Well, bless me, apparently "flyer" is the word for a thing that goes point to point on a body with negligible atmosphere, at least if we take Mark Wade's Encyclopedia Astronautica as authoritative.
Mark Wade said:
Lunar flyers would use rocket power to get crew or cargo quickly from one point on the lunar surface to another. The larger versions could act as rescue vehicles to get crew members to lunar orbit for pick-up and return to earth. Their horrendous fuel requirements meant that they were mainly considered for one-use rescue missions - for example to return a crew from a disabled lunar rover, beyond walking distance back to their lander. Some Apollo variants proposed using leftover propellant from the Lunar Module descent stage to fuel such flyers.
I put in the bold to highlight what I am talking about. I think it would be smart to have a standby Flyer ready to go help some manned remote mission gone wrong. Using them for regular transport though is terribly prohibitive.
I had in mind something like an unmanned version of the
LFV Bell, which perhaps in turn could drop off rovers at distant sites of interest. Obviously that's not "flying" in a conventional sense - yes, it would require some propellant, but we've made certain advances since the 60's in materials and specific impulse...
I don't believe materials are any sort of problem at all; the Wright Brothers could probably have designed a suitable Lunar Flyer, if they studied up on liquid fuel rockets instead of aerodynamics. Well, I exaggerate...although there was a Brazilian or Argentine around their time who some claim was in fact making working LOX engines, but anyway the engine tech of the 50s would be plenty adequate, or the 60s at the latest for hydrogen-oxygen.
Have we really made any significant advances in ISP since the late 60s? Incremental at best, wringing maybe 10 percent more, and at that to do that the engine needs to be sophisticated, with high pressure pumps--the Apollo LM could surely have had a higher performance engine, designed in the early 60s, if the mission planners wanted to risk the possibility of a pump failure. They opted for somewhat lower performance with improved reliability with their ultra-simple pressure fed hypergolic fuel design. The choices of chemical propellant remain the same as what was known back then--every "new" trick I've heard of, such as hybrid solids where the oxidant is a liquid, was studied on paper decades before. To get better ISP than a hydrogen-oxygen rocket such as the 60s vintage Centaur one has to either use fluorine for oxidant or go nuclear--I don't suppose you are proposing a nuclear thermal Flyer?
(And although not on this petite scale, NTR is also 60s vintage tech...) Or one can get fantastic ISP with a Hall thruster, 3000 or more--and really really puny thrust. Great for cruising the asteroid belt over a period of years, useless on the Moon.
Where we really have seen advances over 1960s available tech has been in the matter of avionics. I was stringently cautioned by the authors here against getting too sanguine about it, but surely today we could make a highly reliable autopilot/navigation system that would mass just a few hundred grams and consume a trickle of power, but infallibly guide a Flyer on an optimized trajectory to a feather-soft landing anywhere within its range; just punch in the coordinates. (If they aren't mapped we'd have to include a sensor array, millimetric radar with Doppler capabilities, plus perhaps a visual image processor, to find a perfectly suitable landing spot, and thus also include extra propellant for a hover while it finds the site).
Note that the link you provide to the Bell proposal gives practically no specifications at all--it doesn't say what propellant they wanted to use, how much the flying lawn chair massed, or anything except a bare "80 km range" which I suppose must mean out and back again.
Well, OK, the Moon has an average radius of 1737.1 km (polar radius is a few km smaller, but that's not directly relevant--distance over a particular angle will be greater at the poles, not less, due to Lunar oblateness meaning the poles are relatively flattened, ie lower curvature). And with Wikipedia giving escape velocity, presumably from the surface, as 2380 m/sec, I infer a gravitational potential and thus orbital velocity, at the surface, of -2832200 joules/kg and 1683 m/sec respectively. 80 km circumferential distance implies a half-angle of 0.0231 radians or 1.324 degrees; the orbital energy of the minimum-major axis ellipse that connects a point on the surface to an apolune 40 km away is thus -2768240.8 j/kg, so the kinetic energy on the surface is a bit under 64 kj/kg and the speed would be just under 358 m/sec. That looks very modest, doesn't it? But note that while a gun with this mediocre muzzle velocity would fire a shell to hit some 80 km away (at just the right elevation, that is) we don't want our Flyer to crash at that speed there; we want it to land softly, and that means applying the same delta-V in reverse. Then we want it to come back to base again, which means doing it twice more--total delta-V is thus 1431 m/sec round trip, and that is a big fraction of orbital speed right there.
What sorts of rocket engine and propellant would we have to do the job? Let's say it is a hydrogen-oxygen engine that has exhaust speed exactly 4200, and assume 10 m/sec acceleration, a bit over 1 Earth G, to minimize gravity loss without putting too much stress on anything.
