Auto-Flight
Why would I need one board for each direction? Couldn’t I use a bidirectional foil? Obviously if the foil ventilates then the ama will crash, but if I’m willing to accept that increased risk with a bidirectional board, then the position of the board could just as well be at the midplane right?
Thanks for the kudos Marco. I do not recall saying a proa needs more than one gadget, sorry if I implied differently. We show it offset only because that’s where the aka is. You can mount it almost anywhere, so long as it is near or on the ama. Now a tacking trimaran would need two, I think, but a tacking catamaran might just get away with one, on the centerline. OTOH, a prudent builder might want to build two or even more, each sampling the mean water-to-ama distance in different places around the boat, then average the outputs before applying the force to the boom, all in order to attenuate errors due to wave action. Two Auto-Flights would double the cost though. From $10 to $20. 😊
Mal, thanks for the vote of confidence. Perfectly valid observation. When I have a few minutes I will show the assumptions and calcs I used to approximate the board size, and you can explain to me again where I am insufficiently conservative. 😉
Categorically though, it doesn’t much matter if you build it bigger, say for characteristically light wind or native conservatism, or smaller if your sheet tensions are very small. Of course there are limits and optimizations, but the tolerances should be very forgiving—also very cheap to fix, if I am mistaken. The renderings are of the 5th reiteration of this gadget (can you guess what the working name was?) over the past 4-5 years. I wasn’t happy until I felt I could answers all questions—even yours—and also offer an extremely flexible application.
No one has yet asked me how to adjust AoA or board-to-sheet leverage. Is it that obvious? (I wish!)
Dave
Mal, thanks for the vote of confidence. Perfectly valid observation. When I have a few minutes I will show the assumptions and calcs I used to approximate the board size, and you can explain to me again where I am insufficiently conservative. 😉
Dave
Basically it comes down to this:
Fpaddle = (Fsail x Asail x CEsail) / (Apaddle x CEpaddle x E)
Where:
Fpaddle = force required to be generated by paddle
Fsail = force generated by sail
CEpaddle = the distance of the center of effort of the paddle from the paddle pivot point
CEsail = the distance of the center of effort of the sail from the sail pivot point (i.e. the mast)
Asail = the change in angle of the sail
Apaddle = the change in angle of the paddle
E = the efficiency of the linkage system from the paddle to the sail
Mal.
No one has yet asked me how to adjust AoA or board-to-sheet leverage. Is it that obvious? (I wish!)
Well for the leverage you could move the connectiong point for the sheet down along the rod, which could even be done on the fly if you had a downhaul/uphaul system in place there. Board AoA in an easy way… no idea: how do you adjust AoA? 😊
can you guess what the working name was?
The flying carpet maybe? Though I’d hope it’d be something more original! 😉
Marco
The tricky part in my view is twofold:
- do you have enough power/torque/stroke, as you rightfully noted. And I would think you would.
- do you have the feedback system properly sized (for isntance, you do not want a seesaw effect), and more importantly, does it need to be adjusted for different conditions (windforce, speed, closehauled vs. broadreach, etc)? Only trial and error would tell.
Power is easily solved with paddle size; trial and error as you say. Throw/force ratio ditto, via lever lengths and multipart sheets. The “unknown” is the other, and I think you hit the singular issue on the head—over-control, or “hunting” of the system. This is an issue of all positive feedback systems, and the common solution is one form or another of “dashpot.” See http://en.wikipedia.org/wiki/Dashpot. Shock absorbers on cars are dashpots, as is the little thinghie on the hinge of your glovebox that limits the opening speed of the door.
With Auto-Flight the dashpot function is offered by the extreme paddle taper. The concept here is to reduce/increase control force more gradually as the ama rises and lowers, not all at once. The depth and “gradualness” of this taper is yet to be tested, but again, should be tolerant of pretty extreme variations—and be very cheap to alter.
