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tl;dr: My world has airships using vacuum spheres made out of a super-strong and lightweight material. I'd like to know how versatile such airships could be used, and how big the spheres would be compared to the rest of the ship.


Background & maths:

I'm building a steampunk/magipunk fantasy world that involves lots of flying islands which, naturally, means you need some kind of flight to get around. Additionally, this world features a magical material that is simultaneously both very strong and lightweight (among other unique properties).
It's visually more similar to glass than metal, but for the purpose of this question, let's call it Beskar, because just like the Mandalorian currently carries the Star Wars franchise, I intend for this material to be used to carry airships via buoyancy.

Functionally, this would work via the creation of vacuum-"filled" spheres with a Beskar hull. I haven't decided on an exact density or strength for Beskar yet, thus those are still flexible. However, assume the strength to be sufficient; it should take Hulk levels of strength to break a 1-cm-pole made of Beskar. I don't generally like handwaving stuff or soft magic systems, but I want a super-strong material, so this is going to be as strong as it needs to be.

For a first approximation, assuming a sphere with a radius of 5 meters, we can calculate a volume of roughly 523.6m³. According to some buoyancy calculator I found on the web and assuming an air density of 1.225kg/m³, the mass of the displaced volume (and thus the weight it can carry) equals roughly 640kg.
Assuming that the Beskar hull would be 0.5cm thick (i.e. a hollow sphere with a 5.01m radius), this means we have roughly 525.2m³ minus 523.6m³, or roughly 1.6m³ Beskar. Because the contraption should be actually able to float, I'll declare Beskar to have a density of about 140kg/m³. I'm aware this is lighter than any solid material in the real world (even some aerogels weigh more if my google search is accurate), but what's the point of magic if everything is exactly like in the real world?
(Quick scaling maths: 10m sphere: 6.3m³ or 880kg of Beskar, lifting capacity 5.1 tons. This is a lifting efficiency of 83% as opposed to 72% with the 5m sphere. 20m sphere: 25m³ or 3.5 tons of Beskar, lifting capacity 41 tons, 92% efficiency. These calculations assume the same hull thickness of 0.5cm)


Issue:

Unlike the basic maths above, what I'm actually interested in and can't judge myself is how practical an airship like this would be. Mainly because I don't know anything about ships and their construction. Zeppelins in the real world are gigantic balloons with a comparatively tiny cabin, which is impractical and not what I want (there's a reason Zeppelins are generally not around anymore, except as tourist attractions).

Thus, how viable would an airship with this technology be? Would it just be a little better than a Zeppelin, could it be used as a decent transportation vehicle without being 98% balloon, or would it even be viable as a cargo ship or a military vessel with thick armor plating? And roughly how big would the spheres be compared to the rest of the ship?
Side note, as it's probably relevant: Beskar is obtainable only for significant sums of money, as - while it's far from rare - it is supremely difficult to harvest and process. Thus, I could design such ships to have a supporting skeleton made of Beskar if functionally necessary or the buyer is Beff Jezos, but the floor, walls, etc. would likely be wood or metal. If possible, I'm interested in the viability both with and without a Beskar skeleton.