The elevation for a ballistic trajectory with instant acceleration would be just a hair under 45 degrees--45 degrees minus one quarter the angular distance we want to cover actually, which is to say 44 degrees and a bit under 45 minutes in this case. To reach the coasting speed would thus require a 35.8 second burn, in which time we'd "fall" under Lunar surface gravity to a speed of 58 m/sec so we have to actually angle up a bit and thrust harder (to keep the same time of burn, or else burn longer at the same thrust which complicates the computation I'm trying to do here) to counter that. Over the ground we'd travel a bit over 4 and a half km, so actually we'd subtract 9 km from the total distance--or change the problem so we are going to a point 89 km away, which I will do now since otherwise I'd have to iterate back with revised figures. The fact that we rise 4530 meters also while doing this also changes the problem a bit, because now the trajectory is over a virtual surface with radius raised by that amount, hence the angular distance is lowered (as is the Lunar gravity, and potential is raised). The extra 58 m/sec we need to thrust upward on the other hand raises the total delta-V, by 43 m/sec or 12 percent, and I think that is clearly a bigger increment than the other factors deduct (except the first factor, the extra distance we cover during boost). Delta-V is thus actually 400, and we need to do it 4 times, for a total round trip mass factor of exp(1600/4200) of 1.465, or that is to say a fixed payload and structural mass arriving back at base would mass 68.25 percent of the initial launched mass, thus almost a third of that mass would be hydrogen-oxygen fuel.
Now, considering that I slipped in another 9 km range there, and that for a rescue mission we might be able to send the thing out to the accident site empty of payload and that the mass is therefore greatly lowered on the way out, that isn't so Godawful as I feared. But this presumably is why the Bell proposal had that limited range. We're going to want a rescue craft that can go out to 400 km, what does that mission look like?
I estimate each boost is 820 m/sec, or thereabouts; round trip then would be close to 3300 and 55 percent of launch mass would have to be LH2-LOX propellant. This is still feasible in the sense that a reasonable vehicle could be designed to hold all that propellant I suppose, and that a single stock of that much cryogenic fuel might be maintained at a polar base; just keep it in the shade and the hydrogen boil-off would be modest and facilities to re-liquefy it not unreasonable. So keeping an emergency rescue vehicle handy to retrieve two stranded astronauts whose rover-lab breaks down at extreme range is doable; I don't know about cost though.
OTOH using such jump-bugs for routine sorties is clearly problematic. If the propellant were shipped up from Earth, clearly out of the question! Well, we chose the polar site in the first place, among other reasons, to explore the possibility of Lunar in-situ refueling using polar ice, did we not? I'd suggest that while that might be true, we'd use a up a lot of useful water fast wasting it in this fashion, for excursions that are within range of our wheeled vehicles. Whereas to go far out of their range would use even more propellant.
But wait! What about the less efficient option of refining regolith to produce oxygen and pure aluminum, and then making a slurry monopropellant with powdered Al and LOX?
I can't recall right now just what the ISP of that combination was supposed to be; I think it would be a generous overestimate to guess 200. For the round trip to and from the periphery of 400 km, using the above figures, over 80 percent of the initially boosted mass must be propellant--which is to say, a single rocket boosting at 1 G initially would be slamming the returning crew at 5 Gs on their return. The propellant is indefinitely renewable with enough solar power and a big enough investment in refining equipment, and automated refineries with robot regolith-scooping shovel-vehicles might be set up at many points, so with a network of hundreds of them it might be possible to hop along to any point on the Moon. But these robo-refineries would be kept pretty busy! The terrible mass fraction is offset a bit because the propellant combo is quite dense. OTOH a highly efficient pump for the engine is impossible because the powdered Al would grind up the vanes; it has to be pressure fed, using helium or some other noble gas--argon is apparently the most common element in the Lunar atmosphere. The combustion won't be as efficient as it theoretically might be.
...
At least, at any rate, until they can get some of these...
I'll see your Gerry Anderson rocket-pod-kitbash and raise you egregious defiance of basic physics in an allegedly realistic SF classic:
TV sci-fi shows can play fast and loose all they like; IIRC Moonbase Alpha supposedly had some kind of gravity enhancers to explain why the case wasn't bouncing around--that might have only been in the novelization, I suppose. If they ever mentioned it in viewed canon then they are covered for the Eagles I guess; they might have had some sort of gravity drive.
But 2001 is supposed to be "realistic." Look at that Moonbus though. Or the footage of it hurtling from horizon to horizon; one might then suppose that it is in a suborbital trajectory, right? And the look of the thing is just design aesthetics.
But no...
Here's Heywood Floyd and his minions, walking around inside, pouring coffee, generally demonstrating that that sucker is not in free fall, and those rocket nozzles on the bottom must therefore be constantly firing to levitate the thing.
If you have delta-V to spare for that, you can just push on to a suborbital trajectory and get their a lot quicker.
In the book of course Clarke has the expedition to TMA-1 happen in a wheeled vehicle (sort of a tread-wheel--a wheel where each of eight or so sections is a separate foot on a strut, the better to deal with rough terrain.
So I just wonder who the arty visionary on Kubrick's staff was who came up with this rocket-bus, and whether they had the slightest clue what was head-bangingly wrong with it, and just didn't care, or whether the knowledge never troubled their pretty little minds. I wonder if it was Kubrick himself, and if so did he know better but decide the audience needed the visual sense of progressive motion, and needed it to be fast and yet obviously moonbound, and physics was just going to have to take a back seat to drama cause of ART.
No question it works emotionally.