Analysing Upwind Performance

Just realised that the table I had set out with spaces came out unreadable, so here's another try.


_______________ Strider____ J80

sail area _________ 31_______ 35
LWL ____________ 6.8______ 6.7
WSA (sq. m)_____4.1*2______ ??
WSA (sq. ft)___ 44.7*2______ ??
displacement____ 900______ 1300
area above WL____ 6_______ 5.1

 

Even a little bit of leeway affects the apparent wind adversely. Catamarans go fast
which rotates apparent wind forward, and have less hydrodynamic force to conteract
leeway. When trying to point, both leeway and headway cause the apparent wind to
rotate foward.

The more forward the apparent wind, the higher the lateral component of aerodynamic
force, and hence the more tendency to leeway.

The point at which, with optimal sail trim, all this junk balances out under a specific set
of conditions is the pointing angle of the boat.

AC boats go slower, and have awesome high-lift keels, creating much more lateral
hydrodynamic force. This makes the apparent wind farther aft than in a catameran
zipping forward twice as fast, and making a lot more leeway.

Draw it out, if I am right, even a little leeway hurts your apparent wind, without
headway's compensating increase in apparent wind speed.

 

Actually, I think the case could be made for saying, "The leeway angle should be as great as possible, short of stalling the keel/board."

The apparent wind angle, beta, is best measured from the boat's velocity through the water instead of relative to the boat's centerline - see attached figure. Beta is the sum of the aerodynamic and hydrodynamic "drag angles" [arctan(drag/lift)]. The boatspeed/true wind speed ratio is sin(gamma-beta)/sin(beta), where gamma is the point of sail (head to wind => gamma = 0). Note that what counts is to minimize the drag angle (maximize L/D), regardless of where the boat is pointing! This is why it's more relevant to measure apparent wind from the velocity vector instead of the centerline.

The lift on the keel will be that required to offset the side loads from the sail rig. Below stall, the leeway angle will be proportional to the lift produced by the keel. The other attached figure shows the drag breakdown of a typical foil and an arbitrary increment (CD=0.08) to represent all the other drag contributions of the hull. When considering the foil alone, the maximum L/D occurs at a comparatively small lift coefficient/leeway angle. But when the hull drag is included, the maximum L/D is much lower and occurs at a much greater lift coefficient/leeway angle. The reason is a lot more lift is required to "dilute" the hull drag in the L/D.

Now the drag due to lift is not dependent at all on the area of the keel - it depends (inversely) on the square of the keel depth. But the profile drag of the keel does depend on the area. As does the leeway angle (inversely). So you can make the leeway angle arbitrarily small by increasing the keel area. But if you maintain the same depth, all you're doing is increasing the parasite drag. This is why a fin keel yacht goes upwind better than a full keel yacht of the same depth.

So if you start with a full keel and start cutting away at the the chord of the keel to reduce the area, the lift will remain a constant (it's determined by the sail trim) and the drag due to lift will remain a constant. But the drag will go down and the leeway will go up. Until the keel is so small that it stalls under the applied load. Then the drag will increase rapidly. So you want to stop cutting away at the keel short of that point.

The result is the keel operating at a high lift coefficient, and thus a comparatively high leeway angle.

 

Hmm, ok!

If I understand this properly (no guarantees!) what you're saying is that the
higher the leeway up to a keel stall, the higher the hydro lift, which certainly
makes perfect sense to me! (up to a keel stall, check, points on keel design
well taken -- thanks, I did not know a lot of that stuff)

However, notice that as leeway increases as measured against your total
velocity (the big light blue arrow representing true velocity) rotates clockwise.
So, if we make the simplifying assumption that your Beta remains constant,
the apparent wind is rotating forward, so eventually your sailplan falls
apart.

In the limiting case you have a stall-proof keel, and you're going dead
sideways! Your sailplan is generating no lift at all

Anyways, all I was trying to say is that leeway affects the apparent wind
in some sense 'more' than headway. This means that in a high-leeway design,
the highest angle you can sail relative to TRUE wind is lower, all else being equal.
You may be pointing like crazy against the apparent wind, but that doesn't get
you to the mark!

I am fairly sure that this is what's going on with catamarans.

---

Oh, and furthermore! I see a little more now. The more hydro lift you have,
the more efficiently you sail. Your sailplan "works better," but maximum
pointing isn't about sailplan efficiency, it's about the point where everything
falls apart and you stop going forward!

 

What's going on with catamarans isn't any different than what's happening with other sail craft. I learned the importance of loading up the "hull" when I was working on a landyacht VPP. I had arranged things so that the maximum aerodynamic L/D occurred below the stall angle of attack. I expected the VPP to say the best sheeting angle was that for max L/D, but instead the VPP said performance was better when sheeted past max L/D to the point of stall. What I realized was the extra sheeting was loading up the chassis and inproving its L/D more than was being lost by the rig being oversheeted.

