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## Lunar Swimming

What if there was a lake on the Moon? What would it be like to swim in it? Presuming that it is sheltered in a regular atmosphere, in some giant dome or something.

Kim Holder

This would be so cool.

In fact, I honestly think it's cool enough that it gives us a pretty good reason to go to the Moon in the first place. At the very least, it's better than the one Kennedy gave.

Floating would feel about the same on the Moon as on Earth, since how high in the water you float depends only on your body's density compared to the water's, not the strength of gravity.

Swimming underwater would also feel pretty similar. The inertia of the water is the main source of drag when swimming, and inertia is a property of matter[1]♬ BILL NYE THE SCIENCE GUY ♬ independent of gravity. The top speed of a submerged swimmer would be about the same on the Moon as here—about 2 meters/second.

Everything else would be different and way cooler. The waves would be bigger, the splash fights more intense, and swimmers would be able to jump out of the water like dolphins.

This[2]Not this one. The other one.[3]The simplest approach, which gives us an approximate answer, is to treat the swimmer as a simple projectile. The formula for the height of a projectile is:

$$\frac{\text{speed}^2}{2\times\text{gravity}}$$

... which tells us that a champion swimmer moving at 2 meters per second (4.5 mph) would only have enough kinetic energy to lift their body about 20 centimeters against gravity.

That's not totally accurate, although it's enough to tell us that dolphin jumps on Earth probably aren't in the cards for us. But to get a more accurate answer (and an equation we can apply to the Moon), we need to account for a few other things.

When a swimmer first breaks the surface, they don't have to lift their full weight; they're partially supported by buoyancy. As more of their body leaves the water, the force of buoyancy decreases, since their body is displacing less water. Since the force of gravity isn't changing, their net weight increases.

You can calculate how much potential energy is required to lift a body vertically through the surface to a certain height, but it's a complicated integral (you integrate the displacement of the submerged portion of their body over the vertical distance they travel) and depends on their body shape. For a human body moving fast enough to jump most of the way out of the water, this effect probably adds about half a torso-length to their final height—and less if they're not able to make it all the way out.

The other effect we have to account for is the fact that a swimmer can continue kicking as they start to leave the water. When a swimmer is submerged and moving at top speed, the drag from the water is equal to the thrust they generate by kicking and ... whatever the gerund form of the verb is for the things your arms do while swimming. My first thought was "stroking," but it's definitely not that.

Anyway, once the jumping swimmer breaks the surface, the drag almost vanishes, but they can keep kicking for a few moments. To figure out how much energy this adds, you can multiply the thrust from kicking by the distance over which they're kicking after breaking the surface, since energy equals force times distance. The distance is most of a body length, or 1 to 1.5 meters. As for the force from kicking, random Google results for a search for lifeguard qualifications suggest that good swimmers might be able to carry 10 lbs over their heads for a short distance, which means they're generating a little more than 10 pounds-force (50+ N) of kicking thrust.

We can combine all these together into a big ol' equation:

$\text{Jump height}=\left(\frac{\tfrac{1}{2}\times\text{body mass}\times\left(\text{top speed}\right)^2+\text{kick force}\times\text{torso length}}{\text{Earth gravity}\times\text{body mass}}\right)+\left(\text{buoyancy correction} \right)$
footnote contains some detail on the math behind a dolphin jump. Calculating the height a swimmer can jump out of the water requires taking several different things into account, but the bottom line is that a normal swimmer on the Moon could probably launch themselves a full meter out of the water, and Michael Phelps may well be able to manage 2 or 3.

The numbers get even more exciting when we introduce fins.

Swimmers wearing fins can go substantially faster than regular swimmers without them (although the fastest swimmer wearing flippers will still lose to a runner, even if the runner is also wearing flippers and jumping over hurdles).

Champion finswimmers can go almost 3.2 m/s wearing a monofin, which is fast enough for some pretty impressive jumps—even on Earth. Data on swimfin top speeds and thrusts[4]This paper provides some sample data. suggest that on the Moon, a champion finswimmer could probably launch themselves as high as 4 or 5 meters into the air. In other words, on the Moon, you could conceivably do a high dive in reverse.

But it gets even better. A 2012 paper in PLoS ONE, titled Humans Running in Place on Water at Simulated Reduced Gravity, concluded that while humans can't run on the surface of water on Earth,[5]They actually provide a citation for this statement, which is delightful. they might just barely be able to do so on the Moon. (I highly recommend reading their paper, if only for the hilarious experimental setup illustration on page 2.)

Because of the reduced gravity on the Moon, the water would be launched upward more easily, just like the swimmers. The result would be larger waves and more flying droplets. In technical terms, a pool on the Moon would be more "splashy".[6]The SI unit of splashiness is the splashypant.

To avoid splashing all the water out, you'd want to design the deck so water drains quickly back into the pool. You could just make the rim higher, but then you'd spoil one of the key joys of a pool on the Moon—exiting via Slip 'N Slide:

I 100% support this idea. If we ever build a Moon base, I think we should absolutely build a big swimming pool there. Sure, sending a swimming pool's worth of water (135 horses) to the Moon's surface would be expensive.[7]If you decided to bundle a backyard pool into individual two-liter bottles, and sent them in 3,000 batches of 10 each via the startup Astrobotic, it would cost you \$72 billion (according to their website's calculator). But on the other hand, this lunar base is going to have people on it, so you need to send some water anyway.[8]Sending a supply of water and a filter system is probably cheaper than sending a replacement astronaut every 3 or 4 days, although I encourage NASA to run the numbers on that to be sure.

And it's really not impossible. A large backyard swimming pool weighs about as much as four Apollo lunar landers. A next-generation[9](or, heck, previous-generation) heavy-lift rocket, like Boeing's NASA SLS or Elon Musk's SpaceX Falcon Heavy, would be able to deliver a good-sized pool to the Moon in not too many trips.

So maybe the next step, if you really want a swimming pool on the Moon, is to call Elon Musk and ask for a quote.

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