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with 𝑁 - 𝑒 = realistic energy efficiency of hardware [𝐽/𝐻] - 𝑃𝑈𝐸𝑁 = 𝑙𝑜𝑠𝑠𝑒𝑠 𝑓𝑟𝑜𝑚 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑎𝑛𝑑 𝐼𝑇 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 [%] The realistic energy efficiency of the network can be determined using the market shares of ASIC producers and the energy efficiency of the hardware in operation. 𝑒 =[∑𝑛 𝑆 ∗𝑒 ]+[1−(∑𝑛 𝑆 )]∗𝑒, (4) 𝑁 𝑖=1 𝐴𝑃𝑖 𝐴𝑃𝑖 𝑖=1 𝐴𝑃𝑖 𝑃 with- i=ASICProducer(1,...,n) - 𝑒𝑁 = realistic energy efficiency of hardware [𝐽/𝐻] - 𝑆 =𝑠h𝑎𝑟𝑒𝑜𝑓𝐴𝑆𝐼𝐶𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟𝑖[%] 𝐴𝑃𝑖 - 𝑒𝐴𝑃𝑖 = energy efficiency of 𝐴𝑆𝐼𝐶 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 𝑖 [𝐽/𝐻] - 𝑒𝑃 = energy efficiency 𝑓𝑜𝑟 𝑧𝑒𝑟𝑜 𝑝𝑟𝑜𝑓𝑖𝑡 [𝐽/𝐻] If some of the computing power cannot be assigned to one of the major ASIC producers, we assume this computing power originates from hardware, which generates zero profit. By equalizing EUB and ERM, we derive 𝑒𝑃 = (𝑅𝐵+𝑅𝑇)∗𝑀 ∗ 1 . (5) 𝑃𝑁∗𝐻∗𝑃𝑈𝐸𝑁 𝑡 In terms of the average losses from cooling and equipment, we differentiate between three types of mining facilities according to size, and weight them by their share in terms of computing power 𝑃𝑈𝐸𝑁 =𝑆𝑆 ∗𝑃𝑈𝐸𝑆 +𝑆𝑀 ∗𝑃𝑈𝐸𝑀 +𝑆𝐿 ∗𝑃𝑈𝐸𝐿. - 𝑗 = 𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦 𝑡𝑦𝑝𝑒 (𝑆𝑚𝑎𝑙𝑙, 𝑀𝑒𝑑𝑖𝑢𝑚, 𝐿𝑎𝑟𝑔𝑒) - 𝑆 =𝑠h𝑎𝑟𝑒𝑜𝑓𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦𝑡𝑦𝑝𝑒𝑗[%] 𝑗 - 𝑃𝑈𝐸 =𝑙𝑜𝑠𝑠𝑒𝑠𝑓𝑟𝑜𝑚𝑐𝑜𝑜𝑙𝑖𝑛𝑔𝑎𝑛𝑑𝐼𝑇𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡𝑜𝑓𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦𝑡𝑦𝑝𝑒𝑗[%] 𝑗 The resulting carbon footprint of the Bitcoin network depends on the carbon intensity 𝐼𝑁 of the power mix: 𝐹 = 𝐸 ∗ 𝐼𝑁 . In order to incorporate local differences in the carbon intensity of the power mix, we differentiate among regions and weight them by computing power share: 𝐼=∑𝑛 𝑆 ∗𝐼 +⋯+𝑆 ∗𝐼 . 𝑁 𝑖=𝑅𝑒𝑔 1 𝑅𝑒𝑔 1 𝑅𝑒𝑔 1 𝑅𝑒𝑔 𝑛 𝑅𝑒𝑔 𝑛 17PDF Image | The Carbon Footprint of Bitcoin
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