100 sq. ft of sail area is about 2 HP?

I came across a thread with the title of this message as a very simple post from PAR. It helps a lot, though I am wondering at what wind speed this considered to be true. For instance, Summer in Puget Sound we may want to double, tripple, ... our sail size or even consider a gennaker?

Most of the boats we are considering come with about 1200 sqft of sails. 24HP on some of them, as an engine, would get us up to (nearly) hull speed. Are we going to need a gale to do that?

I realize the math for this can't be simple considering velocity of moving bodies, pressure, force, etc. However, over the centuries someone has to have come up with a reasonable plan that for a certain size boat (defined by length, displacement, under water area, or something) you need this much sail in 10kt winds, X% less in a gale, y% more in 3kts, etc.

No?

 

well PAR, if you can it would be nice to see some tables along these lines....sorry mate, I know you are a busy man, and we seem to trouble you a lot, but there are many people who genuinely appreciate all that you and many other clever people on this forum provide.

it would be an interesting thing to see....

 

Thousands of years of shipbuilding have certainly led to some rules of thumb regarding the sail area needed for a particular hull size.
But I see that you have put some numbers in the title... In that case, if you are looking for a more exact (or scientific, if you want) approach, it is not so straightforward at all.
You could take a look to this post:
http://www.boatdesign.net/forums/sailboats/horsepower-sail-area-equivalence-28551-3.html#post292129
In that case a guy had asked about the equivalence between sail area and propeller bollard pull, but the phisical principles between that one and your question are the same.

 

I think that if a certain sail area can make a hull go at a certain speed, the HP equivalent is easy to calculate.

 

Yes gonzo, but the fact is that another sail type of a different area can drive the hull at the same speed too. Or the same sail, with the same area and a different trim can drive the hull at a different speed.

P.S.
Why "in Spain for a while"? It is a nice country, nice food, nice wine, nice climate, nice all... A place to stay for good.

 

Vague...

Exact numbers is not what I am after. The 100sqft = 2HP was what I could find on the forum. That's a nice round indicator, but at what wind speed can I expect that?

So, my questions boil down to (not expecting heavy math answers):
1) at what wind speed can I expect that?
2) Are most cruising boats designed to go hull speed at 10kts of wind or what? Just an average idea.
3) If I am stuck somewhere with light winds, as a general rule I should plan on adding x% of sail.
4) If I am in a gale, I should plan on reducing to y% of sail. I can get this one from a good storm tactics book so no need to answer here.

 

Different points of sail or trim produce different drive. Area alone is not a direct indication of power. I think maybe you could have a range.

 

Everything's vague when we start throwing numbers at sailboats. Frankly, there isn't much point in trying to equate sail area with horsepower; better to look at a boat's overall performance as there are too many other factors involved. A sailboat's power is much easier to judge by SA/WS (sail area to wetted surface) ratio in light winds, and SA/D (sail area over 2/3 power of displacement) ratio in stronger winds.

 

I'm not the first to come up with this and it is a rough approximation, but effective for comparative reasons. Wind strength would be 12 to 15 knots.

Lets look an example of a light weight 14' planning boat with 75 sq, ft of sail in a nice breeze, full up with a solo crew at 280 pounds or so. This is roughly 180 pounds per HP, which will get this little boat to a S/L of 3 or so. Regular powerboat formulas will make these predictions fairly well. In this example a 13 foot LWL manages slightly better then 12 MPH.

HP per square foot isn't unreasonable, nor unheard of, though it is a rough guess. In the example above (force 4) I used .02 HP per square foot. Had the wind been force six, I would use .07 HP per square foot.

We used these home made VPP formulas before software came along and supposedly made everyone a yacht designer.

 

You can get a lot of data from a wind power website. The comparison between motor and sail area should be at some particular wind speed and it's most accurate with the boat running downwind, as all boats differ in efficiency going upwind.

 

Don't they differ in efficiency going downwind, as well?

 

If you use apparent wind, not so much

 

I don't get this... What efficiency are we talking about here?

 

Precisely

 

I think you're asking multiple questions:

1) what's the relationship (which is indeed a very complex function) between sail area and its ability to generate horsepower. Note, that there is a massive difference in efficiency amongst sails of identical area, so you need to be much more precise about the kind of sail you're talking about.

2) while there are general rules of thumb for sail area for a certain sized boat, given reasonable hull shapes, those tend to be defined by factors other than horsepower. These include cost, easy of handling, fashion (some like old fashioned boats some new ones), and safety reserves. Almost all family cruising boats have far less sail area than is reasonable in even a conservative racing yacht. For example, a 5O5 dingy with no ballast at all has almost the same sail area as a Moore-24 with 1050 lbs of lead, and about the same as a 29' cruising boat. Clearly the sails produce vastly different power, as they are more/less efficient, but also the goals are radically different as are the safety margins.

3) With respect to making a boat perform in a wide range of wind speeds, another part of your question, you'll want to consider a number of ways of radically increasing/decreasing the sail area. For an area with predictable wind speeds (say SF Bay on a summer in July) you can have a boat that doesn't even have a reefing system it simply has small sails. Whereas, if you wish to race/cruise-quickly on that same boat year around, you'll need to increase the sail area by as much as twice to get reasonable performance in the light winds of winter. This is a much longer topic, but it's one of the reasons old boats had removable bowsprits, topmasts, and all manner of other devices - it let them match the sail are to the average conditions.

Hope this helps, although it certainly didn't answer your questions.

In a stab at an answer, you'll really want a graph of HP produced for a given wind speed by a specific sail plan. It will be a different line for each kind of rig (obviously a cat sloop with unstayed mast is far more efficient than a square rigged ship going up wind). The 2HP per 100 Sq Ft is one of a large number of reasonable numbers along one line on one of the graphs you'll need.

If you tell us the kind of rig we could help a bit with the efficiency question, as a lot of simple sloops with alloy masts, single spreaders, and external halyards have similar efficiencies. But, we'd all be guessing what the HP output is of a square rigged ship.

BV