At the same time, I offer this: If the gadget force were huge and the response instant, there’d be no over-control, ever. The system would PUT the ama right THERE by gosh and don’t even THINK about moving. Such a system is not physically feasible and would surely break things at a constant rate, but the example is for alliteration—go to this extreme and the system will not hunt. Now look at the other end of the spectrum and consider a barely-powerful enough, slow as molasses system. This one’s gonna hunt all over the map, likely even cause the very capsize it’s supposed to avoid.
See the trend here? So let’s push the design to the corner of the envelope for high force and quick response. Strong gadget, fast gadget.
Wouldn’t hurt if we sought to optimize the boat under us as well; lean towards a sail which responds linearly to sheet length changes and requires small sheet tension. Work to minimize angular inertia of the boat so the ama can respond faster to changes in the heeling moment from that sail. Practically, this means keeping the ama lighter and using live ballast for higher power in a small boat, and concentrating massive components near the center of roll in a larger one. Please note that these aren’t requirements to the auto-flight system, they are optimizations.
On it, I had a “Regulateur d’allure Navik”. See video here, especially at 2:35 minutes and 4:15 minutes.
http://www.youtube.com/watch?v=P43SaUUa_tYThat thing worked like a charm.
These are wonderful gadgets. As a card-carrying member of the Amateur Yacht Research Society (AYRS) I’ve followed their development for a very long time—and stolen ideas from the very best. The early windvane autopilots were weak and slow, and needed specialized pairing to the boat’s abilities and responses. Later ones became more and more powerful—and faster. Eventually they became, literally, off the shelf devices. You can buy one today here: http://www.selfsteer.com and simply bolt it on to virtually any boat, under a wide range of conditions—with full confidence that it will work. Strong gadget. Fast gadget.
Granted, you system can be much simpler; you do not care about the whole airvane, fletner mechanism. and so on, but you will still have to play with many parameters, some by design and some during operations; size of the blade, angle of attack, length of arm below the pivot point, length of arm to the quadrant above the pivot point, attachement position of the sheet on the boom, etc.
Ideally, you do not want to end up with something like: “I have 4 different positions for the quadrant to adjust the lever arm, depending on wind speed”.
Very much simpler. An auto-steerer must contend with a far wider performance window, and is tasked with holding a precise analog course—through wind and wave. An auto-flight gadget is a simple binary system; it’s either on or it’s off, there are no shades of gray to suss out and react to. Further, it only needs to work—can only work—when there is enough pressure in the wind to fly the ama. It doesn’t need light wind performance, It does not need to work on down-wind courses (These are the the biggest challenges to auto-steer devices) Being a multihull solution, it does not need to work when the boat is going slowly. So, we’ve got reasonable wind pressure. We’ve got significant water velocity. We’ve got a limited length of sheet to contend with. We have a completely controllable righting moment; we can “cheat” the system towards making it easier to fly that ama in marginal conditions, and also to bring on great power from the rig (either via moving live ballast—which is of no use to an autopilot). The autopilot designer has none of these luxuries.
It would be a fun project to work on.
It’ll cost you $10—and a boat—to do so.
Dave
Thanks DaveCulp for posting this great idea!
I can´t wait to see someone try this on a large proa or a scale-model.
This seems to solve a lot of problems for long distance cruising proas.
