Foil for current-driven propulsion?

My last attempt to make you reconsider your position would be to invite you to imagine a windsurfer being in place of Artemis, also equiped with hydrofoil and a high aspect ratio sailplane, also with no wind at all. How would you sail upstream ? My guess is by pumping. How long would you sail like this ? My guess is that depends on your physical conditions.... No pain, no gain !

 

You can only understand the answer to this question when you realise there is energy potential between air and water moving at different speeds relative to each other.

 

The basic situation is that you have air at a different velocity than the immediately adjacent water, so there is energy to be extracted. This energy can be used in different ways, and there is no law of the universe saying you can't use it to go "downwind" faster than the wind itself, though I'll conced that if you insist on a dead "downwind" course, you will slowly drift out to seal

By sailplane, I assume you mean a sail or wingsail. It doesn't really matter. The foils are a distraction. The basic question is whether the boat can obtain a velocity made good, downwind, that is greater than the wind.

Consider a boat that is making 16 knots through the water, at an angle of 135 degrees from the "true" wind, as measured from a buoy that moves with the current, i.e. 10 knots up-current. The velocity made good downwind, relative to the water, is 11.3 knots, which is faster than the current. The apparent wind experienced by the boat is the vector sum of the 10 knot apparent wind a still boat sees, and the 16 knot apparent wind from boat speed, right on the bow. If I've done the trig right, the boat sees an 11.3 knot wind, about 52 degrees off the bow. Seems to me a really efficient boat can sail 16 knots with that kind of wind. It has to be almost as efficient as this gadget:


If the Artemis can do 30 knots, then maybe their boat is really efficient. It's not impossible. But I bet that's the speed through the water, and that the speed made good downwind is a bit less. Unless 42 knots or so is routine, which I suppose is conceivable.

If the air is moving at exactly the same speed as the current, then of course nothing can be done. But that's a different situation.

The physics of a boat on the water doesn't care what the ground is doing. Only the air and water are relevant. If the boat can go downwind faster than the wind when the water is still relative to the bottom, then it can still do so when the water is moving over the bottom. Consider what would happen if that wasn't true. If I had a telescope and a satellite with a big mirror, I could watch the Artemis trying to go up current. From my point of view, relative to the ground I was standing on, it would be going two or three hundred miles per hour to the East. That's awfully fast for a boat, don't you think? I admit that my frame of reference isn't entirely Newtonian, but neither is the shore of the Amazon's, or the water's. Close enough for this thought experiment, though.

If you want a more inertial frame, how about the Moon, which takes a month to complete an orbit, rather then the day the Earth takes to rotate once. The moon's orbital velocity is about 1990 knots (more or less), and the mouth of the Amazon, being close to the equator, is going about 1,000 knots in the same direction. (Both relative to the center of the Earth.) So, if an astronaut with an amazingly good telescope is watching, and the Artemis is much larger than it looks, the astronaut may decide it's going 990 knots to the west. Again, impossibly fast for a boat.

What matters are the relative velocities of the air and the water, and, of course, the efficiency of the boat.

 

Mack:
I was just looking at your original post. You knew enough to ask the question, so I don't think the Dunning-Kruger theory applies here. OTOH, if someone convinces you of something false, and you chase after it... People experiencing the Dunning-Kruger effect are common on forums, though, so it may be tricky to tell which is which unless you're competent enough to answer the question yourself. ;-)

 

This is how it works.

Now, if the thruster reaction represent the current flow, please reorient the arrows and show me how you manage to sail heading the current, without any (True) Wind. We may also note that, if there is no (True) Wind at all, downwind or upwind does not make sense. In the situation described in the video, it is natural to ask yourself :
How to manage sailing downstream ? How to manage sailing upstream ?

 

I see a bunch of lines going every which way, and I have no idea what you mean by thruster reaction. If you find a correct force diagram for a boat sailing upwind, then it will be about right for the situation here, because having the wind 52 degrees off the bow isn't so very different. Keep in mind that the boat has no idea of how fast the land is moving, only what the air and water are doing.
Do you deny that it's possible for a boat to go downwind, via gybing, faster than the wind?

 

Ok, here's a diagram, much simpler than yours. Sorry it's a bit rough from using Paint. When I wrote "current is East", I meant that the current is traveling eastwards. An east wind, OTOH, is coming from the east and going to the west. I could have been clearer about that.

