From 1981 to 2011 the United States had access to one partially-reusable launch stack, the Space Shuttle. The stack consisted on two solid-fueled boosters, a large central fuel tank, and the Orbiter Vehicle (the orbital glider that most people associate with the phrase "space shuttle", since it was the part that astronauts flew to orbit and came home in).
The space shuttle was initially supposed to be fully reusable, but eventually settled on partially refurbishable. The boosters crashed into the ocean, the fuel tank was lost each time, and the orbiter required extensive checks of its heat shield between each flight (and it was a failure of this heat shield that caused the loss of Columbia).
In terms of performance and economics the shuttle cost between $450 million and $1.5 billion per launch (depending on how you accrued non-launch program costs) and could put 27,500 kg of payload into Low Earth Orbit. Its launch cadence (per vehicle) was slow; the refurbishment mentioned above took months.
You'll note that even at $450 million per launch, the Shuttle stack was not competitive with even the most expensive expendable rockets operated by Boeing and Lockheed Martin. Compared to the entry-level prices of $60 million for a Falcon 9, the "reusability" of the Space Shuttle created more expenses than savings.
Half way through 2017 however, SpaceX is now well on its way to replacing the capacity of shuttle at significantly lower costs. The base cost of an expendable Falcon 9 is $60 million, and while SpaceX has not provided firm pricing for its reusable variants, their guidance is that the Gen 1 reusability will provide savings between 10% and 30%, while the long term prospects are savings between 90% and 99%. And this is while delivering 22,800 kg of payload to orbit, fully 80% of the performance for 5% of the cost.
I. How have they achieved this price gap?
The first question is "How does SpaceX make an expendable vehicle that 1/20th the cost of the Space Shuttle stack on a per flight basis?", and this has been answered may times by Elon Musk in interviews. The starting point is that SpaceX does not use traditional aerospace supply chains (grown fat and inefficient on government contracts) but either buys off the shelf technology or builds tools and systems internally with a focus on low-cost production. By example, in a recent interview SpaceX's Chief Propulsion Office Tom Mueller indicated that the marginal cost of production of the Merlin 1-D engines that power the Falcon 9 booster and upper stage were "within factor of 5" of the marginal cost of a Tesla Model 3 sedan (which is $30,000). In a field where rocket engines typically cost hundreds-of-thousands to millions of dollars each, this is extraordinary.
II. Then once the lower base cost is achieved, how do they achieve reusability that lowers costs rather than raises them?
Less damage to Boosters, Rapidly Turns Around
The Space Shuttle boosters crashed into the ocean and required extensive safety checks and refurbishment between launches. The Falcon 9 booster flies under power to either a barge in the Atlantic Ocean or back to its launch pad. Despite years of efforts by NASA, the crash landing and immersion in sea water did too much damage to the boosters to ever allow for rapid reusability. By comparison the Block V version of the Falcon 9 booster is designed to have a 24-hour turnaround with minimal maintenance.
The rapid turn-around is a not-to-be-overlooked part of the 90--99% cost savings that Elon Musk is predicting in the long term. A rocket that flies once per year or less (such as the Space Launch System is predicted to have) still has large fixed costs (such as its landing pad and ground crew) that must be maintained in working order all year round for the next flight. A rocket that flies every month, week, or day uses the exact same amount of launch pad, but the costs are spread out over 10-300x more flights.
Non-Reusable Fuel Tank vs. Eventually Reusable Second Stage
The Space Shuttle fuel tank had no ability to land on its own and could not slow or control its descent through the atmosphere, leading to a full loss every time. NASA never attempted to fix this. Currently the Falcon 9 upper stage is also lost every time, but it doesn't have to be this way forever. The upper stage has the necessary engines and guidance systems to propulsively fly back to earth just like the boost stage does, and developing the ability to do so will be necessary to achieve the >90% cost savings mentioned above. This will be easier to achieve once SpaceX is flying the Falcon Heavy, as it will have a larger performance margin to work with.
Refurbishable Orbiter vs. Rapidly Reusable Fairing/Dragon
Unlike the Space Shuttle, the Falcon 9 stack cannot fly both a crew and a satellite on the same launch. It can fly either a cargo fairing or the Dragon spacecraft, but not both. Until recently the cargo fairing was always lost, but in March 2017 SpaceX announced that they had recovered the fairing. The fairing included guidance boosters and parachutes that allowed it to descend into the ocean, similar to the old Space Shuttle boosters. Long term it probably makes sense for the fairing to incorporate Draco engines (the same as the Dragon spacecraft) for propulsive landing.
Meanwhile the Dragon spacecraft currently uses a heatshield and parachutes to slow down before landing in the ocean (similar to the Apollo capsules). Using this method SpaceX is able to retrieve and re-fly them, and just for the first time re-flew a Dragon to the International Space Station. Meanwhile the next version of the Dragon (Dragon 2) will have Draco thrusters powerful enough to land propulsively like the Falcon boost stage.
Currently the Dragon spacecraft has only been reused once, so it's hard to gauge just how successful SpaceX will be at beating the Shuttle's reusability record on this part of the stack. But there is one part of the design that bodes well. While the Shuttle had thousands of heat-resistant tiles that hed to be inspected individually between each flight, the PICA-X heat shield on the Dragon is a monolithic part that's designed to withstand a certain number of re-entry burns and then be replaced. As a service schedule this should prove much more efficient than the Shuttle system, and should only delay reuse of the craft every 10-20 flights (however many the shield proves to be good for).
The purpose of this essay is not to crow over SpaceX's "victory" over the engineers at NASA. The Space Shuttle design began in 1969 and first flew in 1981. To say that NASA engineers had access to less technology than SpaceX is putting it mildly. They did great considering their political and technological constraints.
The point of this post is to be glad for America. As a nation we are finally within reach of having re-usable rocket stack that can put cargo and crew in orbit once more, with the added benefit of being a fraction of the cost of our old one. Over the next year we should expect Dragon 2 to fly crew to the International Space Station (and possibly beyond) and the Falcon Heavy stack to deliver both larger payloads to Low Earth Orbit than the Space Shuttle and a reusable second stage.
Furthermore the logic of low-cost operations should start to sink into NASA's programming within the next couple years (and hopefully to the private sector as well), and this should deliver a renaissance in terms of space science. When huge chunks of NASA's budget are eaten up trying to develop and maintain a rocket that costs billions to launch and flies once a year, a lot of science gets cut for lack of funding or access to orbit. If the Falcon Heavy can put 20 times a many payloads in orbit for 1/20th the price per kilogram, it suddenly starts making sense to mass produce probes for the asteroid belt, outer solar system, and who knows where else.
The last six months have been a huge boost to the idea that American space has a bright future.