To Infinity Ward and Beyond the Skybox


Originally posted on 6 January 2010 as
To Infinity Ward and Beyond (the Skybox)
The current version has been modified for clarity.

I’d previously written about Call of Duty 4: Modern Warfare 2 in regards to the controversial “No Russian” mission, and the wildly vacillating reaction out among the blogs. Here, I delve a little deeper into the astrophysics behind another memorable scene.


In the “Second Sun” mission of Call of Duty 4: Modern Warfare 2 (COD4MW2), the intrepid & exponentially grizzled soldierheroes with names are left behind for a momentary, establishing vignette in Earth orbit. Sat1, an astronaut on EVA outside the International Space Station, is tasked with looking right, a bold initiative to get eyes on a nuclear missile launch directed at Washington. While normally the United States’ government is pretty great at spying on itself, explaining why NORAD needs to dial-an-astronaut to get snaps of a nuke pointed at the nation’s capital is left as an exercise to the reader.

Oh hey this whole thing has spoilers!

Anyway, let’s have a look at that scene, and then break it down like Ernest William Brown.

Light Pollution

Are city lights visible from space?

Definitely.

Milky Mess

Yes Nick, the skybox looks awful in this video. Yeesh.

EMP-athy

It was observed in 1945 that the detonation of a nuclear bomb high in the atmosphere would cause an electromagnetic pulse (EMP), so naturally today we give all credit to GoldenEye. Still, the nuke sequence in COD4MW2 leads us down a few interesting paths, so let’s have a look. Just recall that I’m no expert on EMPs — I’ve only read about 20 minutes worth of Wikipedia and I only finished Facility under 1:05 once or twice, so grain of salt and all that.

Staggered power grid knockout

After the nuke is detonated, the player witnesses large segments of the Eastern seaboard’s power grid going dark, in a staggered procession emanating roughly circularly from ground zero (Washington, D.C.). My initial thoughts were that an EMP would travel at (or near enough to) the speed of light, so that all power grids within range would fail simultaneously, rather than with a visible delay. However, it seems there are several components to a nuclear EMP. The “E1” component does indeed travel at relativistic speeds, and is capable of overloading electrical circuits. In addition, though, there is a slower-moving “E3” component which bears similarities to solar-based geomagnetic storms, such as the one that disrupted the Quebec power grid in March 1989 (not the last time our lengthy transmission lines caused a few problems). Given that the E3 component can last “tens to hundreds of seconds,” and seems to be more directly associated with power grid failure, it’s possible the cinematics team got this one right and that power loss would indeed expand sequentially. But as there’s a distinct difference between the duration of a pulse-component and its actual speed, and since I really have no idea which of the E1 or E3 components would actually disrupt the grid, let’s call this one unresolved.

Blast radius

In 1962, the United States conducted a high-altitude EMP test code-named Starfish Prime, in which a warhead was detonated 400km over the Pacific Ocean. Immediately afterwards in Hawaii, 1445km away from ground zero, hundreds of streetlights shorted out, television sets malfunctioned, radio communications were disrupted, and burglar alarms were set off. Let’s qualify this as “moderate” damage: not trivial, but certainly nowhere near total grid failure. In CoD4MW2, the warhead is detonated over Washington, D.C., and power outages seem to extend far enough South to disrupt video game studies at the Savannah College of Art and Design in Savannah, Georgia. A handy Google Maps Distance Calculator pegs this distance at approximately 850km. Now, the intensity and spread of an EMP’s effects depend on a number of factors, including altitude of detonation, total yield, the local topology of Earth’s magnetic field, and so on. However, if we wave our hands a lot and assume the Washington EMP was similar to the Starfish Prime event, and that total power grid failure is an order of magnitude greater than the effects experienced in Hawaii in 1962, we can very tentatively assume that “extreme” effects such as grid failure would extend a shorter distance than the full 1445km — say, the 850km or so shown in the game — and that beyond that, equipment would sustain only moderate to trivial EMP damage (e.g., fewer lights going out). So, with a lot of ifs and assumptions, we can say that the extent of the EMP damage as shown in CoD4MW2 seems plausible.

Laterally collateral damage

Moments after witnessing the blast, Sat1 and the ISS are caught in the destructive shockwave of the explosion, and, well, things go bad. Now the ISS, as any country pumpkin can tell you, orbits at a mean altitude of 341km, which places it smack-dab in the middle of the thermosphere. The thermosphere is so-called because, due to the absorption of solar radiation, temperatures can soar to 2500 degrees Celsius. But importantly, “[even] though the temperature is so high, one would not feel warm in the thermosphere, because it is so near vacuum that there is not enough contact with the few atoms of gas to transfer much heat” [emphasis mine]. There’s not enough gas up there to transfer heat, let alone the shockwave from a nuclear explosion (whatever the latter’s altitude).

Spatial Geometry

The problem of altitude comes up again when looking at the apparent size of the Earth as seen by the player. I had been under the impression that, from the ISS, the Earth takes up a massive portion of the sky/viewing sphere; in the game, however, this felt much reduced. Luckily, the ancient Greeks were a very boring people and this prompted an understimulated man by the name of Pythagoras Trigonometry to give his name to the science of triangles.

This is the science

Brilliant science people have previously worked out the formula for the distance to a point on the horizon based on altitude. Referring to the drawing to the left, all we need to know is R (the radius of the body in question) and h (the altitude of the observer’s eye). The distance to the horizon, d, is then defined as:

d = sqrt(h*h + 2Rh) (1)

I’ve used the mean value of 6371.0km for Earth’s radius (R), and the aforementioned altitude of 341km for Sat1’s viewing altitude (h), since they seem to be close enough to the ISS to make the difference negligible. Plugging these values into Equation 1 gives us a distance d of 2112.2km. We can use this to solve for alpha and theta in the above diagram: twice alpha gives the full angular size of the observed celestial body; or to put it another way, theta is the angle of depression between looking tangentially away from the planet, and looking at its limb.

What’s more, we can calculate alpha fairly easily. d is adjacent to alpha in a right-angled triangle, and R is likewise the side opposite alpha. In trigonometric terms:

tan(alpha) = R / d alpha = atan(R / d) (2)

Using this formula and our standard mathulators, we can get a value for alpha of 71.7 degrees. In other words, the angular width of the Earth as seen from the ISS is 143.4 degrees, only a little bit shy of your entire field of vision in one direction; you can also imagine staring straight ahead and tilting your head downwards (depression angle theta) by 18.3 degrees—the resulting (very large) circle would describe the horizon of the Earth as you would see it. Compare that to the images in CoD4MW2, and you can understand the confusion: the Earth as rendered in-game seems far more distant than it should.

Of course, we can do the reverse calculation: if we assume that the angle of depression theta as shown in the game is roughly 45 degrees (which I think is fair), and if we take the Earth’s radius R as a constant (ignoring the flattening of the poles for simplicity), we can determine how high the ISS would have to be in order to provide Sat1 with the vantage point they apparently had. Rearranging the above formulae, we solve for h and find that the ISS would have to be orbiting at an approximate altitude of 2639.0km. This is a far cry from achieving geostationary orbit, which requires an altitude of 35,786km, but it is nevertheless almost 8 times higher than the ISS normally operates.

Missile-aneous

Please take a few minutes and watch this video or any others like it. Think about lofty things. What is lofting them? That is a mystery to science.

If you have significantly more minutes, go watch the heck out of this incredible critique of the entire CoD series. Wonderful stuff.