[Halc (OP)]

The question came up given the realization that if one was on the equator of the moon, one could remain stationary relative to the inertial frame of the moon by running west at about 15 km/hr, which I can still do, albeit not for any extended time.

But I can run that fast here on Earth, not on the moon. Too little gravity up there, and hopping seems the idea method of locomotion up there, and we're not evolved to hop.

So given flat ground, normal atmosphere, and standard running attire (no shoes with wheels or springs), at what gravity (expressed as a fraction of g) can one run the fastest?  Too little and each step takes you airborne with a high probability of not landing on your feet, and with way too much air friction between bounces.  Too high and you'd barely be able to walk without breaking bones.

While we're at it, what sort of physiology has an optimal speed at higher or lower gravity?  Only ground-locomotion counts, not birds or fish or anything which utilizes the medium instead of the ground. I imagine ants could go faster in higher g, Maybe kangaroos would work better at lower g, especially if they could use their tail to maintain proper orientation in flight. They already go 50 km/hr (sustained), and in low enough gravity could probably outrun a cheetah (80, sprint)..

[evan_au]

optimal speed at higher or lower gravity?

Didn't Allan Shepherd hit a golf ball on the Moon? That probably went pretty far, pretty fast!

...but it's not self-powered locomotion...

[Halc (OP)]

Didn't Allan Shepherd hit a golf ball on the Moon? That probably went pretty far, pretty fast!

Pretty far, yes, but not particularly fast. It went far not due to its speed, but due to lack of both gravity bringing it down quickly, and air resistance slowing it as it goes.  I doubt the shot was even half the speed of a typical tee shot on Earth, especially given the cumbersome suit being worn at the time.

Yes, I'm restricting the question to life forms under power of legs, not ballistic objects or vehicles, the ground speed of which is limited only by orbital speed. Yes, one can actually run off Deimos if you can conjure the purchase needed to get up to what would be a running speed on Earth, about a third faster than our guy trying to cancel the moon rotation. The purchase can be had by erecting a circular arch, sort of like a hotwheel loop. Going around that gets you the artificial gravity needed to actually utilize your legs.  For the purpose of the post, we're assuming speed on level ground, not using the artificial gravity of our runner's own centrifugal force.

[Petrochemicals]

This comes back to the transit van in snow question, you need a certain ammount of gravity to initialise friction, a bumble bee cannot run very fast at all due to its air buoyancy,  cheetahs have non retractable claws unique I think among cats to overcome the lack of traction at high speeds.

[Eternal Student]

Hi.

   Straight off the bat you would have thought it was something close to 1g.   

1.  That's the environment we've evolved in.
 
2.  In much lower or much higher g you get all the problems you (Halc) have already mentioned.  You could start to tumble in the air etc.   Human beings are quite good at naturally adjusting their posture and thrust angles to walk and run on slippery surfaces like snow.  We're going to need some criteria to establish when your posture and thrust angles are so abnormal that you wish to stop calling it "running".    At the most extreme, in a very low g environment you don't want to get off the ground at all, you just want thrust in the x-direction and learn to roll.  Since gravity is so low you won't hit the ground with much force anyway.  If you have a good roll technique this could be extremely fast and quite aerodynamic - but I don't suppose you can call this "running".

Best Wishes.

[evan_au]

1g... That's the environment we've evolved in.

Kangaroos also evolved in 1g, but jumping does seem to be more efficient in low g.
- You get to push off with two legs instead of one
- You travel at the same high speed while "resting" (at least until you hit the ground again)

There are some studies on walking and running reduced gravity (no-one is planning to go to Jupiter just yet...)
- A lot of overlap between these two papers...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4163425/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5682019/

[niamul21]

This comes back to the transit van in snow question, you need a certain ammount of gravity to initialise friction, a bumble bee cannot run very fast at all due to its air buoyancy,  cheetahs have non retractable claws unique I think among cats to overcome the lack of traction at high speeds.

I also have the same question Thanks for presenting this one.

