Could solar sails be used as turbines for power generation?

[dansmith170]

TL;DR Summary

Could solar sails be used as turbines for power generation?

It seems as though two advantages to using a solar sail turbine system instead of solar panels would be (1) the sails may not degrade as quickly as the solar panels, and (2) a sail turbine system may be lighter than a solar panel (and therefore less expensive to launch into orbit).

The drawback of using the sail turbine would seem to be that it would generate significantly less power than a solar panel.

I guess the determining factor of whether the "solar windmill" would be preferable would be whether it had a higher Power-to-Weight ratio; that is, if the solar windmill had a very low mass, then it may be a good alternative to the solar panel. My main concern here would be that the solar windmill would apparently need to be much less than a gram in mass to be competitive with the solar panel and that does not appear feasible.

Anyone have any thoughts or insights on this?

Thanks.

 

[berkeman]

TL;DR Summary: Could solar sails be used as turbines for power generation?

It seems as though two advantages to using a solar sail turbine system instead of solar panels would be (1) the sails may not degrade as quickly as the solar panels, and (2) a sail turbine system may be lighter than a solar panel (and therefore less expensive to launch into orbit).

The drawback of using the sail turbine would seem to be that it would generate significantly less power than a solar panel.

I guess the determining factor of whether the "solar windmill" would be preferable would be whether it had a higher Power-to-Weight ratio; that is, if the solar windmill had a very low mass, then it may be a good alternative to the solar panel. My main concern here would be that the solar windmill would apparently need to be much less than a gram in mass to be competitive with the solar panel and that does not appear feasible.

Anyone have any thoughts or insights on this?

Thanks.

You know the drill here, Dan. Post references links to your technical reading, and show your efficiency calculations for the configuration you propose (using LaTeX please).

Thanks very much...

 

[dansmith170]

Citations: https://en.wikipedia.org/wiki/Space-based_solar_power
https://en.wikipedia.org/wiki/Radiation_pressure
https://en.wikipedia.org/wiki/Aluminium
https://www.energy.gov/eere/solar/solar-performance-and-efficiency
https://en.wikipedia.org/wiki/Power-to-weight_ratio
I do not have a specific citation for this, but I estimated solar panel mass at 20 kg.

I do not know LaTeX format very well, here are the formulas I used to estimate power output of a "solar windmill" --

P = VI. (Power, Voltage, Current).
V = NAB(2*pi*f) (V = voltage, N = number of turns, A = area across rotor wire, B = magnetic field, f = frequency of rotation).
Torque = NIAB/R (R = resistance)
Torque = r F (r = radius, F = force)
F = 2IA/c (I = intensity in watts / area, A = area, c = speed of light, F = force)
And I = V/R.

Pick whatever sounds reasonable for the variables, I estimated the Wattage generated as electricity to be 6.5 microWatts - kind of spitballing here. (Although, perhaps this could be increased if resistance was decreased?).

Note: I estimated the force on the sail to be higher than it otherwise would be due to more light being reflected from collector mirrors.

 

[Nugatory]

here are the formulas I used to estimate power output

If you are going to put your radiation-pressure windmill on earth you will also want to include the effects of air resistance, which resists the tendency of the blades to rotate.

If you are going to attach the windmill to a spaceship outside the earth's atmosphere, you will have to do some calculation to see whether the windmill will turn the shaft of a generator relative to the stator, or end up just applying a small torque to the entire spacecraft.

 

[DaveC426913]

If you are going to attach the windmill to a spaceship outside the earth's atmosphere, you will have to do some calculation to see whether the windmill will turn the shaft of a generator relative to the stator, or end up just applying a small torque to the entire spacecraft.

Or just stick a second, counter-rotating windmill on there.

 

[Baluncore]

There will be a problem with bearings in space. Lubrication will be difficult.

Maybe it will need non-contact magnetic bearings, which could be integrated into the alternator, to reduce those bearing problems and use the permanent magnets on the rotor also for suspension.

Will stray iron meteorite dust stick to the magnetic bearings and jam them?

 

[jbriggs444]

If you are going to put your radiation-pressure windmill on earth you will also want to include the effects of air resistance, which resists the tendency of the blades to rotate.

"Resists" so strongly that a Crookes radiometer rotates backward on Earth as compared to its rotation direction in space.

 

[Vanadium 50]

and show your efficiency calculations

Which we don't have.

There have been a half-dozen similar threads from the OP and I am struggling to find one that says "a gizmo this big puts out this many watts". Without that, it's difficult to have a sensible discussion.

 

[hutchphd]

In addition to supplying counter torque to your solar windmill, there is a small matter of linear force. There is no handy dike to attach it to in most regions to mitigate it being blown away.

 

[jbriggs444]

There have been a half-dozen similar threads from the OP and I am struggling to find one that says "a gizmo this big puts out this many watts". Without that, it's difficult to have a sensible discussion.

