Calculating power requirements for catamaran.

[dustman]

The more I look into power requirements for my design the more unsure I become.


I have been relying on Gerr's formula(via Psycho Snail website calculator) for displacement craft, but realized that at higher speeds the numbers don't make sense for a very slim-hulled catamaran, especially after watching numerous videos of slim cats sailing much faster than the sail plan vs disp/length ratio would indicate using said formula.


Is there a formula that would apply specifically to very long slender hulls, say, greater than 20 to 1?



This is all confused even more by reading stuff like: "This means that a catamaran would require four times the power in order to double its speed, whereas a monohull would require eight times the power to double its speed, starting at a slow speed." (Garret, Ross, The Symmetry of Sailing)


From what I can tell most performance cats have greater than 50 and less than 100 square feet of sail area per ton.


And yes I know there are many other factors.


Any insight you have would be greatly appreciated.

[a64pilot]

I’ve never been on a sailing Cat, but if I were designing one, I believe I would try to make it so that one engine running at an acceptable RPM would give me a cruise speed I could live with.
I like the idea of cruising on one, thereby cutting the engine hours you accumulate in half, meaning of course your engines would last twice as long.
I wouldn’t want to size my engines so that it took both to get me what I wanted as a cruise speed

[StuM]

Originally Posted by a64pilot

I’ve never been on a sailing Cat, but if I were designing one, I believe I would try to make it so that one engine running at an acceptable RPM would give me a cruise speed I could live with.
I like the idea of cruising on one, thereby cutting the engine hours you accumulate in half, meaning of course your engines would last twice as long.
I wouldn’t want to size my engines so that it took both to get me what I wanted as a cruise speed

I think he's talking about sail power (area), not engine power.

[css145hs]

A > 20:1 beam to hull ratio? That would indeed be something, tho I can't imagine it would have any usable load capacity. We have 2x40HP being put on a ~10T light displacement 52' 13:1 hull. That's quite a bit of power with both motors going, I have no estimates on motoring speed tho, just my guesstimate that it's on the high end for that form factor.

[kapnd]

You can engineer the hell out of it, and still get it wrong, so I’d be happy with a rough estimate of power required, and overkill it by maybe 20% just to be sure.
IMO the advantages of too much power far outweigh the disadvantages of too little.

[barnakiel]

Cats require less power to drive them to hull speed BUT cats tend to have way more windage.


So .... if you envision driving upwind a bit now and then, you still want the engines to be just as powerful (5hp per ton or thereabouts).


And if you are very smart, you will want to be able to drive under one engine only. So the total hp per ton will often be way superior (compared to same weight monohull boat).


Cheers,
b.

[a64pilot]

Originally Posted by StuM

I think he's talking about sail power (area), not engine power.

I think your right once I reread his post

[dustman]

Thanks for your replies, but am looking for actual data or a formula to use. In the not too distant future I am going to build a very slim-hulled cat and want to properly size both sails and motor. Don't want to undersize the sails because I want to meet my goal of averaging 200 miles a day in the tradewinds, and don't want to oversize because I don't want to have to reef every time the wind picks up a little. This boat would be under 2000 lbs fully loaded, more likely averaging just over 1500 lbs.

[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.

[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.

[Dave_S]

SV Roam do around 200nm per day on a crossing, I think they have around 14 or 15:1 hull ratios, not sure about sail area but probably weigh 7-8ton. With 20:1 you might be looking for ways to slow it down.

[Sailor 99]

Originally Posted by dustman

1) Don't want to undersize the sails because I want to meet my goal of averaging 200 miles a day in the tradewinds,

and

2) don't want to oversize because I don't want to have to reef every time the wind picks up a little.

This boat would be under 2000 lbs fully loaded, more likely averaging just over 1500 lbs

I think that 1 and 2 are in direct conflict with each other. The force of the wind is the wind speed squared. X^2 against what ever sails you have up.

10 knots of wind gives force of 100

20 knots of wind gives force of 400
wind speed double and your force went up by a factor of 4 or 400%

30 knots of wind gives force of 900.
Wind speed tripped and your force went up a factor of 9 or 900%

No sail design is going to allow you to get decent performance at 10 knots without reefing at 20 knots and some serious reefing at 30 knots.

You are also talking about a really light smallish boat. What is going to keep this thing stable in higher winds without reefing... Answer... nothing.

Examples.

A performance oriented 48-52 foot cutter rigged cruising sailing vessel with a cruising displacement of perhaps 45,000 lbs will carry a head sail of perhaps 700 sq ft, a stay sail of perhaps 250 sq ft and a main of perhaps 600 feet and that is a fairly tall rig. That's 1550 sq ft of sail.

These boats run around up on the Great Lakes in 10 to 15 knots of wind with all sails up and its no problem and they can use it.

They run around down in the trades with only a stay sail and a reefed main. Sometimes double reefed. That is perhaps 600 ft of canvas and depending on the point of sail they can be well heeled over. That is a 60% reduction in sail area.

Take something like a 10K lb racing sloop say 34-35 ft.

In 10 knots of wind they might fly 600 sq ft of sail with a big 155% genoa and move nicely. In 25 knots of wind they are barely manageable with a working jib and a double reef in the main. At 30 knots its just go home because pretty much all of the fun just got blown away.

I don't think you can get were you want to go from here. If you don't believe me go talk to a sail maker.


I know these numbers are for mono's but the forces are still there and they are still there except if these get knocked down they come back up. Your cat will not likely come back up

[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.

[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.)

[NPCampbell]

Originally Posted by dustman

I have been relying on Gerr's formula(via Psycho Snail website calculator) for displacement craft, but realized that at higher speeds the numbers don't make sense for a very slim-hulled catamaran, especially after watching numerous videos of slim cats sailing much faster than the sail plan vs disp/length ratio would indicate using said formula.

By higher speeds do you mean beyond hull speed? If that's the case I would agree with you. Most of the quick and dirty formulas are decent approximations for <= hull speed that are based on the hp increasing with the cube of speed for a single hull. At or above hull speed, hull dynamics greatly come into play. How can you generalize stuff like having extra buoyancy aft or sharp overhangs reducing the tendency of the stern falling into the trough of the receding stern wave? Above hull speed you probably require computational fluid dynamics to get accurate numbers. It sounds like you might be comfortable with that? Maybe give one of the freebie CFD programs a try?