Cheers,
Johannes
On another note, with your system the daggerboard has to go in the vaka somehow…
Any proa which flies its ama must have some form of sideforce generation in the main hull. Jzerro and Pacific Bee teach us that having boards in both ama and vaka are a good idea; for instance if down in the ama and up in the vaka, the boat will “heave to” with ama to windward, and maintain that stance aggressively—nearly impossible to put aback. I suspect this is the same with all boards are deployed as well. I also like that they are considering multiple boards for their bigger boat(s). This will allow them to balance their sailplan under lots of different conditions—also make the boat easier to self-steer if that’s an objective
I’m thinking that something along the lines of the rudderboards which Cheers had could be the solution: the rudder only extends along the upper half of the rudderboard. The rear board is fully down, in use as a rudder, and the front board is only down half way for instance, so the control surface of the front board, is still inside the trunk. You’d only need the two rudderboards then, but what I don’t like about solution is that you would reduce the total available steering moment, and you’d be decreasing the average aspect ratio of the boards which are producing your sideforce, particularly if the alternative would have been a high aspect ratio daggerboard…
I tend to use rudderboards as a “default” system. These have been built and optimized by a number of real, on-water boats so are well-proven. There may be more efficient solutions, certainly cleverer ones. I’ve found that it’s a good practice to compare any new scheme against rudderboards, asking myself always “how is this better—or worse—than the default system?” This is not the same as saying they are the best (though they’re pretty darn good!), only that they are a standard, with known capabilities.
Dave
I’m not sure if you understood me correctly. My question is not about how to replace the rudder. Fards, I like them too, but I was wondering what to best do about the sudden lack of a daggerboard when the ama is flying…
I think this illustration of Cheers shows what I was referring to quite clearly: the front rudderboard can be lowered partially without the ‘flap’ of the rudder being exposed to the flow (which can cause problems as we all know). That setup gives you a bit of board area well forward of the midplane, not much, but a bit. Overall I think that’s probably not enough though, and the relatively low average aspect ratio between the two is not that good either.
A daggerboard trunk through the middle of the vaka on the other hand can be difficult. For all boats where the mast(s) is/are mounted on the vaka it’s be possible to sensibly integrate a daggerboard trunk into the windward side of the vaka, provided there is enough space. If you want a rig which is offset to windward like on Russell’s boats, then the placement of a daggerboard in the vaka is a real problem though, because as soon as the board is to leeward of the mast, the potential for a boom-daggerboard collision exists… For boats with cabins, daggerboard placement in the vaka is generally difficult.
I wonder if you could introduce a certain bias in your system, so that the control foil could take over the role of daggerboard as well…
Marco
But Marco, all the boats you mention; Cheers, Jzerro, Pacific Bee, Mbuli, etc—all have rudderbards in their vakas. Not in their amas. We call them “rudderboards” because they are a combination rudder—and daggerboard. Look closely at the Cheers graphic you posted. Remember he’s an Atlantic proa—main hull to windward. You can clearly see his rudderboards in the deck—his vaka’s deck. Mbuli’s are quite visible here.
Volkscruiser cheats—he only has rudders—but they’re in the main hull. the graphic seems to show a single board in the ama as well, but Michael makes no mention of it. JZerro and Pacific Bee—and Madness—have *auxilliary* daggerboards in their amas, and I think these are good ideas, but they are rather controversial because of how they effect sail and helm balance as they are raised or lowered. The boats aren’t designed to get their major leeway resisting from these ama-mounted boards (specifically because they may fly, or at least have their roots ventilated, as the boats “skim.”)
As to aspect ratio and board efficiency, Tiny Dancer uses very high aspect ratio rudderboards, widely separated, in his vaka, and no daggerboard at all.
Regardless, there is no requirement that *any* proa have its leeboards in one hull or the other. There is much precedent for both or either—or none. Most boats—the vast majority of both multihulls and monohulls—carry their daggerboards/keels/rudderboards more or less directly under their masts. A lot of that’s convention, some of it is to do with various sail and/or helm imbalance.
Bottom line, I would certainly not forgo hull flying in order to preserve a windward ama daggerboard. I don’t think any of the above boats would either. 😉
I’m not sure if you understood me correctly. My question is not about how to replace the rudderboards, I like them too, but I was wondering what to best do about the sudden lack of a daggerboard when the ama is flying…
I think this illustration of Cheers shows what I was referring to quite clearly: the front rudderboard can be lowered partially without the ‘flap’ of the rudder being exposed to the flow (which can cause problems as we all know). That setup gives you a bit of board area well forward of the midplane, not much, but a bit. Overall I think that’s probably not enough though, and the relatively low average aspect ratio between the two is not that good either.
