# The Rocket

## Rocket Principles

A rocket in its simplest form is a chamber enclosing a gas under pressure. A small opening at one end of the chamber allows the gas to escape, and in doing so provides a thrust that propels the rocket in the opposite direction. A good example of this is a balloon. Air inside a balloon is compressed by the balloon's rubber walls. The air pushes back so that the forces on each side are balanced. When the nozzle is released, air escapes through it and the balloon is propelled in the opposite direction.

With space rockets, the gas is produced by burning propellants that can be solid or liquid in form or a combination of the two.

## Newton's First Law

Newton's first law can be stated as:

An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an unbalanced force.

This law of motion is just an obvious statement of fact, but to know what it means, it is necessary to understand the terms rest, motion, and unbalanced force.

If an object, such as a rocket, is at rest then the forces on it are balanced. It takes an additional force to unbalance the forces and make the object move. If the object is already moving, it takes such an unbalanced force, to stop it, change its direction from a straight line path, or alter its speed.

In rocket flight, forces become balanced and unbalanced all the time. A rocket on the launch pad is balanced. The surface of the pad pushes the rocket up while gravity tries to pull it down. As the engines are ignited, the thrust from the rocket unbalances the forces, and the rocket travels upward. Later, when the rocket runs out of fuel, it slows down, stops at the highest point of its flight, then falls back to Earth.

## Newton's Second Law

This law of motion is essentially a statement of a mathematical equation. The three parts of the equation are mass (m), acceleration (a), and force (f). Using letters to symbolize each part, the equation can be written as follows:

### F = ma

Let's apply this principle to a rocket. The pressure created by the controlled explosion taking place inside the rocket's engines is a force called thrust. That pressure accelerates the gas one way and the rocket the other.

The thrust for the rocket continues as long as its engines are firing. Because propellant is burned up, the mass of the rocket changes during flight. Its mass is the sum of all its parts. Rocket parts includes engines, payload, control system, propellant tanks, and propellants. By far, the largest part of the rocket's mass is its propellants. But this mass constantly changes as the engines fire since the engines expell the used fuel in the exhaust plume. Thus the rocket's mass smaller during flight. In order for the left side of our equation to remain in balance with the right side, acceleration of the rocket has to increase as its mass decreases. That is why a rocket starts off moving slowly and goes faster and faster as it climbs into space.

Newton's second law of motion is especiaily useful when designing efficient rockets. For a rocket to climb into low Earth orbit, it must achieve a speed in excess of 28,000 km per hour. A speed of over 40,250 km per hour, called escape velocity, enables a rocket to leave Earth and travel out into deep space. Attaining space flight speeds requires the rocket engine to achieve the greatest thrust possible in the shortest time. In other words, the engine must burn a large mass of fuel and push the resulting gas out of the engine as rapidly as possible.

Newton's second law of motion can be restated in the following way: the greater the mass of rocket fuel burned, and the faster the gas produced can escape the engine, the greater the upward thrust of the rocket.

## Newton's Third Law

Newton's third law can be stated as:

Every action has an equal and opposite reaction.

If you have ever stepped off a small boat that has not been properly tied to a pier, you will know exactly what this law means. The boat goes forward, you go backward!

A rocket can lift off from a launch pad only when it expels gas out of its engine. The rocket pushes on the gas, and the gas in turn pushes on the rocket. With rockets, the action is the expelling of gas out of the engine. The reaction is the movement of the rocket in the opposite direction. To enable a rocket to lift off from the launch pad, the action, or thrust, from the engine must be greater than the mass of the rocket. In space, however, even tiny thrusts will cause the rocket to change direction.

## Putting the Laws of Motion Together

An unbalanced force must be exerted for a rocket to lift off from a launch pad or for a craft in space to change speed or direction (first law). The amount of thrust (force) produced by a rocket engine will be determined by the mass of rocket fuel that is burned and how fast the gas escapes the rocket (second law). The reaction, or motion, of the rocket is equal to and in the opposite direction of the action, or thrust, from the engine (third law).

## Rocket Engines and Their Propellants

Most rockets today operate with either solid or liquid propellants. The word propellant does not mean simply fuel, as you might think; it means both fuel and oxidizer. The fuel is the chemical rockets burn, but for burning to take place, an oxidizer (oxygen) must be present. Jet engines draw oxygen into their engines from the surrounding air. Rockets do not have the luxury that jet planes have; they must carry oxygen with them into space, where there is no air.

Solid rocket propellants, which are dry to the touch, contain both the fuel and oxidizer combined together in the chemical itself. Usually the fuel is a mixture of hydrogen compounds and carbon and the oxidizer is made up of oxygen compounds. Liquid propellants, which are often gases that have been chilled until they condense into liquids, are kept in separate containers: one for the fuel and the other for the oxidizer. Then, when the engine fires, the fuel and oxidizer are mixed together in the engine.

