Calculating power requirements for catamaran.

[Sailor 99]

Originally Posted by rob denney

Another example, this time of a multihull, which is pretty close to the spec.

The Ex40 harryproa is an improvement on the original harry, which was 12m (40') long, 6.75 m (22’3″) wide, weighed 800 kg (1764 lbs) with payload 800 kg (1764 lbs). The lee hull was 500mm wide at the waterline, giving 20:1 length to beam ratio. Sail area 42 m sq (452 ft sq) and righting moment 6 tonne metres (44,350 feet pounds). Made 200 miles pretty easily when the conditions were right.

The rig was an unstayed ballestron which worked well. The mast bent and the rig depowered, effectively providing an automatic first reef.

Queen size bunk and a double, plus a reasonable galley, toilet etc. Cedar strip construction.

4 (one a copy) were built, one of which sailed across the Tasman Sea, encountering a gale en route. There are some build pictures at https://web.archive.org/web/20040609...togallery.html

The EX40 is lighter, more robust, has a bigger payload and sail area and is quicker, cheaper and easier to build. There are a number of layouts available, the weekender version is shown.

I am happy to help with sail area and motor size for your cat, but will need more details to do so.

What keeps that boat from falling over on a starboard tack in a big blow? I can only imagine that in a full blow without some serious reefing it would start to fly the starboard hull. Am I wrong?

[tomfl]

Originally Posted by Dark Horse

What keeps that boat from falling over on a starboard tack in a big blow? I can only imagine that in a full blow without some serious reefing it would start to fly the starboard hull. Am I wrong?

No such thing as a starboard tack.

They are able to sail in either direction. This generally involves shunting (the equivalent of tacking or gybing, see diagram), although as with most things proa, there are numerous variations of this as well.

[Just Another Sa]

Originally Posted by Dark Horse

What keeps that boat from falling over on a starboard tack in a big blow? I can only imagine that in a full blow without some serious reefing it would start to fly the starboard hull. Am I wrong?

The exact same hull is on windward side at both starboard and port tack, thus the same available righting moment on both tacks.
You missed the point Harryproa is a shunting boat, neither tacking nor gybing.
Check the website SHUNTING – HARRYPROA

[Just Another Sa]

Originally Posted by dustman

It would have wharram wingsail schooner rig. At the moment my research leads me to believe around 100ft2 would be about right for good all around performance. I would love to have a better formula to go by than the one I'm currently relying on.

100 square feet of sails for 2000 lbs boat is about correct when there is at least 40 knots of apparent wind. Below that it will be very slow.
For a good light wind performance you need at least 400 square feet of soft sails.
Now if all of your sail area is rigid wing, not soft sails, you will get away with something like 300 squarefeet instead in light conditions.
To carry sails without reefing is dependent on righting moment of your boat, which in turn depends on beam, not just weight.
For some boats this might mean 150 ... 250 square feet of sails.
But at higher windspeeds a rigid wing is twice as effective for its area, so 75...125 square feet of rigid wing area is suitable.

Please notice that the maximum lift coefficient of wings is highly dependent on Reynolds number, thus in light air 2 sqft of wing area can match about 3 sqft of sails, but in a decent breeze its equivalent to 4...5 sqft of soft sails assuming it has flaps on trailing edge. If not it will be much closer area wise to soft sails.

Sail area needed for performance does not vary linearly with weight of boat as boat size changes. Bigger boats need significantly less area /weigh than smaller boats.
sailarea^3 / weight^2 would stay much closer at the same number.

[mcarthur]

Not sure it helps you, but I did a little analysis of power catamarans, their engine size, fuel efficiency and power to weight. Now power cat hulls are different to sailing cat hulls, but they’re probably closer than sailing monos.

[dustman]

Originally Posted by Just Another Sa

100 square feet of sails for 2000 lbs boat is about correct when there is at least 40 knots of apparent wind. Below that it will be very slow.
For a good light wind performance you need at least 400 square feet of soft sails.
Now if all of your sail area is rigid wing, not soft sails, you will get away with something like 300 squarefeet instead in light conditions.
To carry sails without reefing is dependent on righting moment of your boat, which in turn depends on beam, not just weight.
For some boats this might mean 150 ... 250 square feet of sails.
But at higher windspeeds a rigid wing is twice as effective for its area, so 75...125 square feet of rigid wing area is suitable.

