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Defence and space

Cost per kilogram: an expendable rocket versus a reusable one

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The prompt

A launch company compares two versions of its rocket and reports in USD. Expendable: a first stage costing USD 40 million, an upper stage costing USD 10 million, and USD 10 million for the nose cone, fuel and launch operations; it carries 20,000 kg. Reusable: the first stage costs USD 50 million to build (it needs landing legs and more engineering) and flies 20 times, each flight needs USD 1.5 million of recovery and refurbishment, the upper stage and the other costs are the same, and it carries 15,000 kg because it keeps fuel for landing. What is the cost per launch and per kilogram of each, and how many flights must the reusable stage make to beat the expendable one per kilogram? (Figures are illustrative.)

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