1960s spaceship design in TV and film was still very much about style -- although thought was now being given to design. Here's the USS Enterprise from the Star Trek television series (1965-1968).
Many of the "big things" (ocean liners, electric locomotives, etc.) which so fascinated people in the 1920s and 1930s were gone by the 1960s, and the Great Depression and World War II had done much to disabuse people of the idea of a utopian future. The new "it" things like rockets and atomic power seemed as bad as they were good. (Remember the V2? And fallout?) But some things seemed to hold a lot of promise, like the computer, even though no one knew yet to what uses it could be put.
Style still tended to rule. The Jupiter II from Lost in Space was merely a flying saucer. But the ships on other series showed clearly that style was still more important than design. The Flying Sub from Voyage to the Bottom of the Sea was inspired by a manta ray, and the Seaview submarine (designed by Jack Martin Smith and Herman Bluemethal) had a nose modeled on a shark and manta-ray fins designed to provide stability. The Proteus submarine in The Fantastic Voyage (designed by Howard Goff) was a Chris-Craft luxury yacht slightly modified for underwater. The Spindrift rocket on Land of the Giants was a kit-bash (sic) of the Proteus and the Flying Sub, slightly modified to be more aerodynamic. The USS Enterprise on Star Trek was inspired by an electric stove coil. These were all "cool looks" that reflected an emphasis on style more than utilitarian design.
The interiors of these ships share many of the same design elements: Lots of glowing and blinking lights, plenty of switches, lots of computers, most equipment sealed behind panels, occasional visible interior bracing (a bulkhead), bucket seats.
Visually, much of the interior design was a reaction to Americans' experiences in World War II. More than 10 million American men had gone to war, and the interiors of their tanks and planes and ships were lined with cables, conduits, steel wires, bracing, and all sorts of equipment. The guts of the tank or the plane had to be exposed, because in a cramped space in the emergency of a battle -- there just wasn't time to unscrew a panel and fix a pump or a short circuit. In the future, though, the assumption was that systems would be far, far more robust. So equipment could be hidden away behind panels. Thus, the "clean look" entered into science fiction visual dogma.
There was also some attempt to think through what style might mean for design. Star Trek was in the forefront of this. The ships in The Fantastic Voyage and Voyage to the Bottom of the Sea were all based on existing theories of aerodynamic underwater design. The SpinDrift was rarely seen on Land of the Giants, and almost never mentioned.
But on Star Trek -- while the Enterprise's design was stylish, Gene Roddenberry, art designer Matt Jeffries, and FX artist Jim Rugg attempted to retcon the design scientifically. The warp nacelles were high and away, they claimed, because the engines generated radiation. The impulse engines were behind the saucer section because that's where the center of gravity on the ship was. A big dish antenna (they'd come into existence just before the war) was needed to communicate with home. Clamshell doors didn't just look cool, they were practical (a dent in a door means it can't be used; a dent in a single slat of a clamshell door means that slat could be switched out and replaced easily without replacing the whole door).
Visually, Star Trek set the tone for much of science fiction for the next half century. That's because designers either copied it, or reacted to it by rejecting it. There's been precious in-between ground, and little that's new (design-wise).
Interestingly, the reason why the Enterprise's bridge is high on the saucer section and exposed to enemy fire (!!!) is because an audience wants to "see the bridge". Just like on an aircraft carrier (the island just up to one side), or an airplane (the cabin is in the nose), or a tank (the driver is in the turret), Roddenberry and Jeffries realized that burying the bridge in the center of the ship (the most logical place for it, given the ability to see outside via television) would violate people's "norm" for "where the bridge should be".
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Typical "clean look" interior spaceship design, courtesy of the deeply influential Star Trek. Everything is concealed behind a wall or panel. Only a few "vital" pieces of equipment jut from the walls. Matt Jeffries argued that the walls were too plain-looking to leave blank, so they got some big styrofoam pieces (the kind motorcycles are packed in), shellacked them, painted them, and put them on the walls.
Notice the bulkheads overhead, showing where the interior bracing is. This is used a lot in sci fi schows of the 1960s.
The bridge of the USS Enteprise, another typical piece of "clean look" visual design. Every panel has glowing buttons and switches on it. Glowing lights are set into the upright panels, and they flash on and off to make it look like "things are happening".
Notice how this is much like a car or airplane dashboard: There may be a "fix engine" light, but it isn't visible until it's lit from behind. The Enterprise's bridge functions the same way.
Note, too, the bucket seating -- a new car design feature of the 1960s considered very innovative.
Funny: My DVD player remote control has more switches, buttons, pads, and sliders than this Enterprise control panel.
Here's the interior of the Proteus submarine (?) from the movie The Fantastic Voyage. It, too, is pretty typical of 1960s "clean look" sci fi ship design. Very little equipment is visible; it's mostly behind panels. Lots of lights, buttons, and switched. Interior bracing is also evident.
Here's the SpinDrift (I just love that word!) from the 1960s television series Land of the Giants. Notice the aerodynamic nature of the craft, which was supposed to rocket into the atmosphere and then drift back down to Earth. The engines look very much like advanced U.S. Air Force turbojet engines, inside an aerodynamic cowling. "Fins control an airplane", the public reasons, and so the SpinDrift has a fin, too. Sci fi always has at least one toe dipped into the pool of reality... OK, sometimes less, but...
Here is the passenger cabin set of the SpinDrift from Land of the Giants. Typical overstuffed leather chairs are given a futuristic look.
Note the geometic (not rectangular) door in the rear, and the hexagonal wall art. This comes from architecture: Modernist architecture loved the "glass and steel box". But that got boring, quick. So Modernist architects quickly began putting "skins" on their buildings composed of repetitive geometric shapes to liven things up.
For example, let's take a look at 2 Broadway, a 32-story office tower built by Uris Brothers and completed in 1959. Notice how much it looks like the SpinDrift passenger cabin? The original facade featured aluminum metal rectangles with rectangular fanlights above and below that covered blue-green tinted windows. (It appeared in the 1960 movie The Apartment with Jack Lemmon and Shirley MacLaine.)
Here are the SpinDrift cabin's control panels. Again, this show reflects the "clean look" design ethic of 1960s sci fi movies and television. Everything is behind a panel. Lots of buttons and switches signal to the viewer "I can control things". Flashing lights are indicators.
The SpinDrift set was cheap, so much of this is merely electronic gear thrown out by the military or businesses. Stripped of its identifying markings and some of its more mundane controls, it looks futuristic (enough).
Another shot of the SpinDrift cabin -- oh no! a giant!
This shot of the SpinDrift cabin again shows the military aircraft-style seating, glowing lights, and "clean look" of typical 1960s sci fi.