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    $\begingroup$ You've said "magic/steampunk". What kind of weapons would be used, and what would armour have to defend against? If we're talking naval cannons, you'd need about one Beskar Sphere per broadside gun, not counting ammunition. If the weapons are crystal staves throwing fireballs and weigh as much as a glass rod, that's an entirely different calculation (and would require different armour approaches). What about propulsion - what is available? Some sort magical directed air, or are we stuck with mechanical linkages and propellers? What generates the propulsive power? $\endgroup$ – jdunlop Jan 22 at 2:37
  • $\begingroup$ Also, the reason Zepplins are not around has little to do with their volume-to-mass ratio, and more to do with a top speed of approximately 120km/h. Carrying provisions and facilities for a two day trip from New York to London is nowhere near as efficient as having people moderately uncomfortable in airline seats for 6 hours. $\endgroup$ – jdunlop Jan 22 at 2:40
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    $\begingroup$ Hydrogen has 93% of the lifting power of vacuum and helium has 86% (en.wikipedia.org/wiki/Vacuum_airship#Principle), so your airship has slightly better payload capacity vs. a real world airship of the same size. It still has the same disadvantages, a large size, which means that it is slow (more surface area = more aerodynamic drag) and vulnerable to bad weather (large cross section = very susceptible to wind). So it's a little better than real world airships but not that much better. $\endgroup$ – GrumpyYoungMan Jan 22 at 2:43
  • $\begingroup$ @jdunlop propulsion on older models or civilian / trade ships would be sails or flying draft beasts. Newer and especially military models would feature magically-powered turbines (weight of the energy source is thus not a concern). Defense-wise, shielding the spheres is not much of a concern, as they're robust enough on their own. Weapons would likely be hand-held devices such as guns or more primitive projectile weapons, or at best maybe some kind of mounted magic railgun (haven't given much thought to weapons yet). [second comment coming] $\endgroup$ – PixelMaster Jan 22 at 2:58
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    $\begingroup$ Airships cannot use sails for propulsion. A sail pulls a boat across water -- it's exploiting the boundary between water and air that a boat sits upon. Without that boundary, using wind is simply ballooning or drifting; none of the classic boating techniques (like tacking) work. $\endgroup$ – user535733 Jan 22 at 3:17
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Let's talk about airship practicality instead of lifting power.

  1. Takeoff and Landing.

    This is, by far, the most hazardous part of an airship journey. Winds near the ground are unpredictable. A single surprise shear can (and did!) wreck an airship in moments. It was a race to get a landed ship into a hangar or properly tied down before that inevitable deadly gust occurred. Similarly, it was a race to get a loaded ship trimmed and back into the air.

    Since the wind in many places (like coastal towns) has some predicable shifts on daily cycles, ships cannot takeoff or land during those known times. Precipitation adds hazards. Lightning is a particular threat, since lightning rods cannot easily be used. Night operations are also very dangerous -- too easy for ground crew to step into a hole on the landing field.

    It's expensive to carry an anchor heavy enough to be useful (and quite rude to drop it upon the town that you are visiting). Therefore your ships will depend upon large local ground crews grabbing lines and using their muscles and mass to drag the ship down from the sky.

    A quiet, small landing field itself needs to be at least 1km on each side. Busy city landing fields will need to be much larger. Your airships are ungainly and slow -- they will approach from random directions as the wind shifts, and beast power will make but a moderate difference due to the enormous aerodynamic drag.

    They will also be slow to rise and fall; as any child who has tried to fight a ball's buoyancy in a swimming pool will attest, it takes a LOT of force to fight buoyancy...and a vacuum ship cannot readily valve gas to lower the ship. (Note to self: Remember to add the weight of the vacuum pump(s) to the dead weight of the ship. And that technology to make vacuum pumps is needed.)

  2. Weather

    During World War I, bad weather destroyed as many airships as combat. An ordinary, unspectacular mid-summer thunderstorm famously ripped apart the USS Shenandoah over Ohio, raining bodies onto the plain, boring farms below.

    Airships depended upon accurate and frequently-updated weather reports from stations along their route. Updating route weather was a primary task of the full-time radioman. Revising the projected route based upon updated weather reports was a primary task of the full-time navigator.

    This means, of course, that you need long-distance communication to share weather data among stations, and a way for those ground stations to communicate (like heliostats or semaphores) with passing airships, both day and night.

    Airships tended to rise during the day and fall at night as the hydrogen heated and valved, then later cooled. Happily, you don't have that problem with vacuum.

    Clouds and fog are an irritation, since they may obscure hazards (the ground, mountains, the stars, landmarks, other ships). But cloudbanks and fogs that last several days are a life-threatening hazard when the ship can no longer measure it's position or altitude. The Graf Zeppelin carried a foghorn to gauge altitude in the fog-prone Rhone river valley.