A daggerboard trunk through the middle of the cabin on the other hand is usually problematic. With a Tepukei-inspired boat like the Delirium concept it’s a non-issue, and with boats where the mast(s) is/are mounted on the vaka (like Mbuli, the Volkscruiser, or Firstborne for instance), it may be possible to sensibly integrate a daggerboard trunk into the windward side of the vaka, provided you don’t have a central companionway. If you do have a central companionway, or want a rig which is offset to windward like on Russell’s boats, then the placement of a daggerboard in the vaka is a real problem though, because as soon as the board is to leeward of the mast, the potential for a boom-daggerboard collision exists…
Marco
No one has yet asked me how to adjust AoA or board-to-sheet leverage. Is it that obvious? (I wish!)
Dave
So how do you plan to control and adjust angle of attack?
Wondering minds want to know…
That is one of the things I am worried about.
For a fixed angle of attack, when the boat speed increases by say 25%, the forces on the immersed paddle will increase by 56% (1.25 ² ), and I am not sure that the tension in the mainsheet will increase in the same manner, does it mean that the system will “automatically” oversheet?...
And added to the above by Laurent, a gust (increasing boat speed) could also come with a change in direction. If the wind shifts back, the boat speeds up, ama lifts, will the system have enough throw to deal with it?
Basically, is it fail safe. If you’re still relying on the crews ‘split second’ reactions to save the boat from capsize, then that’s not ideal.
Of course you could have it dump the sheet completely at full throw, but that would also be a pain if it happens a lot.
I think it’s a brilliant idea by the way!
Why not examine the possibility of placing the lifting foil, foils, to leeward of the vaka? It seems to me the only drawback to the pacific proa as opposed to the cat or tri configurations is the lack of RM. If we are to abandon the simplicity of Tiny Dancer or other two foil boats and add lifting foils why not address the RM issue. Upwind if built light enough and in enough breeze the ama wants to fly. In fact I think most of us have concluded that a safety pod or ama is required to avoid the possibility of capsize on a cruising proa. An angled tapered surface piercing foil on the safety ama placed forward of the centre of gravity, mitigates the possibility of pitch polling, and transforms a pacific proa, to a weight to windward proa, as the angle of heel and the speed of the boat increases. It also reduces the displacement of the boat and could allow for even higher speeds than a conventional proa. It works for Hydropter and Banque Populaire. Down wind an outward angled lifting foil on the ama could be deployed.
On the example I have attached the mast can be canted to vertical or slightly to leeward in light winds. the idea is to present the greatest sail area to the wind, allow the sail to fall into shape ,and to put the weight of the mast to leeward of the vaka .
I have no idea weather the lifting foil to leeward configuration can be made to work on a proa, but I think it is worth examining.
So how do you plan to control and adjust angle of attack?
Wondering minds want to know…
The super-simple version (cast-off oar in a metal tube clamp, temporarily attached to the aka) is simplest; loosen the clamp, rotate the oar a few degrees, re-fasten the clamp. Same method for adjusting the throw and leverage ratio by raising or lowering the oar in its sleeve—also ama flight height; In the article and illustrations we show a fixed height and a fixed AoA (zero) because we think we can, more to the point, that veneer adjustment under way won’t be needed, and that once the system is dialed in, fixed settings will allow all the power and control needed. Remember that the crew has huge control over the force and response speed needed. Moving ‘thwartships and/or adjusting the skipper’s end of the mainsheet, so the ama almost flies to begin with will vastly reduces the amount of power needed (force AND throw). No “dance” is needed, for crew weight shift or for playing the mainsheet—that’s the gadget’s job. the skipper and crew bring the boat to close to flying condition, and the gadget takes over. If the wind increases a little bit at high frequency, the gadget responds. If the wind increases a lot (exceeding gadget throw, for instance, or exceeding gadget force), the crew moves leisurely to windward or the skipper hardens or eases his end of the sheet until the gadget returns to its performance window. “Over correcting” errors are always failsafe; the auto-flight blade leaves the water and mainsheet tension goes to zero
That is one of the things I am worried about.