Let me try an efficiency calculation.

Light moves fast. At the speed of light in fact. (*duh*). As a result, it tends to contain very little momentum per unit energy. By comparison, bullets, bowling balls, cars, cargo ships, water in penstocks and combustion products in gas turbines tend to have lot of momentum compared to their energy. That is because momentum is directly proportional to velocity while energy goes as the square of velocity -- $mv$ versus $\frac{1}{2}mv^2$. The ratio between the energy and momentum is $\frac{v}{2}$.

The faster you go, the less momentum you have per unit energy.

If you harvest the energy of light using a "sail turbine", what you are really capturing is the light's momentum. If the light bounces off your polished sail, most of its energy is retained in the reflected light. You have not captured that. If the light is absorbed by your blackened sail, most if its energy is deposited on the blackened surface, heating it up. You have not captured that. And now you have to dissipate the heat somehow.

The fraction of the light's original energy that is captured in the turbine will be given by the turbine blade's velocity as a fraction of the speed of light.

Note: If you are playing at home, you may notice a missing factor of two here. At light speed, $E=pc$. Our Newtonian prediction was that $E=p\frac{v}{2}$. That is a factor of two error. But let us not quibble over such trifles. [This cancels with the other factor of two discrepancy from ignoring that we get twice the momentum by reflecting the light].

In an ordinary gas turbojet engine, turbine blade tip speeds are on the order of the speed of sound. Call it 300 meters per second. Compared to the speed of light at 300,000,000 meters per second. That is a ratio of a million to one.

So if the sails in a solar turbine are spinning at less than the speed of a jet engine then the turbine will have an efficiency of less than 0.0001 percent.

Plain old solar cells can out-do that by at least five orders of magnitude.Digression alert...

You might object that we can improve efficiency by constructing the turbines from exotic materials. But there are limits to that.

If the tip speed is such that the kinetic energy of the molecules in the tip equals the chemical binding energy holding the molecules in the turbine blade together then the blade will fly apart. This limit turns out to be independent of how big you make the turbine. You can finesse it slightly by making the turbine blades broad at the base and narrow at the tip, but you'll only buy a small factor that way.

No possible chemical binding energy is sufficient to get a tip velocity at a significant percentage of light speed. Not even nuclear binding energies are sufficient.

If you are optimizing ultracentrifuges to maximize the centrifugal acceleration then the way you design around this materials limitation is to shrink the centrifuge. Since tip velocity is limited, you increase acceleration by decreasing radius.

I am not an engineer. But I try to think like one.

 

[russ_watters]

If you are going to attach the windmill to a spaceship outside the earth's atmosphere, you will have to do some calculation to see whether the windmill will turn the shaft of a generator relative to the stator, or end up just applying a small torque to the entire spacecraft.

I'm not sure what there is to calculate. Newton's third tells us that any/all torque applied to the shaft and used to extract power spins the entire spacecraft. You can only get around that partially and temporarily by letting different parts spin-up at different rates (not extracting the power).

 

[jbriggs444]

I'm not sure what there is to calculate. Newton's third tells us that any/all torque applied to the shaft and used to extract power spins the entire spacecraft. You can only get around that partially and temporarily by letting different parts spin-up at different rates (not extracting the power).

Counter-rotating turbines has been mentioned as a possibility. That seems like a good idea.

Or you could rotate the blades on the ends of your Crooks type arrangement to swap the black and silvered sides periodically -- spinning up first one way and then the other.

If you are using Crooks style paddle blades, you could line up a bunch of radiometers. Array the radiometers in a helical pattern with its axis facing the sun. Line the blackened faces up in the center of the helix while the silvered faces are arrayed on the outside. This way the "top" black face shades all of the ones behind it but the silvered faces do not shade each other. You could even put a piece of blackened ship hull (or a solar cell) on top of the helix as a cap to shade all of the black paddle faces. Then you do not even need to paint the paddles.

Rube Goldberg would be proud.

 

[russ_watters]

Counter-rotating turbines has been mentioned as a possibility. That seems like a good idea.

Or you could rotate the blades on the ends of your Crooks type arrangement to swap the black and silvered sides periodically -- spinning up first one way and then the other.

If you are using Crooks style paddle blades, you could line up a bunch of radiometers. Array the radiometers in a helical pattern with its axis facing the sun. Line the blackened faces up in the center of the helix while the silvered faces are arrayed on the outside. This way the "top" black face shades all of the ones behind it but the silvered faces do not shade each other. You could even put a piece of blackened ship hull (or a solar cell) on top of the helix as a cap to shade all of the black paddle faces. Then you do not even need to paint the paddles.

Rube Goldberg would be proud.

@jbriggs444 aren't those all temporary work-arounds that just increase thrust?