[Bored chemist]

Friction is a double edged sword...
The 1000m speed skating record is roughly twice as fast as the 1000m running record.

https://en.wikipedia.org/wiki/List_of_world_records_in_speed_skating
https://en.wikipedia.org/wiki/1000_metres_world_record_progression

My guess (like others) is that we are probably pretty close to optimal for 1G.

[alancalverd]

Wear running spikes or cricket shoes.

If that's not permitted, speed skating seems to be a matter of incremental acceleration. At the end of a running stride you have to prevent yourself falling forward, then push as your center of gravity passes the point of ground contact. With lower g, my guess is that you can run in a more crouched posture and lose less energy per stride in the "prevention of falling" part of the process. Thus your incremental acceleration limit may be greater  even if the increments are smaller.

[Halc (OP)]

Thank you for all your replies. There are no hard rules, but obviously vehicles (powered cars and such) are pointless to ponder.

There seems to be categories of responses:

Traction:
PetroC and Alan mentioned actively gripping the surface if static friction isn't enough. Cleats/claws helps greatly with acceleration. Do they help with speed?  At low enough gravity, they have to, else any effort expended 'running' is going to put you in the air most of the time. Limited time in contact with the ground requires maximum thrust while you're down there, so they very much help with speed and not just acceleration, which is what they're used for at 1g.


Optimal at 1G

Straight off the bat you would have thought it was something close to 1g.

My guess (like others) is that we are probably pretty close to optimal for 1G.

Kangaroos also evolved in 1g, but jumping does seem to be more efficient in low g.

As for an optimal gait at low g, a rolling hop seems natural for humans. The spacemen landed on a rear leg and rolled to the front one in a hop, keeping one leg always forward. This is very similar to a horse canter which is a roll using all four legs in turn, then going airborne. A horse has four different gaits and it's interesting to see where each is optimal.

But the main thing is the optimal-at-1g comments. All creatures have evolved under 1g and are presumably the optimal form for that creature at 1g, but while that might mean that a different form might have evolved at a different gravity, it does not follow that 1g is necessarily optimal for the speed of a given creature in its Earth form.  I suspect a person could run faster (maybe not accelerate harder) under lower gravity, but not under a lot lower gravity. There's a sweet spot somewhere for each creature and it isn't 1g.  The cheetah needs those claws for good acceleration/cornering just like the cleats for sports, but do they help with speed? Might a cheetah run faster given greater traction at 1.2g?  I don't know. Few creatures are limited by traction while running at a stead speed in a straight line.


Not running

The 1000m speed skating record is roughly twice as fast as the 1000m running record.

Human are notoriously inefficient runners. We have massive legs with the muscles far too far down from the hips, as compared to the pencilly legs of deer, cows and birds. All the meat is up in the haunches that barely move, and the part that does move is relatively light stilts.
So yea, it makes sense that a human can move faster via different means like skating (ice or wheels), or via bicycle or something.

54 km/hr is the skating record, which seems awfully slow to me. I can (could anyway) better than that on a bicycle, and I'm no Olympian. Both kinds of skates maximize static friction in one direction and minimize kinetic friction in the orthogonal direction. Both skates and bicycle can select an optimal gear for optimal transfer of work to the surface. They all seem bound pretty much by air friction, so why is the bicycle so much faster? I don't wear a slick air-suit when cycling, and yet I do better than the professional skaters on level ground.  Any ideas anybody?  Is there something inherently more efficient about pumping pedals in a circular motion rather than thrusting feet to the sides? Both are doing the main work by pushing feet down, just like in running. The cyclist doesn't extend the leg all the way like the skater does, but the cyclist can also pull on the upswing, using less natural muscles.
Any ideas?

OK, back to low g: Can a skater or cyclist go faster on the moon, or at 0.8g, or 1.2g?  Just like running, it doesn't seem to be limited by friction. If I run harder, my feet don't slip. But on the moon? Yes, friction would be a big issue and slippage would prevent full thrust.
A hard-working skater would go airborne. There only alternative is to get super low and thrust almost parallel to the ground so there's minimum upward force. Special skates going off the sides of the feet would have to be designed not to slip despite the low weight on them.
The cyclist can have a very long wheelbase to prevent 'wheelies', but something like studded tires are going to be needed to transfer sufficient thrust to the ground. 0.16g is just not enough to get proper traction. Suction cups maybe??? That can't help your speed. Imagine trying to coast with suction cup tires.

