Advice needed on trimaran

2 percent? Alright, that seems easy enough. Thank you.

I'm sorry, I don't quite understand this.

Let's say these are related parameters:
Ama displacement: 200kg = 440lbs
Beam length: 1.5m = 4.92ft
Maximum wind speed with full sails (no reefing): 3 on Beaufort scale (up to 20 km/h).

So how do I determine the sail size that will require reefing only when wind speed exceeds 20km/h?

So, max righting moment is 440lbs * 4,92 = 2162,8 (lbs?)
If sails generate 1.5lbs (with safety) per square feet, then max sail area is 1443,2 square feet (439,9 square meters).

That can't be right... And it doesn't include center of gravity (crew shifting position), height of CE above deck... Factors which can radically change possible sail area...


I must have misunderstood something, at least I tried, but could you please correct me? With the parameters I mentioned before, how do I determine maximum sail area in winds up to 20km/h?

 

you are calculating righting moment vs. overturning moment. they must match in order to stay up-right without reefing.

so max righting moment is 440 x 4.92 ft = 2165 ft-lbs

plus you have weight of crew, say 250 lb, that can get their weight 2 ft off centerline on oppsite side. 250lb x 2 ft = 500 ft-lbs

total righting moment available: 2165 + 500 = 2665 ft-lb.

you need the height off the water for the center of effort for the sails. This should be about the height of one third the way up from the boom to the top of the sail (the centroid of a triangle).

1443.2 SF of sail can not be correct! you must mean 144.3 SF? I will assume that. 144.3x1.5= 216.45 lb later load on sail. lets assumed the centroid of the sail is 7 ft high, so overturning moment is 7x216.45 = 1515 ft lbs. so this is under 2665 ft-lb so you will not have to reef to keep the hull up right. this also means that the ama will have plenty of free board and will not be dragging the beams in the water at this wind speed.

I would also check max over turning of the hull plus ama combo, what we verified above was the ama will not submerge. Take total weight of boat, plus gear and crew, and times the 4.92 beam length. You will want to consider lightly loaded with solo operation, since that is when you are more likely to roll it over. 170 lb solo crew, 250 lb boat weight = 420 lb. times 4.92 ft = 2,066 ft lbs. Still okay for solo operation, and this also means you can fly on one ama since it has 440 lb displacement capacity and your total weight is only 420 lb, so it will stay above the surface.

you will have to make your adjustments for estimated boat weight, and height of CE of the sail. but this is how it works. fairly simple.

 

Thank you, this is a little over my head right now, I'll figure it all out in a day or two.

Just one quick remark - I noticed that you didn't include wind speed anywhere in this calculation, so how does all this calculation relate to the wind speed?

My guess is that pressure on sail (the one you referenced "1 lb per square foot of sail area (plus a 1.5 safety factor)") changes according to the wind speed, right? If so, what is the wind speed 1lb per square foot, and how many lbs per square foot would result with wind speed of 20km/h? Is there some formula?

 

the pressure on the sail is a function of airspeed. The dynamic pressure from airflow is somewhat complicated, it is the half the mass of the air times the velocity squared. Mass of air changes with temp, barometric pressure and altitude. In normal sea level air 1 lb/sf on the sail is about 16 mph as I recall. This means you will want to be reefing (or easing off the main sheet) at about 18 mph relative wind speed (this varies with your point of sail to the wind and your own speed). This is a typical reefing wind speed.

It is not really that complicated, the mast acts like a lever arm that wants to turn the boat over from the force of the wind in the sails, and the weight of the boat and crew against the beam length are trying to keep the boat upright. Force x lever arm = moment. If the overturning moments are larger than the correcting moments, you capsize and you go for a swim.

 

All right, so I'll figure it all out, make some equations, but I think that answers it all. Thank you very much, Petros. So you say that typical wind speed to start reefing is 18mph, that is when wind hits 5 on Beaufort scale? Is this "reef wind speed" for small sailboats such as the one I'm planning, or for most of the sailboats?


By the way, did you figure it all out from basic knowledge of physics, or is it from some book/something you red about sailboat stability?

If I knew the title, I could read it too, so I wouldn't have to ask in every step

 

Give these calculations some consideration. If you like I can do a ballpark example. Based on our previous discussion, what I think you will find is that a trimaran that is as big as you want needs a sail that costs more than your entire budget.

 

I have read many books, plus I have a degree in engineering (where yes, I learned basic knowlage of physics). I have also built some 18 small boats, mostly trial and error, where I also learned a lot about boat behavior. There are n books that are suitable to learn small boat design that I am aware of, most just give general ideas and design ratios. "Elements of Yacht Design" by Larsson and Elliesson is a good general book, get it here: http://books.boatdesign.net/

it is mostly oriented towards large pleasure yacht design, but many of the principles apply to small boats.

Most people will reef sails at 15 to 18 mph, some will go higher, but it makes it difficult to control the sail in such winds. Some do not reef at all, but risk damage to the rigging.

 

Thank you, Petros. I'll try to get hold of that book.

Skyak, thank you for such through info, I'm trying to make these diagrams right now according to your instructions, but I'm failing terribly. Would you be so kind to link to some diagrams for trimarans for me to have an example?

 

this is a "free body diagram" for a sailboat. the idea is to look at the forces operating on the object "free" of outside considerations, it is a look at the forces only. All the forces should balance in a steady state condition. The sum of the forces should add up to zero, and the sum of the moments should add up to zero.

This came off an interesting university website, might be worth a look (though it may also be much more advanced than you need).



http://www.simarnet.com/Yacht_Keels/

 

Thank you. I see that I'm lacking just too much knowledge to understand how to actually use the information you provided into my project.

So to save guessing and asking, I'll go read that book you suggested, and get back if something is still unclear. I just hope that in that book these forces are not only explained, but provides information on how to actually predict them (like how to find center of buoyancy of complex-shaped hull, how to find how much lift and drag sail will provide, and so on).