Thread by @GeorgeWHerbert

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle 😳🙄😂 ok. I’ll do an explainer in a bit now that I’m home and have food

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle Ok. Short Thread: What's the "Flat Earth" approximation in missile trajectories, and why I'd use and mention it.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle So, we all should know that the Earth is a sphere (approximately) and about 40,000 kilometers in circumference. The radius is about 6,400 kilometers. A quarter of the way around is 10,000 kilometers.

Flat Earth simplification assumes we temporarily ignore that it's curved.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle The reason to do that is that certain math in trajectories gets very easy. To do that fully, though, we cheat in several ways.

We assume the earth is Flat.
We assume Gravity is constant with altitude.
We assume Gravity always points straight down towards the flat plane.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle If we do those simplifications, then trajectories of ballistic missiles are calculated the same as for bullets or artillery shells or rocks you throw into the water on a beach. The maximum distance is achieved if you throw up at a 45 degree angle, the math is very easy.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle For short range ballistic missiles, you can hardly tell the difference unless you're the guy in charge of aiming them at a precise target. That guy needs to know the difference. Everyone else, concerned more or less with how far it can go mostly, can ignore that.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle The errors add up the longer range of a ballistic missile you're talking about though.

Dude with a Scud missile? No problem.
A 1,900 kilometer range Pukguksong-3? Not bad.
An ICBM? Nope. The numbers are off by noticable amounts. Embarrassing amounts for professionals.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle The reason we still do it at all is that I can figure out that the maximum range of Pukguksong-3 (assuming that's what flew today) is around 1,850 to 1,900 kilometers with a calculator or if necessary a piece of paper and pencil, in a couple of minutes. Which is useful info.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle Accurate numbers for long range missiles like ICBMs (more than say 90% accuracy for sure), figuring out maximum range really requires a computer program to optimize suborbital trajectory, taking into account curvature, gravity decreasing with altitude, etc. Very hard by hand.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle There are rules of thumb but you really end up with a computer simulation. Oh, and did I mention, you need to take air drag, rotation of the earth, burn time of the missile, and a bunch of other things into account too.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle So in any situation you can get away with it, without being terribly professionally embarrassed, you start with the Flat Earth approximation to hold off the hordes of curious Twitter readers and a few journalists, while you make a run for your optimizing trajectory software.

@nktpnd @NuclearAnthro @wslafoy @mgerrydoyle Hopefully this is an adequate explanation of what the problem is and why the simplification is still used, even by people who are professionals and know it's terrible. It's only slightly terrible for short range & a bit terrible for medium range. But it's not precise. The End.