Windward comparison

[MastMonkey]

Given restrictions on mast height how would the windward ability compare between single masted boat with a low aspect rig and a multi-masted boat with high aspect rigs? Sail area is equivalent.

[Olav]

High aspect ratio leads to less induced drag, so a well designed multi-mast rig might be superior to the single mast with a low aspect sail in this case.

Disadvantages are more weight at the top and therefore a larger heeling moment and - unless we're talking about free standing masts - more windage due to multiple standing rigging.

Therefore I dont't think there's a general answer. It depends on how much the aspect ratios in question differ from each other, how big the difference between rigging weight is, and the boat's stability characteristics. If the aspect ratio difference is not too big the abovementioned downsides may outweigh the advantage of greater aerodynamic efficiency of high aspect sails.

Just my two cents...

[TeddyDiver]

Originally Posted by Olav

a well designed multi-mast rig might be superior to the single mast with a low aspect sail in this case..

Another side too.. Adding sails is like using flaps in an aeroplane and alters the "angle of attack" and compromises the windward ability.. thou depends..

[ancient kayaker]

This is an excellent question which, I hope, will get a full discussion in the forum. I don't have direct experience of either but I have come across several discussions.

Catboats are the most extreme form of large low aspect ratio sail, and in general they do not have a great reputation for upwind performance. Low aspect rigs often employ the gaff rig which also is not preferred for upwind.

On the other hand, multi-masted sailing vessels are not great in that respect either. The closer such a boat sails to the wind the more the sail(s) on the different masts interfere with each other. This was a familiar problem to WW1 plane designers, it's known as the Biplane effect, and biplanes and triplanes soon gave way to monoplanes as construction techniques matured and materials improved.

In a big boat sail handling difficulties become more of a consideration which justifies multiple masts. Sail handling gets a few mentions in Sloop verse Square Rig, Maltese Falcon vs Mirabella

We all know there's more to sailing than upwind performance, but if that is poor the boat will spend most of it's time doing just that. Presumably the boat you have in mind is not large, so the Maltese Falcon is not what you had in mind for a multi-master. You are thinking more along the lines of a yawl, ketch or schooner I imagine. These are discussed at http://www.sailnet.com/forums/boat-r...ter-ketch.html which also has a good explanation of why these rigs have largely been replaced by bermuda sloops and suchlike.

[gggGuest]

Tom Speer will doubtless be along to explain this far better, but I believe as an extraordinarily crude rule of thumb induced drag - that part of drag that aspect ratio affects - is proportional to the chord (~~=foot length) of the sail. So the induced drag from a single sail of a chord of 10 feet is going to be much the same as the total induced drag of two sails of 5 foot chord.

This ought not to be a suprise really: if you bend the same amount of wind then you get the same amount of drag whether you do it with one sail or two.

[MalSmith]

Originally Posted by MastMonkey

Given restrictions on mast height how would the windward ability compare between single masted boat with a low aspect rig and a multi-masted boat with high aspect rigs? Sail area is equivalent.

It depends.

Firstly, if the sails of the multi masted rig are sufficiently separated that they do not influence each other (and they would have to separated a lot), then the total L/D will be as for the individual sail, and the total lift will be the sum of the lift of the individual sails. However, multi masted rigs generally do not have sufficient separation to act independently. The rig behaves as a multi element slotted airfoil. The total L/D will be less than that for an individual sail, and the total lift will be higher than the sum of the lift of the individual sail. So the geometry of the whole rig has a strong influence on the end result.

Secondly, the "windward ability" does not just depend on the rig efficiency. The L/D ratio of the hull/keel system must also be considered. For airfoils generally, it is not possible to improve L/D ratio without sacrificing maximum lift. In order to obtain any benefit from improved rig L/D, the L/D of the hull/keel system must also be sufficiently high, otherwise the loss in total lift does not outweigh the reduced rig drag. Bear in mind that for a typical yacht or monohull dinghy, rig drag is only a small fraction of the total drag of the system, because the L/D of the hull/keel system is poor compared to that of the rig (and the lift produced by the rig and the hull/keel system are equal and opposite).

