3 ms·
Actually, the majority of the weight would be in steel rope. For one type [0], the safe limit is a tensile load of about 134-150 MN/m^2 (= MPa) [1]. At a densi
by throwaway_yy2Di 12y ago
Actually, the majority of the weight would be in steel rope.
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.html 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.html http://www.gabaswire.com/en/overview/grades-of-wire-rope.htm...
- throwaway_yy2Di 12y ago"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. [0] http://www.mcmaster.com/#standard-wire-rope/=upui3o 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)