Other rocket engines use liquid propellants. This is a much more complicated engine, for they require sophisticated valves and pumps to handle the flow of fuel. They also require special mixing chambers and propellant feed lines. Liquid propellants, which are often gases that have been chilled until they condense into liquids, are kept in separate containers: one for the fuel and the other for the oxidizer. Then, when the engine fires, the fuel and oxidizer are mixed together in the engine.

The fuel of a liquid-propellant rocket is usually kerosene or liquid hydrogen; the oxidizer is usually liquid oxygen. They are combined inside a cavity called the combustion chamber. Here the propellants burn and build up high temperatures and pressures, and the expanding gas escapes through the nozzle at the lower end. To get the most power from the propellants, they must be mixed as completely as possible. Small injectors ( nozzles) on the roof of the chamber spray and mix the propellants at the same time. Because the chamber operates under high pressures, the propellants need to be forced inside. Powerful, lightweight turbine pumps between the propellant tanks and combustion chambers take care of this job.

With any rocket, and especially with liquid-propellant rockets, weight is an important factor. In general, the heavier the rocket, the more the thrust needed to get it off the ground. Because of the pumps and fuel lines, liquid engines are much heavier than solid engines.

Hybrid rockets combine elements from both types of rockets. In a hybrid rocket, a gaseous or liquid oxidizer is stored in a tank separate from a solid fuel grain. The major benefit of solid rockets over hybrid rockets (and liquid systems, too) is their simplicity. In hybrid systems, then, it seems that higher complexity is the price paid for better performance. However, note that the performance for these rockets is rival to that of liquid systems. Furthermore, note that hybrid rocket systems require support for only one fluid system, including tanks, valves, regulators, etc. In other words, although hybrid rockets are more complex than solid systems, they compare in performance to liquid systems while requiring only half of the plumbing. This vastly reduces the overall systems weight and cost, while increasing its reliability (there will be fewer parts which could fail). Hybrid rocket systems are also safer to produce and store, can be more ecologically safe with proper propellant choice, and the fuel grain, being inert, is stronger than manufactured solid propellant grains (for solid rockets), and is therefore more reliable.

## Mass

The mass of a rocket can make the difference between a successful flight and just wallowing around on the launch pad. As a basic principle of rocket flight, it can be said that for a rocket to leave the ground, the engine must produce a thrust that is greater than the total mass of the vehicle. It is obvious that a rocket with a lot of unnecessary mass will not be as efficient as one that is trimmed to just the bare essentials. For an typical rocket, the total mass of the vehicle might be distributed in the following way:

• Of the total mass, 90 percent is the propellants; 6 percent is the structure (tanks, engines, fins, etc.); and 4 percent can be the payload.
Payloads may be satellites, astronauts, or spacecraft that will travel to the moon or planets.

In determining the effectiveness of a rocket design, engineers speak in terms of mass fraction (MF). The mass of the propellants of the rocket divided by the total mass of the rocket gives mass fraction:

MF = (Mass of Propellants)/(Total Mass)

The mass fraction of the typical rocket given above is 0.80. From the mass fraction formula one might think that an MF of 1.0 is perfect, but then the entire rocket would be nothing more than a lump of propellants that would simply ignite into a fireball. The larger the MF number, the less payload the rocket can carry; the smaller the MF number, the less its range becomes. An MF number of 0.80 is a good balance between payload-carrying capability and range. The Space Shuttle has an MF of approximately 0.82. The MF varies between the different orbiters in the Space Shuttle fleet and with the different payload weights of each mission.

# Activities and Research

Contributed by Elizabeth Walker, MIT

1. Build a model rocket and launch it in a nearby field.
2. Design and build a device to measure the altitude of your rocket.
3. Research a satellite or interplanetary spacecraft. What type of launch vehicles was used to launch it? What was its mission? How long did it operate? What information did it provide us?

# Problems

contributed by Elizabeth Walker, MIT

1. Explain the difference between how a jet engine, like that described in Theory of Flight, and a rocket engine function. Why don't we use jet engines on rockets?
2. Using what you know about forces, explain whether the rocket in the following situations is balanced or unbalanced. If it is unbalanced, describe which force is greater than the others. Use a free-body diagram to help you.
a. Rocket during launch.
b. Rocket during re-entry.
c. Rocket in orbit at constant velocity.
d. Rocket accelerating in orbit.
e. A Lunar Excursion Module (LEM) sitting on the moon.
3. Why don't we use ailerons, rudders and elevators to control the direction of flight in space?
4. Using what you have learned about Mass Fraction (MF) describe the characteristics of rockets with the following MF's. Will they fly? If so, how much payload can they carry? On what types of missions can they be used?
a. 0.0
b. 0.27
c. 0.49
d. 0.77
e. 0.96

Man-Vehicle Laboratory
MIT Department of Aeronautics and Astronautics
sablan@mit.edu
8 May 1996