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 nonbreaking 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
30foot 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:
 The buoyancy force is assumed to act normal to the wave surface at
the boat location.
 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.
 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
trochoidalshaped 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 30foot boat with a 4foot 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 fullscale 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.
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