How much force would you need to escape earth's gravity by JUMPING?

[Researcher X]

Let's for arguments sake say that we have an invincible superpower humanoid with as much strength as is necessary.

How much force would this guy have to input into the ground to exceed escape velocity?
How much energy is required?
The ground would also pretty much explode under his feet, right? How big would the environmental effects of this be?

 

[enricfemi]

i don't think human being can endure such jump, since the acceleration is much more than the rocket.
of course,except the man has s on his bosom.

 

[Researcher X]

Well, I did say that for arguments sake, the superhero/superpowerful being was invincible. Besides, Superman would just fly out.

Anyway, let's also assume this guy's within human size range and weighs 100kilos.

 

[tanker]

Well, to find how much energy is required, you just calculate how much energy a 100kg mass (i.e. a human) has at escape velocity, which is around 11 000 m/s, since he went from E = 0 J to escape energy. So E = 1/2 mv^2 and all that. So it's about 5 GJ.

Environmental impact? That's roughly the equivalent of one ton of TNT.

As for force, you figure out the acceleration...a jump is about ... 0.1s? We can assume the acceleration is constant in that fairly short period of time so that's about 100 000 m/s^2. Which is about 10 million Newtons for a 100 kg human. Each engine of the Concorde had 170 thousand Newtons, with afterburner. So that's like 30 Concorde engines (on afterburner) on each foot.

Imagine how that feels...

 

[Researcher X]

Thank you. 1 Ton of TNT?

So the ground explosion might be equivalent to a bunker buster bomb going off. I was thinking something so absurd would have a bigger effect. So, if this guy kicked a skyscraper, he could demolish it (but he'd be launched by the kick).


The force... So to do that, that's like one million one hundred and twenty four thousand hundred tons? I converted from the Newtons.

Are you also saying that you'd escape Earth's pull in 0.1 seconds? I'm guessing nobody would see you go. If something like that was caught on film, all you'd see would be an explosion, and anyone within 30 feet would probably be killed or injured by the explosion.

 

[tanker]

Well, yeah. To calculate that force you need how long a jump lasts, while assuming your acceleration is constant during that jump. I assumed a jumping time of 0.1 seconds, so that ten million Newtons (so yeah, around 1 ton of force) would allow you to "jump" out of the Earth with a jump time of 0.1s.

 

[Vanadium 50]

The key is not the jumping time, it's the distance - how far you can move with your feat touching the ground: then equate the work done to escape the Earth's potential energy to the force times distance of the jump. The mass divides out and you get gR = ax or a = g(R/x). Jumping from a crouch gives you a meter of travel or so, therefore you need an acceleration of about 6 million g's. For a mass of 100k, we're talking 6 billion Newtons.

This is far beyond the yield strength of anything he'd be standing on.

 

[Researcher X]

This is far beyond the yield strength of anything he'd be standing on.

Does this mean he'd have to put in even more force than the six billion to get out of orbit, because so much of that force would actually be taken up by the collapsing/exploding ground?

 

[Vanadium 50]

No, it means that he can't get into orbit this way. Instead of propelling himself up, he'll end up pushing the ground he's standing on down.

 

[hamster143]

For simplicity, assume that your legs are weightless and 100 kg weight of your body is concentrated in your torso. Let's say that you start the jump with your knees fully flexed. You need to accelerate to 11 km/s during the time it takes your muscles to move your torso 1 m. Let's also assume that force (and acceleration, f=ma) are constant throughout the move. To address Vanadium 50's point, assume that you're standing on something very heavy and unbreakable.

v = at, L = at^2/2; v and L are known, eliminating t, we get

a = v^2 / 2L = (1.1e4)^2 / (2 * 1) = 6e7 m/s^2 = 6 million g.

Duration of the jump is v/a ~ 180 microseconds.

This crucially depends on having something extremely firm under your feet. Otherwise you'll simply sink into the ground to his knees. Try the same material from which your superhuman's legs are made of.

 

[Researcher X]

Wouldn't weak ground simply reduce the effect, rather than negate it completely? I suppose if you put in enough force, the rebound of the ground would be a gigantic asteroid impact like explosion, which might help propel you into space.

 

[Vanadium 50]

Wouldn't weak ground simply reduce the effect, rather than negate it completely?

The upward acceleration is in response to the ground pushing up. When you jump, you push down, and the ground pushes back up. Exceed the amount of upward force that the ground is able to provide, and you don't go up.

 

[DaveC426913]

Are you also saying that you'd escape Earth's pull in 0.1 seconds? I'm guessing nobody would see you go. If something like that was caught on film, all you'd see would be an explosion, and anyone within 30 feet would probably be killed or injured by the explosion.

I think you may have misunderestood.

The .1s is merely the length of time your feet are pushing on the ground. Once you leave the ground you will be on a freefall path. It'll take much longer than .1s to leave the Earth's atmo.

Earth's escape velocity is around 7 miles per second, so once your feet leave the ground, you'll have to be traveling at least that fast (and that ignores air drag).

At that rate, it would take you something one the order of 14s to escape Earth's atmo.

 

[Researcher X]

So, there's a max jump height on earth, no matter how much power you have. I'd think if you reach a certain level of power, like if your legs were creating extinction level events, the explosion would launch you out of Earth's gravity (very large asteroid impacts launch some debris out of Earth's gravity).

 

[DaveC426913]

So, there's a max jump height on earth, no matter how much power you have. I'd think if you reach a certain level of power, like if your legs were creating extinction level events, the explosion would launch you out of Earth's gravity (very large asteroid impacts launch some debris out of Earth's gravity).

I'm not so sure that it has to waste as much energy as all that - at least in principle. Certainly we can generate huge forces like that with the methods we know already, but the methods we use are poorly-contained (i.e. bombs, etc.).

A well-contained method, sitting on a arbitrarily large block of concrete for example, wouldn't have to be so damaging.


Though, on second thought, there's no way of escaping the idea that what I'm doing is symonymous with postulating a method pf propulsion that can accelerate from 0 to 7mi/s+ in .1s (how many g's is that?) which is a huge specific impulse. Way beyond any technology we can even conceive of, and thus is no different than postulating a science-fiction propulsion system...

So yeah, I guess you're right. Huge explosions are the order of the day.

 

[QuantumPion]

There was a nuclear weapon test where a high-speed camera captured a pipe cover flying out of the fireball. A physicist estimated from the video that the cover may have obtained a high enough velocity from the nuclear blast to get into orbit (or escape Earth entirely, I forgot). Although this was only speculative as he had to extrapolate the object's speed based on one film frame.