Re:Gravitricity
by throwaway_yy2Di on Sunday November 23, 2014 @05:33AM
(#8648367)
"You can't solve this by using shorter cables, because that decreases your energy capacity at the same rate. If you use cables of 1/10th the length (~100 m), you get only 1/10th the potential energy storage per ton. The cable thickness per lifted ton is constant."
This is a simple "figure of merit" for cable in this problem,
cost / (length * load capacity (N))
= cost / energy
For steel rope from [0], it looks like a lower bound of about $1,200/kWh.
[0] http://www.mcmaster.com/#standard-wire-rope/=upui3o
(E.g. item "3440T68", 5/8" plain steel, $5.16/foot for 9,080 lbf lifting capacity;
$5.16 / (9,080 lbf * 1 foot) = $1,509/kWh)
For one type [0], the safe limit is a tensile load of about 134-150 MN/m^2 (= MPa) [1]. At a density of 8 g/cm^3, the limiting length of a uniform cable is ~1.7 - 1.9 kilometers. If you have a stationary, suspended cable of this length, its own weight puts it at its maximum load; it can't lift anything else.
Steel rope on McMaster is around $10,000/ton [of rope]. So, these assumptions are a dead end.
You can't solve this by using shorter cables, because that decreases your energy capacity at the same rate. If you use cables of 1/10th the length (~100 m), you get only 1/10th the potential energy storage per ton. The cable thickness per lifted ton is constant.
[0] http://www.engineeringtoolbox.com/wire-rope-strength-d_1518....
[1] The breaking limit of rope is far higher (~700 MPa), and the breaking limit of a single wire strand -- the tensile strength -- is higher still (1,770 MPa according to [2])
For the cross section area, I'm assuming a circular rope (not accurate).
[2] http://www.gabaswire.com/en/overview/grades-of-wire-rope.htm...