So top of mountain, the energy to carry the windmill up the mountain vs the energy to carry a battery up a mountain is…?
(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.
Let’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 let’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 let’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 human’s energy to get that perfect turbine up to that mountain.
A 10W turbine is currently … ( 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 can’t actually build such a device.
Then compare to carrying a battery.