  3. Navigation

    Daylight navigation in clear air over known landmarks is fairly easy. But the sun goes down, or bad weather obscures the view, or the ship needs to go someplace new.

    Your ships need accurate charts. They need compasses to find their heading. They need accurate precision tools --sextant, clock, ephemeris-- to find their latitude and longitude. They need barometers and lines and noisemakers and a searchlight to gauge altitude.

    Airship navigation is all about probabilities and risk management. If you're flying from Tokyo to Singapore, you don't care what Singapore's weather is right now; you are trying to predict what the weather will be in 30 hours. What direction is the wind likely to be then? Is this the rainy season? How can you approach the landing field from upwind then? Can you arrive three hours before sunset so there's time to land the ship before the winds change? Do the winds near Vietnam indicate a cyclone or not? If a cyclone, which side do you want to ride? How will that change your time of arrival? If you want to avoid dangerous night landings, then is there a safe alternate route that's slower and arrives the next morning? Does the Captain need to make a decision? If so, when is too late for the decision? Are there intermediate stations you can pass over to get updated information?

    You can see why navigation is a full-time job, and why good navigation officers should be well-paid.

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    $\begingroup$ concerning the USS Shenandoah: according to Wikipedia, it apparently got destroyed because it rose and sank too high / too quickly, and the pressure difference got too big. This wouldn't be an issue here. Other than that, I appreciate your input! :) $\endgroup$ – PixelMaster Jan 22 at 10:49
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    $\begingroup$ this is a great answer! only quibble - won't vacuum spheres change in buoyancy depending on temperature? the outside air will get less dense as the temp rises, and therefore the sphere less buoyant - there needs to be some way of controlling this. $\endgroup$ – lupe Jan 22 at 12:15
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    $\begingroup$ @user535733 true, it is dangerous - my point was only that my airships would be much more robust. Of course, that doesn't make navigating any easier, and you can still crash the airship into a mountain, which would damage the ship even if the Beskar parts don't crack. That being said, I fully intended for airships to be piloted only by highly qualified captains. $\endgroup$ – PixelMaster Jan 22 at 12:39
  • $\begingroup$ @lupe, it's a bit less bad than lifting gas, because at least heating the airship itself does not make much difference, which it does with lifting gas. But some method of controlling the buoyancy is needed either way. $\endgroup$ – Jan Hudec Jan 22 at 15:32
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    $\begingroup$ @Nathaniel a method of controlling it is certainly needed. And yes, it is a problem. With lifting gas the ballonets are used that air is blown in, which compresses the gas a bit and reduces the buoyancy (and compensates the expansion with changing pressure). But the pressure differential makes ballonets difficult with vacuum airship. $\endgroup$ – Jan Hudec Jan 23 at 15:34
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16% more functional / versatile than existing helium airships.

This is not the best use of Besker in your world.

As was already pointed out in the comments; Hydrogen has 93% of the lifting power of vacuum and helium has 86%. The improvement from helium to vacuum is a 16% improvement, so that's the performance gain you've got from the real-world. Not much in the scheme of things.

Your armoured battle-air-ships are 16% more practical than the best battle-air-ships we have today. Your freight network is 16% more practical that our current airship freight network. If it's a choice between airships made of besker and isolation - make the airships, but this isn't some groundbreaking technology.

