How dense would an atmosphere (that's presumably non-toxic) need to be in order for a human being (without wings, artificial or otherwise) to achieve unassisted flight (without killing said person from pressure)? Or is atmospheric density unrelated to this?
We call this "swimming" and you'd need an atmospheric density roughly that of water. The pressure needed to get a gas at that density has serious physiological effects, so just compressing the right gas mixture (one selected so as to not produce poisonous partial pressures of any of its components) wouldn't work.
It is certainly possible to put enough oxygen into some liquids that there is the potential of breathing "under water," but I'm not sure that such breathing is actually practical. If you allow limited breathing equipment, it's easy.
The answer to this is as complicated as the equations of flight. Basically there is no single answer, it depends upon many variables. I wrote those detailed answers on the topic of flight for previous questions. So please read these if you are interested in the details:
- A world with 1/3rd gravity but 1/2 atmospheric pressure. Would it be easier to fly?
- Air transport breaks down
- What would humans wings need to be like to fly?
If by "without wings, artificial or otherwise" you meant no bits of vehicle, then the conditions of lunar gravity with Earthly atmospheric density would permit a person with normal musculature to fly wearing only a simple suit with "wing fabric" stretching from the arms to the body.
To accomplish the same feat on a planet with a full 1 g of pull would atmospheric density of greater than 6x that of Earth.
To accomplish the same feat without the wing suit, I don't know. Human arms are not designed to generate lift and most of the arm won't generate lift at all. I am only certain that humans could shape the hand correctly for lift generation and that is not much lifting area. At a guess, you might require another >10x increase in atmospheric density to fly.
My best guess is it would take >60x Earth sea level normal atmospheric density to do this. If Venus were livable, then you could probably fly there with just your arms & hands.
Quick note: you are correct about the relevant parameter being atmospheric density. You can manipulate the density while keeping the pressure the same by using heavy inert gases (aka Xenon) as the mixing gas rather than Nitrogen. But this can only "purchase" 4x the atmospheric density. You'll still need to increase the number of molecules in atmosphere by >15x that of Earth sea level atmosphere.
I was going to break down the details of this solution, but realized that the above references include all the math you need to figure this stuff out.
and I'm feeling lazy today :)
Anyone looking for the details of how to figure this out, please read the three above reference answers.
In order to fly one has to contrast the gravity force.
This can be achieved in multiple way:
- Bernoulli lift force: by having wings and a suitable motion, the resulting force can contrast gravity and enable flight. You have ruled this out.
- Reaction lift force: by using Newton's third law of dynamics, one can generate enough force to contrast gravity. This is the principle used by rockets.
- Drag force: in a fluid moving at adequate velocity, the drag force can contrast gravity (it happens if you are caught in a tornado)
- Buoyancy force: that's what happens when we swim. To have this, the density of the fluid has to be bigger than the average density of the body.
Gases are 3 orders of magnitude less dense than solids/liquids. There is no way a gas alone can make a human fly by buoyancy. And tornadoes are not practical for intentional flight.
To achieve Neutral buoyancy, atmospheric density has to be just over 1000 kg/m3. That's a lot. For comparison, normal atmospheric density is just 1.225 kg/m3, so this is over 800 more dense, and atmospheric pressure (assuming composition is constant) has to be over 800 atmospheres. That's the level of pressure at ocean depths over 8000 m. Not healthy at all.
However, if the nitrogen is eliminated from the breathing mix, and oxygen level is decreased to a trace level that would be tolerable, humans could survive in this environment, at least for a while. I suggest replacing most of the atmospheric content with Neon. As an inert gas, it won't affect body chemistry. Unlike heavier elements like Argon, Neon is thought to not cause narcotic effect, and its molecular weight (20.18) is 5 times higher than Helium, which means we would need 5 times less pressure for the same density.
So, neutral buoyancy neox atmosphere will need to have pressure about 1100 atmospheres (higher than air because neon is lighter).
While living in these extreme conditions is theoretically possible, it was never studied, and some heath problems like High-pressure nervous syndrome are guaranteed to occur.