Marlen et al. To apply these equations, we need to know the towing speed, the drag coefficient, the frontal area, and the angle of attack of the individual components. As mentioned above, the towing speed of a particular gear can be estimated from VMS data.

Very little is known, however, regarding the drag coefficients of beam trawl components. The Reynolds numbers of many of the components are in the subcritical flow range 10 3 —10 5 , where the boundary layer flow is laminar, there is flow separation and the principle contribution to the hydrodynamic drag is from the pressure differential over the components surface.

Hence we use drag coefficients, which are characteristic of this flow regime. For chains, we use values calculated by Xu and Huang , and for some of the ground gear components, we use measurements made by O'Neill and Summerbell Where measurements are not available we use those that have been made for similarly shaped objects such as cylinders, disks, cubes, and spheres and which have Reynolds numbers in the subcritical flow range Hoerner, Table 1 shows the drag coefficients used for the different beam trawl gear components.

No information on the variance in drag coefficients is readily available. Gear components, hydrodynamic drag coefficient, and equation number used to estimate the hydrodynamic drag. The frontal area and angle of attack of components such as the shoes, beam, and nose or wing are well defined and readily measurable, whereas those for components such as the ground gears, tickler chains, chain mats, and electrodes are more variable and depend on the rigging of the gear.

Therefore, we need to look at these components in more detail. To estimate their hydrodynamic drag, we subdivide them into piecewise linear segments and calculate the drag of each segment using equation 2. Given the length of the ground gear sections, the angle of attack of the longitudinal sections was calculated by geometry.

The U-shaped section was assumed to form a catenary. The hydrodynamic drag of the ground gear was calculated as the sum of the drag of the ground gear sections using equations 1 and 2. A chain mat comprises of a matrix of longitudinal and transverse chains that are attached to the ground rope and the beam. Information was available on the number and chain link diameter of the longitudinal and transverse chains but not on their length. The lengths of the chains were estimated from the vertical distances between the point of attachment along the ground gear catenary and the beam longitudinal chains and the horizontal distances between the points of attachment transverse chains.

The points of attachment of the chains along the ground rope catenary were determined by distributing them equally over the width of the trawl. A drag coefficient of 0. For the other part and the tension relief cords the drag coefficient of 1. To estimate the total hydrodynamic drag of a gear, we sum the contributions from each of the individual gear components. Thus, we implicitly assume that there is no hydrodynamic interaction between components and that their contribution is additive.

To assess the validity of this approach, we compare our hydrodynamic drag estimates with in situ measurements of beam trawl drag. Blom , studied the drag of a tickler chain beam trawl and estimated the separate contribution of the shoe tickler chains and net, whereas Fonteyne and co-workers in Paschen et al.

For the conventional beam trawls TBT, TBC , data were from the years to before the transition to pulse trawling. For the pulse beam trawls data were from to after the transition Poos et al. Silt fractions were taken from Wilson et al. Annual swept area ratio SAR of the conventional tickler chain beam trawl TBT, top left and chain mat beam trawl TBC, top right in the period — and pulse trawl PUL, bottom left in the period — and the mud percentage bottom right according Wilson et al.

The components were grouped into four major categories: i ground gear; ii bottom net panels; iii shoes of the beam trawl or nose of the Sumwing; iv tickler chains, chain mat or electrodes, and tension relief cords. The hydrodynamic drag of the individual gear components was estimated by applying the equations described above to the dimensions of the bottom gear components summarized in the Supplementary material SM1.

To obtain an estimate of the variability from the gear dimensions, the hydrodynamic drag of each component was bootstrapped times from a normal distribution based on the mean and standard deviation of the dimensions of the sampled gear components. For each D c , the mean m c was estimated by randomly drawing silt fractions from the observed frequency distribution of silt fraction by gear type.

The sediment mobilization of the different beam trawl types were combined to estimate the sediment mobilization of the beam trawl fleet of the Netherlands when using either the conventional beam trawl or innovative pulse beam trawl by taking account of the proportion of each gear type in the fleet Table 2. Gear types are depicted in Figure 1.