It's easy to get near zero leeway angle on any boat - just luff the sails. But that doesn't do anything for windward performance.

Let's say you employed a jibing centerboard. You could get the situation shown in the attached figure, which has zero leeway. Since the wetted area and depth are exactly the same as before, there's very little change to the drag if the sails are sheeted to maintain the same force as before. So the relationship of the force vectors - and the path through the water - are essentially the same as before. What's changed is the hull orientation relative to the course through the water. If you were to jibe the board the opposite way, you'd end up with more leeway on the hull - and much the same set of force vectors. The point is, leeway angle itself doesn't really tell you anything about the boat's performance.

I think what you're trying to get at is the rotation of the apparent wind vector becomes the limiting factor in high performance craft. And you're right about that. For example, when I put in zero rolling resistance in my landyacht VPP, I still got a finite speed. Beta, being the sum of the aerodynamic and "hydrodynamic" drag angles, was equal to the aerodynamic drag angle, since the chassis drag angle was zero. So when the apparent wind was so far forward that the resultant aerodynamic force was perpendicular to the direction of travel, that was the limiting speed.

But the apparent wind angle depends on the lift and drag, not directly on the leeway angle. It's much the same with sail trim. In order to get the same sail force in the figure below, the sails have to be eased relative to the hull compared to the original case, so their angle of attack is the same. The angle of attack of the sails is roughly independent of the orientation of the hull because they can be sheeted (above centerline if necessary) to get the desired angle of attack.

In the end, it's the lift/drag ratios that determine performance, not the leeway angle or the sheeting angle themselves.

 

> What's going on with catamarans isn't any different than what's
> happening with other sail craft

Then, why do they tend to not point at well? I think you may answer this in your remarks, though. I think it's simply because they don't generate as much hydrodynamic lift as keelboats, and I think that's what you're saying. We're just coming at the same information from two different angles. Heh heh. Angles.

It's foolish of me to suggest, and I apologize for doing so, that there's any specific thing that causes something else. It's a complex system where all the parts interact to create a specific performance profile.

By the way, it's perhaps worth pointing out that the lateral hydrodynamic force ALWAYS equals the aerodynamic lateral forces unless the boat is accelerating sideways. Leeway is caused by the boat "slipping sideways" until enough lateral hydrodynamic force to balance the aerodynamic. Lifting keels/boards exist to provide "free" lateral force in the right direction, so you don't have to do it all with bulk resistance (or whatever the right word is).

You know this, I am pretty darn sure, but I am not finding it particularly clear from your postings.

 

I don't think the difference is in the lift. As the apparent wind comes forward, the crew sheets in the sail to maintain the same angle of attack - that's what you're doing when you trim by the telltales. So the lift vector stays the same magnitude but changes direction. This actually increases the required hydrodynamic lift, as you can see in the diagrams by decreasing beta.

Instead, the difference is in the drag. A keelboat has a very distinct increase in drag with speed - much more than increasing by the square of the speed. A catamaran's drag does not increase as rapidly with speed. And a landyacht or iceboat's drag increases very little with speed. The less the drag increases with speed, the more it makes sense to foot rather than point. A modern multihull can point as high as a monohull, but if they do, they don't go to weather any faster than a monohull. So they foot for better speed and Vmg because they can. If a keelboat tried the same trick, it wouldn't pick up enough speed to make up for the extra distance.

If the drag increased with the square of the speed so the lift/drag ratio stayed the same, the polar plot of the yacht's performance would consist of two circular arcs. The point of sail for best Vmg would be 45 degrees plus beta/2, implying that a lower performance yacht would actually need to foot rather than point. But beta isn't constant as the point of sail changes - it increases as the keelboat tries to foot, and that drives them to point instead.

However, the theory shows that there's something fundamental about sailing 45 degrees to the true wind for best windward performance. The optimum is going to be in that neighborhood no matter what kind of sailing craft it is.

The notion that a multihull can't point is flat out false, so I disagree the premise of your original question. In my F-24 trimaran, I routinely sail up through the lee of bigger monohulls, sailing both higher and faster. The misperception that multihulls don't point well is a left-over from the early first generation mulithulls that had excessive windage and wetted area (due to V-shaped sections), and whose designers thought they could get away with shallow keels or no board at all. Or they were designed with no boards for the purpose of sailing off the beach like the Hobie 16. Today you see more attention paid to rounded topsides for less windage, semicircular sections, and deep daggerboards to reduce induced drag. As a result, modern multihulls point much the same as performance monohulls.

 

> The notion that a multihull can't point is flat out false

First of all, did I miss it, or have you not mentioned this helpful datum before? This is something I did not know, and was assuming was the other way about.

Secondly, with regard to drag. Is the point here that for multihulls that speed is cheaper with regard to drag, so by sailing deeper they get enough extra speed to give greater VMG? Or, another way to put it, those neato polar graphs "lobe out" farther further off the wind than a monohull?

