So top of mountain, the energy to carry the windmill up the mountain vs the energy to carry a battery up a mountain isâ€¦?

(hint: do the math)

For the purpose of a human climbing a mountain, gravity barely alters in the few K feet moved. So Force in easily assumed a constant.

Energy = Force x distance.

So take say a turbine, say assuming a super efficient strong perfect wonderful turbine, you can design able to withstand the winds of a mountain top, somehow you figure how to anchor it so its not blown over, and so it weighs 1Kg.

Letâ€™s assume you raise it up 3000ft / 1000M, against the gravity (not actually a constant but pretty constant so near Earth) of 9.8m/s2. So energy to raise up the mountain is 1Kg x 9.8m/s2 (the mass x gravity = Force) x 1000M (distance) = (Energy) 9.8KJ

Watts = Energy / time.

Then letâ€™s pick say a time that turbine is there, say a lunch spot, shall we call that 1000 seconds or 16.7 minutes? So then the Watts = Energy / time = 9.8Watts.

So now we are getting there, Watts = Volts x Current (V x A) so letâ€™s hold the Volts at 5V, so the amps need to be (9.8/2) = 2A.

So now your perfect super light, super strong, turbine is needing to make 2A output to make just the electrical energy to match just the perfectly efficient humanâ€™s energy to get that perfect turbine up to that mountain.

A 10W turbine is currently â€¦ ( I could not fine one so find a nearby match)

I found a 15W turbine, weighs 12oz excluding all of the necessary attachments to hold it down, this is just the blades and generator part. So it sounds like you canâ€™t actually build such a device.

Then compare to carrying a battery.