3 ms·

>Consider the "Tyranny of Rockets" problem: if you want to send a rocket up 1 km, you need X fuel. But to get to 2 km, you need way more than 2X fuel- because y

>Consider the "Tyranny of Rockets" problem: if you want to send a rocket up 1 km, you need X fuel. But to get to 2 km, you need way more than 2X fuel- because you first have to carry all that extra fuel up 1 km, which takes more energy/fuel, before you can use it to go the other km. And if you want 3 km up... well, you get the idea. It's exponential in cost. Is this correct? I know how the Tyranny of the Rocket Equation relates to mass, but I've never heard it used in terms of altitude before. Using the kinematic equations, it seems the initial velocity required to reach height 2X would actually be less than double of that for just X. However, I'm not sure if that also applies to rocket launches and if it does how it relates to fuel requirements. Feel free to correct me if I'm on the completely wrong track here.

CydeWeys 7y ago
It's not correct. The rocket equation is exponential for delta-v, not for altitude. Getting to 2km could easily be free once you've hit 1km, if your rocket is traveling fast enough at 1km when it cuts out to coast much higher. It's getting to, say, 2 km/s that takes more than double the fuel of getting to 1 km/s. It's not a simple relationship though (like say the inverse-square law); it's related to propellant velocity, which for chemical rockets is in the neighborhood of 4 km/s. Reaching velocities greater than your propellant velocity is where the exponential ramp really starts to take off. And no, it's not just mass either. If you have a rocket that sends mass M to velocity V, then double the size of the rocket and it'll send mass 2M to velocity V. The rocket equation tells you the ratio of fuel mass to payload mass required to reach any given delta-v. That's what grows exponentially as the desired delta-v grows.

3 ms·

>Consider the "Tyranny of Rockets" problem: if you want to send a rocket up 1 km, you need X fuel. But to get to 2 km, you need way more than 2X fuel- because y

by theLotusGambit 7y ago

CydeWeys 7y ago
It's not correct. The rocket equation is exponential for delta-v, not for altitude. Getting to 2km could easily be free once you've hit 1km, if your rocket is traveling fast enough at 1km when it cuts out to coast much higher. It's getting to, say, 2 km/s that takes more than double the fuel of getting to 1 km/s. It's not a simple relationship though (like say the inverse-square law); it's related to propellant velocity, which for chemical rockets is in the neighborhood of 4 km/s. Reaching velocities greater than your propellant velocity is where the exponential ramp really starts to take off. And no, it's not just mass either. If you have a rocket that sends mass M to velocity V, then double the size of the rocket and it'll send mass 2M to velocity V. The rocket equation tells you the ratio of fuel mass to payload mass required to reach any given delta-v. That's what grows exponentially as the desired delta-v grows.