Large vessels tow their TBT at an average speed of 3. The difference in towing speed between gear types is less in small vessels: 2. The mean towing speed of PUL trawlers does not differ between rigging types. The estimated hydrodynamic drag of the different gear components that are in close contact with the seafloor, and therefore relevant when assessing the impact on the mobilization of sediment, is presented in Table 3.

For small vessels, net panels have the largest contribution for all gear types 1. For large vessels, the net panels have the largest contribution for the pulse trawl types 1. The largest difference in hydrodynamic drag between gear types was observed for the gear component that plays a role in the stimulation of flatfish.

Significant differences were also observed for the ground gear drag. For small vessels, the estimated hydrodynamic drag of 4. The fleet estimates take account of the number of vessels using a particular gear type Table 2 and the silt content where the gear types operate.

The comparison of modelled hydrodynamic drag with experimental measurements in the literature is presented in detail in Supplementary material SM2. Although the experimental values are of combined hydrodynamic and geotechnical drag, we isolate measurements for tickler chains, chain mats and the gear netting at higher speeds where we assume the contribution of geotechnical drag is minimized.

The correspondence for tickler chains and chain mats is reasonably good. The ratio between the modelled and measured drag of Blom , tickler chains is 1. The discrepancy is larger for the netting panels, and the modelled drag of Blom net is 1.

The silt fraction of the fishing grounds of PUL is intermediate. Small vessels, which mainly fish within 12 nautical miles from the coast, trawl sediments with a lower silt fraction when compared to large vessels using the same gear type, except for small TBC trawlers that fish in areas with a slightly higher silt content.

Figure 4 shows the estimated sediment mobilization and the contribution of the main gear components for the gear types taking account of the modelled hydrodynamic drag and the silt fraction distribution of their fishing grounds. Small vessels mobilize between 4. Sediment mobilization by large vessels, estimated between 4.

The relative contribution of gear components to the sediment mobilization reflects the differences in hydrodynamic drag of gear components by gear type. The bars show the standard deviation of the sediment mobilization of the whole gear.

Taking account of the proportion of vessels deploying a certain beam trawl type Table 2 , the sediment mobilization of an average vessel of the Dutch beam trawl fleet is estimated at 9. For small vessels, sediment mobilization of a conventional beam trawler 4. To contextualize these values, if we assume the sediment has relative density of 2. The application of our methodology to the Dutch beam trawl fishery in the North Sea showed that the innovative pulse trawl that replaced mechanical stimulation of sole by tickler chains or chain mats with electrical stimulation reduced the hydrodynamic drag of the gear and the amount of sediments mobilized in the wake of the trawl of large trawlers but not of small trawlers.

Among the conventional beam trawlers, TBC mobilizes less sediments, despite the higher hydrodynamic drag, than TBT because this gear type is used on fishing grounds with low silt content. Pulse trawls are more efficient to catch the target species sole Poos et al.

The lower hydrodynamic drag of the pulse trawl is due to the combined effect of the replacement of tickler chains running perpendicular to the towing direction with longitudinal electrodes and the reduction in towing speed. The reduction in hydrodynamic drag is to some extent counteracted by the larger twine surface area of the pulse trawl nets and the larger surface area of the ground rope in pulse trawls. The use of pulse gear requires a rectangular matrix of electrode arrays to generate a stable electric field, constraining the type of ground rope to be used.

Three types of ground ropes evolved. The reduction in catch efficiency, however, may be compensated by the smaller disk diameter of the additional sole-rope, which is expected to better follow the bottom profile and reduce the possibility of the fish escape underneath the sole rope. The different ground rope rigging types used are related to the fishing grounds. Vessels from the northern harbours predominantly use the U-shaped ground rope and sole-rope.

In the mid-south and mid-north vessels use a rectangular or U-shaped ground rope and the vessels from the south use rectangular ground ropes. The overall hydrodynamic drag of tickler chain and chain mat beam trawls is comparable, but drag varies between individual gear components. Chains are contributing nearly equally to the overall hydrodynamic drag while the netting panels are more important in tickler chain trawls. The ground gear is conversely causing a higher drag in chain mat beam trawls.