Please notice that the maximum lift coefficient of wings is highly dependent on Reynolds number, thus in light air 2 sqft of wing area can match about 3 sqft of sails, but in a decent breeze its equivalent to 4...5 sqft of soft sails assuming it has flaps on trailing edge. If not it will be much closer area wise to soft sails.

Sail area needed for performance does not vary linearly with weight of boat as boat size changes. Bigger boats need significantly less area /weigh than smaller boats.
sailarea^3 / weight^2 would stay much closer at the same number.

Thanks for the reply.


So I ran the calculations on Gerr's formula, at 1500lb, 40' LWL, and 7.5 kts(approx. 200 miles a day if average speed) it comes out to 1520 watts. Also according to Gerr, 100ft2 of sail area represents 1500 watts with a force 4 wind(The nature of boats, pg 164). From what I've seen watching the weather almost every day for many moons, the trade winds on my planned crossing routes average in the upper force 4 range. I also imagine that the hulls Gerr's equation is designed for are monohulls with less than optimum performance at anything but low speeds. The 40' hulls I am envisioning would look something like a cross between a hobie 16 and tiki 38 hull, with no accommodations or storage. Except for really light air I can't imagine a situation where these hulls would not be considerably more efficient than the hulls those equations are meant for.



Am I missing something here?

[dustman]

The beam would be 20', and the schooner rig would have a low CE.


The Wharram wingsail is not a true rigid wing sail and is reefable, supposedly fairly easily.



I'm also trying keep the masts pretty short and keep weight to a minimum. More sail means more beefy structure and more weight, more weight means more materials and more rigid materials. All this equates to increased cost and complexity and reduced ease of use and safety.



I want safe, simple, frugal, even if it means I get around a little slower. But I really don't feel like if I stay in the tradewind belts that 200 miles a day is a stretch. But, alas, I have little first hand experience, so here I am to make sure I'm not getting ahead myself.

[dustman]

Originally Posted by Dave_S

1500lbs, I'm was imagining something bigger.

Just a thought. Nothing to back it up but.....

If starting from scratch I'd be inclined to have more sail area if possible with 4 reefs and use 1st reef as the normal setup, then in light air you could shake the reef out. You would carry some more weight as a penalty.

It seems strange to me to have a sail set up that no reef is good to 25kn. I guess much less for you so maybe not so important.

I'm also not sure what a sailmaker might think or if they could design the sail to have good shape at 1st reef. I would think you could.

I'm thinking full battens, with the first reef attached to the lowest batten. According to some Wharram people the sails are flat cut for some reason. I think I would add a boom along with the battens, those sails seems way too baggy in certain points of sail.

[dustman]

I guess a question I should be asking is how much less efficient are sails when heading downwind acting as a drag device than when acting as a wing on a reach?

[Pauls]

You are looking for a precise formula for sail area/displacement. The flaw in this goal is that weather is constantly changing. A given sail area is only ideal for a given wind speed on a given course relative to that wind. Because both wind speeds, courses sailed and sea conditions change, so does the need for a sailboat to change its sail area.

If you design your boat with a sail area/displacement that you think is OK for average conditions in your area then you will be under canvassed when conditions are below average. That means you will be under canvassed about 49% of the time. Do you want that?

Design the boat with a good large sail area/displacement. You CANNOT generalize about this. It is the ratio of the center of area of your sail plan to the righting moment of your boat.

You are going to have a relatively low sail plan by necessity, due to the restrictions of staying the rig with a proa. The lower sail plan will reduce the center of area of the sails and allow more sail area for the same righting moment.

Honestly, reefing is not difficult. With a large rig, if you don't want to reef you can sail reefed down. But the large rig gives you the option to increase sail need it, and you are going to need it frequently. There is very little downside to a larger rig, and lots of downside to a too small one.

Finally, instead of using websites for data, I strongly suggest you buy the books you need and study them. Start with Gerr's "The Nature of Boats". It is excellent, very readable, and covers many aspects of boat design. By the time you finish it you will have refined many of the issues you are looking at.

[rob denney]

Originally Posted by Teleman

Rob: Trying to estimate the space in the EX40 accom hull. Is there standing headroom on the middle floor space, or only in the hull?

(Apologies for thread drift.)

Standing headroom is only in the hull and the large hatch on the version shown. Because the rig and rudders are in the lee hull, the windward hull sees far lower loads than a cat or tri so there are more options for the cabin, including a pop top, bimini or simply a higher roof.

