The interaction between a breaking wave and a boat hull is a complex phenomenon. A mathematical model of this event is probably beyond current capability. However, what we are really interested in is obtaining a good estimate of the maximum load for use in designing the drogue and the attaching equipment. Fortunately the model tests have revealed a very important fact which permits us to greatly simplify this problem. The tests clearly show that whenever the boat is struck by a large breaking wave (large enough to cause capsize without a drogue) the boat is driven up to wave speed before the drogue builds up any appreciable load. Thus in estimating the maximum drogue load we can assume that the boat is moving at wave speed and calculate the force necessary to decelerate it. From the model tests we have determined which forces are important during the deceleration process. These forces are shown on Figure 10. There are two distinct phases. In the first phase, the boat is riding on the breaking crest and the drogue must pull it backward over the top of the wave. The important forces are the horizontal component of the buoyancy force (FB) and the inertia force (ma) as the boat is decelerated by the drogue. in the second phase the boat has been pulled over the top of the wave and is being dragged through the fast-moving water of the breaking wave crest. The important load during this phase is the hull drag force (FH) . The relative speed between the boat and the water is several times the hull speed of a displacement hull, so the drag force will be high.

A simple breaking wave simulation using the forces shown on Figure 10 is included in Appendix B. It is assumed that the event begins with the boat riding the wave crest at a certain angle to the horizontal and moving at wave speed (V3) . This phase continues until the boat is pulled through the wave crest for a specified distance. Then the boat is assumed to be essentially level at the top of the wave and is pulled by the drogue through water moving at wave speed. Wave height does not appear in this simulation but is represented by the assumption that the height is sufficient to drive the boat up to wave speed.

Model test results of drogue load against time were checked against this simulation. In general the correlation was acceptable. A typical comparison is discussed previously in this report. Although the simulation is highly simplified, it does logically represent the important forces and it should be highly useful in predicting maximum loads and in obtaining an understanding of the influence of various parameters on the maximum drogue load during a wave strike.

Figures 24A and 24B present calculated maximum drogue loads for a variety of conditions. As a reference for comparison purposes the following conditions were chosen:

- 30-foot boat, displacement 7500 lbs.
- 4-foot diameter parachute-type drogue
- 250 feet of 3/4-inch nylon towline (K=200 lbs/ft)
- 200-foot wave length 300 lbs. of wind drag
- Slope of boat on wave crest = 20 deg. (SL=-.36)

A breaking wave with a wave length of 200 feet will have a crest velocity of 32 ft/sec. Full-scale experience and model tests clearly show that such a wave can capsize a small sailing yacht. The breaking waves in the Fasten storm may have been even of longer wave length but no actual data were obtained. A 4-foot diameter drogue was chosen as being near the minimum acceptable size for a 7500 lb. boat. The towline elasticity represents the dynamic behaviour of 250 feet of 3/4-inch nylon double braid, the smallest line with adequate strength. The 20 degree slope of the boat when riding at wave speed on the wave crest is a reasonable value obtained from model test.

Figure 24A presents drogue load against time for the reference conditions. The load peaks at 5600 lbs or 75% of the displacement. This compares with a maximum load of 1500 lbs for the same boat and drogue riding on regular 20-foot waves with a length of 200 feet. As mentioned previously, it is felt that the 1500 lb. figure may be too high because more damping exists in the real case than in the simulation. However, there is no reason to believe that the 5600 lb. figure is too high.

Figure 24B shows the effect of drogue size on maximum load. Increasing the drogue diameter from 4 feet to 12 feet increases the load by 50%. It is clearly advisable to use the smallest drogue which will prevent capsize.

Figure 24C shows the effect of towline stiffness on maximum load. Some sailors believe that a highly elastic towline will reduce the drogue load. This may be true in regular non-breaking waves, but in a breaking wave strike the effect is small because the boat rides the wave front and stretches the line until the load builds up. Actually the model tests show that a highly elastic line is very undesirable because the boat may be capsized before the load builds up.

Figure 24D shows the effect of wave crest slope on the maximum drogue load. Ref erring to Figure 10, Phase 1, for a brief instant at the start of the event the boat is poised on the wave crest and is moving at the same speed as the wave. There is no significant vertical velocity or acceleration. The forward component of the buoyancy force is a function of the wave slope. This is a large force, equal to half the displacement at a slope of 27 deg. (SL=-.5). For the type of wave used in this investigation the model often reached a slope of 20 degrees before being pulled over the crest.

Figure 24E shows the effect of wave crest velocity on maximum drogue load. This is an important variable because the boat must be decelerated from this speed by the drogue, and both the inertia loads and the hull drag are a function of this velocity. Figure 24E also shows a scale f or the wave length of regular waves which would correspond to a particular crest velocity. However, a breaking wave is formed by the addition of two or more storm waves. For a storm such as the Fastnet we have no information on the crest velocity of the dangerous breaking waves. It is reasonable to believe that the velocity would be no higher than that of waves with the longest length and probably would be somewhat lower.

An increase of crest velocity from 30 to 40 ft./sec. would increase the maximum drogue load by 35%.

Figure 24F shows the effect of boat size or displacement on drogue load. For this simulation it was assumed that all the pertinent variables were scaled up with boat size. The drogue diameter was scaled up as the boat length or as the cube root of the displacement. The hull drag factor, towline elasticity and wind force were also scaled up.

If the displacement is increased from 7500 lbs. (30foot boat) to 30,000 lbs. (48-foot boat) the drogue load is increased by a factor of 3.4. Here we must make a judgement based on experience. The incidence of breaking wave capsizing decreases sharply with an increase in boat size or displacement. Many 30 to 40-foot boats have been capsized but very few boats over 60 feet have been capsized by a breaking wave. It is apparent that there are few breaking waves with enough momentum in the crest to drive a 60-foot boat up to wave speed. Thus in choosing a drogue size it is reasonable to decrease the relative size as displacement increases. With this policy the maximum drogue load need not increase as much as shown on Figure 24F.