Analysing Upwind Performance

[Skippy]

Be careful about taking that analogy too far. The high-pressure (windward) side of the wings is the undersides, not the upper surfaces. In sailing, you lose power when you pinch because the true wind direction doesn't change, and by sheeting in, you're turning the sail's power to a less favorable angle. Whereas on gliding, you stall when you nose up too high because your power source is gravity, which is then similarly in a less favorable direction. But that's a gravitational issue, not an aerodynamic one.

"has anyone tried hiking to leeward in light winds?"
Not me personally, but yes, people have mentioned doing that with good results.

"OK, why do I feel like I'm about to be blasted by those who really know what they are saying"
A good sense of intuition?

[CT 249]

But as Tom mentioned (and I gave figures to indicate the F18's good wsa v a Flying Dutchman) a good modern multi may not actually have significantly higher wsa. In fact some of them have such small foils (to reduce) wsa that the small foils may be the problem, perhaps.

Our Formula 16HP has foils that extend about 18" below the hull, and they are comparatively big for a performance cat. In contrast monos from Laser to International Canoes and skiffs have big foils. Only the modern Moth lacks a deep CB, partly because it's a small low-drag boat with a low-drag rig and it's also not at its best in light airs.

I assume that the multi's small foils "rotate the lobe" to favour footing - does that sound right Tom?

[jam007]

Reading this thread I was inspired in making the graph below.
It shows Velocity made good and Boat speed for different boats and headings.
As shown has the SeaCart 30 (A racing trimaran) a higher TWA for its maximum VMG since the boats speed increases rapidly with higher TWA angles.
All boats has a minimum AWA when they stop going forward. That is when the part of the sailforce directed forward at the smallest possible sheeting angle just is sufficient to counteract the aerodynamic drag form rigg, sail and hull. In the graph the VO60 seems to come close to this minimum angle as the speed slows rapidly as the AWA gets close to 20 degrees while the SeaCart 30 seems to have a few degrees left to pint before that.
The data on SeaCart 30 and VO 60 is taken from the homepage of SeaCart 30 and is for 10 knots of true windspeed. The data on the Dinghy from Marchaj's "Sail Performance".
I have included the leeway angle in AWA. Iow. AWA is calculated from the direction of motion.

I have searched for ACC yatch data and would really like to plot them. Can anyone direct me to where I can find a polar for ACC yatch? (Does not have to be exact, no secrets revieled )

[tazmann]

Hello
As far as upwind performance, there are to many varables to say any one thing is the cause but you should be able to point higher than 50% granted your boat speed will suffer. Cats are usualy designed for off the wind performance, You cannot compare to the J80 for upwind light air sailing, Thats what there built for. I raced santana 20 one design for a few years and its amazing the deference between the same boats , it all boils down to rig tuning and sail trim ( if the boats and sails are equal) for the wind and sea condition. The first couple races all the other boats were pointing 10-15% higher and going faster than I was (real frustating) so my learning curve went way up. I guess what Im trying to say is you have to learn you particular boat, what works on one doesnt allways work on the other. With cats you should be able to fall off the wind and go for boat speed make a few tacks and come out ahead of the J80
Tom

[tspeer]

Originally Posted by CT 249

...
I assume that the multi's small foils "rotate the lobe" to favour footing - does that sound right Tom?

You do want to foot in a multihull. You can pinch with the monohulls and go at comparable speeds. However, it's better to foot off for better speed. It's not so much that the lobe is rotated, it's more like the lobe is extended.

A fun sport in a modern mulithull is to pick out a larger monohull going to weather, and climb up under their lee until you pass in front, sailing both higher and faster.

[Jocko]

Originally Posted by tspeer

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."

Disagree: Edmond Bruce's tank testing showed, and he firmly believed,published that leeway angles > 5 degrees were undesirable. His statement to this is basically that greater leeway than this meant too little board area/too large sail area and vice versa.

Originally Posted by tspeer

... Note that what counts is to minimize the drag angle (maximize L/D), regardless of where the boat is pointing!

Totally agree! Amen - I'm with you on this.

Originally Posted by tspeer

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.

