[maxwell86]

No, because people buying a luxury air yacht care about going from A to B.

If your claim is that there is a market for luxury air yachts that are extremely expensive to maintain, require a huge crew 10x larger than a yacht, are 10x "smaller" than a yacht, and can't remain stationary somewhere nor from A to B, but instead only can go "wherever the wind goes", then I don't believe you.

Feel free to prove me wrong. But the amount of yachts in Montecarlo during the F1 grand prix suggests that a significant market of the luxury yacht market does care very much about going from A to B, and about being able to remain stationary in their yacht somewhere.

So not being able to go from A to B and having to put your "yacht" inside a crappy hangar without views to be able to stay at one particular place pretty much kill the idea.

[phreeza]

OK fair enough, I was thinking more about the operations within a day, when the travel style of a Goodyear blimp would be sufficient. But you are right that long distance point-to-point travel would likely be a requirement for the longer timescales.

FWIW I'd be really interested in a writeup of your actual napkin math that convinces you of the infeasibility so strongly.

[maxwell86]

The math is simple, its just the Archimedes principle, fluid drag force basics, and power law of propelers and jet engines.

Archimedes says:

m = V * (density air - density helium)

that is, the total mass that you can carry (including helium, propellers, fuel, all of it), scales linearly with the volume V of the balloon, and the difference in densities between the gas inside and outside.

There is little that you can do about the density difference beyond heating helium to make it larger, but at equal temp on the ground its 0.1, so you end up with:

m = 0.1 V

so if you want to carry 120'000 kg, then you need 1'200'000 m3 of helium.

That's a lot of helium. If you put it in a ball, the radius would be 66 m. or 132 m diameter. The wind surface of the ball would be 13'685 m2.

The force of air on a ball is obtained from the definition of the drag coefficient:

F = density_air * C_d * v^2 * A

The C_d is worse at low Reynolds number, so lets fix that at 1.0 (worst case, it gets slightly better as the flow speed increases, but whether its 1 or 0.8 it doesn't really matter).

So if you want to stay stationary at 20 m /s winds (72 km / h), then you need to apply a force of

F = 1.225 kg/m3 * 1.0 * 20^2 * 13'685 = 6.7 MN

The power required to produce similar thrust via a propeller is more or less

P = sqrt(F^3/(rho * A_propeller))

so with 10x 2m diameter propellers, you'd need

P = sqrt(6.7^3 MN / (1.225 * 10 * pi * 1^2)) = 2.8 MW

of power. If you actually wanted to move against the wind at 70km/h you'd need almost 6 MW.

That's not "a lot" but is not "nothing either".

If you take Rolls-Royce AE 2100 engine powering the C130 Hercules, each engine produces 7.5 MW. These engines aren't "silent", so riding in this thing isn't going to be nice, but no engine in this league is silent.

Considering that you also need electricity and other stuff on board for a crew of 20-40 people...

You end up that for 120 tons, you need at least one cargo aircraft propeller engine to be able to move at 70km/h against the wind (which is pretty slow). You might want two, you know, in case one fails, and the wind carries you to antarctic.

From those 120 tons, you need to subtract the helium, the propellers, the crew, etc. to get to the effective weight that you can carry.

If you wanted to go faster, notice that the drag increases with velocity square. You can try to reduce the surface like zeppelins do, but the surface is still going to be pretty big, because "volume" is what make these flight.

Also if you reduce the surface in travel direction, you are going to increase lateral surface cause that's how volume works, and that's going to make it worse when you have cross winds.

For any reasonable speed you might be looking at close to 20 MW of power, which is 777 jet-turbine like amounts of power.

So why doesn't make sense to build this to go from A to B?

Cause physics. If you want this to "float" (you can't really call this flying), you need absurd amounts of volume, and it turns out, that moving things with a large volume through a fluid requires a lot of energy.

You could do a more detailed analysis, improve the performance of every single component by 10x, but you can't change the physics.

