Solar Turbines on the moon

Question

Related to other questions about power generation on the moon. URL's will be added shortly...

Given that force is experienced by objects hit by sunlight, such as a solar sail, would a turbine of some form be plausible as a power generation option.

This could take the form of a horizontal carousel of "blades", or a mast with a set of blades such as wind turbines on Earth.

Essentially, can I get some pointers as to: whether it's viable, whether it's been proposed, whether there is something significant that would prevent such development from being possible, etc.

Answer 1

This is an interesting question (to me at least) so I'll try an answer. I'll address the following aspects

• ...would a turbine of some form be plausible as a power generation option.
• ...whether it's viable,
• whether there is something significant that would prevent such development from being possible

Sure it would work in principle. You would have to rethink what the blades look like. Wind turbine blades and even windmill sails work in fluids that flow around the blades. The forces on the blades (producing torque at the axis) are best understood and optimized using fluid dynamics. So you would have to probably abandon the notion that you're making a turbine proper.

Without going into detailed design, let's calculate the mechanical force that light can produce on a surface².

• Radiation pressure from momentum of an electromagnetic wave
• Poynting vector

gives us $P = I/c$ where $P$ is pressure, $I$ is the intensity of the light and $c$ is the speed of light. Note that this is wavelength-agnostic. If we use the solar constant¹ of 1360 W/m^2 and 3E+08 m/s we get a pressure of 4.53E-06 Newtons per square meter.

Now a 20% efficient solar photovoltaic panel gives us 270 watts/m^2, and we'd like to get something comparable our solar paddle wheel.

How do we convert that force of 4.53E-06 Newtons per square meter to watts per square meter? We multiply by velocity. The power we put into something is the force we apply multiplied by the speed that it's already moving when the force is applied.

You can push on a fixed wall all day with 1 Newton, but produce no power. But if you can push with 1 Newton on a bicyclist who's moving, you transfer power. And if the bicyclist is moving twice as fast and you can still manage to push with 1 Newton, you double the power!

So speed is the key. The power you generate is directly proportional to the speed the blade is moving.

The faster the paddle is moving - receding from the Sun, the more power we produce.

Do we violate conservation of energy? No! The light reflected by the receding paddle is Doppler-shifted to longer wavelength. Now we're really extracting substantial energy from the light when the paddle is moving fast.

Let's say your paddle is moving backwards at 1% the speed of light. That Doppler-shifts the reflected light by 2% lower in frequency, and therefore 2% lower in energy. That's 0.02 * 1360 W/m^2 = 27 W/m^2 or 1/10 of what a solar photovoltaic panel would produce with no moving parts.

We can recalculate that here:

Let's say your solar paddle wheel has mirrored blades, reflecting back towards the Sun. Now we pick up a factor of 2 because we reverse the momentum (F = dp/dt) of the photons. We're now at 9.05E-06 N/m^2. Let's say the paddle is moving backwards at 1% the speed of light or 3E+06 m/s. The power is then 9.05E-06 * 3E+06 = 27 watts, the same number we got by just calculating the energy loss of the reflected light due to doppler shift.

But could you make one?

A mechanical system involving paddles moving at three million meters per second poses several problems.

If your paddle wheels were macroscopic, they would fly apart - there are not likely any known materials with tensile strengths able to hold a big paddle wheel together if it was meter sized.

Maybe you could nano-fabricate zillions of tiny wheels with edge velocities of 0.01 c that would hold together, tiny spinning dust particles or very large molecules, but that will take some serious development.

You might propose that you need some reliable micro-power source that runs during lunar night, and the infrared radiation from the Earth (which is probably roughly of order 10 watts/m^2) can't be harnesed with solar photovoltaics because of their large band gaps requiring visible or near infrared only, but a simple Stirling engine could use collected infrared light from the Earth and make mechanical power by re-radiating it to the "cold of space" and that could turn a generator.

I think there's no situation where you could even attempt to develop a solar photon paddlewheel power system that would work that could even come close to existing technologies.

Alternatively

If you put your paddles in a glass container and added some low-pressure gas, you could make a Crookes radiometer At low speeds (below the speed of sound) these can produce much more power than a device based on solar photon pressure because they convert sunlight to heat and transfer that heat to moving matter.

But if you are going to convert sunlight to heat and transfer that to moving matter, might as well make a solar thermal Stirling engine generator.

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¹Why were solar constant measurements before TSIS-1 all about 0.3% high?

²see also

• this answer to Is Electromagnetic Propulsion Like Radiation Pressure propulsion?
• this answer to Kinetic reaction from emission of electromagnetic radiation and links therein