5.2 Boat & Drogue in Regular Waves
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        In a storm, the boat and drogue must ride for a long period of time in large non-breaking waves, possibly as high as 20 to 30 feet. There are many reports of the towline chafing and breaking or the drogue being ripped to pieces after several hours under these conditions. We are interested in understanding the cyclic motion of the boat and drogue, and the variation of load and slack in the towline.

        Exploratory calculations were made using several mathematical models. The model finally chosen is shown on Figure 21. It is intended to represent a condition in which the wave length is much greater than the length of the boat; for example, a 30-foot boat riding on waves with a wave length of 200 feet or more. Experience suggests that this condition exists in all storms where there is a significant possibility of breaking wave capsize. Several simplifying assumptions can be made with this wave and boat geometry:

  1. The buoyancy force is assumed to act normal to the wave surface at the boat location.
  2. Pitching motion of the boat is neglected since the period of the wave is far greater than the natural period of the boat in pitch.
  3. Since the drogue is far behind the boat the towline load is assumed to be horizontal. Vertical components of load are neglected.

        A typical program is included in Appendix A for a boat riding on regular waves with a trochoidal-shaped profile. Similar programs were studied for waves with profiles of a sine wave, a cycloid, and certain arbitrary shapes intended to represent photographs of particular storm waves. Variation of boat displacement, drogue size and geometry and towline elasticity were also studied.

        Figure 22 shows the drogue load and towline slack for a 30-foot boat with a 4-foot diameter parachute drogue in regular trochoidal waves with a wave length of 200 feet and wave heights of 10 and 20 feet. Figure 23 shows the same boat and drogue in waves with a length of 80 feet and a height of 8 feet. The drogue exerts a load as the boat passes over the wave crest and the towline goes slack as the boat traverses the trough. Similar results are obtained with a variety of wave shapes. The peak load increases as we increase the boat displacement, drogue size, and stiffness of the towline.

        No full-scale data are available to check the validity of this simulation, but sailors who have used drogues under storm conditions report that the peak loads did not appear to be high and the towline did not seem to go very slack. This suggests that there is more damping in the actual case than in the simulation, which makes sense because there are small surf ace waves superimposed on the large wave and these are not included in the simulation. Also in the actual case the waves are not regular and this would diminish the cyclic motion. It seems reasonable to conclude that the simulation could be considered a worst case, and the calculated cyclic loads could be used as design loads for fatigue strength and chafing resistance. Actual loads should be somewhat lower.