Fascinating wind machine, perhaps a hoax

A fascinating passage in Anis Aouni's narration in the video about the Saphonian wind machine is this:


He responds by saying that it does not involve rotation.

So there!

But we wonder, "So how does it nutate"?

Trying to transition from the design taught by the patent to what seems to be the current generation design, it seems is if it nutates because the fulcrum slide makes it notate.

So how does the wind get into the picture?

Well, fancifully, we might think that the wind makes it nutate after "we show it how" with the rotating fulcrum slide.

It is tempting to make the comparison with the class of induction motor that has zero torque at zero speed. We have to push it to start it running. (Many years ago some electrical clocks were driven by a synchronous form of such a motor. You had to start them by spinning a little knob on the back. If you wanted, as a joke, you could start them to run backward.)

Of course the electromechanical phenomenon by which they would develop torque at a non-zero speed is well understood. (It is the same phenomenon by which motors that start automatically in fact develop their real torque. I studied it in engineering school.)

So perhaps I am just missing the comparable phenomenon for a wind-driven nutating disk. After all, I didn't study wind-driven machines in engineering school. Perhaps the mechanical engineers did.

Perhaps once the wind-to-nutation phenomenon is "breathing on its own", the fulcrum slide could be withdrawn. Perhaps it is only needed at startup.

Best regards,

Doug

Just a quick note. This is fluid dynamics and not pure mechanics. The wind is not stable and the flow of air around the sail is likely to be turbulent. That alone would be sufficient to start nutation.

Hi, Jerome,

Jerome Marot said:

Just a quick note. This is fluid dynamics and not pure mechanics. The wind is not stable and the flow of air around the sail is likely to be turbulent. That alone would be sufficient to start nutation.

Click to expand...

That might well be.

Best regards,

Doug

It is interesting to consider the scale of wind power we are dealing with here.

Imagine a small conventional bladed turbine (perhaps a laboratory test unit) with a blade circle diameter of one meter (3.28 feet). We consider it to intercept a "column" of moving air in the wind with a diameter of one meter.

Assume that the speed of the wind is 10 miles per hour (4.47 m/sec). This is slightly above the speed at which large commercial turbines typically develop their largest power coefficient (extract the largest fraction of the kinetic power in the intercepted wind.

For that wind speed, the kinetic power in our "one meter diameter" column within the wind would be approximately 42.7 watts.

The Betz limit predicts that the most power we could extract from the amount of intercepted wind at that speed would be 59.3% of the contained kinetic power, or 25.3 watts.

Large bladed turbines achieve maximum power coefficients of perhaps 0.50. If our little turbine did as well (I have no idea how that actually scales). it would extract from the intercepted wind 21.3 watts.

Note that the kinetic power content of a cylinder-shaped "column" of air within the wind, for any wind speed, goes as its area. Thus, for a hypothetical test turbine with a blade circle of diameter 2 meters, all the power figures shown above would increase by four times. The power output for a power coefficient of 0.5 would be 85.3 watts.

We hear various claims about the power coefficient of the Saphonian machine, but they seem to center on the notion that it extracts twice as much power from the wind as a conventional bladed turbine. That would mean that it could approach extraction of all the energy from the intercepted wind column.

That would be a wondrous feat indeed. It would mean, among other things, that the air from the intercepted column, after its encounter with the Saphonian machine, would be "spent", without kinetic power, and thus would have zero speed. It therefore would not "leave the field of battle" and would of course prevent any further air from passing through the machine. Thus the machine could not perform this wondrous feat for but an instant.

Best regards,

Doug

Especially for those with some electrical background, I'll present a situation from electrical engineering that is conceptually somewhat parallel to the matter of not being able to extract the full kinetic power from a wind stream. The parallel is hardly exact, technically, but I think it helps us to see the basic "challenge".

************

Suppose we have a DC power, perhaps for use in a laboratory. We know that as we increase the load on it (that is, draw current from it) its voltage "sags". If the decrease in voltage is linear with the current drawn, Thévenin teaches that we can consider it to have this "equivalent circuit":


VT is the "Thévenin source voltage", and RT is the Thévenin internal resistance. VO is what we often call the "open circuit voltage" of this equivalent circuit, since it is the voltage we see at the output terminals when they are open (that is, there is no load connected).

We can lean about the load behavior of such an equivalent circuit with some extreme cases. Here is the first:


Here our "load" is an open circuit (no load at all). We see that the load current, IL, is thus zero. The load voltage is the open circuit voltage of the circuit (duh!). The load power, PL, is the product of the load voltage and the load current. Since the load current is zero, the power into the load is zero. (A good thing, given that there really is no load!)

