Is the concept of my flying carpet possible?

Question

My planet is tidally locked to its sun. It has a slightly thicker atmosphere than Earth. Over the planet’s sun-side surface, there would be no wind because that area is in the middle of a big cyclone/anticyclone. (I'm not sure if that works yet.)

The Aliens living there are using some sort of light glider to travel over big distances from one city to another.

The concept is very simple:

1. Two snake-like weights on each side.
2. A middlepart with some steering mechanics in the front in shape of a manta ray (not shown)
3. A thin, flexible, black plastic between the weights.

The sun shines onto the plastic. The plastic heats up the air beneath it. The air expands and carries the weight of the construction. When it flies, it looks like a straight worm that hangs in the air whilst looking at the ground in a very slight angle. It has trouble landing. That's why it doesn't. It will fly slowly past a bridge and passangers just jump onto it.

It should be able to travel over long distances without droping in altitude.

---

Questions

1. How exactly can I get the energy of the sun through the "carpet" into the air below?
2. How many gallons of air must there be under the carpet per pound of weight and under which circumsances (temperature and pressure of the air)?
3. What other circumstances in a world would be practical for my flying carpet to work?

---

I had to finish the question in a hurry and will adjust it later if wished.

Answer 1

The principle seems similar to a solar balloon, which is an hot-air balloon where the air is heated primarly by the Sun. The Wikipedia page linked has several formulas that should be useful to you.

Your design is open on the bottom while existing solar balloons are closed. This is probably critical to keep the hot air inside long enough to reach the right temperature and is probably going to be a major difference. If you are able to tweak the composition of your atmosphere you might make it more responsive to heat dilation, lowering the required temperature, but I'd bet this would not be possible with Earth's atmosphere.

On the other hand, the air will be really hot on the day side of a tidally locked planet. It will receive heat from the ground as well, although how much is hard to say. Ground heat might be the force that makes it all work but you'll need to reach a compromise with how people will survive there in the first place.

To make it steerable you'll need some kind of propulsion. If you have an excess of hot air letting it out would propel the vehicle in the opposite direction. Alternatively you can use a (solar.powered?) mechanical propulsion like fins or a propeller.

Conclusion: "Flying carpets" will need some assumptions on the local climate and physical properties of the atmosphere and the ground. They will probably need to be incredibly large to carry a modest weight. You might however convince a reader that they work because you have some qualitative arguments, even if the numbers would not add up.

Answer 2

So basically you are trying to make a solar-powered balloon, stretched as a carpet.

Balloon floats because air captured in it is less dense than air around it.

So answering question 3:

• in world with atmosphere with big thermal expansion coefficient. The bigger difference in densities of gases inside a balloon and outside of it, the bigger lift force.
• in world with great gravity. The greater gravity, the greater buoyancy (balloon uses it). BTW. there is no buoyancy in zero-gravity.
• in world with more dense atmosphere higher buoyancy can be achieved (water produces bigger maximum possible buoyancy than air), although air density on it's own does not produce buoyancy (only with correlation with thermal expansion coefficient that produces densities difference).

As to question 2 (I'm not using imperial units here. This is why: https://www.goodreads.com/quotes/8417995-in-metric-one-milliliter-of-water-occupies-one-cubic-centimeter):

Problem with carpet is that most of the heated air beneath it escapes it immediately. I see two possible solutions - capture part of heated up air by shaping your carpet more like a container, or make atmosphere so dense (it will prevent heated air from escaping a bit on it own) with so high thermal expansion coefficient and so great gravity, that this thin layer of heated air would be able to lift whole carpet.

Let's see it it is anyhow doable with some maths.

Some symbols with meanings:

m - mass of carpet

g - acceleration of gravity

Fb - buoyancy force

Vu - volume of heated air under carpet needed to create this force

Rd - difference in densities between heated and cold air (beneath and over carpet) - it gets bigger with air's thermal expansion coefficient growth

Q - gravity force acting on carpet

If your carpet will weight W, then we need to create force greater than W*g to lift it.

This force will be Fb = gVuRd, so:

Fb > Q

gVuRd > m*g

Vu*Rg > m

(Vu*Rd)/m > 1

About thermal expansion coefficient you can read here: https://en.wikipedia.org/wiki/Thermal_expansion#Volume_expansion This coefficient for gases usually is around 0,01 - 0,02 / K that means, when you heat some volume V of gas by 1 kelvin, you get 1,02V in the end. Let's call this coefficient "B".

This means, that Rd (mo - mass of air over carpet, mu - mass of air under carpet, Rn - density of air over carpet, like in normal conditions):

Rd = (mo/Vo - mu/Vu)

Rd = (mo/Vo - mu/((1+B)*Vo))

Rd = Rn - Rn/(1+B)

So the bigger B, the bigger Rd, and Rd tends to Rn, so to value of density of air above carpet.

So all in all you have:

(Vu * (Rn - Rn/(1+B)))/m > 1

Let's count volume of air under carpet for some example values:

Vu - searched

Rn = 6 g/L (sulfur hexafluoride, one of most dense gases I know about)

B = 0,02 (upper regions of common coefficient)

m - 1000kg (rather small unit assuming aluminum as constructing material, 6 passengers probably)

So:

Vu > m / (Rn - Rn/(1+B))

Vu > 1000[kg] / (0,006[kg/L] - (0,006[kg/L]/1,02)

Vu > 8500000 L (dm3)

So assuming that under your carpet you'll add a wall to keep averagely 10dm (1m) of hot air under carpet (it will be more in the middle, and less on the sides, but I can't calculate this), your carpet would have to have 850000dm2 or 8500m2 of area. Pretty much impossible with 1000kg. But if you'd add a wall that will keep 100m of air under it, it will have to have 85m2 area, so... pretty big carpet you'd have. But possible I think.

Let's mess a bit with entry values:

Rn = 10

B = 0,05

m = 250kg (ultra-light sun-forged meteorite metals alloy)

We get Vu > 525000dm3

So with wall keeping avg. 1m or air beneath, area of carpet should be 525m2 Well.. maybe...?

If we would do:

Rn = 600 (least dense liquid I found has ~616: https://en.wikipedia.org/wiki/Isopentane)

B = 0,1 (this seems so extreme extreme to me that I don't know If it is possible in conditions any carbon life we know of can survive)

m = 10kg

Vu > 1100dm3, so with 0,5dm of air beneath it in average it's area could be 22m2 So extreme...

As to question 1:

Another thing is heating the air - there are two ways that come to my mind. solar powered peltier modules or Stirling engine. Both will transport heat from upper surface of carpet to bottom one. Both can be powered with super-efficient solar power driven energy source, but since this civilization is bound to their sun so tightly, than this is probably not a problem.

Afterword:

Our planes have MUCH more efficient ratio of mass/(wings)area, so maybe just make them all use solar powered planes...?