The flapping foil propulsion drive based on Cardan gear mechanism

[Victor R]

What I don't understand, Victor, is your aversion to rails. Yes, they add an unsightly transverse frame, which is draggy, particularly if underwater. But doesn't your mechanism trace the same transverse path in any event? Let its motion trace out an invisible rectangle in a transverse plane. Just put rails above and below. How is it different?

Hi Horton HCCI, thanks for your question.
I have nothing against guides, but they are not used in this mechanism for an important reason.
In the mechanism, as I already mentioned, the direction of thrust is changed by rotating "that invisible rectangle that traces the fin's movement" at a certain angle relative to the boat's centerline.
If there are guides, they would also need to be rotated by the same angle, which means a rotating base for the guides would be needed.

Instead, the Cardan gear mechanism's property is used - the plane in which the fin reciprocating motion occurs rotates to the desired angle when the central gear rotates to the same angle. A swivel base is not required for this.
For steering on the move, a turning angle of +- 40 degrees is sufficient. For mooring, the angle can be up to +- 180 degrees (180 is also needed for reversing).

 

[Victor R]

There's a lot of fiendishly little devils in the details

You're absolutely right!
One such detail is the need to adjust the optimal fin angle of attack on the fly depending on the boat's speed. To achieve this, it is not enough to simply regulate the speed of the electric motor.
You also need to adjust the fin's angle to the flow direction while it oscillates. This is truly difficult. To simplify matters, you can only adjust the fin's angular oscillation amplitude on the fly.
How would we change it? There are two shafts - the first (master driver) is located in the mechanism for moving the fin (since this is where the greatest load is); second slave, dependent on the master, in the fin angle pitch mechanism (less load here).
An differential gearbox is located between the drive and driven shafts. This allows the driven shaft to be adjusted for lag (or lead) relative to the drive shaft during movement, thereby changing the fin's oscillation angle from zero to the maximum allowable by the geometry of the mechanism.

 

[Horton HCCI]

In the mechanism, as I already mentioned, the direction of thrust is changed by rotating "that invisible rectangle that traces the fin's movement" at a certain angle relative to the boat's centerline.
If there are guides, they would also need to be rotated by the same angle, which means a rotating base for the guides would be needed.

Instead, the Cardan gear mechanism's property is used - the plane in which the fin reciprocating motion occurs rotates to the desired angle when the central gear rotates to the same angle. A swivel base is not required for this.
For steering on the move, a turning angle of +- 40 degrees is sufficient. For mooring, the angle can be up to +- 180 degrees (180 is also needed for reversing).

OK. I don't understand the details, but I'll take your word for it. . Are you using two fins, or one? If two, could you obtain steering by stopping or reversing one foil while applying power to the other? One advantage of dual foils, as I know you know, is that you can make their motion opposed and synchronized. This means that, where your lift vectors are oriented in unhelpful directions, like athwartships, the transverse vectors cancel each other out, leaving only the thrust vector in the direction of forward motion. Like a keel or daggerboard in a sailboat going upwind, except the lift vector from the opposite side is used to counteract what would otherwise be a heeling force . Keeps the stern from yawing around. I think your earlier model prototypes are dual-fin, yes? I have no idea how you reverse thrust, but I think your claim is that you do.

 

[Victor R]

I don't understand the details, but I'll take your word for it

I drew a diagram explaining the change in thrust direction from 0 to 180 degrees towards one side; towards the other, the picture should be mirrored.

How the plane of fin oscillation rotates at the same angle as the central gear of the Cardan mechanism is rotated, I think it will be clearer from the animation of the same mechanism with an external central gear:
Tusi couple - Wikipedia https://en.wikipedia.org/wiki/Tusi_couple#/media/File:TusiCouple.gif
Tusi couple Tusi couple - Wikipedia https://en.wikipedia.org/wiki/Tusi_couple

 

[Victor R]

advantage of dual foils

Yes, a balanced drive requires two fins operating synchronously in antiphase. This significantly complicates the drive mechanics.
But with an electric drive, it's simpler to use two separate single-fin drives and synchronize their operation not mechanically, but through an electronic control system. And I view my drive as part of such a system.

 

[Horton HCCI]

I drew a diagram explaining the change in thrust direction from 0 to 180 degrees towards one side; towards the other, the picture should be mirrored.

Aha. I guess I thought you were keeping your same transverse path on your earlier animations/diagrams, and were proposing to present your foils trailing edge to the flow. That struck me as non-optimal, but would probably work to some degree. Another approach might be to use a fully symmetrical, reversible blade, tapered equally at both ends, like a yuloh, yes? A lot of compromises there, but maybe some advantages as well.

Am I right in thinking that a main goal of your setup, aside from curiosity and the "fun" of doing the math is as a more efficient means of providing thrust vectoring for high maneuverability in restricted spaces? If so, what's the main advantage over other approaches like Voith-Schneider and azipod? Thrust efficiency/size/weight? Reduced complexity? Remains to be seen? Would the mechanism be retractable, like bow and stern thrusters in a ship, or are you seeing it as main motive forward thrust as well?

No need to pursue practicality, of course, and there's a lot to be said for just trying to explore the concept and see what might be learned.