For a fixed angle of attack, when the boat speed increases by say 25%, the forces on the immersed paddle will increase by 56% (1.25 ² ), and I am not sure that the tension in the mainsheet will increase in the same manner, does it mean that the system will “automatically” oversheet?...
A very good point and I’m glad you ask. As either boat speed or wind speed increase, all forces also increase. As both the blade and the mainsail are simple 3D foils, their forces increase linearly (not in lockstep of course, but one isn’t rising exponentially, compared to the other.) The entire system becomes more loaded up—and the boat accelerates.
That’s the simplest version. Of course there will be transient loads, differences in efficiency between cloth sail and wooden blade, etc. These issues are dealt with by brute force approach—the gadget is sized and geared to be to more powerful than necessary in every likely situation (either by brilliant design or by “trial by axe and spokeshave” experimentation. The former is nicely challenging from an armchair view, the latter more satisfying, plus anyone with even rudimentary axe skills can do it) If over-powered, the ama *will* rise, the gadget *will* lift out of the water, and the force available *will* be reduced from 100% down as far as 0% if needed. This without the skipper’s input. Assuming rudimentary intelligence, he/she will know when flying is hopeless, or the system needs some settings adjustment, etc. It’s important to note that the system does not need adjustment while under way—if it is sufficiently powerful for the boat and conditions. I’ll speak more about the boat “requirements”—we’ll call them “gentle suggestions” in order to be optimized for automatic flight control.
It is when the system is under-powered (as when the wind is too light, or the crew is sitting too far to windward, or the boat is standing still and the gust hits) that the system will oversheet the main, calling for more power that is just not there. A stop could be fashioned, but simpler will be if the crew moves inboard so the ama can fly, or the skipper sheets out until the gadget reaches the end of its throw and “turns off” (becomes ineffective). No system works in *all* conditions. This gadget only controls the ama’s flight, it does not increase its ability to fly.
Dave
And added to the above by Laurent, a gust (increasing boat speed) could also come with a change in direction. If the wind shifts back, the boat speeds up, ama lifts, will the system have enough throw to deal with it?
I would say that there will always be conditions (very gusty day? Very high winds, blocked/uncovered by high cliffs nearby?) when it simply wouldn’t be prudent to sail under automatic control of any kind. You probably disconnect your car’s cruise control in heavy traffic, and the offshore guys rarely sail into crowded harbors under auto-pilot.
In answer to your question though, let’s walk through it; The boat is sailing in some wind (call it 10 kts) This is enough for flight so the gadget is hooked in and is controlling the sheet—thus the ama flying altitude. Big gust hits (120% - 150% are typical, let’s call it 150%, 15 kts. Sail force increases to 225% of where it was. The ama is already flying so we don’t have reserve RM we can get to quickly. We’ve more or less stipulated we aren’t paying close attention or we’d have eased the sheet when the gust arrived, so let’s presume we also haven’t the presence of mind to round the boat up, so the ama rises, perhaps to the point where the auto-flight blade leaves the water altogether. With no force from the gadget, the mainsheet is effectively “dumped,” there is no tension on it at all. Its AoA thus its force is reduced to some very low number and the ama begins to crash back down—re-immersing the auto-flight blade and all is good with the world again.
The important question you ask is, what if the throw is insufficient to de-power the main enough to avoid capsize? Very good question. The answer depends on your risk tolerance, if you build the auto-flight gadget very large, it can have very great power (power = force X throw) You can then “gear” the system to have the max likely force needed, leaving lots of extra capacity to design in a very long throw. You have designed for the exceptional “100 year storm” scenario and you sleep well. OTOH, if you want the highest average performance from your boat, want to avoid giant power hogs that need their full capabilities only very rarely, you might build your gadget smaller, less powerful and with less maximum throw. You will rely on your own ability, during that rare “white squall moment” to have the presence of mind to dump your end of the sheet—As I might add, you’d need to do for any other boat you might sail. The gadget will have given you a significantly longer reaction time to suss out that Something Bad is happening and that Something Should be Done about it.
