On April 12, 1981, while everyone's attention was focused on the still-climbing STS-1, another significant moment was happening mostly out of sight: the recovery of an orbital-class booster by flotation with the intent to reuse it. But almost 20 years earlier, a nearly identical plan had been formed to recover Redstone boosters and reuse them, going so far as drop, float, and practice booster recovery with the United States Navy.
(cover image: SRB Splashdown superimposed with "Water Impact" drawing of Redstone Booster)
The first instance of recovered and reused rockets that this author knows of is some of Dr. Goddard's early rockets—he would do so to save money. He did so both with rockets that were failures (see his A3) and attempted to design ones that could be parachuted and reused (see his A5) [1: Alway, Peter. Retro Rockets: Experimental Rockets 1926-1941. pp26, 28].
The next instance is, much like the Redstone family, part of Von Braun and his team's space flight revolution. To support the development of the A4/V2 rocket, the team had been using a rocket they deemed A3 but which proved unsatisfactory. It was replaced by their A5 which could be recovered by parachute and water landing for reuse, probably, in part, due to the extremely incremental approach to development that would later pit Von Braun's methodology against George Mueller's [2: Ibid. p66].
The effort to reuse Mercury-Redstone boosters occurred at the dawn of manned spaceflight, somewhere around 1961. Despite being considered a success, its results weren't adopted for reasons which I'll consider towards the end of this post. Also, linked here, is a more philosophical piece on why reusability has, thus far, been limited in operation.
I've found two reports on the project to recover Mercury-Redstone boosters. One is a summary of the project and its results as included in a larger summary of the Mercury program, linked here. The other is from a 1962 conference on reusable concepts and research and includes both diagrams and photographs, linked here. A compendium of presentations from the conference, including plans to attach giant Rogallo wings to the Saturn I, is linked here.
There were two prongs to the research: tests with the thrust unit of a PGM-11 Redstone missile (serial number "RS-33" although a list of Redstone Serial Numbers indicates there was only a CC-33) and tests with an H1 engine. The tests on the engine were a series of immersions, treatment for corrosion, disassembly and inspection, then test firings. The program calculates that the cost of this work on the H1 engine was 5% the cost of a new engine.
The booster used in all of the tests was not a space launcher but a military Redstone reserved for training use. However, the report states it was "altered in weight and configuration so as to simulate MERCURY-REDSTONE," so perhaps it was extended to match the length of the MRLV. After successful drop tests in a quarry near Redstone Arsenal (identified via this document), an operation testing retrieval was conducted with the Navy. The pictures come from that, although they are of an extremely poor quality and I am searching for better ones.
First, a recovery ship had to be adapted. The Landing Ship, Dock (LSD) type was chosen because they had an open deck that could be flooded and the booster floated into. To support the booster when it was not floating, the LSD required two "saddles" in the well deck.
After a booster had landed in the water, the LSD would dispatch smaller craft to safe and tow the Redstone. A Landing Craft Personnel, Vehicle (LPCV) was used in the tests. I've identified the second picture in the series as the LPCV towing the booster (the booster either being out of frame, at the starboard hip of the LPCV and hence out of sight, or being in the overexposed region of the image).
When the LPCV's bow was even with the stern gate of the LSD (the gate used to dam off the well-deck), it would disconnect the tow line and reverse away from the booster and LSD. Swimmers from the LSD would approach the booster and attach two sets of three lines to a six-place connecting web.
The six lines attached to the booster were used to float it over the saddles while the well-deck was still flooded. Once it was in position, the well-deck could be emptied.
Once emptied, the booster would sit in two saddles, one fore and one aft. The project concluded a freshwater rinse was sufficient to prevent corrosion from the sea water.
In addition, parachute designs were drawn up, equipment bays designed, and the whole project appeared to have promise when the funding apparently ran out. So why wasn't it a higher priority?
I believe the primary reason was money. In an unusual twist, however, I think there was too much money being put into NASA to make the funds required to achieve reusability a worthwhile investment. The tight, and very public, deadline for the moon landing probably compounded this. Building any launch vehicle requires massive investment, but, in order to achieve space flight your rocket only has to be able to launch once. Spending money on making your rocket launch more than once is technically unnecessary and an investment that carries additional risks. In short, NASA needed rockets that would successfully launch in order to achieve their pressing goal--any additional ability of the launcher was a further risk.
Another reason was the choice of vehicle itself. The Redstone was too little of a booster to see much use past the early days of the space program. And, it was too late of a study to make use of the results. The last use of a Redstone-derived launcher for satellites was in 1958, further Mercury-Redstone Launch Vehicle flights were cancelled in 1961, and the missile would be out of production by 1964 . With Saturn I development begun in 1958  and Titan III in 1959 , the community's focus was probably on heavy-launch vehicles and the possibilities they were opening up. Additionally, Marshall Space Flight Center (MSFC) was overseeing the design of the Saturn rockets. The Redstone's meager lift capability meant little interest in further developing it. The joint US Army - Australian Project Sparta would not be started until 1966, two years after the missile was declared obsolete . The study's use of the Redstone booster meant results that were, at best, only analogous to other vehicles.
