Quick and dirty experiment.
Get a bathroom scale. Big pieces of cardboard to flap.
See how much you can reduce your weight. Bet it is barely noticeable.
Off-topic, I know, but gosh! I love Heinlein’s earlier stuff! 
You can do something like that right now - “free fall” in an enclosed room, into a fan blowing upward. Try flapping your wings and see if that makes any difference.
But your experiment proves only that big pieces of cardboard are wrong solution for ornithopter wings.
That’s not a very good analogy. Your arms would need to be strong enough to push wings with enough surface area to displace enough air to “climb” against gravity. So roughly something with about the surface area of 1/2 a hangglider on each arm. No easy task.
Since you weight 1/6 as much on the moon, my WAG is that you would need wings about 1/6 the surface area of 1/2 a hangglider on each arm.
Not sure if that’s a completely apt comparison either - hang gliders don’t fly by flapping - a wing that flaps may not need to be the same size as one that glides.
I know, which is why I put in the bit about inevitable inefficiencies. The problem is that there’s a certain speed/resistance ratio at which your arms produce their maximum energy output. Larger wings are more energy efficient but wings large enough to grip enough air would have an impossibly high resistance to work against. Wings small enough to beat at the optimum human rate waste virtually all their energy throwing a small volume of air back at higher speed. Which is why a helicopter requires much less power than a jet-powered VTOL. You could fly by flapping your arms even in Earth gravity IF there was such a thing as 100-foot long wings that weighed nothing and a zero-weight zero friction loss mechanism that would gear down your flapping to a six-beat per minute stroke. Effectively that’s what the Gossamer Condor does. Now as to whether lunar gravity makes enough difference to put it in the realm of the possible… my guess would be take the amount of difference even the best wings you can flap in Earth gravity make (five or ten pounds?) and that’s pretty much what your gross weight would have to be in order to fly.
Let’s do some back of the envelope math.
Take a 150 lb adult, strap on 50 lbs of wings. 50 lbs is a conservative number, assuming some composite material frames and synthetic feathers, and fully articulating like bird wings.
That’s 200 lbs. 1/6 of that is ~34 lbs in order to break even. So you would want 40 to 50 lbs to have reasonably responsive flight.
Can you lift 40 - 50 lbs with your arms and shoulders? Could effective gearing be instituted in the wing set to allow you to flap them while exerting less overall force?
Heinlein cites a wing loading of 1 lb per square foot. Birds have from 1 to above 2 lbs per square foot.
So maybe it depends on how much flapping vs how much soaring (riding thermals).
Yes, but not for very long. (I base this on a recent project where I was installing drywall on a ceiling).
He also mentions a higher than normal air density as well. It’s a solid fact that it’s easier to fly in denser air whether you’re using an airplane, glider, or rotorcraft.
I’d say with 1/6 and a good design it would be a matter of getting the air dense enough to support a human with a wing small enough to be human powered. Human beings can certainly tolerate air at higher than sea level pressures, although you may need to undergo decompression before returning to a lower pressure (it all depends on just how dense an atmosphere you need, and what it is composed of)
Flapping is much more efficient for keeping something aloft; it’s less efficient for forward motion.
I imagine that they would probably utilize the feet as well in this flying scheme… Big fins like a diver wears that you can paddle to produce some extra forward thrust for speed to help your wings produce lift.
And wouldn’t these wings have to be positioned on the lower back or waist, where the center of gravity is? Seems that could make the flapping mechanism rather difficult to pull off.
Tell that to an Arctic Tern.
Maybe for really small things like bugs and birds, but not for big things in thin atmospheres.
Otherwise, where are all the helicopters that work by flapping?:dubious:
We haven’t built flapping-wing aircraft to this point because we simply don’t have the technology; aircraft wings are already among the most complex mechanical structures we commonly build, and a fully articulated wing would obviously be twice as complicated.
We don’t see wheeled animals in nature, either; we build wheeled vehicles- but a vehicle with legs would be capable of traversing ground that no wheeled vehicle ever will.
Actually, the first ornithopters capable of manned flight were built in 1870. Practical fixed wing aircraft ended up dominating, mostly because they are much simpler.
I don’t imagine the technology would be much more complicated than a helicopter. I think mostly they haven’t been developed because they look sort of…ridiculous. Flying in an aircraft that shakes up and down as the wings flap might be a bit uncomfortable as well.
Thats because its pretty darn hard to biologically evolve wheels or propellors.
Again I ask, if its more efficient why aren’t we doing it?
Most birds- raptors, at any rate- flap in more of a forward-back stroke than an up-down one. I can’t find a video, but if you watch a falcon fly its wings move in an almost totally lateral action.
OK, I’ve been giving this some more thought.
A 165 lb. human weighs about as much on the Moon as a medium/large Andean Condor weighs on Earth. The condor manages to soar beautifully with a wingspan of 9-10 feet. That suggests that a human could do it on the Moon, in air the same density as Earth’s, with a wingspan not much larger than that, if the wings were as good as a bird’s. 9-10 feet is pretty big, but not as big as a hang glider.
Now, could a human flap those wings fast enough to take off? I’m not sure how to find the answer to that. Comparisons to a climber don’t seem very apposite, because the climber applies muscular force almost entirely through the hands. That’s not at all the case with flapping wings. But I do know that birds have freakin’ huge pectoral muscles, so my guess would be that a person with great upper body strength could do it, but not necessarily an average person.
As others have noted, humans’ legs are much stronger than our arms, so an easier way to fly would be with big flippers, kicking like a diver. I think this could work quite well, especially if one also had a fixed gliding wing attached to one’s back. I’m not sure how the takeoff would work, though–could you jump high enough to give the flippers ground clearance? Perhaps on the moon you could.
WF
As a point of reference, even the smallest helicopter (250 pounds empty) needs about 40 horsepower to hover and manuever.
Humans put out a fraction of a HP TOTAL.
The one sixth g thing buys you something, but not nearly enough IMO.
You can’t assume that a helicopter is a model of efficient powered flight. How many horsepower do you think a condor puts out?