How Rocket Motors Work
 
by William Colburn
 
 
This is a description of  rocket motor operation, without mathematics and theoretical discussions, to show how they work explained through experience and research. English units are used as well as assumptions made to simplify the explanations.  
 
 
What’s Going On
 
“When push comes to shove” describes Isaac Newton’s answer to rocket propulsion-  “For every action there is an opposite and equal reaction” is exactly what he said. So when you fire a rifle, the kick you feel is Newton’s reaction from the action of the bullet being accelerated out the barrel. You could measure that “kick” in pounds with a scale. Now if it was kept up for some time, it would be just like a rocket motor and the “kick” would be called “thrust."  
 
 Another way to look at it, and more accepted in this modern world, is that the operation of a rocket motor is due to conservation of momentum. That is a term that just means that parts of a system, when put in motion, and their momenta (pretty much velocity times their mass) added up, it equals the original momentum. So stuff shooting out the rear of a rocket has negative momentum. So the vehicle itself then must have positive momentum to equal that, the negative amount being exactly the same as the positive amount.  
 
When you look at momentum instead of thrust, then the quality of the motor you are looking at is exhaust velocity. Here are three kinds for your appreciation: Effective Exhaust velocity is what you really get from a vehicle; Theoretical Exhaust velocity is what the Chemistry and Thermodynamics tell you; Characteristic Exhaust Velocity applies across the board to all vehicles with the same propellants and eliminates the motor characteristics, so you can compare propellants.  
 
You can see what many scientists of the early 20th century did not, rocket propulsion  is completely independent of the atmosphere you are in and works equally well in a vacuum. (We will show later that this statement is not entirely true!)
 
Can the rocket go faster than the gas it shoots out the rear? It turns out that if a rocket is flying in a vacuum outside of a gravity field, if it has 2.72 times as much propellant as its mass, it will get up to exactly the speed of its exhaust gas. If the ratio is about 7.5, it will get up to twice the speed of its exhaust, and at 20 times the weight of the inert vehicle, it will be going at 3 times the exhaust velocity.  
 
Traveling in a gravity field and inside the atmosphere spoils the heck out of those numbers. In a gravity field, for every second you are rising vertically, you are also “falling." This means you have to subtract from your vertical speed, whatever “falling” speed you might have gotten in the same amount of time. For a short rocket flight, you can guess closely what that might be by subtracting the weight of your rocket from the thrust it produces, which reduces the acceleration by one gravity.
 
The air is even worse if you are a rocket vehicle, because it will probably be traveling at greater than Mach 1. As a rocket gets close to Mach 1, the “drag” gets to be very high. It is caused by the force of the air compressing on all parts of the rocket- the nose, the fins and the air friction on the body, fins and nose. In a vehicle launching a satellite, the first stage, the booster, may spend as much as 30% of its propellant overcoming this “drag."  
 
As an example of how dramatic both those effects are, if you launched a V-2 from the earth it can go up about 120 miles. If you launched a V-2 from the airless, low gravity moon of earth, it could reach the earth, 286,000 miles away!  (The V-2 was the first ballistic missile, created in Germany in WWII, and used very extensively in upper air research by the USA, the Soviet Union and Great Britain.)
 

Part 3:
 
The Nozzle
 
This is the important part of the rocket motor that makes it efficient and gets the most out of the propellant. It includes three sections: the converging (tapers inward), the throat (the smallest part seeing the highest temperature and erosion stress), and the diverging (tapers outward, allowing the gas to expand to the local pressure). Other terms for these parts  are: nozzle entrance and nozzle exit and expansion section.  
 
The converging section accelerates the hot gases to a higher velocity. If the internal pressure in the motor is greater than twice (about) the external pressure (atmospheric pressure) then the gases will accelerate to their maximum speed, called the sonic velocity, at the smallest part of the convergence. The nozzle approach velocity is kept low, at  a local Mach 0.2 or so. The smaller the nozzle throat, the lower the Mach approach number. There is an optimum size for each propellant combination and for each solid or hybrid rocket motor propellant grain design. (A “grain” refers to the solid mass of propellant in its final monolithic form in the motor) As liquid motors become smaller(both mono and bi propellant) they need smaller diameter nozzles in comparison with their chamber diameters. Solid propellant motors need to have nozzles that are at least 1 ½ times smaller in diameter than the core or hole that goes down the center of the propellant grain. A higher ratio applies for hybrid fuel grains and nozzles.  
 
The nozzle throat controls the amount of mass that flows through the nozzle per unit of time. So it controls both the thrust and the pressure inside the rocket motor. Choosing the correct diameter for the throat is a large part of rocket science. Since you can tell what the thrust might be in two different ways, one using the amount of propellant used per second and the second using how much pressure there is in the chamber, you can make the thrust level match the chamber pressure you need to create within the strength limits of the motor. The throat needs to resist heat and erosion of high velocity gases. Refractory metals (tungsten, molybdenum), ceramic coatings (silicon nitride), graphite and carbon-carbon (fibers of hydrocarbon decomposed to make carbon fibers under heat and pressure)  as well as silica filled phenolic have all been used as nozzle throat materials. In most Bi-Liquid motors, the throats will be cooled by one of the propellants  and be made of the same material as the chamber. Special cases are HTP (High Test Peroxide) and Ammonium Nitrate Solid Propellant motors where the temperature is low enough that steel nozzles and throats will suffice.