 

[jbriggs444]

@jbriggs444 aren't those all temporary work-arounds that just increase thrust?

I thought the goal is to eliminate net torque. Net thrust is a different task.

If the craft is in orbit about a planet, the effect of net thrust will approximately average itself away over the course of an orbit. One might modulate the exposed surface area for better stationkeeping.

 

[russ_watters]

I thought the goal is to eliminate net torque. Net thrust is trickier.

I see them as connected, when fixing one problem just transfers the problem to something else.

If the craft is in orbit, the effect of net thrust will approximately average itself out over the course of an orbit.

I'm thin on orbital dynamics, but doesn't that just increase the eccentricity over time?

 

[jbriggs444]

I see them as connected, when fixing one problem just transfers the problem to something else.

Say we have a symmetric craft. For the sake of having something definite, it is a circular cylinder with one of the circular faces facing the sun. We will call this face the "top".

We mount a radiometer on the top, somewhere off center, almost on the rim. It is oriented like a paddle wheel with its axle parallel to the top and at right angles to a line of radius.

We blacken the "front" side of the paddle blades. [The "front" is the side that moves toward the sun]. Or we shade them. The "front" sides are toward the middle of the craft. The "back" sides are toward the rim.

We mount a second radiometer on the top, diametrically opposite to the first so that it is symmetric in all respects.

By symmetry, any thrust from light will supply zero net torque to the craft as a whole. However, one radiometer paddle wheel will rotate in one direction and the other paddle wheel will rotate in the opposite direction. We can theoretically harvest a tiny amount of power from each.

I'm thin on orbital dynamics, but doesn't that just increase the eccentricity over time?

I believe that you get eccentricity. Perhaps you get an eccentricity that will precess. I am also thin on orbital dynamics. But I would expect that any progressive eccentricity (which I do not believe would result in the first place) could be dealt with by rhythmicly shading the silvered sides of the two radiometers in time with the orbit.

 

[russ_watters]

@jbriggs444 i'll bow out here as i believe the OP has triggered a game of "find the flaw in the PMM" except that he's getting us to play for him. The game is won/lost when the PMM gets so complex that someone accidentally rounds-off the violation.

 

[Bystander]

@jbriggs444 i'll bow out here as i believe the OP has triggered a game of "find the flaw in the PMM" except that he's getting us to play for him. The game is won/lost when the PMM gets so complex that someone accidentally rounds-off the violation.

Close it?

 

[BWV]

P = VI. (Power, Voltage, Current).
V = NAB(2*pi*f) (V = voltage, N = number of turns, A = area across rotor wire, B = magnetic field, f = frequency of rotation).
Torque = NIAB/R (R = resistance)
Torque = r F (r = radius, F = force)
F = 2IA/c (I = intensity in watts / area, A = area, c = speed of light, F = force)
And I = V/R.

With ChatGPT there is no need to learn Latex, it can do it all, just in the Bing AI extension told it to 'convert these equations to latex code for a bulletin board:' and copied and pasted your text:\begin{equation*} P = VI \qquad \text{(Power, Voltage, Current)} \end{equation*}

\begin{equation*} V = NAB(2\pi f) \qquad \text{(Voltage, N = number of turns, A = area across rotor wire, B = magnetic field, f = frequency of rotation)} \end{equation*}

\begin{equation*} Torque = \frac{NIAB}{R} \qquad \text{(R = resistance)} \end{equation*}

\begin{equation*} Torque = r F \qquad \text{(r = radius, F = force)} \end{equation*}

\begin{equation*} F = \frac{2IA}{c} \qquad \text{(I = intensity in watts / area, A = area, c = speed of light, F = force)} \end{equation*}

And

\begin{equation*} I = \frac{V}{R} \end{equation*}

 

[dansmith170]

So if the sails in a solar turbine are spinning at less than the speed of a jet engine then the turbine will have an efficiency of less than 0.0001 percent.

Plain old solar cells can out-do that by at least five orders of magnitude.

I am not sure if this is entirely accurate. The efficiency calculation you outlined seems to say that efficiency will depend on the momentum transferred. But the energy produced depends on a current that is caused by rotation, where that rotation is caused by a momentum transfer, so I do not think the energy output can be put in terms of momentum.

Power = Torque x angular velocity.

Let's suppose torque is about (10 microNewtons * meters) (a fair supposition according to Wikipedia).
If we can increase angular velocity to 1 million rpm, our power output should be 1 Watt. A solar sail efficiency in outer space may be about 35%. Meaning that for 1360 Watts from the sun, about 476 Watts turns into power generated. If this is correct, then the "solar windmill" will only be about two orders of magnitude different from the solar panel.

If the "solar windmill" can be made sufficiently lightweight (low mass), then it should generate more electricity per kilogram, and could therefore be a preferable alternative to solar panels.

