Building on my previous question would an actively camouflaging airship cast a shadow, how much energy would it take to have the airship's shadow disappear? Some metrics you might want to know: The airship is about 300 meters long, and about 40 meters wide. The airship has an area of about 11000 m2, and has a cruising altitude of about 1000 meters. It will use high power LEDs with an efficacy of about 200 lm/W. The airship has a power output of about 2500 MW (three nuclear reactors supplemented by solar panels).
closed as too broad by L.Dutch♦, Azuaron, Amadeus, sphennings, Vylix Sep 7 '17 at 3:05
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The sun has an intensity of up to 1KW/m2. As a result, for each m2, you need a 1KW light (collimated presumably). As a result, your airship needs to output 11MW of light energy.
To put that in perspective, if you use incandescent bulbs (5%) efficiency, then you'll need 200MW electricity. This is about the combined output of two A4W nuclear reactors from a Nimitz class aircraft carrier.
LED's are a fair bit more efficient, coming in at somewhere in the 80% range (from memory), so you'll only need 14MW of electricity. A single engine powering this could be the 18KU44 diesel engine which has 18 cylinders, weighs 210 tonnes and is some 12 meters long.
If you have 100% efficient solar panels and 100% efficient lights, then you can do this without any generator needed.
This doesn't actually answer your specific question, but it is far too long for a comment and justifies the answer, "it doesn't matter."
Nothing is perfect, especially invisibility.
Removing a shadow on the ground has some remarkable technical problems.
Bright light source
The first problem is that to remove a shadow you would need a light source almost as bright as the sun itself. So long as the airship is directly between the sun and an observer on the ground the airship would be invisible. But "directly between the observer and the sun" means the observer is standing within the shadow of the airship. If the observer stands anywhere else, the light becomes a very bright beacon.
Shielding around the light would keep it from being too visible at obtuse angles, but you'd never be able to hide it completely.
As the airship travels and the planet rotates, the angle between the airship and its shadow changes. This means the light must rotate (and do so very quickly) to keep up. You would either need to rotate the light all the way around the ship, or you would need a variety of lights with better-than-average brightness control between them to keep the shadow illuminated, making it even harder to keep the light hidden from observers (you could have multiple lights burning at the same time).
The Shape of the Shadow
The goal is to keep the shadow illuminated like the land around it. That means only the shape of the airship wants to be illuminated. Any land that falls within the beam of light that isn't shadowed by the airship becomes over-illuminated, creating a travelling halo on the ground. Not as easy to see, but once seen, just as easy to track.
Complicating this is the shape of the shadow changes with the pitch, roll, yaw, and altitude of the airship. I'm not convinced we have the technology today to create such well controlled light (and if your people did... why are they using airships? Technology dichotomy!)
The brightness of the moment
The strength of sunlight changes. It changes during the day from dark to bright to dark again. Clouds, depending on their nature and altidude, blowing dust, pollution, smoke from forest fires, etc. will all change the light level — all of which your light source must compensate for.
On a side note, your airship would need to either be grounded during dust/smoke or turn the light off completely as the beam of the light would be an arrow, pointing the ship out. Have you ever played with a flashlight on a foggy night? Yup, that's the problem.
Clouds, birds, and other airships
You're not just streaming a single light to hide the shadow, or even a bank of lights. You'd need to use a very high number of lights with the ability to detect changes in illumination between the sun and the airship so the shadow on the ground can change in part. In other words, if a normal, commercial airship passes between your ship and the sun, your lights would need to track the shape of that second airship (which might not completely shadow your airship) such that its shadow appears correctly on the ground. Same thing for clouds and birds. Now your lights are fluctuating almost moment-by-moment.
In the end your multiple lights would be very bright and, unlike the sun, almost constantly flickering. Rather than help hide your ship, they'd probably paint a target on it.
I love the idea of a stealth airship, but everything must have a weakness or it's unbelievable. Casting shadows sounds like a pretty good weakness, especially since the calculation of where the airship is in the sky isn't trivial at all.
This plot line has actually been addressed in the Star Trek the Next Generation episode, "Identity Crisis". Geordi discovers the invisible alien creatures by an unknown shadow. He has the computer estimate the 3D shape of the alien from the shadow, which the computer cannot do without some parameters (the approximate size of the object). Otherwise you can't know, in your case, the distance from the shadow on the ground to the airship (all three dimensions are involved, so it's easier to explain with polar coordinates and a vector).
(This idea was also touched on in "The Shadow" (e.g., see the 1994 film), but other than to add some drama, the effect of clouding a mind to not see the body but the inability to hide the shadow was pretty much glossed over.)
Picture a beam of light coming from the Sun and hitting the airship; other beams of light, parallel to the first, proceed unimpeded.
The difference between the area illuminated by the passing beams and the one not illuminated by the intercepted beam is the shadow visibility.
So one thing you might try is to supply your invisible airship with almost invisible Fresnel diffraction wings, arranged around and below the airship. If they were, say, nine times as wide as the airship, and redistributed light with a 90% efficiency - even with perfect mirrors you won't be able to go much higher than that - you will have, instead of a 0% luminosity shadow, an area ten times as large with 81% of the normal luminosity.
You can do better than that at next to no cost by redistributing the light not uniformly, but with radial symmetry. The areas next to the outer border have their luminosity diminished very little, then more and more going towards the center. This way, there's no stark contrast anywhere.
Of course, seeing this thing over, say, a uniform desert would be hopeless. But going over any panorama reasonably varied should not be so noticeable.
Except from those directly underneath: they would see something between them and the Sun.
And, from a side, you'd see something as well.
All the answers here are elaborate but I think the real answer here is to address the problems with the question
First off; A photon (particle of light),as far as we care here, travels in a straight path. A photon's path can be changed when it collides with a particle.
When you see a rock sitting in a desert, what you are seeing are the photons from the sun hitting the rock and being reflected into your eye. The color is caused by different wavelengths of the emitted light being absorbed by the rock and not reflected back into your eye. This is why if you shine a bright enough light at something all you see is white.
To create invisibility: requires an object to emit all the photons that would pass through the object to a viewer's eyes to be emitted by the object at the viewer's eyes.
That's it, that's the simplest cheapest way to achieve invisibility. What makes the broad concept of invisibility harder is now you got to worry about unknown number of viewers, angles, and shadows.
So to create general invisibility: you got to achieve; all photons that collide with the object must be absorbed and emitted directly on the opposite side of the object continuing the angle of its capture.
Now to calculate energy cost: you need to come up with a system that captures a photon on one side and emits a photon on the other continuing its capture angle. Then you need to determine how much energy an area of this system uses. Then you need to multiply that by the surface area of your object. Also the number of light sources in your objects area will most likely affect your operational cost. (if anyone here could actually answer this they would be rich and own their own country and this question would be in the physics stack)
Now at the answers here: There are plenty of theoretical ways to achieve this; LEDS, lasers, light transmitting compounds. All of which would certainly have different operational costs. However, none of these can be claimed as 'THE' way to achieve invisibility. The first problem is a photon is smaller than an atom so no matter what you do, no current technology can be minimized to the point of achieving this effect in its broad description. All of them will result in some kind of fractal because they are trying to approximate a unit and units smaller than they can accurately observe.