How high could someone jump in Earth's gravity if an electric motor lifted 90% of their weight?

Question

• Context:

It still is in the early works, there is barely anything to talk about the worldbuilding. But what I can say is that I'm interested on replacing hydraulic exoskeletons with a simpler back-pack-like that have drone electric engines.

These electric motors would lift the equivalent of 80-90% of the user's weight (including its own electric engines and power source.

Something like this, but smaller, since they don't need to take off:

• The idea:

The idea is that since 90% of the user weight is reduced, they would be able to jump and climb buildings like super humans.

However, it still is earth's gravity, and they are still just electric motors. So they still need to accelerate the same amount of mass with just their legs.

The only thing similar to this idea that I could find was a video of a Lunar Gravity Simulation that is just a person connected to a tether/exoskeleton that slows down their jump and fall to, well, simulate how they would be on the moon.

However, as you can see on the video itself in slow motion, once the person inside the suit jumps, her body lifts a little bit inside the suit, letting me to believe that maybe she would be able to jump higher. But how higher I can't tell.

How high these people would be able to jump with an electric motor lifting 90% of their weight? It would be significant enough? Or this thing would just be able to help them climb something?

Answer 1

Unfortunately, the naive answer of 10x is incorrect, and likely a drastic overestimate.

Muscle force decreases with contraction speed, reaching zero at a relatively low velocity. In other words, muscles have a maximum contraction speed. (This is one of the reasons why humans throwing fastballs is somewhat impressive.)

Say you can jump 100cm. That's a velocity on liftoff of ~4.4m/s^2. (...well, kind of. There's some center of mass trickery that goes on.)

For an apples-to-oranges comparison, here indicates that male V0 (for horizontal leg movements - again, apples-to-oranges comparison) is ~8.16m/s^2. In other words, at ~8.16m/s^2 your leg muscles are providing a net zero force. (And you'll asymptote towards that speed, hence that's an overestimate.)

10x height (10m) would require a velocity on liftoff of ~14m/s^2.

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In order to jump higher, you'd likely need mechanical advantage of some sort or another, not just compensation for weight.

Answer 2

When an object is projected up with initial energy E, it reaches a maximum height of $h=E/g$, neglecting losses due to drag and under the assumption that the gravity can be considered constant.

Since in your case the net force acting on the object is $0.1g$, your object will reach an height 10 times higher when putting the same energy in the jump.

Answer 3

Suppose, a human of 100kg would be able to jump 1 meter upward. On Earth, where g=9.81, your human can apparently produce the following amount of gravitational potential energy:

E = weight * height * g = 100 * 1 * 9.81 = 981 Joules

Suppose you have help, that is 90% of the energy is provided by a motor. You will have ten times the amount of energy. Height will grow proportionally,

h = 9810/(100*9.81) = 10.0 meters.

Now let's say this electromotor would add 6kg to your weight. In that case

h = 9810/((100 +6 ) * 9.81) = 9.43 meters.

Of course, when your person is an athlete who can jump 2m, the height reached would be doubled, 18.86 meters. In fact the weight does not matter: when the person can jump x meters, he will jump 10x meters with 90% help. The lighter your athlete is, the more +6kg for the engine will count, though..