"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))
The is the same as the cost / energy stored. The denominator is simply the work equation (distance * force) -- the mechanical work the cable can do before it runs out of length.
= cost / energy
This is actually sort-of constant, since the denominator is ~proportional to the cable volume. (The load capacity is ~ the cross sectional area d^2).
For steel rope from [0], it looks like a lower bound of about $1,200/kWh.
This is a simple "figure of merit" for cable in this problem,
The is the same as the cost / energy stored. The denominator is simply the work equation (distance * force) -- the mechanical work the cable can do before it runs out of length. This is actually sort-of constant, since the denominator is ~proportional to the cable volume. (The load capacity is ~ the cross sectional area d^2).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)