Re: Cheap power 5 cents per unit from the jet stream could supply all world needs
- From: "Bret Cahill" <BretCahill@xxxxxxx>
- Date: 3 Oct 2006 17:35:26 -0700
So we assume a very light but strong cable. 35000 ft of it (7 miles!)
If a 100,000 psi tensile strength steel cable was of uniform cross
section 7 miles would be too high even assuming the only force was the
weight of the cable and the cable was vertical.
Assume 1in^2 cross section:
7mi X 5280'/mi X 12 in/ft X .25 lbs/in^3 = 111,000 lb cable
Since the cable will be at at angle to the vertical, drifting at least
several miles down wind, it may be anywhere from ten to 15 miles long
with a horizontal force component as well.
Titanium might work but at $10 million / cable, or 40 cents/watt it's
kind of expensive.
Maybe carbon fiber . . .
Maybe increasing the cross section as you went up .. . ..
I'm leaving the rest of the back of envelope calculations to others.
Setting up the free body diagram:
Fx at the anchor = - Fx at the rotor
The weight of the cable is uniformly distributed on the curve, a
hyperbolic cosine, in the -y direction.
Fy at the rotor = weight of the cable + weight of the rotor
Assume Fy at the anchor = 0
Fy at rotor/Fx at rotor = tan theta = the slope of the line at the
rotor.
Determine the weight of the cable by the arc length, dl = (dx^2 +
dy^2)^0.5
etc.
Bret Cahill
.
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