Again from Bruce: his tank testing showed that airfoil theory didn't necessarily apply to keel design - especially w.r.t. surface piercing foils. Indeed, his testing showed that surface piercing foils operated most efficiently with aspect ratios near unity. I believe that monohulls with deep keels (ACC et al) would probably be far enough away from the surface piercing realm as to believe that span loading was key. I believe that Cheekee Monkey now has foils outboard, similar to many modern tris - they perhaps don't need(benefit from) the aspect ratio beneficial to monohulls.

Originally Posted by tspeer

... So if you start with a full keel and start cutting away at 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.

Stop! The drag (wetted surface) will go down, but the leeway (increasing) will necessarily increase the hull's drag. Total drag - determining the all important hull's L/D ratio - will not necessarily improve. I believe this is where Bruce and Speer diverge, no? Is it not reasonable to believe that increasing the leeway beyond 5 degrees creates a greater drag penalty from the hull than improvement from the foil? Hence the optimum shown in Bruce's tank testing?

Originally Posted by tspeer

...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.

At this point, the hull would likely be slewing sideways at something like 15 degrees when equipped with high aspect ratio foils, or 25 degrees if equipped with low aspect ratio/full keel equipment. Surely that angle is going to overwhelm the drag numbers.

Originally Posted by tspeer

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

Say it ain't so!

[tspeer]

My main point is, for the designer, reducing leeway does not necessarily improve performance. You can make the leeway arbitrarily small by adding more lateral area. But this extra wetted surface will slow you down.

The article I've seen by Bruce on optimum centerboard size ("Design for Fast Sailing", AYRS, p. 65 - 68) had a geometric aspect ratio of 3. He assumed the board had an effective aspect ratio of 6 because of the end-plate effect of the hull, but his data had an average lift curve slope of 0.064/deg, which implies an effective aspect ratio of 3.24 (an Oswald efficiency factor of 1.08).

When he looked at sizing the centerboards, he maintained the aspect ratio, thus increasing the depth for the larger board. This is not the same as maintaining the same depth and cutting away at the chord. Under his assumption of constant aspect ratio, the board alone reached its optimum L/D at 6 degrees, and this stayed the optimum angle because he maintained the aspect ratio. Had he maintained the same depth, he would have gotten a different result.

Here's Bruce's table:

AR = 3
Angle(deg)____0_______2_______4_______6_______8______10______12
CL___________0_______0.14____0.26____0.39____0.52____0.64_____0.73
CD___________0.035___0.037___0.042___0.059___0.085___0.123____0.161
L/D__________0_______3.8_____6.2_____6.6_____6.1_____5.2______4.5

Here's the same table multiplied by the areas Bruce examined (3, 6, 9) to get the lift and drag divided by the dynamic pressure. The necessary lift area will be proportional to the sail area at a given boat speed/wind speed ratio.

Boards sized as Bruce sized them (constant aspect ratio):
AR = 3__________Area = 3_____e = 1.08_____Depth = 3__________________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10______12__________10.15
Lift Area________0_______0.42____0.78____1.17____1.56____1.92____2.19___________1.94
Drag Area_______0.105___0.111___0.127___0.180___0.261___0.378___0.495__________0.387
Profile__________0.105___0.106___0.108___0.136___0.181___0.257___0.338__________0.263
Induced_________0.000___0.006___0.020___0.045___0.080___0.121___0.157_________0.123
L/D_____________0.0_____3.8_____6.1_____6.5_____6.0_____5.1_____4.4___________5.0

AR = 3__________Area = 6_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________4.97
Lift Area________0_______0.84____1.56____2.34____3.12____3.84_____4.38__________1.94
Drag Area_______0.210___0.223___0.255___0.361___0.522___0.756____0.989_________0.306
Profile__________0.210___0.211___0.215___0.271___0.363___0.515____0.676_________0.242
Induced_________0.000___0.012___0.040___0.090___0.159___0.241____0.314________0.064
L/D_____________0.0_____3.8_____6.1_____6.5_____6.0_____5.1______4.4__________6.3

AR = 3__________Area = 9_____e = 1.08_____Depth = 5.20_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________3.26
Lift Area________0_______1.26____2.34____3.51____4.68____5.76_____6.57__________1.94
Drag Area_______0.315___0.334___0.382___0.541___0.783___1.134____1.484_________0.365
Profile__________0.315___0.317___0.323___0.407___0.544___0.772____1.013_________0.321
Induced_________0.000___0.017___0.060___0.134___0.239___0.362____0.471_________0.044
L/D_____________0.0_____3.8_____6.1_____6.5_____6.0_____5.1______4.4___________5.2

For his notional design, he needed a lift area (CL*Area) of 1.94, and for these designs the best choice was the area 6 board, operating at an angle of 5 degrees.

