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The ancient Titans of myth were real, and their imprisonment in the cells of Tartarus ironically saved them from the global flood that wiped out the Olympians who defeated them. Now in the modern day, melting polar ice is slowly cracking open the entrance to their prison in what is now called Antarctica, and the Titans have emerged to reclaim rulership of a world that has forgotten the terror of being beneath the feet of giants the size of mountains. Opposing them are the armies of the modern-day world, who will run out of ammunition before depleting the Titans' numbers enough to defeat them, and a nascent population of superhumans created using genes spliced from an Olympian body found buried in the Siberian ice.

The Titans vary in size (and their size is often variable even for an individual), from being only three meters tall at their smallest, to the 300-500 meter juggernauts capable of leveling cities with enough effort, to Kronos himself, towering at over a mile in height. Some of them are capable of flight, and in their efforts to subdue humanity, will make no effort to mitigate the damage of their passing.

So, the question is: If a flying Titan of say, 300 meters in height, with a similar proportional body profile as a human, flies in an upright position (standing upright, rather than a Superman pose) at about the same speed as a commercial jet, Mach 0.8-0.9 or so, a hundred meters or so above the ground, how much damage would you expect to occur from the displaced air? Would it be devastating or a nuisance? How do the figures change if 1.6 km-tall Kronos attempted the same feat? What if they were supersonic, flying at Mach 1.5 or so? There is no apparent exhaust being used to propel them, so we're only dealing with the displaced air.

EDIT: I've been advised to narrow the focus of the question, so let's just go with with the question of a 300-meter Titan flying at Mach 0.8 about a hundred meters above the ground.

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    $\begingroup$ This is a pretty cheesily awesome scenario but a tricky physics question. I was thinking of modelling the wind of passage like an explosion as felt 100 meters away. But I am not sure that is accurate because the passing titan is not a single energetic event - energy is continuously added. I look forward to an answer featuring math. $\endgroup$
    – Willk
    Sep 26, 2021 at 15:20
  • $\begingroup$ You should work with only one parameter at a time (e.g.: locking size or speed temporarily and ask about the other), it will be both easier for you and for the others :). If you get a formula or a scale to work with in the answers, you'll be able to close your predictions with other neighboring values. $\endgroup$ Nov 4, 2021 at 11:28
  • $\begingroup$ @JoinJBHonCodidact if a single mathematics equation is able to do the heavy lifting, all of those are trivial additions. $\endgroup$
    – IT Alex
    Nov 4, 2021 at 17:47
  • $\begingroup$ @JoinJBHonCodidact I took your advice and narrowed the focus of the question, though at this point I doubt I'm going to get any answers. $\endgroup$ Nov 4, 2021 at 19:01
  • $\begingroup$ To improve readability I'd recommend that you delete the bits of your question that are no longer relevant. If anyone cares about how the question has changed over time they can read the edit history. $\endgroup$
    – sphennings
    Nov 4, 2021 at 19:18

1 Answer 1

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Using this, we can calculate the drag.

Using a density of 1.2kg/m3, air, a velocity of 300 m/s, a drag coefficient of 1.3, and an area of 22500m2 (assume a human surface area is 1m2, 2 meters tall, the titan is 150^2 times larger in surface area) we get a drag force of 1645312500N, or 1.6*10^9 N. It's one hundred larger than the force of the Saturn 5 launch.

Saturn 5 was pretty big.

Our building's shaking! The roar is terrific! The building's shaking! This big glass window is shaking. We’re holding it with our hands! Look at that rocket go! Into the clouds at 3,000 feet! The roar is terrific! Look at it going! You can see it. Part of our roof has come in here.

This will probably enough to kill anyone within a mile, deafen people at five miles, and wreck buildings for a much larger radius.

Fd = 1/2 * ρ * u² * A * Cd is the equation. Velocity, u, is squared so damage will increase a lot with that- double the speed, quadruple the force, and area is squared from height, so increasing the height five times will increase the forces 25 times. It won't increase the volume damaged as much, since volume increases by the cube (hence why nuclear bombs tend to have lots of little ones, not one big one) but will still do a lot of damage.

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  • $\begingroup$ Those numbers are a bit suspect, as at 1.2 kg/m^3, your titan is a veritable light-weight with a density similar to that of air, but at 3000 m/s s/he is travelling at a velocity of about 9 times the speed of sound. $\endgroup$
    – Penguino
    Nov 4, 2021 at 21:01
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    $\begingroup$ The density is the density of the air, not the titan, since the titan is displacing the air. The 3000m/s is fixed, I added a 0. $\endgroup$
    – Nepene Nep
    Nov 4, 2021 at 21:40
  • $\begingroup$ Yes - my error on the first half - and now your conclusion seems reasonable $\endgroup$
    – Penguino
    Nov 4, 2021 at 22:36

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