##
How Newton powers your Rocket

The primary goal of a rocket engine is to generate thrust. While most people know what thrust is, many people (including Aerospace Engineers) struggle with how thrust is actually made. To understand this you have to understand Newton’s laws of mechanics, specifically the second and third laws:

** Second law**: The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object

**Third law**: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

These two equations combined are literally what drives the rocket forward. By throwing mass (propellant) out the back of the engine, the engine generates a force on the rocket (third law). This force then accelerates the rocket forward (second law).

## The Rocket Equation

Engines do this with combustion and nozzle design. The combustion creates a lot of hot gasses in the combustion chamber which create high pressure in the engine. Since the pressure in the combustion chamber is much higher than the surrounding atmosphere pressure, the hot gasses find a way to escape and relieve the pressure difference out the back of the engine: generating thrust. [caption id="attachment_4429" align="aligncenter" width="400"]

Pressure inside and outside a Rocket Nozzle[/caption]

This thrust is formally calculated with the Rocket Thrust Equation.

[caption id="attachment_4425" align="aligncenter" width="214"]

Thrust = Momentum Thrust + Pressure Thrust[/caption] The left side of this equation is the thrust term, measured in Newtons or Pound-Force. The right side of the equation is broken into two parts: The Momentum Thrust term and the Pressure Thrust term. The momentum thrust term is calculated by multiplying the propellant mass flow rate (m-dot) by the exhaust velocity (ue), this represents the propellant being thrown out the back of the engine. The Pressure Thrust term of the equation multiplies the exhaust area of the nozzle (Ae) by the difference in pressure between the exhaust gas at the exit of the nozzle (pe-pa). While it is very difficult to physically measure some parameters on the right side of the equation, Thrust is easily measured. So Engineers typically use this equation to determine other rocket parameters like exhaust velocity and pressure at the nozzle exit.

## Pressure Thrust

While majority of thrust comes from this momentum thrust term(m-dot * ue) but the pressure thrust term is not insignificant, and becomes very important to analyze as you try to get all the performance you can out of an engine. The analysis and discussion of Pressure Thrust is fairly complex and requires an entire discussion in itself. Pressure thrust comes from the fact that at the exhaust plane of the engine the hot gasses had not been expanded enough and are usually at a higher pressure than the surrounding atmosphere. When the high pressure thrust reaches the exit nozzle, if it hasn’t already been expanded to match the ambient pressure (which is the most efficient) it will add additional thrust from the pressure difference and continue to expand after it has left the nozzle.This expansion becomes particularly apparent when a first stage engine, optimized for thrust at sea level, reaches the upper atmosphere. [caption id="attachment_4431" align="aligncenter" width="240"]

Saturn V main engine in the upper atmosphere[/caption]

## Combustion Makes Thrust

Most conventional propulsion devices use a form of chemical combustion to generate thrust. Combustion typically requires two chemicals: a Fuel and an Oxidizer. Many familiar propulsion systems, like Jet Engines for example, use the Oxygen in the atmosphere as an oxidizer. This is useful since jets fly in the thick lower atmosphere where there’s no shortage of oxygen to fly through. The problem arises when you start getting vertical: oxygen becomes scarce very quickly as you ascend. This means no matter how much fuel you have, you have nothing (oxygen usually) to burn it with. This is where rockets come into their own since they carry both the oxidizer AND the fuel, a one stop shop for generating thrust. This means they can fly anywhere, from the thick lower atmosphere, to deep space, and even

underwater without affecting thrust too much.

## The Thrust Equation and Small Rockets

You may be asking yourself, why go through all this complex analysis for rocket engines, which are very complicated and difficult to work with when there are plenty of other simpler propulsion systems out there. The fact is there aren't many ways of getting around using rocket propulsion for space and near space applications givin their low weight, efficiency, and ability to generate thrust regardless of their surroundings. And once you understand the basic mechanisms of thrust, Momentum Thrust and Pressure Thrust, you can then exploit their strengths and weaknesses to get your rocket higher. Small scale rockets do have some definite limitations when it comes to efficiency and propellant capacity. However, their small size also means there’s a lot of opportunities for innovative launch methods for getting through the thick, propellant draining, lower atmosphere. For instance you could use a

high altitude balloon to get your rocket very close to space, or use an aircraft launch system similar to this: [caption id="attachment_4433" align="aligncenter" width="300"]

An air launch system can bypass the thick lower atmosphere[/caption]