The results of the current study are representative for the Dutch beam trawl vessels targeting sole and will likely be representative for the entire North Sea beam trawl fleet, which is largely comprised of Dutch owned vessels that were re-flagged to exploit the UK, German, and Belgian quota.

We must be aware of the limitations of our approach. The of silt fraction estimates are interpolated values from a range of data sources complied by Wilson et al. We downscaled these data to the resolution used in our study 0. There are also a number of uncertainties associated with the hydrodynamic drag estimates. For many of the gear components, their drag coefficients are estimated from experiments; i on idealized bodies that are similar to, but not exactly the same as the gear component e.

The approach further assumes that the hydrodynamic drag of the individual gear components are additive and that there is no interference between them Paschen et al. All these factors will affect the hydrodynamics, and the corresponding drag estimates and sediment mobilization estimates must be used with caution. Indeed, the validation of our approach showed, through comparison with literature estimates, that realistic hydrodynamic drag estimates were modelled for gear components, such as beam, shoes, wings, electrodes, tension relief cords, etc.

However, further research is required to study the hydrodynamic drag of components such as the beam trawl net panels. The discrepancy between the modelled and measured drags may be due to the fact that the typical beam trawl towing speeds are greater than the maximum speed of about 4 knots 2. This differs from the otter trawl nets used by Reid , whose netting panels will have a larger angle of attack and hence will be less streamlined and in turn will have a greater drag. Chafers and dolly ropes were not included in the analysis, but may in turn increase the drag of beam trawl nets.

Hence, because pulse trawlers have a lower total catch volume than conventional beam trawlers van Marlen et al. The accuracy of the model predictions will also be affected by the quality of the gear component data. The dimension of the various beam trawls in this paper have been presented to active fishers and gear manufacturers and we are confident that they are representative of the fleet, in particular for the pulse trawls PUL and the tickler chain beam trawls TBT used by large vessels. The sample size of the TBC and the TBT used by the small vessels was limited rendering the quantitative results for these trawls less certain.

In spite of the limitations of our approach, our model-based estimates of the difference in the amount of sediment mobilized in the wake of a tickler chain beam trawl and a pulse trawl, showed good agreement with in situ field estimates Depestele et al.

Hence, although there is uncertainty associated with some of the hydrodynamic drag estimates, we expect that our methodology provides a good approximation and will be particularly useful in capturing the relative differences between gears. We are confident that our approach provides reasonable estimates of the quantity of sediment mobilized by different gears, which, as we have shown here, are particularly useful when used with information on different gear types, spatial and temporal fishing effort data and spatial sediment data, to estimate the differential impact of trawling at the fleet level.

This will provide policymakers and fisheries managers with a quantitative means to assess the physical impacts of different fishing gears and fishing methods across sediment types. It will allow the ranking of gears in terms of their impact and permit a direct comparison with the physical impact of natural events such as storms and tides and of other uses of the seabed such as mineral extraction and mining.

Accordingly, it will permit a rationale and objective approach to fulfilling the requirements of the Common Fisheries Policy and the Marine Strategy Framework Directive. Our approach could also be used to provide estimates of trawling-induced sediment mobilization for mechanistic models of biogeochemical cycles de Borger et al.

Furthermore, the hydrodynamic drag estimates will provide a better understanding of the forces required to tow a trawl gear across the seabed and contribute to the development of fuel-efficient gears that will reduce CO 2 and NOx emissions by the fishing industry. Primary VMS-data and catch and effort data of the mandatory logbook are subject to confidential agreements. An exerpt of anonimised data will be shared on reasonable request to the corresponding author.

Rijnsdorp, A. Sediment mobilization by bottom trawls: a model approach applied to the Dutch North Sea beam trawl fishery. Lokker Cooperatie Westvoorn , H. Drijver and a number of individual skippers are gratefully acknowledged for providing information on gear dimensions. We tank Niels T. Hintzen for providing an updated data set with swept area ratios by grid cell for conventional tickler chain and chain mat beam trawl.

