How quiet can I make 800 million lbs of jet thrust? (Or; noise levels of ridiculously giant heavier-than-air ships)

Factual Questions
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Silly, esoteric technical question time! Some background: I’ve been playing a bit of Cyberpunk 2077. Which, befitting the aesthetic of the genre, features some giant cargo airships with video billboards mounted on the side cruising lazily over a dystopian city. Example here.

Nifty. Now, ever the sucker for ridiculous fictional flying machines, did a little digging through video clips and the game’s asset models, and made some estimates. Judging by the 40’ shipping containers on the airship in the game, these vessels (about 25x35x186 meters in size) would carry roughly 20,000 tons worth of cargo. And I’m guessing, if only for the convenience and lack of any better knowledge, that it weighs that much empty. So, 40,000 tons, deadweight.

This is obviously a heavier-than-air vessel, but it also has no lifting surfaces, and this setting has (to my knowledge) no type of true science-fictional “anti-gravity” technology. So, they must be airborne by thrust alone.

40,000 tons—or 80,000,000 lbs—of thrust, by my figuring, just to stay airborne. By comparison, the first stage of a Saturn V produced 7.5 million lbs of thrust.

Now, all else aside, my question is: what is the minimum amount of noise you could make, producing that much thrust, from a source that size?

I see that the engines of the Saturn V’s S-1C, mentioned above, produced ~200 decibels of sound—whereabouts the term “sound” is less applicable than the term “sanitary, hands-free meat pulping force.”

I could presume—or at least suppose—that if you were producing 40,000 tons of thrust from an exhaust nozzle that was very huge (like…the size of Wales), it might not actually be very loud at all.

But the 2077 Airship only has five (unidentified) structures on it’s underside which you could readily say even look “engine like,” and they’re 13 meters across—unless you’re only counting the “indented ring” in the middle of the structure, which would seem to look closer to the actual diameter of an engine nozzle, and are only 9.26 meters in diameter. Illustrated here.

I simply don’t know how to go about calculating this. (I also don’t know if there are any applicable “exotic but not physically-impossible” technologies an author might conceivably use to get such a craft airborne, within the constraints of shape and size of the in-game airship, that would be any less noisy or destructive than riding 40 kilotons worth of hot air/plasma directly over a major city at low altitude. I’m guessing “not really,” but hey…maybe I’m wrong)

So…would anyone care to take a crack at this one?

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Aaaand…looking at the thread title, I now realize that I accidentally put in an extra zero in there.

Off to a great start!

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So, acoustic radiation–the technical term for “sound”-- from a propulsion system comes from multiple sources: one is the bulk movement of air, which creates interactions with the surrounding still air that are approximately white noise (essentially noise with a constant power spectral density across some range). Another is the narrowband frequency noise that comes from periodic sources such as rotating machinery, the interference between main and tail rotor blades in a helicopter, acoustic resonances, structural-acoustic interactions, et cetera. And the third are self-interactions between wavefronts, and particularly supersonic waves which can produce very intense shock-shock interactions (which is the crackling sound you hear at rocket launches). There are other ancillary sources such as interactions between hot exhaust and cold ambient air but these three will dominate. Sound is measured as a quality called the Sound Pressure Level, which is just the fluctuation in pressure relative to some base value, resulting in an an acoustic power spectral density; this is where the “decibel” measurement comes from (which is not a fundamental unit itself but a logarithmic factor relative to the base level; in air that is 20 𝜇Pa, which is the lowest level that sound can be detected by the human ear).

Presumably the propulsion systems lifting these cargo airships are not using any kind of supersonic nozzle design because of the undesirable characteristics and would be using some kind of low bypass turbofan engine for high specific thrust, so we can dismiss shock interactions as a source of acoustic energy. Similarly, although the rotating of a turbofan will create high frequency noise, it would presumably be designed to minimize that and other resonances because that would actually represent an energy loss and/or potentially destructive interactions. Which leaves the bulk movement of air. Depending upon how distributed the movement is and how fast it is moving relative to stationary air will dictate how loud it is; the slower the air is moving and more that it is spread out, the lower the SPL will be just because the energy is distributed. However, the propulsion system would have to develop enough momentum to lift 40 kilotons of mass, which is obviously a hell of a lot of energy, and the relatively small size of the outlets means that the exhaust would have to have a lot of momentum to maintain flight. If you calculated the amount of kinetic energy and just spread it over a flat spectrum you’d get some rough estimate of the SPL although in the real world the energy will go preferentially into some energy bands over others, generally with a high amplitude in the low frequency but some mid-range concentration of acoustic energy.

Realistically, such vehicles (and the “helicarriers” in The Avengers) are impossible in practice. Not only would they consume prodigious amounts of power but the acoustic output would be deafening to both anyone on board the vessel and certainly to those below it, and not withstanding the dynamics of having to constantly suck in the volume of air to keep it suspended. The few aircraft that are capable of sustain propulsive hovering without very large or multiple rotor systems, e.g. the AV-8B ‘Harrier II’, F-35B ‘Lightning II’, et cetera, have extremely large fuel consumption and low weight limits for sustained hovering. Even helicopters and titlrotor aircraft lik ethe V-22 ‘Osprey’ tend to transition into forward flight quickly because of the fuel consumption in hovering flight, although they do get some advantage from being in the ground effect zone where recirculation reduces end-tip losses. A straight-up hovering craft unable to use ground effect would require enormous constant power which would be converted to high acoustic radiation.

Note, this is also the reason that “flying cars”, even if technically feasible, would not be practical or desirable. The noise pollution alone would be onerous in an urban or suburban area, notwithstanding the fuel consumption and potential for death upon even the occasional catastrophic propulsive or structural failure. Such vehicles may see limited use as emergency medical or police vehicles–essentially replacing the helicopter with something slightly less invested in killing its crew and passengers at the slightest provocation–but without some technomagical means of silent propulsion would just not be practical for everyday transportation.

Stranger

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80,000,000 lbs is 3.6E7 kg, or in Earth’s gravity 3.5E8 N.

Thrust (F, in newtons) is mass flow rate (i.e., of the air blown through the jets) times exhaust velocity (v).

Flow is density (p) times exit area (A) times velocity (v). Therefore F=pAv^2, and v^2=F/¶

We know that p=1.225 and A=664 m^2 (5 circles of 13 m diameter). So v=656 m/s.

That’s over mach 2. So the vehicle will be constantly be generating supersonic shockwaves from the exhaust. As a point of comparison, note the XF-84H Thunderscreech, a piddly prop plane that shed shockwaves from its propeller. It could be heard from 25 miles away and induced nausea and seizures among the ground crew.

This would be orders of magnitude worse, due to the increased exhaust speed and sheer volume of exhaust needed. And it’s a best-case scenario: I used the maximum possible area and assumed cool, high-density air. If you tried to do it with a rocket or the like, it would get even worse.

That said, I think your premise is a bit off. I’m pretty sure there is some form of antigravity in the game universe.

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All nice ways of saying: sound IS moving (vibrating) air: you cannot move air without making sound.

Even a gentle breeze is loud when it blows in your ear.

Even if you move air without mechanical components (like a pressurized container like a CO2 bottle) it will be incredibly loud quite easily.