In terms of strength/kg, besker sounds like an amazing material, up there with carbon nanotubes and graphene on the specific strength scale, if you have floating islands you need to connect:

  • spin some besker into something resembling steel rope, string it between the islands, and build yourself a ski-lift-like transportation network. Or
  • build a bridge made of besker between islands. This stuff should be able to span dozens of km without supports. If the islands drift in the wind, the besker sounds strong enough that it should stop that and keep the islands in a rigid formation.
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    $\begingroup$ Correction – it's 7% more efficient. If we were to return to airships today, we'd probably go back to hydrogen. The issues with Airship disasters were largely due to design flaws like single-cell balloons, and ridiculously flammable coatings (the Hindenburg's skin could apparently be used as a fire starter). We don't use airships today not because of the flammability of airships, but because even with 200% the lifting capacity of helium and no fire risk, they'd not be our choice – they're large, slow, and have difficulty with winds. $\endgroup$ – Dan W Jan 22 at 14:02
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    $\begingroup$ Also keep in mind that no matter how strong the material is, a hydrogen- or helium-filled balloon will need a significantly thinner shell, because the load on it is much less, further reducing the difference in performance. $\endgroup$ – Jan Hudec Jan 22 at 15:23
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    $\begingroup$ @DanW The commercially-available-today cargo airship produced by Lockheed Martin, LMH1, actually uses helium, so the answer is correct. aviationweek.com/aerospace/… $\endgroup$ – user662852 Jan 22 at 16:25
  • $\begingroup$ @user662852 - yes, but we use helium because we have an irrational fear of hydrogen. Because we don’t use many airships - people distrust airships anyway, and they’re impractical - we can afford helium, but if they took off seriously, we’d have to switch to hydrogen. There’s a similar irrational fear of hydrogen in cars, even though studies suggest they’d be less dangerous than petrol. $\endgroup$ – Dan W Jan 22 at 18:14
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    $\begingroup$ The added security from using helium must be significant, as that's what all current airships use. Hydrogen would be significantly cheaper, and 10% extra lift is a lot. That said, the modern constructions are designed to actually require thrust to take off, which makes maneuvering easier. $\endgroup$ – PMF Jan 23 at 20:55
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As I calculated in my previous answer

Let's take the ideal case where the volume in the balloon is completely devoided of air, the balloon doesn't let any air leak in and can withstand the outer pressure. This means that a cubic meter of that void will have a lifting force equivalent to the weight of the displaced air, which means about 12 N. This means that to lift a 100 kg load the balloon would need a volume of about $1000/12 \approx 84 \ m^3$.

This is the most compact balloon you can get, because any other lifting gas will be denser than vacuum. However, a vacuum is the only one to require additional structural reinforcement, because the whole structure will need to withstand atmospheric pressure, while any other gas would provide that for free. If you don't provide that, this will happen

enter image description here

In short, what you gain with lifting power you lose with non-paying load.

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Alternate Vision:

FLYING WINGS: With such a strong, light material, why not make very thin (relatively), light airships akin to giant flying wings that happen to be buoyant if they stop moving? Flying wings have a fairly large internal volume and low drag. They would have all the best qualities of an airplane and an airship. Due to the strength and lightness of beskar, irregular shapes can be "filled" with vacuum (or multiple small pockets of vacuum). The same super-strength means the ships would use their vacuum tanks as armor against attacks. Since it is aerodynamic, it's fast, plus if punctured the aerodynamics should keep it airborne even if it loses buoyancy (at least long enough to go a ways and land). You might be able to overload your airships and use aerodynamics to compensate for the excess loads (give enough thrust).

GENERATING VACUUM: Creating a vacuum in real life is a lot harder than it might seem. But what if this weren't a problem? If you have extremely efficient pumps for creating vacuum (like teleporting out air) you could pump air in and out of your vacuum chambers to allow the ships to effortlessly control buoyancy. In fact ammonia has been proposed as a lifting gas specifically because it can be condensed by refrigeration to reduce lift, and then evaporated to re-inflate emptied lifting chambers for superior control. Since you aren't actually using a lifting gas, yet seem to be able to easily create vacuums, this would simply involve filling with regular air and then expelling it at need. This also means you could fill an airship on the ground for stability, then empty the air for take-off/flight.

