It’s been over a year since the last science post, so I had probably better either a) make another science post or b) rename the site. What I’m about to talk about is more science fiction than proper science, but I was wondering about it and did the research and it’s close enough to the real thing to pass for it if you squint a bit, and most importantly it ends the science drought.
The hokum military fantasy plotline of Call of Duty: Ghosts is kicked off when the baddies hijack a US space station to drop a number of very heavy objects onto the continental United States, devastating the country and providing the developers with an excuse for one of the more mediocre first person shooters I’ve played in recent years. As with most concepts explored in Call of Duty, while the way its portrayed in the game is complete nonsense the idea of launching weapons into space that can bombard targets below is a legitimate one that’s been around for a very long time –since before we actually got into space in the first place, in fact — and Ghosts even references a specific one: its Loki satellite has an obvious link to Project Thor, a proposal originating from the 1950s but which was being mentioned in news reports as recently as four years ago under its sexier nickname: Rods from God.
As the particular variant of kinetic bombardment that’s been drawn up by the US, Rods from God is by far the most well-known version of the kinetic bombardment idea, even worming its way into popular consciousness via “entertainment” products like CoD: Ghosts and the execrably awful GI Joe: Retaliation. The idea is that you would have a pair of satellites in orbit: a command and control satellite that handles targeting and guidance and a launcher satellite that houses the actual projectiles, which in this case are long, thin rods composed of a very dense material (tungsten is the one usually cited due to its frankly ludicrous density of 19.3 g cm-3 – for comparison, lead clocks in at a measly 11.3 g cm-3) and whose only attachment would be a set of small fins required to steer the rod through the atmosphere to its target. The high material density is required to maximise the projectile’s mass, and hence its kinetic energy once it strikes its target; kinetic energy is a function of mass times velocity squared, and the velocity of something dropped from orbit is in theory going to be pretty damn fast.
Now, the popular depictions of kinetic bombardment mentioned above portray these rods as being absurdly destructive, striking with the force of a nuclear weapon and wiping entire cities off of the map. The reason I’m writing this post is because I got curious: tungsten may be dense, and orbital velocities may be pretty fast, but how much kinetic energy would one of these rods actually have once it reached the Earth’s surface? The rods can vary in size, but the larger versions are mentioned as being 6m long with a 30cm diameter, giving them a mass of roughly 8,000 kg. Assuming we want our rod to hit with the force of a small nuclear weapon (15 kilotons of TNT, say, or 63 terajoules), we’d have to ensure that it hits the Earth’s surface travelling at a velocity of
For reference the fastest man-made object in existence is the New Horizons probe, currently in the penultimate year of its journey to Pluto and cruising at a cool 16.26 kilometres per second relative to the Sun — and it managed that only with the aid of a gravitational slingshot provided by Jupiter. Clearly, then, the idea of one of these rods striking with the force of a nuclear weapon is somewhat overstating their destructive capacity, especially since you’d lose a lot of the kinetic energy on the way down thanks to the Earth’s atmosphere. The question now is: how much kinetic energy would one of these rods realistically have once it reached the surface? There’s a bunch of complicated ways we can figure this out, but I’m going to cheat and simply assume that the rod is going to be slowed down enough by its passage through the atmosphere that it will be moving at terminal velocity when it hits the ground. The equation for working out terminal velocity is
Where m is the mass of the object, g is its acceleration due to gravity (9.81 m s-1), ρ is the density of the medium through which the object is falling (in this case air with a density of 1.225 kg m-3), A is the projected area of the object (the rods are very long and thin and present only a small surface area along their direction of travel), and Cd is the drag coefficient of the falling object (I’m using the drag coefficient of a cone, since my assumption is that the tip of the rod will be cone-shaped). Plug all of these numbers into the equation and the terminal velocity of the rod comes out at
This gives the rod a kinetic energy of around 14.5 gigajoules, which sounds like a lot but which, when converted to something more analogous to explosive force, is equivalent to only 3.46 tons of TNT. That’s plenty of power, more than enough to wreck a small neighbourhood, but a single kinetic impactor isn’t going to be destroying a city any time soon.
More than that, though, there’s the question of practicality to consider. Rods from God do have a couple of advantages over regular missiles – dropping them from space would give any prospective target little to no warning before they struck, and the sheer density of the rod would give it an awful lot of penetrating power ideal for destroying hardened targets – but they have to be weighed up against the massive disadvantages inherent in the concept, first and foremost of which is that in order to drop an 8 ton rod onto somebody’s head you first have to lift it up into orbit. With typical launch costs currently standing at around $5,000 per kilo at the cheap end, putting just one of these rods into orbit would cost a whopping $40,000.000. Putting a whole array of them (plus launch system) up there would be ruinously expensive – and before you say “But Hentzau, a single stealth bomber costs a billion dollars,” you have to bear in mind that that price tag includes the R&D and engineering work required to develop the bomber in the first place. There would be similar costs involved in developing a kinetic bombardment array that would massively inflate the cost, and all for something that has less destructive capacity than a WW2-era Lancaster bomber, and whose job can easily be performed by much cheaper conventional missiles and/or bombs. Little wonder, then, that the Rods from God concept has never made it out of the pages of science fiction.