Basically, is it fail safe. If you’re still relying on the crews ‘split second’ reactions to save the boat from capsize, then that’s not ideal.
Of course you could have it dump the sheet completely at full throw, but that would also be a pain if it happens a lot.
If it requires split second reactions form the crew, then in my view it has failed. Simple as that. 😉
I think it’s a brilliant idea by the way!
Thank you.
Dave
Hey guys,
I’ve attached a way to adjust the AoA of the system while it’s in operation. This setup also makes the foil part of the system auto-shunting.
I’ve attached a sketch of the AoA control for the foil: essentially the rod with which the control foil is attached to the boat is placed infront of the CE of the foil. This means the lift creates a moment attempting to move the rear of the foil upwards (decrease AoA). To counter this force, we have our control line, which is attached to the top of the board. The lift and resulting moment keeps that line taught. If we pull the control line in a bit, we bring the rear of the foil ‘downwards’ increasing AoA.
If we shunt, then the board will be backwards to the flow, as soon as there is any flow whatsoever, the board will flip over to the other side by itself, but since the length of the control line stays the same, the AoA setting is the same for the new direction of travel as it was before. This naturally only works with a symmetrical foil section.
Overall this complicates the system slightly, since you need to add one more rotational degree of freedom to the movement of the control foil. In my opinion the live-AoA adjustment alone is not worth it, Dave has suggested a much easier way to allow AoA adjustment with the system at rest (just use a clamp); but if we had an easy way to swap or shunt the mainsheet with regard to this mechanism, then I’d say it’d be pretty appealing…
Cheers,
Marco
Edit: True autoshunting of the mainsheet is impossible; you have to have user input of some kind—I had a bit of a brainlapse there. 😛
I suspect that the sheet control foil shown is too small to do the job. I think that you would need to use the full extent of the lateral resistance area to derive enough force to get enough sheet travel.
This post will put some of you to sleep; it’s OK to skip it. Consider just reading the asterisked (**) paragraphs. 😉
Sheet-to-tiller steering has been around forever. Several rules of thumb have been established: A system working near equilibrium, with sheet and tiller loads as small as practical, will result in better performance. This makes intuitive sense: If the control forces are small, components can be smaller, so lighter and cheaper. Inertia is smaller so response can be faster.
**An ordinary boomed mainsail requires most of its sheet load to pull the boom down, not in. A wingsail sheet, OTOH, needs no down force at all. Better, it can be aerodynamically balanced, reducing sheet load even further—to only a few ounces if desired.
There are simple solutions for reducing sheet loads; wishbone boom, balestron rig, sprit boom, even junk rig. We chose one of the commonest—a simple boom vang.
**The second caveat it to ask the system to work within as small an operating window as practical. It is possible to design hydrofoils that will fly a boat at 3-4 kts boat speed, and also at 30-40 kts. Designing a single system to do both is difficult.
The auto-flight system shown is meant to control flight of the ama of a smallish proa from perhaps 5-6 kts boatspeed up to about 20 kts.
The proa design is meant to be generic; the Auto-Flight gadget is the subject, not the proa. The identical gadget should be able to be walked to and bolted onto any multihull its approximate size and mass.
Here are some working numbers. Change them to suit yourself:
LOA = 18’
BOA (center-to-center of hulls) = 10’
Mass = 400 lbs including 175 lb crew and 225 lb boat.
The proa is a 75/25 weight distribution Pacific proa, meaning its at-rest CG is 2.5’ to windward of the centerline of the vaka.
