3. Rocket Science

Problem:

How do rockets work?

Background:

In popular culture, the phrases “rocket science” and “brain surgery” are used to represent any task that requires great intelligence or skill. The purpose of this post is to show that rocket science isn’t that hard. You can make rockets too! In addition to this, there are a few common misconceptions which I will clear up.

Solution:

As with most problems in physics, the first place to start is Newton’s laws. Newton’s 2^nd law is commonly stated as force equals mass times acceleration, F = ma. This statement is almost true. The true statement of Newton’s 2^nd is that the change in momentum is related to the force. Momentum is, in turn, the product of mass and velocity. A force can be generated by a change in velocity (acceleration) or a change in mass. The ingenious method employed by rockets is to use a mass change instead of an acceleration change to generate force. This can be illustrated by the example below.

A rocket uses its nozzle to accelerate the flow at exit to a high speed above the inlet velocity. Due to the shape of the nozzle the speed at exist must necessarily be higher than the speed at the inlet. (See solution section of this post for the proof.) Applying Newton’s 2^nd law to a fluid element and making simplifying assumptions relevant to this problem, we can derive this equation

F = mt*v +p*A (Equation 1)

Where mt, is the mass flow rate. It represents the rate at which the rocket is losing mass. The net momentum flux, mt*v, results in a force on the rocket (thrust) which accelerates the rocket forward. In addition, the pressure causes a force on the rocket which is proportional to the nozzle area. There is a common misconception that the pressure at the nozzle exit causes thrust. The equation demonstrates that the fluid flux, alone, is enough to produce force in the rocket.

Model Limitations:

A major limitation with the usefulness of Equation 1 is lack of information. It would be very difficult or impossible to know all of the values for velocity and pressure. However, given this information, the force can be calculated exactly.