There’s got to be what, probably one or two Metalocalypse fans in the readership? The rest of you will probably be pretty confused, but bear with me. Quick primer: the show is about an absurdly successful but actually incompetent death metal band called Dethklok.
The season finale was last night. Holy cow that was a great episode. The last five minutes are worth their weight in gold. I won’t say what happens for the benefit of those who watch the show but haven’t seen the finale yet, but it’s brutal stuff. The body count is even higher than usual and my own favorite character is at minimum horribly injured and possibly dead. From that show, I expect nothing less. I hope he survives, but I can’t wait for next season either way.
Anyway, the band Dethklok is tremendously rich. Rich enough in this episode to play a concert from a rocket-supported platform high above the desert. Assuming they’re rich enough to afford it, are the laws of physics going to let them do such a thing?
Newton’s laws are what we need to use. If you want to exert an upward force on the rocket platform, you’re going to have to exert a downward force on the rocket fuel you’re throwing out the bottom of the rocket engines. Let M be the platform mass and you have:
Write out the momentum p of the fuel explicitly and you’ll get:
Where v is the exit velocity of the fuel from the rocket engine. For the space shuttle it’s about 3560 m/s at sea level. So that mass derivative of the fuel is just the burn rate. Doing the math, and assuming the platform mass was 10 tons you’ll need a burn rate of:
Well it’s not that unrealistic. The problem is that to keep the platform up, you have to bring all those kilograms of fuel with you on the platform. And the more fuel you have, the heavier the platform will be and the higher your burn rate will have to be. Working out the details is something we can save for later, but suffice it to say that the concert had better not run very long. But one song? Sure, I’m willing to give the cartoon the benefit of a doubt and call it plausible.