I'm not seeing how drag makes the boat point less well. Well, it depends on definitions, perhaps. If 'pointing' simply means how far up it goes without starting to go backwards, anyways. If 'pointing poorly' means, instead, that the boat goes forward at high angles (the sails are pulling), just really really slowly, I guess I'll buy that.

I've been thinking entirely about how far up it can go and still be going forward, which as far as I can tell depends (almost) entirely on apparent wind and sailplan. Or, perhaps I am thinking of how far up it can go and still have the sails applying lift forward of the beam, which is almost but not quite the same thing.

 

I observed the same thing Tom, as I mentioned above in #50:

Obviously if you manage to create more wind (greater apparent wind) as many lighter-weight, slender multihulls do, then your chances for greater performance are enhanced. But you must make efficient use of this increased wind. This is the job of the sailing technic (helmsman), and a function of the rig design itself.

Most competitive multihulls can create a substantial amount of apparent wind. And they generally utilize it most effeciently by sailing no higher than 45 true, tacking thru 90-100. This generally maximizes their VMG. However, I have been in numerous situations where, if we slowed down to a speed just barely above that of a real competitive monohull, we could work our way to windward of him, and boy were they surprised! (I must admit it took a moment of inattentiveness on their part to pull this off...playing the slightess wind shifts). We concentrated on getting the greatest driving efficiency from our rig at these higher pointing angles...proper slot, proper sail shape for this higher incidence angle.

 

Yes, that's it exactly.

You're getting closer. As the boat slows down, it takes a larger leeway angle to produce the necessary lift to counter the sails. Eventually, the keel stalls, and the boat really starts going sideways - using drag to counter the sails as well as (greatly reduced) lift.

If it weren't for the keel stalling, then it would be due to the net aerodynamic force coming abeam. That's what limited the speed when I put in zero rolling resistance in my landyacht VPP.

 

So, which happens first? I see a couple of scenarios as a boat heads up (slowly) until it starts to pinch. I don't think these are not readily distinguishable from the deck, I think you'd have to do Science:

1) the keel stalls first, the boat starts to skid sideways, causing the sails to luff
2) the sailplan falls apart first, the sails start to luff before the keel stalls (and then as the boat slows, the keel stalls)

do you have a sense of which one happens first on real boats? Or, does something else happen?

 

Something else. The crew trims in the sails to keep them from luffing. Keel stalls, sails stay full. Both leeway angle and apparent wind angle increase.

You seem to think the sails will be luffing at the limit of a yacht's abilty to point. I suppose there are boats that won't allow the sails to be sheeted in adequately, and for them luffing might be the limiting factor. But you certainly can't generalize that.

Go try it out for yourself. Pinch up and watch what happens.

 

Well, in all the boat's *I* have driven, which ain't that many to be sure, the jib starts to get soft and fall in right around the time the boat stops wanting to go forward. These are various ratty sails on charter boats, some genoas sheeted to the spreaders. Smaller jibs that certainly COULD be sheeted in more if only the crummy old boat had a track there etc.

So, sure, in theory on a boat with the right setup you could simply keep sheeting in until the net lift was aft of the beam, and then the keel stalls, and you start slithering around the water.

I guess I am asking about, say, a Santa Cruz 27 with a beat up dacron 135% genoa sheeted to the spreader, and it is unreasonable to expect you to know if the keel or the sail stalls first It sounds like the answer might well be 'it depends on your boat.'

 

Tom, what about multihulls? Doesn't a catamaran hull stall out before the daggerboard? And doesn't it generate fairly good lift below its stall angle? With a monohull, it seems like the hull never generates enough lift to make a difference.

 

Pointing ability

By way of comparison, if you view a sailboat's upwind performance as being analogous to a glider's (engineless plane) descent profile, the ability of your boat to climb to windward is identical to the pilot's ability to fend off excessive altitude loss. A gliding pilot with sailing experience sees up as windward, down as leeward - managing that glide angle requires controlling two factors simultaneously: lift and drag. The sailor must also control the lift and drag forces of underwater components to effectively/optimally sail upwind. Here is where the connection lies. A cat in a light wind has too much drag from being cursed with wetted area - hence the angle suffers. (Not a cat sailor - has anyone tried hiking to leeward in light winds? - wouldn't it make the cat perform more like the tri?) The cat improves its' angle in stronger winds by creating underwater lift with less drag when its' wetted area decreases.

My suggestion - focus on making the underwater parts most efficient - foils! and hull drag, with windage a close second (third? - I've lost count)

Next - the suggestion that 50 degrees is good since the idea of 45 + half the drag angle is optimal is only a player for the 'rocket' ships like ice yachts and land yachts which can achieve speed increases when they fall off the wind. Most sailors don't see much speed increase when the angle grows - unless you're on an awesome cat - hence most people benefit more from angle fixation, as per the AC crews. (OK, why do I feel like I'm about to be blasted by those who really know what they are saying)