Now we go to the other extreme.


We have applied to the output terminals an extreme load: a "short circuit". If this were an actual power supply, it would either blow its internal protective fuse or blow up. but this is only a theoretical model of such a power supply.

We see the load current, IL, and the load voltage, VL. We see again that the load power, PL is the product of the load voltage and the load current. The load voltage is zero, so the power into our "load" is zero.

Next we will show the general non-extreme case:


Here the load has a resistance RL. We see the various relationships. We could easily calculate the power into the load, but I chose not to clutter up the figure with that. Suffice it to say that, since there is a non-zero load voltage, and a non-zero load current, there is a non-zero power into the load.

Now if we looked at the load power as a function of the load resistance, we could find through (the) calculus for what value of RL would the load power (for this power supply equivalent circuit) be the greatest. It turns out that tidily this is when RL = RT: the load resistance is the same as the internal resistance of the source.


We see in fact that this maximum amount of power that can be extracted from this source is VT^2/2RT.

The condition for maximum power extraction, Rl=RT, is most often spoken of as "impedance matching". Impedance is a quantity that, in AC circuits, plays somewhat the role of resistance (but not exactly). A special case of an impedance is when it is in fact a resistance.

For an AC source, the Thévenin equivalent circuit is an AC voltage source in series with an impedance., the "internal impedance" of the source.

So we might expect that the maximum power could be extracted from such an AC source when the impedance of the load is the same as the internal, impedance of the source. But not so. Rather, the condition for maximum power extraction is when the impedance of the load is the complex conjugate of the internal impedance (don't ask).

So to speak of the situation we see above, in a DC circuit, as "impedance matching", which is in a way technically accurate, is the result of years of authors showing off their sophomore year electrical engineering vocabulary.

But back to things Saphonian. The very situations that limit the extraction of energy from our little, power supply equivalent circuit at the extremes of "load" are like the very things that limit the extraction of power from the wind at the extremes of load, which are:

• If the wind machine gets the benefit of the full "free velocity" of the wind, it's because it exerts no back force on the wind to slow the wind down, and thus the wind exerts no force on it. So in this case, no power is extracted from the wind.

• If the wind machine gets the benefit of the full "force capability" of the wind, it does so by "stalling" the wind (as the side of a barn would). Thus there is the highest possible force but no motion. Again this means that in this case, no power is extracted from the wind.

Now the situation that is conceptually parallel to the "matched load resistance" in my electrical example is the case to which the Betz limit applies. The analysis is more complex than in the electrical case, in part because the energy in moving wind varies as the cube of the velocity, and because we have the matter of wind "escaping" the turbine in the face of the back force exerted by the turbine. Thus, for example, the optimal case is not where the outgoing wind has half the velocity of the incoming wind but rather 1/3.

Best regards,

Doug

Jerome Marot said:

I have little doubt that it is possible to create some electricity with that machine. Anything that moves will be able to create electricity when there is enough wind. This is not the question. The question is whether that machine would be practical and the probable answer is no.

First, efficiency is probably rather low, contrary to what the inventor claims. Second, the main problem with small wind turbines is not efficiency (there is plenty of wind), but maintenance costs. Optimal small wind turbines do not use a complicated combined mechanic hydraulic conversion.

Here, courtesy of wikipedia, a 5 KW Darius Turbine for residencial use. 5KW typically covers the needs of a single house.

Click to expand...

I like this idea, Jerome! I would love to have free electricity and I do not imagine it would cause a significant loss of birdlife! I wonder why I see none where I live?

asher

Asher Kelman said:

I like this idea, Jerome! I would love to have free electricity and I do not imagine it would cause a significant loss of birdlife! I wonder why I see none where I live?

Click to expand...

Because it is not free. If you run a wind turbine like this one, the wind may well be free, but initial costs and maintenance are not. Maintenance, in particular, can be quite costly for wind or water turbines: they are mechanical devices and are submitted to wear and tear. In many cases, the cost are not competitive with mains power.

On top of that, local regulations may not permit you to erect wind turbines near your home. There are some reasons for that: noise (some small wind turbines are quite loud, although most commercial ones are designed to minimise that impact) and safety in areas where windstorms are common. There is also an impact of wind turbines: they extract energy by slowing the wind. If you have one, you'll get all the winds. If all your neighbours have one as well, you may well find out that your turbine is a lot less efficient.

This being said, wind power is probably the most promising technology for renewable energy generation. The world record is Denmark, with 39% of the country electricity being produced in this way.