AIRCRAFT: Making irregular shapes would require rather more material, and you said it was expensive. Have you considered this for craft that aren't QUITE airships? A large section of an aircraft filled with such a chamber would mean that the total mass of the craft was lighter, allowing you to carry dense payloads easier. Also, in the event of loss of power, an aircraft that is not quite buoyant might be able to glide to ground like a feather. Large, light aircraft might be able to go fast when desired, but also move quite slowly if needed, so they might be very good for making VTOL/STOL planes that can fly fast, then loiter in an area using minimal power (unlike the beasts that modern armies use, requiring massive engines, jets, and huge propellers).

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  • $\begingroup$ A craft can be aerodynamic or usefully buoyant, but not really both. Air is about three orders of magnitude less dense than any other thing you might typically want to carry. So if you want to support the cargo with buoyancy, the craft still needs thousand times more empty space than is occupied by cargo, and this increase in volume will be accompanied by huge increase in drag. Aerodynamic lift is just that much more efficient (at the cost of requiring constant power supply) $\endgroup$ – Jan Hudec Jan 22 at 15:40
  • $\begingroup$ @Jan Hudec The OP's combination of ultrastrong ultralight and magic with vacuum suggested something at the edge of buoyancy, which is why I also suggested the near-buoyant aircraft, or something that was fundamentally an aircraft but with airship properties. I'm not an engineer, though, so I can't say what would work with magical materials and engines. $\endgroup$ – DWKraus Jan 22 at 22:02
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The problem is that vacuum doesn't gain you all that much over filling your balloons with hydrogen or helium. Air is a mix of roughly 80% N2 and 20% O2 (with a bit of other stuff I'll neglect for simplicity). The molecular weights of N2 and O2 are 28 & 32, respectively. Thus the average for air is about 29.

Air at 0 °C and sea level pressure weighs 1.293 kg/m^3. Thus if you have a balloon that holds a perfect vacuum (and the balloon itself is weightless), then it can lift 1.293 kg for every cubic meter of balloon.

Hydrogen has a molecular weight of 2. If that balloon is filled with hydrogen, it will weigh 0.089 kg/m^3, so it can lift 1.204 kg for every cubic meter. Likewise for helium, it would lift about 1.1 kg. Which shows that there's not a great deal of advantage to be gained by using vacuum.

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With your numbers, hydrogen-filled airship is still superior!

Ok, so you say a 5 m radius balloon evacuated balloon needs a shell 5 mm thick with average density 140 kg/m³ (it would probably not be solid, but a honeycomb structure; and then it can be thicker, because you need thickness for strength in bending), which weighs 220 kg.

But a 5 m radius balloon filled with hydrogen only contains 46.6 kg of hydrogen. So if you can save 50 kg by using less strong shell, you are better off.

Can you? Sure!

  • The vacuum shell needs strength in bending (otherwise it would crumple upon light distortion). Strength in bending comes from one side of the material to resist compression while the other side resists tension (and the middle does nothing, which is why honeycomb structure would be better than solid shell). So more material is needed than for pure compression or tension. I am not sure just how much the strength in bending needs to be though; that's not a straightforward calculation.
  • If beskar is anything like common strong materials, it is much stronger in tension than in compression.
  • The hydrogen-filled balloon only needs to withstand maybe ⅕ of the pressure differential. You can keep the hydrogen pressure just a little above the ambient by filling and emptying the balancing ballonets inside and venting some hydrogen in emergency.

This together means that the shell can be at least one, but probably two orders of magnitude lighter. Even normal fabric balloon would weigh only around 40 kg at the size and you have much stronger material. That is, you save at least 200 kg by supporting the structure from inside with 50 kg of hydrogen. A gain of 150 kg of payload!

Control

Then there is the question of control. Hydrogen airships have ballonets inside the lifting balloons that air blown into them. This maintains the pressure with changing altitude and allows adjusting the pressure and therefore the lift. This works because the ballonets are flexible.

But your vacuum shells are not flexible. You could have flexible balloons inside that you fill with ballast to reduce the buoyancy, but emptying them again requires strong vacuum pumps. The blowers for ballonets in helium-filled airship can be light, because they don't need to work with big pressure differentials.

