2c:null 2d:["$","title",null,{"children":"Gravity Storage | Bob Kerns | Observable"}] 32:T5c5,Gravity storage is a simple idea, so why don’t we see real implementations yet? It turns out to be a deceptive problem. You can store as much energy as you want for as long as you want, by raising lots of heavy blocks and lowering them again. But how much weight? And, importantly, how fast can you do it? The analysis below assumes ${tex`n`} pickers—basically overhead cranes with a motor/generator hoist. The pickers pick from a common pool of blocks, raising or lowering them in ${tex`t_{descent}`} seconds, then moving to the next block in ${tex`t_{pick}`} seconds. The pool of blocks may be shared divided between. pickers; the analysis is the same. The per-picker output is intermittent, unless you feed them with conveyors. For this scenario, set ${tex`t_{pick}`} to 0 by checking the ${tex`Continuous`} checkbox. If multiple blocks can be on a picker at once, multiply the number of pickers by the number of blocks in transit. The density of concrete is around 2.4 ${tex`\dfrac{kg}{l}`}. We start out with 3.0 on the assumption that a denser mateiral will be used, such as iron ore (around 3.0). You can try it out on other planets by altering the value of ${tex`g`}. The cost estimate for the hoist covers just the motor/generator, associated electronics, etc. Costing the beams would require specific structural analysis. Likewise for the support structures for the blocks, ec. The very approximate hoist cost is included to give a sense of how costs vary.33:[] 30:{"id":"0ed915f57bd0e99c","slug":"gravity-storage","title":"Gravity Storage","thumbnail":"f2c13adbd07b5c52de14f5f15ec87bce1fa860f65d76f4800dc2c506c16454fc","access_level":"public","create_time":"$D2023-01-07T01:19:38.115Z","update_time":"$D2023-01-09T07:35:23.495Z","view_time":null,"first_public_time":"$D2023-01-09T07:25:08.794Z","has_unpublished_edits":null,"fork":false,"stars":3,"starred":false,"owner":{"type":"team","id":"a2a391e81ef70f60","login":"bobkerns","name":"Bob Kerns","avatar_url":"https://avatars-next.observableusercontent.com/d3d634f0561198d48f6c5a897f4009b95f14b0014fb7d85f3b6cc5415336b639","tier":"starter_2024"},"version":299,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"c30fe465bb675dbe","login":"bobkerns","name":"Bob 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Math.log})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"viewof block= Inputs.form({\n x: Inputs.range([0.5,10], {label: tex`block\\ width\\ (m)`, value: 1, step: 0.1, transform: Math.log}),\n y: Inputs.range([0.5,10], {label: tex`block\\ length\\ (m)`, value: 1, step: 0.1, transform: Math.log}),\n z: Inputs.range([0.1,5], {label: tex`block\\ height\\ (m)`, value: 0.5, step: 0.1, transform: Math.log})\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"viewof stack = Inputs.form({\n x: Inputs.range([1, 10000], {label: tex`Rows`, value: 100, step: 1, transform: Math.log}),\n y: Inputs.range([1, 10000], {label: tex`Columns`, value: 100, step: 1, transform: Math.log}),\n z: Inputs.range([1, Math.floor(h / block.z)], {label: tex`Layers`, value: 10, step: 1, transform: Math.log})})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"viewof g = Inputs.range([g_earth/10, g_earth*100], {label: tex`g`, value: g_earth, transform: Math.log})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":277,"value":"viewof t_descent = Inputs.range(\n [Math.ceil((2 * h) / g_earth), Math.ceil((200 * h) / g_earth)],\n {\n value: Math.ceil((20 * h) / g_earth),\n label: tex`t_{descent}\\ (s)`,\n step: 1\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":281,"value":"viewof continuous = Inputs.toggle({ label: tex`Continuous`, value: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"viewof t_pick_raw = Inputs.range(\n [\n continuous ? 0 : Math.ceil((2 * h) / g_earth),\n 10 * Math.ceil((2 * h) / g_earth)\n ],\n {\n value: continuous ? 0 : 2 * Math.ceil((2 * h) / g_earth),\n label: tex`t_{pick}\\ (s)`,\n step: 1,\n disabled: continuous\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":122,"value":"viewof pickers = Inputs.range([1,Math.floor(Math.sqrt(stack.x*stack.y))], {label: tex`pickers`, value: 1, step: 1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"tex`blocks = ${blocks}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"tex`\\dfrac{Mass}{Block}\\ (tonne) = ${block_mass / 1000}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"tex`Stack\\ Height = ${stack.z * block.z}\\ m`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":84,"value":"tex`Footprint = ${stack.x * block.x}\\ m \\text{ x } ${stack.y * block.y}\\ m = ${stack.x*block.x*stack.y*block.y}\\ m^2`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"{\n return tex`Run time = ${dec(t_run / 3600)}\\ hours`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"tex`Power = ${si(power, \"W\")}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"tex`Hoist\\ Power = ${si(hoist_power, \"W\")}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":233,"value":"tex`Hoist\\ Cost = \\$${Math.round(\n ((hoist_power * cost_per_watt)) * pickers\n).toLocaleString()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"## Appendix\nInports and infrastrucrure","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":73,"value":"g_earth = 9.80665","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"blocks = stack.x * stack.y * stack.z","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":135,"value":"block_mass = block.x * block.y * block.z * d * 100 * 100 * 100","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":141,"value":"t_run = blocks * (t_descent + t_pick) / pickers","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"dec = (n, d = 2) => n.toLocaleString(undefined, {minimumFractionDigits: d, maximumFractionDigits: d})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"block_energy = block_mass * h * g","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"power = (block_energy * pickers) / (t_descent + t_pick)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"si = {\n let si = (v, u) => {\n let ss = (s, p) =>\n `${dec(v / Math.pow(10, s))}\\\\ \\\\text{${p}${u}}`\n return v < 0\n ? `-${si(-v, u)}`\n : v < 1e-27\n ? ss(-30, 'q')\n : v < 1e-24\n ? ss(-27, 'r')\n : v < 1e-21\n ? ss(-24, 'y')\n : v < 1e-18\n ? ss(-21, 'z')\n : v < 1e-15\n ? ss(-18, 'a')\n : v < 1e-12\n ? ss(-15, 'f')\n : v < 1e-9\n ? ss(-12, 'p')\n : v < 1e-6\n ? ss(-9, 'n')\n : v < 1e-3\n ? ss(-6, 'μ')\n : v < 1e0\n ? ss(-3, 'm')\n : v < 1e3\n ? ss(0, '')\n : v < 1e6\n ? ss(3, 'k')\n : v < 1e9\n ? ss(6, 'M')\n : v < 1e12\n ? ss(9, 'G')\n : v < 1e15\n ? ss(12, 'T')\n : v < 1e18\n ? ss(15, 'P')\n : v < 1e21\n ? ss(18, 'E')\n : v < 1e24\n ? ss(21, 'Z')\n : v < 1e27\n ? ss(23, 'R')\n : ss(24, 'Q')\n }\n return si\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":224,"value":"hoist_power = block_energy / t_descent","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":241,"value":"cost_per_watt = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"t_pick = continuous ? 0 : t_pick_raw","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1"}} 31:"$30:body"