The rocket equation
Rockets work by flinging stuff out of the bottom of the rocket at high speed, propelling the rocket up. Newton’s third law states that for every action, there is an equal and opposite reaction, which is the basic concept that describes how a rocket works. If the force coming out of the rocket nozzle is greater than the force due to gravity sticking the rocket to the ground, then the rocket will lift off.
This doesn’t mean the rocket will reach orbit; it will just lift off. The key is to keep the stuff coming out of the rocket nozzle, and a chemical reaction between a fuel and an oxidizer achieves this. The mixture is pumped into the combustion chamber, and the chemical reaction products are forced out of the nozzle at high speed. That stuff has mass and acceleration, so multiplied together, it gives a force. This force pushes against the mass of the rocket, which is held down by the acceleration due to gravity.
This sounds nice and simple; the problem is it’s rocket science, so it’s not so simple. The mass of the rocket changes as the fuel is oxidised and thrown out the nozzle. To get the rocket, precisely the payload, into space and orbit the earth, it must go fast, around 7.6 km/s. That’s a lot of force to get a rocket from the ground to that velocity.
How much fuel do you need?
Konstantin Tsiolkovsky is generally credited with developing the rocket equation, which he published in 1903, a long time before the first rocket flew. If you know the velocity you want the rocket to travel and the engine’s performance, then you can figure out the amount of fuel required. The velocity is critical because it determines if you’ll make an orbit. To get to and stay in a low-earth orbit, you need to travel at around 7.6km/s.
Rocket engines are designed to get as much oxidised product out of the combustion chamber as fast as possible, hopefully, all in one direction. Another important attribute that measures the effectiveness of the engine is the exhaust velocity of the gases leaving the nozzle. This is typically around 2.8 km/s. If you know the mass flow rate of the engine, which can be calculated from the rate of fuel and oxidizer being used, then you can calculate the force that the engine generates, called thrust. It will fly if the engine’s thrust is equal to or greater than the force holding the rocket to the ground. Remember, the rocket’s mass is reduced as the engine uses fuel.
The diagram below is based on the following equation: the rocket equation written to find the wet mass. The dry mass is the weight of everything except the fuel, and the wet mass is the dry mass plus the fuel. Delta velocity is the desired velocity, and the exhaust velocity is fixed at 2.8 km/s for this diagram. You can adjust the dry mass and delta velocity sliders to see how much the wet mass is.