Safety

And don't forget the added safety. Penetrating an evacuated shell (you are fighting with the ships, aren't you?) would trigger very fast rush of air. That would create strong forces that would be likely to further tear the shell and probably lead to fairly quick collapse of the damaged balloon—and corresponding sudden loss of lifting force.

But hydrogen-filled airships are, from practical experience from WWI, quite difficult to shot down. Penetrating the lifting balloon causes leak, but since the pressure difference is small, the damage is less likely to propagate, especially if you add some rip-stop structure. And the leak is slow enough that you won't come falling down, just start to very slowly sink. During the first world war, fighters often poured hundreds of bullets into a bombing airship and it still made it home!

Of course you want to have the airship composed from multiple lifting balloons either way. But the collapse of an evacuated lift balloon is always going to be more abrupt and therefore cause more problems.

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  • $\begingroup$ I suppose hydrogen-filled balloons are better (unless I turn Beskar into Mary-Sueium and give it a weight of basically nothing). But the important question is: which is cooler? ^^ $\endgroup$ – PixelMaster Jan 22 at 17:40
  • $\begingroup$ @PixelMaster, I don't find vacuum airships very cool and the extremely strong material they need throws off the power balance a lot (it should, of course, be used for a lot of other things too; in many domains it would pay off more than airships, especially weapons and armour). $\endgroup$ – Jan Hudec Jan 22 at 18:54
  • $\begingroup$ It is of course used in other fields as well, but that's not the point of the question. $\endgroup$ – PixelMaster Jan 22 at 18:56
  • $\begingroup$ @PixelMaster Dragon- (or large bird-)towed airships sound much cooler even if filled with completely mundane helium. Or dragon-towed gliders maybe even more so—dragons use dynamic lift, so they can pull a fixed-wing heavier-than-air glider. And while sails don't work, you can have large ox-powered propellers for slowly flying, but high capacity merchant airship. $\endgroup$ – Jan Hudec Jan 22 at 18:56
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Other answers are right at pointing that vacuum zeppelins would be just about 16% better than helium ones. However, there's still one important difference between vacuum and gas that affects the way a zeppelin flies: In gas airships buoyancy is constant, independent of altitude, buoyancy will be higher at low altitudes and the airship will tend to remain at a constant equilibrium altitude.

In our world airships, gas in bags is at the same pressure of external air, and if managed properly (e.g. avoiding too fast descents) also at the same temperature. Since gas and air density is inversely proportional to pressure and directly proportional to temperature, density of gas and density of aire change equally. Since buoyancy equals the weight of displaced air, that weight remains constant and buoyancy is constant at all altitudes and temperatures.

However, in a rigid vacuum balloon, volume is constant, but air density varies with altitude and temperature, increasing buoyancy at lower altitudes where air is denser. An airship would float more at lower altitudes and sink at higher altitudes, tending to remain at a constant level.

That could be an advantage, specially if all air islands are at the same level, but could be a disadvantage if the airships are expected to go down to earth lever.

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Let me note that, according to our finite element analysis https://arxiv.org/abs/1903.05171 , vacuum balloons can be made using commercially available materials. Our article also contains references to other people's work on the topic. Improved altitude control (via pumping air in and out of the balloon) can be one of the advantages of vacuum balloons.

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  • $\begingroup$ What do you mean exactly by "our" do you mean "our" as in a specific group you are a part of or affiliated with? if yes then please state that explicitly. $\endgroup$ – Topcode Jan 24 at 0:41
  • $\begingroup$ @Topcode : by "us" I mean the authors of the article - me and A. V. Gavrilin $\endgroup$ – akhmeteli Jan 24 at 0:45
  • $\begingroup$ yeah, you should probably add that at the end of the post, something like (This article was partially written by me) or something along those lines $\endgroup$ – Topcode Jan 24 at 0:51

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