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A Comprehensive Guide to the Physics of Running on the Moon



One day people will be permanently on the moon. Law? One day it will happen. So how will we live on the moon? And perhaps a more important question – how do we go there ? To prepare for our lunar colony, let me look at three movements we can do on the moon: jump, run, and turn.

Let me note that this analysis is inspired by Andy Weir's latest novel Artemis ]. I will not spoil the plot except to say that there is a girl moving on the moon. Weir does a pretty good job and describes what would be different if you moved the moon compared to the earth.

What is different about the moon compared to the earth? The biggest difference is the gravitational field on the surface. On Earth, the field has a magnitude of 9.8 Newton per kilogram (we use the symbol g). This means that a free falling object (no air resistance) would have a downward acceleration of 9.8 m / s 2 . On the moon, the gravitational field is about 1

.6 N / kg, so the vertical acceleration of a lunar object is much less than one on Earth.

There is another important difference to the moon: it does not have any air. If you're a human jumping, maybe that's no big deal. A terrestrial, jumping human does not move fast enough for air resistance to play a significant role. On the moon, however, the same human would probably want to wear a spacesuit. This suit would both increase the effective mass and reduce the freedom of movement for a moving person. Oh, if there's a lunar base, there'd probably be air in it, so you would not have to wear a spacesuit if you did not think it looked cool (it would).

Jumping to the Moon

I will start with the simplest jump in motion. Suppose that during a normal human jump a human pushes with a maximum force over a certain distance to the ground. This distance is from the lowest position in the projection squat until the feet are no longer in contact with the ground.

Now for some starting values ​​(you can change them if you want). I'll say that this maximum bounce is three times the weight of the person (the weight on Earth) and the jump distance is 15 centimeters – that's just a guess. With these values, I can not model the movement of a jumping human on Earth. I only calculate the total force as either the force pushing upwards plus gravity while it is "in contact" with the ground or just gravity afterward. It should be a fairly simple numeric calculation.

I'll make a few changes for a jumping human on the moon. Obviously the gravitational field will change – but also some other things. I assume that the person wears a space suit, so this will increase the total mass (but not the maximum bounce). Since a spacesuit is bulky, the jump distance will also be smaller. OK, let's get to him. Here are two jumpers (Moon and Earth). If you want the code for this calculation, go here.

That's what it would look like (with spherical people for simplicity).

Here is also a diagram of the vertical position of the two jumpers. [19659010] A few things to notice. First, the earth jumper starts at a higher speed. Why? Because the lunar jumper has more mass (spacesuit and stuff). Second, the lunar jumper both rises higher and remains much longer off the ground due to the lower vertical acceleration.

But wait! How about a real video of a lunar jump? Here is a video of John Young's famous "spring greeting" during the Apollo 16 mission.

Pretty cool – but without a spacesuit, a human could probably jump even higher. Here's an old NASA movie of a jumping human in simulated moon gravity. The method of NASA (very creative) to simulate the gravity of the moon, is to let the a-human largely horizontally float through strings and then move on a mostly vertical surface to move

Running on the moon [19659006] It's not really a spoiler, but one of the first scenes in the book Artemis has the main character (jazz) on the surface of the moon. For some reason (read the book), she starts running in her spacesuit pretty quickly. So, how about running on the moon?

Yes, there is a video of real astronauts moving in a way that could be called "running" – but I still want to model that movement. I have previously built a model of a running man and now I can just change something to fit the moon. Here is my previous article on a running human model. Some important points aspect of this model (remember, it's still just a model).

  • A human is jumping on the ground like a ball. It consists of two parts: contact with the ground and movement through the air.
  • The part where the human being does not have contact with the ground has to take a minimum of time so that the human being can change his feet from front to back.
  • During contact with the ground, humans can only exert maximum force.
  • The contact time with the ground decreases with linear running speed.

All this together means that as the runner moves faster, a larger component of the compressive force must be applied in the vertical direction to lift the person off the ground as the contact time decreases. Finally, the human achieves a maximum speed using all the force in the vertical direction. You can see my model code here.

But what about walking on the moon? The big difference is the time. Since the gravitational field is small, the human is in the air for a much longer time with a smaller vertical thrust force. This means that more of the maximum force in the horizontal direction can be used to increase the horizontal speed.

OK, but what about a plot? Here is my running model on Earth as well as on the Moon. I raised the Moonman's mass to simulate a spacesuit, and I also increased the "step-time" man has on the ground to account for a voluminous suit that would require more leg swing.

Here is a diagram of the speed as a function of time for these two runners

The Earth person reaches a speed of almost 10 m / s, but the Moonman can easily exceed 15 m go / s. But wait! It is even better. This requires the same kind of running style for both gravitational fields. On the moon, however, it is very likely that there are more efficient running styles that exploit the low gravitational field.

It's probably not very surprising that people have already explored the idea of ​​running in low gravity. Just take a look at this NASA test with the same "horizontal running" sprint as in the spring video.

Oh, there is also this interesting paper that looks at the theoretical and simulated running speeds on the Moon – "The Preferred Running Speed ​​of Actual Moon Gravity," from the Journal of Experimental Biology. For this study, they put actual people on treadmills while flying in an airplane in parabolic orbits to produce a lower apparent weight. But really, who knows how it will really work until we take it seriously to be on the moon.

Running and Turning

Running in a straight line could be fun for a short time – but if you really want maneuvers around you, you'll eventually have to turn around. Would the moon turn differently than on earth? Of course. Consider a man walking in a circle on the surface of the earth. Here is a top and side view with a force diagram.

The key idea here is that you need a "sideways" force to make a turn. The direction of this torque is towards the center of the circle you are going to hit. Also, the magnitude of this force depends on the running speed and the size of the circle in the following manner.

For example, faster running speed means greater power, and a smaller radius (sharper turning) also means greater power. The force that presses people into a circular path is the friction between the feet and the ground. But of course you already know that – if you try to turn on a low-friction ice, it does not work so well, right?

Here's the last important point – the size of the frictional force is proportional to the force with which the ground slides on humans . In the case of maximum friction, the order would be:

But what about the moon? What changes? The first is the gravitational force. With a lower gravitational force on the moon, a lesser force of the ground will affect humans. This of course means that a lower frictional force is used for turning. Oh, add the fact that man may run faster and you get a major reversal problem.

So walking on the moon will be different than walking on the earth. I am quite excited to see what cool tricks we can imagine in this lower gravity environment. Oh, being on the moon would be cool too.


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