 

This diagram has been made in order to investigate the role of a side force, when considering the question of sailing without wind, as given by Will in his post. He has proposed to study the role of side thrusters, that is why you see here "thruster reaction". Still, these arrows can also represent the current flow (remplace "thruster reaction" by "current flow", in the discussion that we have). I don't deny that it is possible to go faster than the wind especially when there is no wind at all. I just never said that. The videos whose links are given in a previous post give examples of how to make a way @sea without wind. The windsurfer pumps lateraly. The surfboarder pumps vertically. Olympic sailing series, very used with light winds, do sometimes pump their boat to make their way, in the absence of wind. I pump my 18' cat when there is no wind. Everybody pump. In that case, we can say that our speed is an infinite time the speed of the wind, so three times or five times, or ten times the speed of the wind do not really matters. If you follow this diagram, you will be able, yourself, to determine yourself the correct force diagram for a boat sailing upwind. I don't have the solution, but I know how to find it, again, with a little work. I'm just sharing a start here. A diagram that everybody can use to come to the solution by themselves. It is what you told to Mack, speaking about the Dunning-Kruger effect, isn't it ?
With this diagram, and without writing any equations, you are able to make your own conclusions about
- the question posed by Mack
- Artemis in the Amazon river
- Artemis in Gibraltar
- the question posed by Will in his post.
- a bunch of question that can be posed that way

Lines are made in order to manage
-Addition of vectors
- Projection of vectors.
This is a very common representation of a mechanical system @equilibrium (constant speed of its parts). It is a geometric representation that is "analyticalized" in every Velocity Performance Predictor. It is a "visual VPP". If you are not familiar with this kind of representations ( which may be the case, considering your reaction to "this bunch of lines", together with the fact that I had only one rightfull comment from Doug from the whole of you ), let me explain what is represented here.

The filled arrows represent speed vectors. As you can see, there is no indications of referential at all. In general, it is assumed to be Galilean. (we are not talking about satellites in orbit, and we neglect the Coriolis Effect due to earth rotation, we neglect the effects of general relativity, considering that the speed we are talking about are small compared to the speed of light). I may recall that any referential moving at constant speed relatively to any Galilean referential is also Galilean. The referential choosen here is attached to the boat, whose movement will be thus investigated at constant speed. The magnitude of these speed vectors are arbitrary choosen. What is important is their composition and direction, that helps drawing the force vectors applied to the mechanical system. These force vectors are represented by the empty arrows. Both their magnitude and direction are important.

The "Sailplane drag force" (SDF) is oriented downstream to the boat speed and that the "Sailplane lift force" (SLF) is normal to the boat speed. In magnitude of SDF is smaller than of the SLF. The smaller the magnitude of the SDF is, the greater the aerodynamical aspect ratio of the sailplane is. The sum of the two vectors SDF and SLF gives the "Total sailplane force" vector (TSF), excerted by the sailplane on the boat (assuming that the sailplane is rigidly attached to the boat). This TSF vector is split into two vectors : "The Sailplane heeling force" (SHF) vector, perpendicular to the axis of the boat, and the "Sailplane drive" '(SD) vector, on the axis of the boat. Depending on the direction of the boat speed, the SHF vector will be windward or leeward oriented. SHF is associated by the name with the heel, as it is a force that is generated by the sailplane at an higher altitude than Center of Gravity, which is responsible for the heel of the boat. The lift force being, by definition, normal to the incoming flow (which is here, again, the direction of the boat speed), the SD can be oriented in the fore direction of the boat, corresponding to a true drive force, or, can be oriented in the aft direction of the boat, which will correspond to a counter-drive force. Here, SD is a drive force, pointing toward the boat, in consistency with the filled blue arrow, representing the forward speed of the boat (FSB). Please note that SD and FSB are in opposite directions, because of the choice of referential made, attached to the boat.

For the boat system to be in equilibrium, the sum of the forces vectors should be equal to zero. In fact, the sum of the forces moment should also be zero, but I arbitrary choose the application centers of every forces to be sure to have also a zero moment applied on this representation of the system. In reality, these application centers vary with the boat speed. It also should be noted that the application center of the boat drag force and the application center of the sailplane forces are not the same. The magnitude and the direction of the force vectors may be affected, but this approximation is sufficient to study qualitatively the problem posed. Not quantatively. Again, it does not say anything about the magnitude of the boat speed. You can go 5 times the speed of the wind (which is null in this case, but... anyway), this model will only demonstrate how the boat will make is way.

The equilibrium considerations given, the "Boat resistance" vector (BR), is determined, as being opposed and equal in magnitude to SD. This boat resistance vector represent the projection of the sum of all the drag forces generated by the boat parts, in presence of the fluid and the air. Here, the boat is considered as bare hull and deck, without foil, nor rudder, nor daggerboard, nor crewmembers, nor rigging. So the "Boat drag force" vector (BDF) is determined as a vector, oriented like the boat speed vector, whose projection gives BR. BDF is the sum of the hull and deck windage and the hull drag. BDF has also a projection perpendicular to the boat axis, which is represented here by the pink "Boat side force" vector (BSF). To equilibrate (in plane view) the boat, it is seen that we should finally add, to our mechanical system, counter forces, opposed to the sum of BSF and SHF. Without daggerboard (again, taking advantage of the question of Will on his thread, about the use of side thrusters to sail without wind), I determine the "Thrusters reaction" vectors (TR), whose sum is equal and opposed to the sum of BSF and SHF ; BSF+SHF = -2 x TR, where bold characters stands for vector notations. The center of applications of TR are choosen on the boat axis, equally distant to the center of application of the aerodynamic and hydrodynamic forces. This ensures that the sum of the moment will be zero, and that the mechanical representation will be one of a system @equilibrium ie consistent with the choosen boat speed vector. Again, speed magnitudes are not demonstrated here.