Additionally, it may be that the rpm can be increased beyond 1 million rpm. Further, torque may be able to be increased by either increasing the radius of spin or by adding mirrors to increase light intensity (and therefore the force of light) on the "solar windmill."

https://en.wikipedia.org/wiki/Radiation_pressure
https://en.wikipedia.org/wiki/Solar_irradiance
https://www.solar.com/learn/space-based-solar-vs-conventional-solar-how-are-they-different/

 

[Vanadium 50]

If you don't like our efficiency calculations, show us your own. No handwaving, no disconnected equations, no pages of text, no explanation why you shouldn't need to do this. Just "Power out = ...",

 

[jbriggs444]

I am not sure if this is entirely accurate. The efficiency calculation you outlined seems to say that efficiency will depend on the momentum transferred. But the energy produced depends on a current that is caused by rotation, where that rotation is caused by a momentum transfer, so I do not think the energy output can be put in terms of momentum.

Power = Torque x angular velocity.

Let's suppose torque is about (10 microNewtons * meters) (a fair supposition according to Wikipedia).

For what moment arm and what sail area? The figure seems to be in the ballpark for a one square meter sail area on a one meter radius turbine.

If we can increase angular velocity to 1 million rpm, our power output should be 1 Watt

Sounds about right. One million rpm is about 100,000 radians per second.

So roughly one kilowatt of input power and one watt of harvested power. 0.1 percent efficiency.

Now, what kind of acceleration are we talking for the blade tips of the turbine. $a=\frac{\omega^2}{r}$ =
10,000,000,000 m/s². About one million g's.

You can get ultracentrifuges to do a million g's. But not with a one meter radius. And probably not with only 10 microNewton-meters of frictional resistance.

All for that one watt of power.

A solar sail efficiency in outer space may be about 35%. Meaning that for 1360 Watts from the sun, about 476 Watts turns into power generated. If this is correct, then the "solar windmill" will only be about two orders of magnitude different from the solar panel.

Sorry, the assertion of 35 percent efficiency is incorrect. Please provide either a reference or a calculation.

One of your references quoted 34 percent efficiency for solar cells. Not solar sails.

 

[dansmith170]

If you don't like our efficiency calculations, show us your own. No handwaving, no disconnected equations, no pages of text, no explanation why you shouldn''t need to do this. Just "Power out = ....",

Okay, solar windmill -->

Efficiency = Power out / Power in x100 = (9.4 W / 1360 W) * 100 = .7%

 

[jbriggs444]

Okay, solar windmill -->

Efficiency = Power out / Power in x100 = (9.4 W / 1360 W) * 100 = .7%

This "solar windmill" that produces 9.4 W from a 1 square meter capture area. Reference please.

 

[dansmith170]

Now, what kind of acceleration are we talking for the blade tips of the turbine. $a=\frac{\omega^2}{r}$ =
10,000,000,000 m/s². About one million g's.

You can get ultracentrifuges to do a million g's. But not with a one meter radius. And probably not with only 10 microNewton-meters of frictional resistance.Sorry, the assertion of 35 percent efficiency is incorrect. Please provide either a reference or a calculation.

One of your references quoted 34 percent efficiency for solar cells. Not solar sails.

34% efficiency for the solar panels, that is what I meant --

https://www.solar.com/learn/space-based-solar-vs-conventional-solar-how-are-they-different/

Would you say more about the acceleration of the turbine blades, why is 1 million g's a problem?

 

[dansmith170]

This "solar windmill" that produces 9.4 W from a 1 square meter capture area. Reference please.

I do not have a reference, I calculated power output with Torque x Angular Velocity. Supposing there to be 1 million rpm of the armature, and 10 meters for radius of the turbines, at 10 microNewtons of forces from sunlight per meter squared, that is 9.4 Watts per square meter.

 

[berkeman]

1 million rpm of the armature

Say what?

 

[Vanadium 50]

Say what?

We're clearly in fantasy land. Even if the idea were sound, which it is not, not only will steel flow like water at these forces, for blades of a few meters weighing a few hundred kilos, it will take a million years or so to spin up,

 

[dansmith170]

In addition to supplying counter torque to your solar windmill, there is a small matter of linear force. There is no handy dike to attach it to in most regions to mitigate it being blown away.

Perhaps the Earth's gravity could be used as a kind of tether?

 

[russ_watters]

I do not have a reference, I calculated power output with Torque x Angular Velocity. Supposing there to be 1 million rpm of the armature, and 10 meters for radius of the turbines, at 10 microNewtons of forces from sunlight per meter squared, that is 9.4 Watts per square meter.

I believe you are trying to disconnect power out from power in by assuming that you can increase the rpm without a drop in torque. You can't with a wind turbine either.

This game is over.