Windmills in Red Mars

Note: this post is based off a recitation problem I wrote when I was TAing graduate heat transfer last semester. At some point I hope to upload some of the problems I wrote, including this one, which should provide a more structural/mathematical approach to answering the question (rather than just the conceptual approach provided here).

In high school, I read the science fiction novel Red Mars by Kim Stanley Robinson, which chronicles the efforts of a colony of astronauts to terraform Mars (that is, make it more Earth-like, and therefore habitable to humans). Red Mars is fairly far towards the “hard” end of science fiction, meaning that the story is fueled, as much as possible, by actual science that we currently have a strong understanding of. To give recent Hollywood examples, The Martian is representative of hard science fiction, while Interstellar is representative of soft science fiction. This distinction is important because when something doesn’t click as being realistic (in terms of the science) in soft sci-fi, you’re expected to continue suspending disbelief, while if something doesn’t click as being realistic in hard sci-fi, it means the author messed up.

I read Red Mars many years ago, and in the intervening time I’ve forgotten most of the book. However, there is one plot point I still remember, because I disagreed with my high school science teacher about its scientific accuracy. At one point in the story, the colonists distribute windmills all over the surface of Mars which power heaters, with the intention of raising the average temperature of Mars. This post is concerned with the question of whether or not such a scheme could actually raise the surface temperature of Mars. Later in the story we find (spoiler alert) that the proponent of the windmill distribution plan didn’t care about their ability to raise the planet’s temperature, he wanted to use them to distribute plant life (algae? I don’t remember exactly) around Mars. That’s all fine and good, except that 1. some scientists in the story later find that the temperature of Mars has risen by some small (but apparently measurable) amount that they attribute to the windmills, and 2. the plan should be thermodynamically sound if we’re to believe that the other colonists could be convinced to go along with it, regardless of the plan’s true goals.

My science teacher argued that the plan is unsound, because wind is kinetic energy that will eventually be viscously dissipated and converted to heat anyways, so the windmills are pointless. My argument was that a Mars with windmills will be less windy on average (and therefore have less kinetic energy in its atmosphere) and because of conservation of energy its reasonable that the drop in kinetic energy would be accounted for by a rise in thermal energy (i.e., Mars would be at a higher temperature). For a long time I couldn’t reconcile these two viewpoints, however with some simplifying assumptions, we can capture the physics of the situation in a way that is compatible with both arguments.

Our Mars model has two forms of energy: kinetic energy (how windy it is on Mars) and thermal energy (how hot Mars is). The other important piece to know is that the only way Mars can exchange energy with the universe is by radiation: it absorbs energy radiated from the sun, and radiates out infrared radiation to the universe. The energy it receives from the sun should be constant, but the energy it radiates away is a function of its temperature (the hotter Mars gets, the more it radiates away). That means that Mars has some equilibrium temperature, at which the rate it loses energy to the universe is equal to the rate it absorbs energy from the sun. This system is self-balancing (or has negative feedback, to use control theory terminology): if Mars’ temperature rises above the equilibrium, it radiates away more than it absorbs, so the temperature lowers back to the equilibrium value. And vice-versa if Mars’ temperature drops below the equilibrium value. What is not defined by our simple model is how fast this happens, we just know that given enough time, Mars will reach its equilibrium temperature. From this perspective, my science teacher’s argument is correct, and even if you convert kinetic energy to thermal energy, in the long run the Martian temperature remains unchanged. However, this is only the long term behavior. When the windmills are deployed on Mars, they act to convert some of the kinetic energy in the wind to thermal energy. They will continue this conversion process until the wind on Mars reaches a new, lower, “post-windmill” value. Immediately after the windmills have converted the kinetic energy to thermal energy, they will have temporarily increased the average temperature of Mars.

So the full picture of this simple model for Mars is that with the windmills, the average temperature of Mars could be changed temporarily by converting kinetic energy to thermal energy, but in the long run the equilibrium temperature of Mars is determined by radiative exchange with the universe, which the windmills can’t (directly) address. In terms of how this fits into how realistic Red Mars is, I would say that on the first point, there could be a tiny (temporary) increase in temperature due to the windmills, but on the second point, at least one of the colonists should’ve had a strong enough understanding of thermodynamics to explain that this plan would ultimately be futile, and resources should be diverted to a different endeavor. So unfortunately, for this small corner of the story, it seems that Kim Stanley Robinson messed up.