It is no accident that most modern sailing boats are sloop rigged. The sloop rig is a slotted airfoil system that has about the right balance of L/D for this application. High performance catamarans tend more towards una rigs. Very low drag rigs (e.g. solid wings) are really only of benefit for land and ice yachts, who's "hulls" have much higher L/D ratios.

The commonly observed poor windward performance of cat rigged boats is not due to aspect ratio. It is due to being a single element (non slotted) airfoil, which cannot produce as much lift as an equivalent sloop rig.

[tspeer]

Originally Posted by MastMonkey

Given restrictions on mast height how would the windward ability compare between single masted boat with a low aspect rig and a multi-masted boat with high aspect rigs? Sail area is equivalent.

Given the same span, and sufficient wind, the heeling moment would be the same. Presumably, the height of the center of effort can also be made to be the same, too, so the lift will be the same between the rigs. So what's important is how the drag varies between the rigs.

In principle, they could be nearly equivalent with regard to lift-induced drag. In the 1920s, Max Munk showed that if you have more than one lifting surface lined up downwind, the total induced drag of the assembly depends on how the total lift is distributed over the maximum span, and it doesn't matter how the lift is divided among the various surfaces.

In practice, things are different. When you consider the apparent wind angle, the multi-masted boat becomes a multiplane, with cross-wind separation between the surfaces. This reduces the induced drag for a given span. The longer the boat, the larger the separation would be.

The parasite drag is also important. A multi-masted rig will have smaller diameter spars, but it will also have more shrouds and other rigging.

And then there's the ability to control the sail shape, including twist. A large chord single sail may be harder to shape than a more moderately sized sail of the multi-mast rig.

So there's no way to generalize. I suspect it depends on how tall are the masts you're talking about.

[MastMonkey]

I wish I could give a specific example or numbers. This was a hypothetical question that occured to me as I contemplated design features I would desire in a boat. One desire would be for free standing mast. Doing the calculation though for some projected sail areas it seemed difficult to accomplish without having to divide the rig or have a very low aspect ratio sail. My thought was that with a multi-masted rig, something I would actually prefer, taller, thinner sails could be used. I wondered though if doing so would offset the penalty incured in additional drag and turbulent interaction between the two sails.

An additional thought occured to me that the multi-masted rig with taller sails might have a light air advantage over the single sail due to its height. Given a tall triangular sail, at the very top where there is maximum spacing between the lifting surfaces would it be most efficient?

This is all new to me, so thank you everyone for the generous responses.

[tspeer]

Originally Posted by MastMonkey

...Doing the calculation though for some projected sail areas it seemed difficult to accomplish without having to divide the rig or have a very low aspect ratio sail.

Aspect ratio is often misunderstood. Aspect ratio is really the nondimensional form of the square of the span. If you can get a low aspect ratio sail to set properly, I don't see any reason why it would have more drag than two closely mounted sails of the same height and total area.

My thought was that with a multi-masted rig, something I would actually prefer, taller, thinner sails could be used. I wondered though if doing so would offset the penalty incured in additional drag and turbulent interaction between the two sails.

Taller sails are a different matter. Physically taller would be more efficient. The downside is taller has more heeling moment, so you can't use as much lift. So there's a compromise between taller for less drag vs lower for more power. The more efficient the hull, the more the optimum favors the taller rig.

An additional thought occured to me that the multi-masted rig with taller sails might have a light air advantage over the single sail due to its height. Given a tall triangular sail, at the very top where there is maximum spacing between the lifting surfaces would it be most efficient?

In principle, the spacing in the streamwise direction doesn't matter.

I think the decision as to one mast or more has more to do with the size of the sails and their ease of handling, etc.