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Jun 24, 2017, 02:48 AM
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# The vicious math of Falcon 9

The story sounds great until you realize in order to reuse the 1st stage, they have to throw away 34% of the payload, according to Kiwipedia. There are no dual geostationary satellites at a time or payloads of opportunity like the Arianne 5.

Given this fact, let's calculate the cost of launching the same mass with reused 1st stages & expendable 1st stages. The shotwell said it costs "less than half" to reuse the 1st stage, which we'll assume means half. The 1st stage is 2/3 of the total cost, so that gives a total cost of 2/3 / 2 + 1/3 as the cost of a flight proven booster.

So the 1st launch of 1 payload costs 1 for each system. The later launches cost .667 for flight proven & 1 again for expendable. With these parameters, the cost/lb for flight proven approaches but never goes below the expendable system. The problem is the discount for a flight proven rocket exactly matches the reduction in payload.

As soon as the flight proven booster gets anywhere below 1/2 the cost of a new booster, it saves more than the reduction in payload & it becomes favorable. Just reducing the refurbished cost to 40% of a new 1st stage would barely start breaking even after 7 launches. If they miraculously got it to 10% of a new 1st stage, they would start saving huge amounts of money after 3 launches.

Even in the miraculous case, they wouldn't start saving money until 3 launches. So far, they've only gotten 2 launches from the reused 1st stages, so they're losing a huge amount of money. The future is still heavily dependent on new Falcon 9's being much cheaper than other rockets, with the hope that someday they can reuse just 1 booster for a whole year with much lower refurbishment costs.