But suppose he had compared the boards on the basis of constant depth and varied the chord to change the area. Here's what his table would have looked like:

Boards sized keeping the depth the same:
AR = 6__________Area = 3_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________10.15
Lift Area________0_______0.42____0.78____1.17____1.56____1.92_____2.19___________1.94
Drag Area_______0.105___0.109___0.118___0.158___0.221___0.318____0.416__________0.325
Profile__________0.105___0.106___0.108___0.136___0.181___0.257____0.338__________0.263
Induced_________0.000___0.003___0.010___0.022___0.040___0.060____0.078__________0.062
L/D_____________0.0_____3.9_____6.6_____7.4_____7.1_____6.0______5.3____________6.0

AR = 4.83_____Area = 3.73_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________8.01
Lift Area________0_______0.522___0.969___1.453___1.938___2.385____2.721_________1.94
Drag Area_______0.130___0.136___0.149___0.203___0.287___0.413____0.541_________0.287
Profile__________0.130___0.131___0.134___0.168___0.225___0.320____0.420_________0.225
Induced_________0.000___0.004___0.015___0.035___0.061___0.093____0.121_________0.062
L/D_____________0.0_____3.8_____6.5_____7.2_____6.8_____5.8______5.0___________6.8

AR = 3__________Area = 6_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________4.97
Lift Area________0_______0.84____1.56____2.34____3.12____3.84_____4.38__________1.94
Drag Area_______0.210___0.223___0.255___0.361___0.522___0.756____0.989_________0.306
Profile__________0.210___0.211___0.215___0.271___0.363___0.515____0.676_________0.242
Induced_________0.000___0.012___0.040___0.090___0.159___0.241____0.314_________0.064
L/D_____________0.0_____3.8_____6.1_____6.5_____6.0_____5.1______4.4___________6.3

AR = 2__________Area = 9_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0_______2_______4_______6_______8_______10_______12__________3.26
Lift Area________0_______1.26____2.34____3.51____4.68____5.76_____6.57__________1.94
Drag Area_______0.315___0.343___0.412___0.608___0.902___1.315____1.720_________0.387
Profile__________0.315___0.317___0.323___0.407___0.544___0.772____1.013_________0.321
Induced_________0.000___0.026___0.090___0.202___0.358___0.543____0.706_________0.066
L/D_____________0.0_____3.7_____5.7_____5.8_____5.2_____4.4______3.8___________5.0



If you only looked at the area 3, 6 and 9 boards, it might look like the previous result. But this is only because the profile drag is increasing rapidly at the higher angle of attack. The true optimum is at 8 degrees angle of attack. Had the profile drag not been increasing as it did, the chord could have been cut some more, making the angle of attack even higher.

When the drag of the hull is factored in, that also drives the optimum angle of attack higher because the extra induced drag due to the extra lift is offset in the lift-drag ratio by the higher lift.

Note also that the induced drag area is the same for the different aspect ratios when the lift area and depth are kept constant. Induced drag for the same lift depends on depth and not planform area or aspect ratio. This is a fundamental problem when trying to design a shallow-draft keel.

I submit that keeping the depth constant and varying the chord is the way a typical designer actually works. The depth is set by considerations like the desired stability, water depth, etc. So what the designer is free to vary is the chord.

[farjoe]

Originally Posted by tazmann

Hello
You cannot compare to the J80 for upwind light air sailing, Thats what there built for.
Tom

The interesting question is WHY?

It is not the weight. It may be the lower immersed are(some do not agree) and lower windage. The sail area is similar. Daggerboard area is lower and probably the surface finish is inferior due to the fact that the J80 cannot retract it.

What are the parameters which make boats like the J80 "built for upwind light air sailing"?

farjoe

[tspeer]

Oops - I forgot to correct the angles of attack for the different aspect ratios.