Even if you just want to lift cargo, and barely move it from A to B, this wouldn't make sense, because the surfaces created by the huge volume would mean that you need absurd amounts of power to just stay stationary in case of "mild" winds. Even if you had enough power, wind changes direction quickly, but the huge propellers required for this don't. So if you need to lift heavy cargo, you probably need to position it with < 1mm tolerance, cause by definition you can't move heavy cargo after you position it, so you gotta get it right (e.g. something like a highway bridge).

You can't do that with this thing either cause of physics (big area, movement very sensitive to wind, impossible to control).

For the luxury thing, you end up much better with a luxury private jet, or a private 787 or whatever. The C130 Hercules, can take off with 137 tons, is orders of magnitude faster and cheaper, and only needs a crew of 3!

For transporting a bridge, you end up much better with a bunch of heavy cargo helicopters.

---

Instead, if you just "float" somewhere, and you don't care were, balloons and zeppelins are pretty good.

They aren't as good as a modern glider obviously, but they benefit from working with the physics and not against them.

Other vehicles that "float", like boats and submarines, exploit the fact that water is way denser than air, yet even they have pretty big submerged volumes, but luckily for them water doesn't change direction as fast as wind does.

[phreeza]

Thanks for writing this all out, but I think your initial calculation is off by an order of magnitude, no? You need 1m^3 of helium to lift a kg.

I don't have time to work through the rest now but I'll give it a shot tomorrow.

[maxwell86]

If you heat the helium enough, yes.

But even with 1 order of magnitude less volume, the fluid dynamics are still really bad.

These things "fly" like a brick, we are just making this brick lighter and lighter, but a brick is a brick.

We'd have to shape the helium into an airfol (an helium airfoil) to solve the main drawback.

[phreeza]

Well you don't have to really heat it, it's just room temperature. The kind of density you are talking about is only reached well below 100K.

So here is my take on your estimate:

First of all, I was thinking more about an RV-sized gondola. So something like this [0].

The axles are rated for 30000 lbs together, so let's say 15000 kg fully loaded. This includes ridiculous stuff like marble countertops, so there is likely a lot of headroom for trimming weight.

Taking that into account, and the room temperature helium density, we get 15000 m^3 of volume.

Then I would argue that taking a sphere is really not the right approach, because it has poor drag coefficient and also having this elongated shape is what gives you control authority (try steering a circular boat with a rudder, any rudder you apply will just make you spin). The argument about crosswinds also does not really apply because you would always point the nose at the apparent wind, not dead at the direction you want to go. Same as a boat in current or an aeroplane. The exception are gusts of course, and I do see those could pose a problem.

So let's take an ellipsoid with a 1:2 aspect ratio. you need semi major axes of a=b=12m and c=24m to get ~15000m^3 volume. So this thing will definitely not fit in your garage, but it will fit into a pretty standard barn that any rural construction crew builds routinely.

The frontal area is then pi*(12m)^2 = 452 m^2. The drag coefficient for such an ellispoid is somewhere around 0.1 from what I can tell. Can get even lower for a proper airfoil shape but let's go with 0.1 to account for stuff like the gondola etc.

For 20m/s, (way faster than any water-based yacht can travel) gives a force of

1.225 kg/m3 * 0.1 * (20m/s)^2 * 452 m^2 = 22 kN

and a corresponding power needed of

sqrt((22kN)^3 / (1.225 kg*m^-3* 10 * pi * 1m^2)) = 0.5 MW = 700hp

That seems like a very realistic power requirement for such a vehicle, the RV I liked to earlier has 600hp. Might have to be a bit more because the prop area is perhaps a bit much here, but that scales linearly so I don't think thats a huge problem.

Of course if you want to maintain TAS much above 20m/s things escalate quickly. For 40m/s:

1.225 kg/m3 * 0.1 * (40m/s)^2 * 452 m^2 = 88 kN

sqrt((88kN)^3 / (1.225 kg*m^-3* 10 * pi * 1m^2)) = 4.2 MW = 5200 hp

which does indeed seem excessive. But I think for such a craft 20m/s would actually be acceptable. Can't fly it in a storm and can't compete for speed, but both those things are true for leisure sailing yachts.

[0] https://www.entegracoach.com/motorhomes/cornerstone/