I think I'm coming to appreciate the Cardan mechanism/Tusi couple as having an advantage over a simpler articulated crank without gears, in that the joint between the central rotary arm and the extended arm is essentially powered rather than passive. Does that make sense? Fair assessment?

Have you considered/tried the external central external gear route? I assume it has a larger footprint, but I see some advantages in perhaps providing more support to the mechanisms and maybe reducing some of what I expect are pretty high reciprocating loads. Don't know how that would work with reversing thrust, or how/whether your "slave" mechanism for importing pitch would be incorporated.

 

[Horton HCCI]

Yes, a balanced drive requires two fins operating synchronously in antiphase. This significantly complicates the drive mechanics.
But with an electric drive, it's simpler to use two separate single-fin drives and synchronize their operation not mechanically, but through an electronic control system. And I view my drive as part of such a system.

Good call on this. I'm actually reminded of a very old patent for a diesel-type free piston / gas turbine engine that proposed a rotary generator to both smooth piston motion and potentially synchromize multiple free pistons: US1785643A - Internal-combustion power plant - Google Patents https://patents.google.com/patent/US1785643A/en?inventor=walter+noack&oq=walter+noack. It could conceivably be a combination motor/generator, I'd think.

Possibly use electrical resistance (back EMF?) to cushion the reciprocal loads?

 

[Victor R]

a diesel-type free piston / gas turbine engine

I think a better comparison would be the ABB Dynafin trochoidal propulsor, which has several fins, each driven by an individual electric motor, but all moving in sync:
https://irso.info/wp-content/uploads/2-11-Viherialehto-S-ABB_DynafinTM.pdf

 

[Victor R]

what's the main advantage over other approaches like Voith-Schneider and azipod?

A tricky question that can cool creative ardor .
One can only assume that in a design with a reciprocating fin motion, less energy is wasted on unproductive water swirling than in a design with a circular fin motion or a rotating propeller.
On the other hand, it's clear that the Voith-Schneider design with circular fin motion is preferable from a mechanical standpoint.
Therefore, attempts are being made to improve the Voith-Schneider design by modifying the fin motion so that it mimics the motion of a flapping foil while maintaining circular motion.

This is the so-called trochoidal propulsor.

This video shows testing of such a propulsion system in the form of an outboard motor.
ADV's Trochoidal Marine Thruster

Have you considered/tried the external central external gear route?

Do you mean a drive with an external central gear of internal gear engagement, like in the Tusi couple animation?
There are some design solutions that could be adapted, such as:
the ornithopter wing mechanism;
the internal combustion engine design.

 

[gonzo]

Do all the models use stiff fins?

 

[Victor R]

Do all the models use stiff fins?

I currently have one model. It uses a fin with a hard, replaceable shell with a NASA-0018 profile, 3D printed from ABS plastic. The fin measures 400x120x22 mm, an area comparable to a rowing oar blade.

 

[gonzo]

I wondered if there had been any experimentation with flexible blades. Maybe on the trailing edge.

 

[Victor R]

I wondered if there had been any experimentation with flexible blades. Maybe on the trailing edge.

Yes, of course they were, here's one of the articles:
The effect of chordwise flexibility on the thrust and efficiency of a flapping foil.
The article provides the following conclusions:
Chordwise flexibility in flapping foils, if properly selected, is shown experimentally to improve efficiency with a small
decrease in thrust coefficient. ... Overall, flexible foils can be very efficient propulsors, and are shown to be competitive against rotary propellers.

 

[Horton HCCI]

One can only assume that in a design with a reciprocating fin motion, less energy is wasted on unproductive water swirling than in a design with a circular fin motion or a rotating propeller.

I find myself in complete agreement with this. Especially with Voith-Schneider types, although I'd agree it seems like the same issue with rotrary props. I think I read somewhere the most efficient prop is a single blade with a counterbalance. There actually were some back in the day.

On the other hand, it's clear that the Voith-Schneider design with circular fin motion is preferable from a mechanical standpoint.
Therefore, attempts are being made to improve the Voith-Schneider design by modifying the fin motion so that it mimics the motion of a flapping foil while maintaining circular motion.

OK, so these seem like the same thing as Voith Schneider. What am I missing? Bigger circle, but are the blades not still rotating over their circular travel? What's different?

Do you mean a drive with an external central gear of internal gear engagement, like in the Tusi couple animation?

Exactly this. Let's see if I can do this...
Tusi with external gear:

I can't seem to get a screen capture of your Cardan gear mechanism, but it's above. 4R across in both instances. 1R on the Cardan central arm, but there's your slave mechanism.....Yah, OK, the external gear is a lot bigger overall. What I'm worried about is the forces out on the end of your arm extension on reversal. The turn is pretty abrupt (I assume the same) with the big external gear, but the force isn't all cantilevered on that joint. I dunno, maybe it doesn't make that much difference, or maybe my concern is misplaced.

 

[Horton HCCI]

OK, here we go--same radius, same 4R travel, superimposed:

Yep, a lot bigger, although the "slave" pitch control mechanism adds quite a bit. Or is that more compact on your actual unit?

Actually, if we superimpose your 180 degree turn over things, we get:

Unless I'm going cross-eyed, the total sweep of the Tusi external gear and the Cardan gear mechanism are the same.

What I don't know is how on earth you would get a "slave" mechanism to work with the Tusi external gear. But you could use a servo out on your foil mast, right?