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SpaceX boosters return by landing nicely thanks to an elaborate guiding system. This requires, well, a guiding system (so, more electronics, more opportunities for failure and massive engineering headaches), and also additional fuel.

The Space Shuttle boosters were also reusable, but simply parachuted at sea. This required a parachute, but no complex electronics and no additional fuel.

What is the benefit of SpaceX's method compared to that of the Space Shuttle, as it comes to reusable boosters?

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In addition to the answers to this near-duplicate question, you should note that a solid rocket casing is much sturdier than a liquid fueled stage. The shuttle SRBs were deformed by the force of the water impact and had to be re-rounded as part of their refurbishment; a Falcon 9 first stage would be completely crushed in a similar parachute landing, not to mention impact and seawater damage to the engines.

The guidance system duplication doesn't seem to have been a headache at all for SpaceX. Electronics is light compared to everything else, and the guidance system needs to be quite reliable to carry out the primary mission anyway.

The fuel reserved for the recovery system is a significant hit, but it does gain them flexibility; Falcon 9 always has the option of flying in the expendable mode for bigger/higher-energy payloads. STS couldn't replace the SRB parachutes with additional solid fuel.

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    $\begingroup$ The flexibility is an important point indeed. They can expend, land on a drone ship very far out, land on a drone ship somewhere half way, or return to launch site. See USSF-44 for example, which they are constantly tweaking. At one point, they were talking about finishing A Shortfall Of Gravitas and do a triple drone ship landing, the current plan seems to be to do a dual drone ship landing for the side boosters and expend the center core. $\endgroup$ Jan 28 at 19:04

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