Aldridge J. Assessment of the physical disturbance of the northern European Continental shelf seabed by waves and currents. Continental Shelf Research , : — Google Scholar. Amoroso R. Blom W. Weerstand van boomkortuigen. Rijksinstituut voor Visserijonderzoek Report TO Weerstandscomponenten van een boomkortuig voor kW. Rijksinstituut voor Visserijonderzoek Report TO Bolam S.

Differences in biological traits composition of benthic assemblages between unimpacted habitats. Marine Environmental Research , : 1 — Brent R. Algorithms for Minimization without Derivatives. Brylinsky M. Impacts of flounder trawls on the intertidal habitat and community of the Minas Basin, Bay of Fundy. Canadian Journal of Fisheries and Aquatic Sciences , 51 : — Clark M.

The impacts of deep-sea fisheries on benthic communities: a review. Collie J. Indirect effects of bottom fishing on the productivity of marine fish. Fish and Fisheries , 18 : — Impact of bottom trawling on sediment biogeochemistry: a modelling approach. Biogeosciences Discuss , : 1 — Environmental impact of bottom gears on benthic fauna in relation to natural resources management and protection of the North Sea. NIOZ Report Pulse trawl fishing: characteristics of the electrical stimulation and the effect on behaviour and injuries of Atlantic cod Gadus morhua.

Depestele J. Comparison of mechanical disturbance in soft sediments due to tickler-chain SumWing trawl vs. Measuring and assessing the physical impact of beam trawling. Eigaard O. Estimating seabed pressure from demersal trawls, seines, and dredges based on gear design and dimensions.

The footprint of bottom trawling in European waters: distribution, intensity, and seabed integrity. Engelhard G. One hundred and twenty years of change in fishing power of English North Sea trawlers. Blackwell Publishing , London. Google Preview. Ferro R. Fonteyne R. Huidige vistuigen en visserijmethodes in de Belgische Zeevisserij. Rijkstation voor Zeevisserij, Oostende. Haasnoot T. Fishing gear transitions: lessons from the Dutch flatfish pulse trawl.

Harris P. Seafloor Geomorphology as Benthic Habitat. Elsevier , London, UK. Hiddink J. The sensitivity of benthic macroinvertebrates to bottom trawling impacts using their longevity. Journal of Applied Ecology , 56 : — Global analysis of depletion and recovery of seabed biota after bottom trawling disturbance.

Hintzen N. VMStools: open-source software for the processing, analysis and visualisation of fisheries logbook and VMS data. Fisheries Research , — : 31 — Hoerner S. Fluid-dynamic drag. Published by the author. Horwood J. Advances in Marine Biology , 29 : — Jennings S. The effects of fishing on marine ecosystems. Advances in Marine Biology , 34 : — Jones J.

Environmental impact of trawling on the seabed: a review. Kaiser M. Prioritization of knowledge-needs to achieve best practices for bottom trawling in relation to seabed habitats. Fish and Fisheries , 17 : — Lambert G. Implications of using alternative methods of vessel monitoring system VMS data analysis to describe fishing activities and impacts. Lucchetti A. Impact and performance of Mediterranean fishing gear by side-scan sonar technology. Canadian Journal of Fisheries and Aquatic Sciences , 69 : — Mayer L.

Effects of commercial dragging on sedimentary organic matter. Marine Environmental Research , 31 : — Mazor T. Trawl fishing impacts on the status of seabed fauna in diverse regions of the globe. Fish and Fisheries , 22 : 72 — Mengual B. Ocean Dynamics , 66 : — O'Neill F. The physical impact of towed demersal fishing gears on soft sediments. Cod-end drag as a function of catch size and towing speed.

Fisheries Research , 72 : — The mobilisation of sediment by demersal otter trawls. Marine Pollution Bulletin , 62 : — The hydrodynamic drag and the mobilisation of sediment into the water column of towed fishing gear components.

Journal of Marine Systems , : 76 — Oberle F. There are 12 components in state vector ; thus, the virtual control inputs of all of the state variables can be defined as. Then, the tracking error of the trawl system can be written as. The midwater trawl system is a high-order nonlinear system. To obtain the control instruction of the whole system, the state space model is divided into six subsystems. The principle of system division is that the lower-order subsystem stabilization relies on the next higher-order subsystem.