The difficult economics of developing reusable rockets naturally played a role as well, but I'm interested in why this specific project has been generally forgotten. The Mercury-Redstone Launch Vehicle used ballast in its design, which meant that replacing the ballast with a recovery system didn't face the usual dilemma of increasing payload at the expense of reducing launch capability. This is a rare condition for a space launch vehicle, in my experience. If one were to do the math I expect that it is more immediately profitable to replace, after every launch, a more powerful launch vehicle (if one replaced the ballast with fuel) or a launch vehicle capable of carrying more payload (if one replaced the ballast with payload) than it is to develop a successful recovery system. The last relies on frequent reuse to recoup its high development cost, a premise which the space shuttle showed could be undone by other factors that affect launch rate. Thus, there is a substantial risk that one cannot recoup the high development costs needed to perfect a recovery system when compared to the lower risks and increased profits of replacing the ballast with fuel or payload.
Besides NASA's then-prodigious budget, the Redstone's semi-retired status, and the Redstone's unique opportunity to replace ballast with a recovery system, the project used the boost portion of a PGM-11 Redstone, meaning the results had to be extrapolated to apply to the space launch versions. Reading the report, it is clear that as much as possible was done to make the unit a clear analogue to a space launch version, but there is always room for surprises between mock-ups and reality.
For example, drop tests of the booster were conducted from 25 feet to simulate the estimated descent rate of a space launcher under parachute. During development of the Space Shuttle's Solid Rocket Boosters, a 48,000lb SRB "drop test vehicle" (SRB-DTV) was dropped from NASA's NB-52B to test the parachute systems . The empty weight of an SRB was 190,000lbs . Additional drop tests were conducted from a height of 200 feet using a scale model and pressure tests were conducted to verify reusability of up to 20 times . Still, in operation, the boosters were damaged by impact and seeping seawater, requiring the parachutes be redesigned . Given the extent of the SRB tests and the fact that operations still required changes it would make sense that the Redstone project's results would have required further modifications after entering service. More cautious members of the spaceflight community may have been pessimistic that the results were as good as they seemed.
Another example: the solid rocket boosters used in the shuttle program never reached their goal of "wash, dry, and fly" because of complications—meaning the assessment that the Redstone only had to be flushed with freshwater after immersion may have been overly optimistic too . Such optimism would have been impossible to prove right/wrong short of an actual demonstration, requiring funding diverted from another project.
The conference proceedings do note that "A program of this nature is needed in the near future possibly in the form of subscale test vehicles, but preferably through recovery of operational vehicles most closely approaching expected future vehicles." This clearly rang true with the SRBs and could explain the success SpaceX has shown given their incremental approach to recovering operational hardware.
Finally, as the report indicates, the Redstone booster was chosen for the project because its structure was conducive to the stresses of a water landing and flotation. Few launch vehicles are.
The Atlas rocket, which was the Redstone's successor for manned launches and a successful satellite launcher, with its "balloon tanks" almost certainly would have required an extremely slow descent and gentle landing. Even if it survived the landing, it would have required some pressurization system to keep its tanks "inflated" or risk damage like what is pictured to the right. UPDATE: I've since learned of studies for adding wings and jet engines to recover Atlas boosters, conducted by Convair under Air Force SR-89774. See To Reach the High Frontier: A History of US Launch Vehicles p92, Launius and Jenkins, eds. Images of a model here.
NASA's third manned launch vehicle, a variant of the Titan II was not as delicate and a portion of it even recovered from the Gemini 5 mission, albeit damaged from its unarrested descent and landing.
Famously, solid rockets are well-suited to this kind of recovery and reuse. The steel casings of the space shuttle SRBs were recovered on almost every flight , although they required significant refurbishment before reuse. The Ariane V boosters, while not reusable, can also be recovered via floatation .
Prior to the Falcon 9's successful landings, it simulated landing on the ocean surface. No Falcon 9 survived the fall from vertical to horizontal after engine cutoff, demonstrating the significant structural demands for reuse placed on a liquid fuel booster. Additional problems could arise from leftover fuels if hypergolic or presented with an ignition source.
In short, it seems the reusability project may have been 'short-circuited' by the generous funding available for MSFC's giant rockets and tight deadline to use those rockets, the use of a launch vehicle with little growth potential and lift capacity, a launch vehicle unique for its under-utilization of onboard weight, and the need to extrapolate its results to other launch vehicles.
Addendum: Which Ship?
Between the images and specific references in the reports, I believe I've identified the ship involved. The report is explicit in calling the larger ship an LSD (Landing Ship, Dock) and that it either had or was accompanied by an LCVP (Landing Craft Vehicle, Personnel).
In 1961-1962 there were three classes of LSD in service: Ashland, Casa Grande, and Thomaston. I believe the horizontal lines on the stern gate in the first picture identify the LSD as one of the Thomaston class. The lines appear to extend the full length and to the full height of the stern gate. As can be seen in the picture of the Ashland class USS Belle Grove, below, it is clear the horizontal grid lines on the stern gate do not extend the full height—it is the same for the Casa Grande class.
In 1962 there was a Thomaston class landing ship named USS Fort Snelling in service. It was home-ported in Norfolk, VA . The booster project tested sea recovery practices 50m offshore from Norfolk. Looking at all landing ships in service at that time, no others make as much sense to be abbreviated "FS."
Given the photographic evidence, the plausible abbreviation, and the appropriate location at the time, I thus believe it was the USS Fort Snelling that took part in the project.