B Mobility in a Strong Gravity Environment vs. Moving Mass?

[shintashi]

TL;DR Summary

Figuring out how biological strength should vary in High G's

This is a basic conundrum that has bothered me for years:

if you or a species like you is "adapted" to Twice Gravity (or any other multiple of 9.8m/2 squared) and your life functions and capacities are near identical,

How strong/fast are you? Compared to 1G?

See, this is the issue of mass vs. weight, power lifting vs. long distance jumping. Standing freely without collapsing under your own weight, vs. sprinting.

Gravity exerts itself on all your molecules equally, not just the ones on the surface. If something is 200kg, or about 440lbs in 1 Earth Gravity, it should theoretically be 880lbs in 2G's,

but in 2G's how much harder would you or any machine have to throw it in order for it to traverse the same distance?

Practically speaking, if a human began with a 4.54 kg stone,
which is about 10 lbs on earth, in 2 Gs, that object is "20 lbs", but wouldn't the Arc of hurling it Require FOUR, not TWO times the kinetic energy to produce the same acceleration, and wouldn't the parabola be shaped differently?

Thus I began to question, would someone who could jump 2 meters from standing, in order to also jump 2 meters from standing in 2Gs, require the same strength that would propel them 4 meters on Earth but also lift 4, not two times as much?

Thus double vs. quadruple problem leaves me confused. How strong/fast would a humanoid have to be?

Would it be some strange hybrid like x2.83 (the multiplicative average of x2 and x4?)? Would everyone just be exponentially stronger but the same speed, or gradually slower but the same strength?

in 10Gs,
would a person have the power to move "10 times faster", on Earth, and thus be 100 times stronger,
or would they be "10 times stronger", on Earth, but only 3 times faster on Earth, and move 1/3rd an Earther's speed on their 10G Homeworld?

 

[jbriggs444]

If you are going to keep your balance and avoid falling, 2 g's means that you fall $\sqrt{2}$ times as fast. So [all other things being equal] you have to be about 40% faster to successfully deal with this problem.

Of course, all other things are not equal. Things do not scale neatly by a single factor.

 

[hutchphd]

Watch the films of the astronauts on the moon to get a feel for the opposite case of smaller g. Slower and higher jumps
In some ways beings can compensate for more g by being smaller in stature (better strength to weight) and quicker as @jbriggs444 mentions. Since $(muscle strength) \alpha (muscle X- section)$ and $(mass)\alpha (volume)$ you should be half as tall and have a faster internal clock by$\sqrt2$.
Of course as Galileo pointed out your bones may need a different shape. This is actually very instructive to think about ...

 

[A.T.]

Figuring out how biological strength should vary in High G's

We had related discussions about the question of jumping in lower G:
https://www.physicsforums.com/threa...ump-21-times-higher-than-on-the-earth.774140/
In short, bio-mechanics is complex and doesn't result in simple scaling laws.

And if you are also asking about evolving in and adapting to higher G environments, that makes it even more complex. The higher G affects many processes and the evolution of other life forms that you are adapting to as your food, prey, predators.

 

[DrStupid]

Watch the films of the astronauts on the moon to get a feel for the opposite case of smaller g. Slower and higher jumps

They are not only slower because of the reduced gravity but also due to the space suits. Are there films of the Apollo astronauts with full equipment on Earth for comparison?

 

[hutchphd]

They are not only slower because of the reduced gravity but also due to the space suits

Well they don't jump as high because of the heavy suits. But their slow motion trajectory as they hop (or lope) indicates specifically the lower gravity.
On Earth they can't really either hop or lope because the Earth weight of the total suit is 180lbs...hard to hop carrying someone on your back.

 

[DrStupid]

But their slow motion trajectory as they hop (or lope) indicates specifically the lower gravity.

That applies to the center of mass but not as much to the legs and even less to the arms. It would be interesting to know to what extend the impression of slow motion is caused by gravity and by the suits.

 

[russ_watters]

This guy's skipping looks stiff to me, but not really slow-motion:



A few notes:

• The extra mass of the pack means accelerations would be slower/less explosive than without it, but once in motion the lower gravity means less effort is needed to stay in motion.
• He's not hopping very high, because he doesn't need to, but he is definitely in contact with the ground less than someone running on earth. My suspicion is that if gravity were much higher than on Earth or you were carrying a pack, running would be near impossible and you'd have to stick to a fast walk so a foot was always touching the ground. Maybe there's videos of soldiers trying to run or march fast in full gear...

 

[A.T.]

This guy's skipping looks stiff to me, but not really slow-motion:

Another thing to keep in mind: They weren't on the Moon long enough to adapt or optimize their locomotion. They trained underwater, but that is obviously very different because of the drag.

 

[hutchphd]

.
Here's video of a few famous falls. $\sqrt 6=2.45$ seems about correct for slo-mo for these

.

 

[DrStupid]

This guy's skipping looks stiff to me, but not really slow-motion:

But you see another effect. During normal walking the legs are moving like pendulums. On the Moon the pendulum frequency is by a factor 2.45 slower than on Earth, resulting in a corresponding reduced walking speed. That would be the missing slow-motion movement. As the guy's in the movie try to walk much faster, their legs get out of sync and they start jumping.