[Eternal Student]

Hi.

Well, you ( @Halc ) seem surprisingly interested in this.
   I've had a quick glance at whats on the web.   A similar question has been asked on Quora and Reddit.

https://www.quora.com/Is-it-possible-to-run-very-fast-in-a-low-gravity-environment

https://www.reddit.com/r/askscience/comments/j4ss3/which_would_be_the_ideal_amount_of_gravity_to_run/

    I've had a glance through those replies.  The majority seem to think a slightly higher g environment would help.  At least that's their opinion for a 100m sprint where acceleration is everything.  The main argument being that friction force is improved so you get a better horizontal acceleration.   The inertia of your own body is determined, of course, just by your mass and has nothing to do with the gravity.  So you have more horizontal acceleration just from Newton's   F = m.a.

    The opinions shift a little if you're considering a distance run and sustaining a top speed.  The energy you waste bobbing up and down as you run can't be easily ignored.  What's important is that you have to find that energy from your own chemical stores you can't sustain anaerobic respiration and build up lactate indefinitely.   It's generally thought that fatigue is not important for the 100m sprint (on earth) but starts to become important after 200m.   For any long distance run, reducing the rate of energy consumption becomes more important than having good friction and good acceleration at the start of the race.   For this a slightly lower g environment is likely to help.   You can bounce further between each hop off one leg and effectively reduce the rate of energy consumption per metre.  That means you could sustain more metres per second.
   In very low g or very high g environments running just goes badly wrong

I'll continue to keep an eye open for more authoritative articles but you know it will be hard to find data for any experiments have been done on running in low and high g environments.  We don't have sports scientists with fully functional labs on the moon just yet.

Best Wishes.

[Halc (OP)]

The majority seem to think a slightly higher g environment would help.  At least that's their opinion for a 100m sprint where acceleration is everything.

Ah, but I'm assuming you're already up to speed. 'How fast can you run at such and such g', which is a different question than  'How quickly can you cover short distance X from a stop at such and such g'. Hence my hesitation about the claws/cleat which help only with acceleration, not speed, at least not near 1g.

Thanks for the reply. I'll look at the posts, but I hesitate to get any answers from quora.

I did think about why bikes are faster than skating. Biking seems almost 100% efficient, almost all the mechanical energy going into forward thrust, whereas the skater is thrusting against his own inertia, sending his center of gravity from side to side. That's a lot of work, even though half of it is negative work being done. The human body doesn't capture negative work very well. Again, a kangaroo does. They're designed to absorb the energy of coming down and bounce back up again, using energy only to add to it a bit. Hence the skater wasting a lot of energy that the cyclist doesn't.

[gem]

HI all

Halc

I did think about why bikes are faster than skating. Biking seems almost 100% efficient, almost all the mechanical energy going into forward thrust, whereas the skater is thrusting against his own inertia, sending his center of gravity from side to side. That's a lot of work, even though half of it is negative work being done. The human body doesn't capture negative work very well. Again, a kangaroo does. They're designed to absorb the energy of coming down and bounce back up again, using energy only to add to it a bit. Hence the skater wasting a lot of energy that the cyclist doesn't

Bikes have gears which would account for the faster speed 

rather than straight comparison of energy efficiency

https://www.popularmechanics.com/adventure/outdoor-gear/a22061530/how-bike-gears-work/

[alancalverd]

You'd need to modify the atmosphere of your g--altered planet.
At low g, you'll have to increase the oxygen content to match the optimum partial pressure of 220 mb, and at very low g you may find the total pressure even of 100% oxygen is insufficient to fully inflate your lungs. Conversely at high g you will experience increased drag (directly proportional to air density) that will offset any advantage from ground friction.

