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Context: Robots and exoskeletons in this fictional scenario are having a "boom" because of some random super battery that can store a lot of energy, but it can only release it in really small quantities during a long period of time. So the idea is that it can power an exoskeleton, but you need a pneumatic/hydraulic cylinder to make it useful. Like a normal battery, but with a really long duration span.

The thing is that I can't make heads of the amount of energy/bars I would require to store in a pressure cylinder (hydraulic or pneumatic) in order to make cylinder actuators (hydraulic/pneumatic pistons) to work as fast (if not faster) than the human muscle.

After all, it is about military exoskeletons that need to help the squishy hummies to survive during combat.

Don't worry too much about the battery itself, but about the forces (if you can), for example "if we take into consideration AA batteries, you would require the cylinder to be this size", or something like that.

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    $\begingroup$ linear actuators and pistons are two very different things, linear actuators are powered by electricity instead of pressure. $\endgroup$
    – John
    May 22 at 23:39
  • $\begingroup$ Which muscle? How light is the piston? If the piston is light enough then then a trivially minimum amount of energy. It seems like you're not asking about the amount of energy to move a piston, but about the amount of energy needed to power a suite of power armor, for some unit of time. $\endgroup$
    – sphennings
    May 23 at 1:54
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    $\begingroup$ It is completely unclear what you are asking. In particular, the phrase "the amount of energy over bars I would require to store in a hydraulic pressure cylinder in order to make the cylinder actuactors (hydraulic pistons) to work as fast if not faster than human muscle" is completely opaque. In a first approximation, any hydraulic system will respond very much faster than any animal muscle -- the speed of sound in hydraulic oil is very much greater than the speed of neural transmission. $\endgroup$
    – AlexP
    May 23 at 3:40
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    $\begingroup$ P.S. I think that I understand the problem to be that you have a battery technology which provides very large capacity, but limited maximum discharge current. If my understanding is correct, then the requirement to increase the maximum discharge current is an electrical problem, to which any normal engineer will seek and design electrical solutions instead of going into hydraulics or pneumatics, and have the limited current battery charge a supercapacitor or a small battery with large maximum current. Electrical solutions have the great advantage of having no moving parts... $\endgroup$
    – AlexP
    May 23 at 3:48

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Energy isn't your problem. A tiny votive candle has enough chemical energy to blow up your house, if you could magically convert it all into mechanical work all at once. Mechanical power is the problem.

Mechanical power output is the rate of energy output over time, multiplied by the efficiency of the power supply (a dimensionless value between 0 and 1 that measures how much of the energy makes things move and how much of the energy just makes things hot). An efficiency of 0.3 is "good" for a well-engineered machine in good working order, so if you want the total power output including waste heat, multiply all the following numbers by 3 or 4.

Averaged over a few minutes, for a robot the same approximate size as a human, your power supply needs to be able to output about 5 watts of mechanical output power per 1kg of the robot or power-suit's total mass in order to duplicate the power output per unit mass of a human athlete. (This is about the mechanical power output of an elite athlete sprinting or cycling.)

To do a 1-meter jump-and-reach, it needs to achieve a vertical velocity of 4 meters per second, an output of 16 Joules per kilogram. It needs to do this in between 1/10 and 1/4 of a second, indicating a peak mechanical power output somewhere on the order of 100 watts per kilogram for momentary feats of athleticism like jumping and striking. This is a rough estimate of the mechanical power output of an elite basketball player doing the takeoff for a slam dunk. Much of the energy used by the athlete (or the robot) might come from spring-like energy left over from a previous smaller jump: energy momentarily stored in the slight stretching of the large tendons of the legs for the athlete, or perhaps pneumatics or even literal springs for the robot).

To lift a heavy weight as well as a human athlete, power probably won't be your issue. Muscles are force-limited, not output-power-limited. An elite weight-lifter doing explosive squat lifts has a power output of about 5-10 watts per kilogram body weight during the lift itself.

If your robot can move like a human athlete, it needs big feet: for every human mass of robot, you need a human foot equivalent of extra boot surface area. If it doesn't have big feet, it won't be able to get enough friction on the ground to do its athletics and it'll tend to sink into soft earth.

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