From the target trajectory to the control instruction , the six subsystems are based on the dynamic equations of the trawl net, the two otter boards, the trawler, and the two trawl winches, respectively. Based on the physical relations of the six subsystems, Figure 3 shows the demand relationships of the key virtual control inputs. The Lyapunov functions, which are related to the control objectives, can then be built with the following steps.

Step 1. For the first subsystem, the Lyapunov function is given by The time derivative of is The virtual control inputs can be defined as where the control parameter. Equation 11 is plugged into 10 , and the derivative of is. Step 2. For the second subsystem, the Lyapunov function is given by The time derivative of is The traditional backstepping method can only be applied to the strict feedback form of nonlinear systems.

However, in 14 , the high-order state variable appears. Thus a new variable is introduced, which is defined as. The new virtual control inputs can be embodied as where the control parameter. Equation 15 is plugged into 14 , and the derivative of is where.

The variables and are the ideal position vectors of the two otter boards. To deduce their expressions from , these two otter boards are assumed to move at the same depth underwater such that and in the -direction. In addition, assuming that the extension ratios of the ropes are consistent in three directions, the variables and in the - and -directions can be expressed as. Step 3. For the third subsystem, the Lyapunov function is given by The time derivative of is The two virtual variables can be defined as where the control parameters ,.

Equation 20 is plugged into 19 , and the derivative of is. Step 4. For the fourth subsystem, the Lyapunov function can be defined as The time derivative of is In 23 , the high-order state variables and appeared. Similar to Step 2 , new variables can be introduced as The corresponding virtual control inputs can be defined as For one vector , two expressions can be derived from Unfortunately, the tensions of the two warps are not equal when the vessel is turning, which leads to a conflict in solving.

Moreover, 25 is based on the physical interpretation of force and displacement; however, the physical interpretation of is the -coordinate, the -coordinate, and the yawing angle of the vessel on the target trajectory. Therefore, the physical meaning of 25 in the -direction is not correct. Take , for example; the trajectory tracking error of the trawl net can be used as control inputs. Then, the output of controller for can be expressed as where the control parameters are the nonlinear functions of.

Considering the physical significance of and , the deviation between the actual tension and the ideal tension of the warps can be used as control inputs. The controller outputs for and are similar to Plugging the expressions of these variables into 23 , the derivative of can be found by. Step 5. For the fifth subsystem, the Lyapunov function is given by The time derivative of is Three virtual variables can be defined as where the control parameters , and ,.

Plugging 31 into 30 , the derivative of is found as. Step 6. For the last subsystem, the Lyapunov function is written as The time derivative of is The controlled quantities of the trawler and two winches can be defined as where the control parameters , and ,. Thus, the three-dimensional trajectory tracking controller of trawl system has been acquired. To indicate the trawl system stability under the bounded input signal and external environment disturbance, three disturbance terms are added to the state model.

Then, the expressions of , , and in 7 can be rewritten as where , , and are the disturbing forces on the trawl net and two otter boards. For the condition that nonzero bounded disturbances often exist in trawl system, the Lyapunov function can be defined as. Through 39 it can be seen that the tracking error is global uniform ultimate boundedness, and the state of the system converges to the origin of a small domain in the stable area in the presence of interference with an unknown upper limit.

The trawl system is assumed to move in the uniform flow. The parameters of the trawl system are listed in Tables 1 and 2. The simulation time is set as. Figure 4 shows the trajectory tracking of the trawl net when the approached control algorithm is adopted. It can be seen that the trawl net tracks the target trajectory of 40 well. Because the coordinate values of the trajectories are much larger than the tracking error, the tracking errors in three directions are individually shown in Figure 5.

