-By Nikhil Menda
Rocketry is generally regarded as hard and rightly so. It is after all, rocket science.
However, I believe that the science behind rocketry is fairly simple, and the hard part is actually the rocket engineering.
The how and the why behind rockets is something that most people already know. You've probably heard of Newton's third law, where every action has an equal and opposite reaction. It's a simple statement, but also a very powerful one. Pretty much every rocket engine relies on this principle, all they do is throw something out back which in turn makes them move forwards.
Party balloons can act like rockets too. Fill one up and then instead of tying the balloon, let it go. The balloon throws the air out the back, which makes it moves forwards. Just like a rocket.
But how do we get from flying balloons around in a kid's birthday party, to a rocket that flies people into space? Well we're gonna need a lot more thrust.
It turns out that Newton can help us here again. When we say thrust, we are essentially talking about Force. The same force that Newton's second law tells us how to find. He shows us that the change in momentum of a an object is proportional to the force experienced by the object. $F = (\triangle Mass * Velocity) \div time$
In the world of rockets, this translates to saying that the thrust of an engine depends on the mass of the gas particles thrown out, and how quickly they are being thrown out. We generally see this term written in the form of mass flow rate, $\dot{m}$ (pronounced m dot), which makes the equation above look like $F = \triangle \dot{m} * V$ (where V is velocity of the gas particles thrown out).
However, there is one more term that we cannot forget about. When you fill the balloon up, what you are doing is increasing the pressure in the balloon. This pressure builds up and once you let the balloon go, the pressure forces the gas out of the balloon to make it quickly and give us the force we wanted to make our balloon rocket fly. However, some of you may notice the relationship between pressure and force, we define pressure as a measure of the amount of force applied over a certain area($P = F/A)$. We can use this relationship to figure out the amount of force that's contributed by this pressure in our balloon by multiplying the pressure of the balloon at the mouth, by the area of the mouth. In traditional rockets, we call these terms the nozzle exit pressure, and the nozzle exit area($F = (P_{exit} )*A_{exit}$). Now there's one more thing to remember, while the pressure from the nozzle exit contributes to the thrust, there could still be pressure from the surroundings or atmosphere pushing against this thrust. So the force from the pressure term is actually $F = (P_{exit}-P_{atm} )*A_{exit}$
Combining these two forces gives us the total thrust produced by the rocket engine.
$F_{thrust} = \triangle \dot{m} *V_{exit} + (P_{exit}-P_{atm} )*A_{exit}$
So now we know how to find the thrust of a rocket engine, and more importantly, we know the parameters we need to change to increase the thrust of a rocket engine.