Sail area is ~130 sq ft; the single mainsail is 20’ on the luff and 7.5’ foot. It’s center of effort then is ~9’ above the boom and ~3.5’ aft of the mast CL.
Boom is ~5’ above the boat’s center of lateral pressure
Sheet is attached to the boom ~6’ aft of the mast CL.
Auto-flight blade is about 6” X 24” and has an area of~.5 sq ft. It’s CLP is ~18” below its pivot point and the top of its arm is ~36” above the pivot point. The auto-flight’s useful range of motion is ~+/- 45 degrees, yielding a max throw of just under 3’
The mainsheet is double-ended, one end attached to the auto-flight arm and the other held by the skipper. It is inherently a 2:1 advantage which doubles the force of the auto-flight but halves its throw. Thus the effective “gear ratio” of this auto-flight system is 1:1; the force developed by the blade is equal to the force delivered to the boom.
Crew will be assumed to be in one of 3 locations; 1) sitting on the tramp or seat, ~2.5’ to windward of the vaka CL; 2) sitting on the ama with his center of mass directly above the ama’s CL; and last, 3) wholly in the vaka, with his CG directly over the vaka’s centerline.
In position 1 the boat+crew’s CG is 2.5’ outboard of the vaka centerline thus max RM (when the ama just leaves the water) = 2.5 X 400 = 1000 ft-lbs. In position 2) the CG is 6.25’ outboard of the vaka centerline, thus max RM = 6.25 X 400 = 2500 ft-lbs. In position 3 the CG is 1.25’ outboard of the vaka centerline so max RM = 1.25 X 400 = 500 ft lbs.
How much wind will it take to hit these targets (fly the ama)? With the CE of the sail 14’ above the boat’s CLP, we’ll need 1000/14 = ~72 lbs sail force = ~55 lbs.sq ft =~12-13 kts apparent wind to fly the ama in position 1 (we’re assuming a lift coefficient of 1.0). Position 2 = 2500/14 = 179 lbs = 1.4 lbs/sq ft = ~20 kts apparent. Position 3 = 500/14 = 36 lbs sail force = ~.28 lbs/sq ft or about 8 kts apparent.
**It’s important to note that, with the crew fixed in these positions, the wind force must be capped—anything above that created by these numbers must be dumped, or the boat capsizes. Therefore, the sheet tensions generated at these sail forces will be the working tensions on the auto-flight system; they set a maximum design size for the system’s scantlings and the blade’s size.
In condition 1 above we will see 72 lbs total force from the sail, perpendicular to the boom and centered 3.5’ aft of the mast. The sheet is attached to the boom 6’ aft of the mast, so assuming we have succeeded in avoiding the need for down-force on the sheet, and assuming the sheet lead is perpendicular to the boom, the force on the sheet is ~42 lbs. Condition 2, with 179 lbs total sail force = ~105 lbs on the sheet and for condition 3 with 36 lbs of sail force we’ll see about 21 lbs sheet force.
We have too little information to accurately predict the boat speed under each of the above conditions, but a (very) rough-cut estimation might be something a good bit less than the apparent wind speed in each situation, but surely more than half of it? Bruce number is not high at 1.2, but the boat is pretty clean, skinny, and after all will be flying its ama. This might lead to boat speed estimates of 10 kts, 17 kts and perhaps 5 kts, respectively?
Meaning our little ½ sq ft auto-flight blade, again working at a CL of about 1.0 (perhaps it’s a Speer reversible asymmetric section, set at zero AoA, relying on the boat’s leeway to give it ~5-7 degrees working AoA) creates a force of about 100 lbs at 17 kts, about 35 lbs at 10 kts and about 9 lbs at 5 kts boat speed.
**So Mal is correct, our blade needs to about 50% larger in size, to perhaps 0.75 sq ft. Add a 33% safety margin and build it 1.0 sq ft. Perhaps 8”chord by 34”depth (~1/3 larger than shown) Nothing like as big as the primary daggerboard though.