The mean absolute errors of tracking error in the -direction, -direction, and -direction are Obviously, the tracking errors of the horizontal displacements are much larger than those of the vertical displacement, mainly because the horizontal positions of the two otter boards have no direct relation with the trawl net, and the control inputs of the otter boards in the - and -directions are derived from assumption in Moreover, Figure 5 shows that the track error is cyclical; in a real-world situation, the large size of the trawl net can compensate for the tracking error in the horizontal directions.

Figure 6 shows the trajectories of the two otter boards. It can be seen that the curved shapes are similar to the trajectory of the trawl net. This movement coordination between the otter boards and the trawl net is beneficial for system stability. Figure 7 illustrates the velocity curve of the trawler.

Although the trawler has frequent speed changes, the velocity is in a reasonable range. The average speed is 2. Figure 8 presents the dynamic changes of the lengths of the two warps. The maximum and the minimum lengths of the two warps are reasonable and bounded.

Figures 9 and 10 are the thrust change curve of the trawler and the torque curves of the winches, respectively. It can be seen that these control signals have varying degrees of trembles. Compared with the response times of the ship propeller 0. To further illustrate the performance of the improved backstepping method and test the robustness and adaptive ability of the proposed controller, a traditional linear PID controller based on the proposed simplified model is considered.

A simulation contrast verification is presented while considering the interference of the external environment. The target trajectory for the comparison simulation uses 40 with a shorter simulation time. The disturbing forces and are considered as the same constant value, which is in the -direction and -direction.

Respectively, acts on the left otter board over the period of , and acts on the trawl net over the period of. Consider that the resistance coefficients of the otter board and the trawl net are time varying, and and are redefined as where , , and. When disturbing forces are exerted on the trawl system, the trajectories of the trawl net are produced by these two controllers, as shown in Figure Figure 11 a is the simulation result of the linear PID controller, and Figure 11 b is the simulation result of the improved backstepping controller.

It can be seen that when the disturbing forces exist, the path deviation in Figure 11 a is significantly less than the deviations in Figure 11 b , and the path deviation in the -direction is larger than the deviations in the - and -directions. After the disturbing forces disappear, the path deviation is quickly eliminated under the action of the improved backstepping controller, whereas the control process of linear PID controller is very slow.

By adjusting the PID parameters, the oscillating amplitude of the path curve cannot be eliminated effectively. In this paper, a three-dimensional trajectory tracking control approach of a midwater trawl system is proposed. First, according to the actual working status of a single-boat midwater trawl system, a four-material-point simplified model is presented. Second, a compound nonlinear controller is designed, based on the backstepping method.

In the process of recursion, the high-order state variables are gradually eliminated. The theoretical identification and simulation illustrate the effectiveness and convergence of the proposed control method.

The movement consistency of the trawl net and otter boards is displayed. Under the action of an external disturbance, the depth displacement of trawl net is larger than the horizontal displacements. Compared with the traditional linear PID control method, the improved backstepping control strategy has higher control precision and stronger robustness.

In the future, an experimental demonstration will be presented. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors.

Read the winning articles. Journal overview. Special Issues. Academic Editor: William MacKunis. Received 09 Apr Accepted 11 Aug Published 07 Sep Abstract An improved backstepping control method for three-dimensional trajectory tracking of a midwater trawl system is investigated. Introduction Single-boat midwater trawl systems have occupied an important position in pelagic fisheries.

Three-Dimensional Kinematic Model of the Trawl System A trawl system is a combination of a rigid body and a flexible body. Figure 1. Figure 2. Figure 3. Quantity Symbol Value Mass of trawler ton Mass of otter board ton 5. Table 1. Table 2. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. Figure 9. Figure Trawl system tracking trajectories with disturbing force.

References H. Ablow and S. Gobat, M. Grosenbaugh, and M. Gobat and M. View at: Google Scholar F. Hu, T. Tokai, and K. Johansen, O. Egeland, and A.

#### Bottom trawls impact the seafloor and benthic ecosystem.

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Recommendations binary options | Xu, M. Very little is known, however, regarding the drag coefficients of beam trawl components. Table 3. Journal of Sea Research46 : — Figure 1. For many of the gear components, their drag coefficients are estimated from experiments; i on idealized bodies that are similar to, but not exactly the same as the gear component e. |

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