Worth reviewing the IOC's discussions on records during the Mexico Olympics. There is no doubt that athletes quickly acclimatised to the lower air pressure, so competition was reasonably fair  but there was some concern that the lower g and reduced drag at altitude could make some records inaccessible to future competitors   

[Petrochemicals]

Thank you for all your replies. There are no hard rules, but obviously vehicles (powered cars and such) are pointless to ponder.

There seems to be categories of responses:

Traction:
PetroC and Alan mentioned actively gripping the surface if static friction isn't enough. Cleats/claws helps greatly with acceleration. Do they help with speed?  At low enough gravity, they have to, else any effort expended 'running' is going to put you in the air most of the time. Limited time in contact with the ground requires maximum thrust while you're down there, so they very much help with speed and not just acceleration, which is what they're used for at 1g.

As you say it is the problem of traction at high speed. A planes propellor usually limited in rpm maybe because of its own own self destruction usually has a variable pitch unlike a standard boat impellor. The airplane propellor angle to the vertical increace at high speed to take greater bites of air to gain traction. A propellor could not function with a great pitch at slow speed much like a bike from stand still at a very high ratio gear.

[Halc (OP)]

I've had a quick glance at whats on the web.   A similar question has been asked on Quora and Reddit.
https://www.quora.com/Is-it-possible-to-run-very-fast-in-a-low-gravity-environment
https://www.reddit.com/r/askscience/comments/j4ss3/which_would_be_the_ideal_amount_of_gravity_to_run/

I looked through these. A lot of similar responses, and further exploration into the matter seems to require some actual tests or a good simulation or something.
A lot of the same mistakes were made as well in the responses, like assertions of gravity-dependent atmosphere when the OP clearly specified this to be normal.

You'd need to modify the atmosphere of your g--altered planet.

Yea, like that. Read the OP Alan. The atmosphere is normal, by whatever means necessary.

Also, many seem to miss where I stated in my OP that this question is about max speed, not max acceleration.

Bikes have gears which would account for the faster speed

So do skates, as I pointed out in post 9. The 'gear' of a skater is the angle of the skate relative to the direction of motion, almost perpendicular at first, but almost parallel as the higher speeds are achieved.

[alancalverd]

from: alancalverd on 01/04/2022 15:23:20
You'd need to modify the atmosphere of your g--altered planet.

Yea, like that. Read the OP Alan. The atmosphere is normal, by whatever means necessary.

Whilst the question may be fairly easy to solve for anaerobic acceleration (sprinting), maximum speed may require a transition to aerobic exercise  (as in skating and cycling). So it's a complicating factor - the result depends on what you mean by "normal".

As I said earlier, if g < 0.2g_earth then the total pressure won't inflate your lungs adequately even with 100% oxygen. If g>>g_earth you may have problems with nitrogen dissolving in your blood  - not sure how this affects the ability to exercise but any divers may have an opinion.

[alancalverd]

So given flat ground,

......in a rotating space station of infinite diameter....... Of course. Silly me.

[Bored chemist]

So given flat ground,

......in a rotating space station of infinite diameter....... Of course. Silly me.

Or even...

(large enough that it's locally pretty flat)

as specified.

[evan_au]

The human body doesn't capture negative work very well. Again, a kangaroo does.

The human anatomy does have some mechanisms to capture the energy of impacts and reuse it - the Achilles tendon will absorb some impact energy, and release it again when the foot leaves the ground.
Some marathon runners from Africa prefer to run in bare feet, but for the rest of us, running shoes assist with storing the impact energy.

Special skates going off the sides of the feet..

My understanding of ice skates is that they apply enough pressure to the ice to change the state from solid to liquid, even though the temperature does not change appreciably, and is still below 0°C. That reduces friction significantly (but not to zero, because then they would have no acceleration).

On the Moon, the gravitational force on a human body is about 6 times less than on Earth, so this would require a skate contact area that is 6 times less - maybe 3 times shorter, and half of the width? (Assuming normal atmospheric pressure, so the ice doesn't sublimate.)

Both kinds of skates

This site quotes 5 types of modern ice skates (ignoring the traditional bone skates):
https://en.wikipedia.org/wiki/Ice_skate#Types_of_ice_skates