 

@MacktheYounger

Diagram of my proposal to for a water current driven craft. I chose the Skysails concept as the line attached to the kite(s) allows for relatively large distances between the two water bodies that have to be moving at speeds relative to each other.

Note the "control pod" in the diagram i copied from Skysails. The pod contains the mechanisms to control the kite's attitude. They are represented by the little black blobs in my picture. The launch and recovery system will need some more work.

 

I got my head round the concept with this comparison, which might be helpful:

My little boat has modest sails, which form a relatively decent (aero)foil.

It also has a rather fine ash leeboard which is a rather good (hydro)foil.

With some wind, in still water, it sails upwind rather well, using lift generated by the true and by the virtual wind. But not directly upwind.

The leeboard also generates lift, from the virtual current generated, which helps the boat move in the upwind direction, resisting leeway.

I haven’t the focus or the energy to join in detailed discussion of vectors, I’m afraid, but it seems to me that Artemis is doing exactly the same, but upside down, sailing upcurrent in still air.

The wing(aero)foil on Artemis l is doing the same job in the same way as my leeboard, generating useful upcurrent lift from the virtual wind generated. The (hydro)foils are behaving as the sails on my boat; they are generating lift in the water, with an upcurrent component, from the real and virtual current.

I presume the initial down current run of Artemis is necessary to generate the virtual wind and momentum to get the system up and running, in a similar way to bearing away after going about in my boat, to get the sails and leeboard foil working, and then pointing higher as my speed increases.

Of course, in this comparison, the devil is in the detail of the vast differences in relative viscosities, magnitudes of forces, efficiencies and sizes of foils involved, but I am happy that Artemis is theoretically able to do what is suggested, though the video and commentary is carefully framed; They do not say this has actually been achieved, only that it is (theoretically) possible. I think the video is particularly unhelpful, composed mainly of soundbites and pseudo-scientific graphics.

 

Actually, if the boat can sail downwind, faster than the wind, that's the whole story. The relative motion is what matters. The boat isn't in contact with the bottom, unless it drops an anchor, so it's not affected by any frame of reference issues like that. It sails faster than the wind, downwind, and therefore up current. As I mentioned, if you're going to measure from some arbitrary point, why not from my house? In that case, the "wind" will be hundreds of miles per hour. Or measure the wind from Alpha Centauri. It's just as relevant. The only things that matter, when you look at speed through the water, are the air and the water and the boat. Once you know the speed through the water, you can do a vector sum with the speed of the current and find out that you're going up-current at 1.3 knots.

 

Flotation:
I've seen schemes like this. I think, if you dig into it, you'll find that the submerged foil doesn't need to have anywhere near as much area as the "Skysail", because the water is 816 times as dense. (varies, and is a bit more in salt water). If you're going to have a ship, you can just use a centerboard or something like that, if you're going to go upwind. I suspect a typical ship's hull is sufficient for reaching. The ship's velocity isn't nearly what the airspeed of the "Skysail" is, so the board or foil will have to be much larger than 1/816 of the "Skysail's" area, but it will still be substantially smaller than the "Skysail".
Hypothetically, if the wind was consistent enough and the control algorithms were good enough, you could dispense with the ship and fly the cargo between the chute and the foil in the water. Seems like it would be awfully tricky, though. If they do get these good enough, maybe we'll see an attempt on the sailing speed record using this trick. Assuming they don't disqualify it.

 

In my diagram both foils (or kites or sails, whatever you want to call them) are underwater. As is the payload. The same principle should work in media with different densities such as air and water and if that's the case differences in foil size should relate to difference in density indeed.

As the original question was a about how to make use of water currents I took the liberty to exclude air altogether.

The kite shown in the diagram probably is not the ideal shape, some more ridgid materials might also be better to achieve optimal efficiency. As a diagram to demonstrate a principle I though the image of a controllable kite was sufficient.

Moonshot #1 is under development to make an attempt at the sailing speed record based on this principle. It is controlled by hand, not algorithms as that would make it illegal.

 

Moonshot videos:

 

Do "realizing the energy potential" means skipping corroborating calculations and judging with a wet finger? ? Do you mean this kind of potential energy ?