The change in angle of attack comes from the change in the angle of the wake left by the board. The board sails in a crosswise-current of its own making, and the shorter the board, the larger this adverse current is for the same lift. This self-induced current shows up as a change in leeway.

Boards sized keeping the depth the same:
AR = 6__________Area = 3_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0.00____1.57____3.21____4.81____6.42____8.05_____9.78___________8.18
Lift Area________0_______0.42____0.78____1.17____1.56____1.92_____2.19___________1.94
Drag Area_______0.105___0.109___0.118___0.158___0.221___0.318____0.416__________0.325
Profile__________0.105___0.106___0.108___0.136___0.181___0.257____0.338__________0.263
Induced_________0.000___0.003___0.010___0.022___0.040___0.060____0.078__________0.062
L/D_____________0.0_____3.9_____6.6_____7.4_____7.1_____6.0______5.3____________6.0

AR = 4.83_____Area = 3.73_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0.00____1.68____3.40____5.10____6.80____8.53____10.32__________6.81
Lift Area________0_______0.522___0.969___1.453___1.938___2.385____2.721_________1.94
Drag Area_______0.130___0.136___0.149___0.203___0.287___0.413____0.541_________0.287
Profile__________0.130___0.131___0.134___0.168___0.225___0.320____0.420_________0.225
Induced_________0.000___0.004___0.015___0.035___0.061___0.093____0.121_________0.062
L/D_____________0.0_____3.8_____6.5_____7.2_____6.8_____5.8______5.0___________6.8

AR = 3__________Area = 6_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0.00____2.00____4.00____6.00____8.00____10.00____12.00__________4.97
Lift Area________0_______0.84____1.56____2.34____3.12____3.84_____4.38__________1.94
Drag Area_______0.210___0.223___0.255___0.361___0.522___0.756____0.989_________0.306
Profile__________0.210___0.211___0.215___0.271___0.363___0.515____0.676_________0.242
Induced_________0.000___0.012___0.040___0.090___0.159___0.241____0.314_________0.064
L/D_____________0.0_____3.8_____6.1_____6.5_____6.0_____5.1______4.4___________6.3

AR = 2__________Area = 9_____e = 1.08_____Depth = 4.24_______________________Design Pt
Angle(deg)______0.00____2.43____4.79____7.19____9.58____11.95____14.22__________3.91
Lift Area________0_______1.26____2.34____3.51____4.68____5.76_____6.57__________1.94
Drag Area_______0.315___0.343___0.412___0.608___0.902___1.315____1.720_________0.387
Profile__________0.315___0.317___0.323___0.407___0.544___0.772____1.013_________0.321
Induced_________0.000___0.026___0.090___0.202___0.358___0.543____0.706_________0.066
L/D_____________0.0_____3.7_____5.7_____5.8_____5.2_____4.4______3.8___________5.0

The difference isn't so pronounced - it's now 7 degrees, not 8 - but it's still 37% higher than the 5 degrees that was Bruce's optimum angle.

[RHough]

Sailing to windward is L/D pure and simple. You need low L/D to go to weather, the higher the L/D the higher the boat points.

If you can increase lift without increasing drag you point higher. If you can decrease drag at the same lift you point higher.

If your boat doesn't point as high as another, your L/D ratio is lower than the other boat's. Not a tough concept.

[RHough]

When looking at the sail plan going to weather the rig used to be considered a semi-span as far as AR is concerned. The water plane became the centre and any gaps between hull and sail foot treated like a gap in the wing.

Thus a sail with measured AR of 2 would be assumed to have an AR of 4 for induced drag calculation. Is that model still used?

When two sails are some distance apart fore and aft (Freedom Cat Ketch) are they considered separately? In the opposite case of an IOR sloop where the sails overlap for most of their length how is AR determined?

[tspeer]

Originally Posted by RHough

...
Thus a sail with measured AR of 2 would be assumed to have an AR of 4 for induced drag calculation. Is that model still used?

Unless the lift can be carried right down to the surface, the effective AR is nowhere near doubled. Even if you don't have a gap, if the lift drops off due to the wind boundary layer near the surface, you lose the effective span extension.

