Subject: [harryproa] Lucs Proa
From: "Rick Willoughby rickwill@bigpond.net.au [harryproa]" <harryproa@yahoogroups.com.au>
Date: 4/28/2016, 4:45 AM
To: "harryproa@yahoogroups.com.au" <harryproa@yahoogroups.com.au>
Reply-to:
harryproa@yahoogroups.com.au

 

Luc
I had some time and enough interest to take a closer look at the reserve buoyancy question.

The conditions considered:
Hull length 15m
Maximum beam 0.43m
Boat displacement 1000kg all carried on this hull
Total Volume 2000 litres
CoE 7m above water level
Sail Area 30sq.m
Hard chine flat bottom
Sailing to windward at 50 degrees to waves and 30 degrees to apparent wind. (This may not necessarily be the worst case.)

With 100% reserve buoyancy the boat starts to dive above 12kts of wind.

With 200% reserve wind gets above 15kts before diving begins.

With 300% reserve, wind can get to about 20kts before the hull dives. The peak vertical acceleration in this case is 1.7g so this might be a limiting factor. For a 1000kg boat with flat bottom and rocker there would be significant dynamic lift with the forward motion associated with 20 knot wind that this model does not take into account. Also I do not check that there is sufficient righting moment to carry full sail for given wind strength. In all probability the sails would need reefing and then the CoE is lower.

Some points to note:
1. The lower the reserve buoyancy the smoother the ride. In 12kts wind the boat with 100% reserve buoyancy will have peak vertical acceleration of 0.3g while the 300% reserve gives peak vertical acceleration of 0.5g.

2. One of the not so obvious aspects with only 100% reserve buoyancy when in bigger waves is that the upward acceleration of the CoG is always less than 1g but the downward acceleration can equal 1g if the hull becomes fully airborne. That results in net negative heave. Meaning the hull rides deeper in the water.

2. The hull with lower reserve buoyancy has less added drag from pitching up to the point where the heave is net negative.

3. For generating wave height in this model I assume open water conditions and wind speed for wave generation equals apparent wind speed for determining wave height and wave celerity.

4. For the proa I have taken the LCG to be the middle of the boat.

5. The metacentric height for the chosen waterplane is 87m. Being so high means that it can submerged the nose in a gust and still recover statically. Dynamically it depends on the shape of the deck as well, particularly when forced into the back of a wave when running. The model does not consider any dynamic downforce caused by submerging the deck. However I know from experience that a flat deck will dig in and drive deeper.

In summary this confirms what I had expected from my experience with particular hulls.

One way to increase reserve buoyancy without increasing deck height, length or waterline beam is to flare the sides. This also reduces the wetter surface compared with vertical sides. You could also just put more volume in the ends using raised foredecks and leave the middle lower. The height in the bows has much more influence on avoiding a dive than the volume in the middle:
http://cf.gcaptain.com/wp-content/uploads/2013/09/PX121-Pacific-Radiance-InAir-PS-Fore-Low.jpg

Rick

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Posted by: Rick Willoughby <rickwill@bigpond.net.au>
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