[dustman]

Originally Posted by Pauls

Finally, instead of using websites for data, I strongly suggest you buy the books you need and study them. Start with Gerr's "The Nature of Boats". It is excellent, very readable, and covers many aspects of boat design. By the time you finish it you will have refined many of the issues you are looking at.

I own The Nature of Boats, The Symmetry of sailing, and The Sailors Bible. The nature of boats I have read through, still working on the other 2. Any other good books to recommend?

[Just Another Sa]

Originally Posted by dustman

Thanks for the reply.

So I ran the calculations on Gerr's formula, at 1500lb, 40' LWL, and 7.5 kts(approx. 200 miles a day if average speed) it comes out to 1520 watts. Also according to Gerr, 100ft2 of sail area represents 1500 watts with a force 4 wind(The nature of boats, pg 164). From what I've seen watching the weather almost every day for many moons, the trade winds on my planned crossing routes average in the upper force 4 range. I also imagine that the hulls Gerr's equation is designed for are monohulls with less than optimum performance at anything but low speeds. The 40' hulls I am envisioning would look something like a cross between a hobie 16 and tiki 38 hull, with no accommodations or storage. Except for really light air I can't imagine a situation where these hulls would not be considerably more efficient than the hulls those equations are meant for.

Am I missing something here?

Haven't read the book, so cannot comment on that directly.
But there are too many ways to link power for the case. It could mean at very least any of the following:
1) The kinetic energy of certain volume of moving air divided by the time it takes to pass a a certain area perpendicular to the direction of flow.
When that power is multiplied by 16/27, it gives maximum theoretical power a turbine could extract from the air flow according to the Betz law.
Not very useful at all for sails or sailboats.
2) the propulsive power, calculated by multiplying component of aerodynamic force directed to the direction of motion of the boat, and speed of the boat.
3) required shaft power to rotate a propeller which would produce same speed as the sails are producing. Same as case 2 multiplied by assumed propeller efficiency.

None of them are very useful, and sails power at the same wind varies a lot depending on point of sail and speed of the boat. It's definitely not just a function of sail area and either true or apparent windspeed.
Furthermore any such formula would also depend on units used, are you sure you are using the correct units the formula was intended for?

I have a lot of experience on 25 foot long trimaran having beam of 20 ft and sailing weight of 960 kg + crew weight. It has 32 square meters of sails (344 sqft) and carries full sails up to 20 knots of true wind or about 30 knots of apparent. Fully reefed main alone was 11 sqm or 108 sqft, and together with storm jib it could handle any wind I ever met.
As a tri it has a lot less wetted area than your cat in light winds, and it would be dead slow with fully reefed main alone in light winds. Would have to guess something like less than 3 knots boatspeed in 8 knots of true. Some cruising monohulls of same length would be almost twice as fast.
Vertical distance from lowest point of jib to the highest point of full main was about 11,1 m or 36,4 feet. The rig was fractional.
It would have been a better boat with 40 sq meters of sails and closer to mast head rig than 7/8 with no disadvantages.
less than 20 sqmeters would alredy be slow to the extreme in light conditions. 32 sq meters already was irritatingly small sail area in those conditions.
100 sqft or 9.1 sq m would be less than used in storm jib and trysail combined for such boat.
Or compare with hobie 16 having 218 sqft of sails. https://www.hobie.com/sail/hobie-16/
Your boat has more than 15 times righting moment and you want much smaller sail area for it?!?
Makes no sense at all if you also want reasonable performance, not a boat just capable of drifting.

[Just Another Sa]

Originally Posted by dustman

I own The Nature of Boats, The Symmetry of sailing, and The Sailors Bible. The nature of boats I have read through, still working on the other 2. Any other good books to recommend?

If you want formulas only one comes to mind:
Aero- hydrodynamics of sailing by C A Marchaj
Not including the modern era foilers, but looking at things from the scientific point of view, thus also having formulas.

[Pauls]

Let's keep this simple. SA/Displacement is a ratio of power (sail area) to displacement. SA/D varies greatly, depending on the targeted use of the boat. You know what you want your boat to do. Look at the SA/d of comparable boats designed for similar use, and use that information to make a decision on the SA/D for your design. This is simple. And it is reality based. Making comparisons based on real world performance is a very solid, realistic approach.