31 March 08 Weekly Whiffle

Dear all,

I’m interested in reading all of this. I’m afraid I will not be an early adopter but might be a close follower.

Another idea I considered, and most likely without merit, but the idea is this. I found a company that makes a pourable two- part closed cell foam that does not expand.   My thought was this. Fill in the area in the rear tank which is lower than the floor with closed cell foam to make the two level. Finish the closed cell foam with epoxy to seal. Then make opening in the rear cockpit bulkhead and the transom. I would then add long air buoyancy bags fore to aft, along the inside of the cockpit. You lose some cockpit utility and when you cruise everything needs to be in dry bags.
This sounds like the final result might sort of approximate the Hartley W ... except they use permanent side flotation tanks and smaller holes.  I wouldn't do this nor recommend it... It would weaken the structure of the boat and wouldn't improve the self drainage if at all... in fact I think the boat would sink lower as air bags would tend to pull upwards away from the floor and would require greater depth of water to be effective than the fixed tank. It would get water out fast once underway but would seem to me to have significant disadvantages, and is really serious and unnecessary surgery on the boat, not to mention not covered by the rules. Al's note: side buoyancy also tends to make the boat want to invert/turtle and might well make it hard/impossible to get back onto the board from a swimming position that you sometimes can end up in.

My thought would be that upon righting the boat the water would automatically flow aft and I would hope out. I would make the opening large enough that the water flow would be very fast. How fast? Good question.
As noted in my initial email I think the boat will only recover to the sink depth it would achieve if you got in and opened the floor bailers.... I kind of suspect this will result in about 4" of water in the boat .... and should be the depth eventually achieved after natural drainage of the likely higher post-capsize water level through the drain tubes. But the head difference is very small and thus the driving force to drain relatively low. The real advantage of stern drainage comes when the boat starts moving and some 'suction' effects start to come into play to remove the water.

A 4” round hole say 24” long offers a volume of 4.93 liters x 2 = 9.86 liters. That would be the bottle neck. The volume shouldn't much matter, it's the flow rate through the opening that should be most relevant... and one could jam a lot of water through two 4" dia. holes.

I guestimate that if you had 6” water in the cockpit you would have 424 liters of water also 424 kgs or 932 lbs. ( 72” long x 60” x 6”) Here’s where it gets tricky and keeps me awake at night.   To clear the boat of the water you need to slightly sink the transom. The water rushes aft further sinking the transom. Will there be enough floating moment ( sorry, real engineers) in the aft half of the boat to clear water?
Not sure what you mean by clear the water. I don't think you can clear the boat of water ... with you and crew in it and an open hole to the lake it can only recover to the equilibrium position as noted above. That however should be less water than after the capsize which is anywhere up to a foot. Say the back tank is 5' wide and 2' long. Probably about 1.5' high. Completely submerged, that will provide about 940 lb of buoyancy.   The advantage of the drain tubes comes in rapidly clearing the water once the boat is moving... it usually takes some time to drain through the floor bailers once sailing.... stern tubes would just significantly decrease that by allowing the water to exit the boat quickly... not so much by gravity, but what would seem to me primarily the suction forces created by the boat motion.

My concern is that upon the initial slosh aft the back of the boat would sink and then a certain equilibrium achieved where no water would leave.   Any part of the boat that is out of the water is of no value in terms of lifting the partially sunk part.
This would seem true whether a drainage tube exists or not.

If I were doing this as an experiment, I would do the following.

1)       On the average capsize with a boat that has air tanks in good working order, what is the volume of water in the boat, and therefore the weight?
2)       Given this volume of water, and the top of the rear bulkhead as a limiting factor ( more than that the water sloshes over), where would the water reach in the cockpit? In cross section, the water would look like a triangle.
3)       Given this information, you could determine the weight of water per linear inch of cockpit which would increase as the measurement moved aft.
4)       The next question would be, what volume of air do you need to offset a liter, and therefore the total volume of water in the cockpit?
a litre of air would displace a litre of water... but that is not presumably what you mean?
5)       More importantly, what is the volume of air in a Mk II and where is it in the boat? Where is it in reference to where the water is in the cockpit?
6)       I would think that it would be important to match flotation volume to water volume and that the volume of air should have a positive lifting value versus the water in the cockpit.
7)       If you could demonstrate that with the average or even worst case water volume in the cockpit, sloshed to the back of the cockpit, at max. height, that there was a positive lifting energy (sorry, real scientists) versus the weight of the water, then you could argue that there would be a positive flow out of the cockpit.

Regardless of boat position there should only be positive water flow out of the boat if the level of the capsize water is higher than the boat would normally have with the bailers open ... i.e. with empty Mk III boat and bailers open ... no water... Get in and wait and eventually you have what? 4" depth?. Any water level higher than that after a capsize will want to flow naturally out of the boat... but the boat cannot completely drain no matter what static position you put it in. The rationale for the stern tubes is not self drainage but get the boat moving and add the suction and dynamic effects that allow the bailers to work. Big drain tubes .... now you have fast drainage.   That's how it seems it would work to me anyways.

The good news is that once water began to flow that the ratio of weight to buoyancy would only get better. Sounds like an excellent Calculus problem. Unfortunately I’m a liberal arts major from Farmville, Va.

I think until we can answer these questions, or perhaps even more relevant questions posed by a real engineer or scientist, that any change to the boat would only be an educated guess. This is why I hesitate to do anything. I like the idea of the bailers (Al's note: drain tubes???). I think it would add to safety, I think it would work, but I think there are some fundamentals that need to be looked at first.

Kind Regards to all

Richard Johnson

That is quite an experiment and some pretty mean calculations. I'll make only slight claim to being a real engineer and alas, I've forgotten most of the calculus that got me through engineering school (which for their continued reputation I will not name) but I'll take a stab at this. I might have to make a few assumptions that will no doubt be appalling to the more learned but please bear with me (not to mention forgive).

Firstly .... the formula for drainage from a tank at atmospheric pressure (hopefully fairly safe to assume) is generally dictated by the following differential equation:

to make things more difficult, however, the tank (cockpit) volume is also changing as we sink the stern, but if we consider it to primarily be triangular under the conditions described then it is clear that we can use the following:

Secondly the rearward sloshing of the water can probably best be approximated by this graphical relationship

Combining these two aspects, we can quickly see the water volumetric shape closely resembles the following

A little bit of elementary calculus will help define the volumetric change rate of the cockpit water with time

After expanding the formula with some turbulent fluid flow relationships primarily defined by:

... the next step clearly is substitution into the original differential equation for drainage, integrating, and solving for the resulting unknowns to easily provide the answer. Rather than bore you with the final calculations, the results of this are probably best illustrated in pictorial form.

One more commonly sees another method of calculation utilized by those not so enamoured with the intricacies and joys of integral calculus.

PS ... the only part of this bs I even partly understand is the first equation... which actually is for drainage out of a tank. It's amazing what Googling 'calculus equations' can come up with. I doubt this adds much to the discussion but I had fun with it. Enjoy.

cheers

Andrew
W9657