The figure below shows what a lifting line analysis predicts for the minimum induced drag for sail rigs designed for different amounts of gap. This is not the increase you get when you design for no gap and the move the rig up, instead each point is a different design that is the best you can do for a gven luff length. Given that the foot of a typical sail is around 5% of the span or more above the surface, the drag is almost the same as for a surface designed without the reflection plane.



For more sail-like lift distributions,

the induced drag with gap tradeoff looks like this:

When two sails are some distance apart fore and aft (Freedom Cat Ketch) are they considered separately? In the opposite case of an IOR sloop where the sails overlap for most of their length how is AR determined?

Munk's stagger theorem says that when multiple surfaces are lined up in the streamwise direction, the induced drag is the same as for a single surface with the same total loading. It doesn't matter how the surfaces are spaced or how the loading is distributed between the surfaces.

So the appropriate aspect ratio to use is the square of the maximum span divided by the total area.

[RHough]

Originally Posted by tspeer

Unless the lift can be carried right down to the surface, the effective AR is nowhere near doubled. Even if you don't have a gap, if the lift drops off due to the wind boundary layer near the surface, you lose the effective span extension.

Thanks! If I had thought it through a bit more I'd have seen that. "Carry the lift down to the surface" is the best description of why the AR is not double that I've ever read.

Originally Posted by tspeer

Munk's stagger theorem says that when multiple surfaces are lined up in the streamwise direction, the induced drag is the same as for a single surface with the same total loading. It doesn't matter how the surfaces are spaced or how the loading is distributed between the surfaces.

So the appropriate aspect ratio to use is the square of the maximum span divided by the total area.

I'm getting this ... almost. Cat Ketch two sails of 150ft^2 each and 30ft span would be 30^2/300= AR 3:1 correct?

Sloop with 150ft^2 main and 150ft^2 genoa overlapping 50ft^2 (150% of J) would be either AR 3:1 also or would it be 30^2/250 = AR 3.6? Is the total sail area used or the projected area?

I used to design RC sailplanes so I'm trying to turn my head sideways to understand sails in terms I'm more familiar with.

Thanks again for a very informative response.

[gggGuest]

You're getting very deep in the theory of foil performance boys. This tends to be based on steady flow and constant speeds. All well and good, but there are traps waiting. A few years ago on a fast dinghy I designed I had to switch from a smallish high speed section daggerboard to a larger low speed section.

The problem was, although the board was just fine moving along, it had a horrible propensity for stalling coming out of tacks and the like, leaving the boat dead in the water for seconds or worse until normal service could be resumes. So in the end the major factor on design wasn't L/D or anything else,but purely the problem of getting through tacks...

And of course in practice our boat may not - even will not - be travelling at constant speed and direction, but instead have both heading and speed constantly changing as it runs through waves and responds to wind changes.

That's why, although I would never want to work without the theoretical background, it has got to be very strongly balanced against and founded in empirical data. The problem is just too complicated. This is, incidentally why the Bethwaites are so strong. They have the theoretical background, but they also have an enormous body of empirical data which no-one else has done, and tend to be guided more by the real world outputs of the empirical data.

[RHough]

Originally Posted by gggGuest

And of course in practice our boat may not - even will not - be travelling at constant speed and direction, but instead have both heading and speed constantly changing as it runs through waves and responds to wind changes.

Of course. However, one does not have to build 10 sailplanes to discover that AR 20:1 has a flatter glide slope than AR 6:1 if one knows some theory.

I don't expect to create a polar diagram of a boat's performance on paper and have the real boat perform exactly as predicted. In my RC sailplanes I was able to select an optimum AR for a given span that performed as predicted. It is certainly possible to predict that one design will have a higher L/D than another.

In non human carrying designs it is possible to do things like calculate max loadings on a spar that the planform can generate then build a series of wings with the safety fudge factor progressively reduced until the spar fails to check the validity of the calculations. I don't have the budget to build multiple rigs and test to failure on a full scale boat.

In the case of a foil stalling out of tacks, I would look for foils that operate far from the stall in steady state so they can tolerate a higher AOA change before they stall. I'd also look at how many degrees AOA has to be reduced before flow is re-established and select on the basis of broadest range with smallest hysteresis loop area. I'd look at what works in aerobatic aircraft rather than sailplanes.