# Rocket Propulsion Tutorial

SpaceX Merlin Engine

The Cambridge Dictionary of Space Technology defines a rocket as a propulsive device using a mixture of propellants which,upon ignition, provide a reaction force to propel a vehicle suchas a missile, aircraft or spacecraft.

Typically, two separate chemical propellants are used, a fuel (such as liquid hydrogen or kerosene), and an oxidizer (such as liquid oxygen or nitrous oxide), which provides the oxygen to sustain a burning reaction.

Rockets differ from similar propulsion systems such as gas turbine engines (jets) in that they carry both their fuel and oxidizer on board, thereby needing no intake oxygen to operate. Also, the performance possible with rockets make them ideal for vehicles such as spacecraft, which need to achieve large changes in momentum and high final velocities.

A rocket operates according to Newton’s third law of motion, which states, generally, that for every action there is an equal and opposite reaction. In a chemical rocket, the fuel and oxidizer are combined in a combustion chamber, where they are exposed to a source of ignition, causing a violent chemical reaction which produces hot, rapidly expanding gases. These gases are accelerated through a throat and nozzle, where they are ejected at very high velocity, thereby imparting
a change of momentum to the vehicle.

For the purposes of this discussion, there are three major types of chemical
rockets: solid propellant, liquid propellant, and hybrid propellant.

A solid propellant rocket, commonly called a “rocket motor,” is likely
a composite propellant, with both the fuel and oxidizer pre-mixed
together with a firm, rubber-like putty called the binder. This mixture is
then formed into the shape of the engine
casing itself, and contains an empty space or port down the center of the putty
which serves as the combustion chamber.
The Solid Rocket Boosters (SRBs) on the Space Shuttle are the most notable of this
type of system, using aluminum powder as a fuel and
ammonium perchlorate
(NH4ClO4) as an oxidizer.

 Liquid- and Solid-Propellant Rockets.Note the different combustion chambers and the significantincrease in complexity required for a liquid system. Hybrid Rocket with molded plexiglass fuel module (left) and N20 oxidizer canister (blue, right). (Image credit Hypertek.)

A liquid propellant rocket, commonly called a “rocket engine,” keeps its
fuel and oxidizer in separate fuel tanks, then, through a series of pumps, valves
and injectors, combines the propellants in a combustion chamber. Liquid systems
tend to have better fuel efficiencies (in terms of
impulse per unit weight) than solids,
but are considerably more complex and thus more prone to failure. The Space Shuttle
Main Engines (SSMEs) are the most recognizable implementation of a liquid propellant
system.

Hybrid propellant rockets typically utilize a solid fuel and a liquid
or gaseous oxidizer. Fuel in a hybrid can be almost anything combustible, but the
most common is rubber or, specifically,
(HTPB). While rubber may seem a strange choice for use as a rocket fuel, it is
interesting to note that the binder
used in the shuttle’s SRBs is, in fact, a polybutadiene. Hybrid oxidizers are similar
in nature to liquid systems, although N20 (nitrous oxide) is commonly
chosen for its ease of handling and storage. Hybrids are seen as being more versatile
than solids due to their ability to throttle, stop and restart, and safer than
liquids since the propellants are, separately, totally inert. Currently, however, little
experimentation has been done with large-scale hybrids.

Most commercial hobby rockets use some form of solid propellant, either black powder
or a HTPB-Ammonium Perchlorate composite. A few companies are now producing high-power hybrid
motors for the hobby market which are considerably less expensive per flight than composites of comparable
performance, but require a complex system of ground support equipment (GSE). The
most well-known commercial application of a large hybrid motor is
Scaled Composites’ suborbital rocket glider,
SpaceShipOne.

## Rocket Performance

When designing or selecting a rocket propulsion system for an aerospace vehicle,
various performance parameters must be addressed. These include such concerns as
final velocity desired, maximum acceleration, maximum altitude, payload and vehicle mass, and fuel mass
budget and volume constraints, to name a few. In order to understand and compare
the performance characteristics of different systems, the following principles
must be discussed.

### Force

In physics, a force acting on a body is that which causes the body to
accelerate; that is, to change its velocity. The concept
first appeared in Newton’s second law of motion of

classical mechanics,
and is usually expressed by the equation:

$F = m a$

where

F is the Force, measured in
newtons (N),
m is the Mass, measured in kilograms (kg),
and
a is the Acceleration,
measured in metres per second squared (m/s2).

[Review SI Units of Weights and Measures.]

### Thrust

Thrust is the force that propels a rocket. The diagram to the right
shows a rocket’s combustion chamber with an opening, the throat and

nozzle, through which the expanding gases can escape.

(Diagram credit Robert A. Braeunig.)

The thrust force is a product of the exhaust velocity (Ve)
and the mass flow rate (q) of the ejected propellant,
plus the difference between the atmospheric pressure (Pa) and the pressure
of the exhaust gases (Pe). Exhaust pressure (Pe) is affected
by the expansion ratio of the rocket nozzle, defined by dividing the area
of the nozzle’s exit (Ae) by the area of the throat (At).

Thrust is therefore expressed by the equation:

F = q Ve + (Pe – Pa) Ae

A nozzle is said to be optimized for its operating
environment when Pe = Pa.
Assuming an optimized expansion ratio, the thrust equation can be reduced to its
simplest form:

F = q Ve

where

F is the Thrust force, measured in newtons (N),
q is the Mass Flow Rate of the ejected propellant, (kg/s),
and
Ve is the hot gas Exhaust Velocity

relative to the moving vehicle, (m/s).

This looks very similar to the Force equation above (F = ma), and upon
closer inspection it becomes clear that Thrust is simply the acceleration of a
given mass of propellant out the back end of the vehicle which, in turn, pushes it
forward.

### The Thrust Curve

As a rocket motor fires, its instantaneous thrust can be measured and recorded over the
duration of the burn. This data can then be plotted on a graph with thrust (in
newtons or pounds) on the vertical scale and time (in seconds) on the horizontal
scale. This graph is commonly referred to as a “thrust curve”, and is used as a
visual means of comparing two different rocket motors. (See Fig. 1)

Typical thrust curve.
(Credit ThrustCurve.org.)

You can see from the graph that the thrust spikes sharply at the beginning of the burn, and
then gradually begins to taper off. This spike is the point of maximum thrust, and it
occurs in this example at about 0.3 seconds into the burn.

### Total Impulse

The area under the thrust curve is called the total impulse. It is the product of
the thrust force integrated over the burn time, and is expressed by the equation:

or

I = F t
(assuming constant thrust)

where

I is the Total Impulse, measured in newton-seconds (Ns),
F is the total Thrust, in newtons (N),
and
t is the burn Time, in seconds (s).

Total impulse is the best means of comparing one rocket motor to another.
It is proportional to the total energy released by all the propellant in a propulsion system.
More total impulse means more velocity and altitude for vehicles of equal mass,
or more payload for flights of similar altitude.

You’ll also see in Figure 1 the line of average thrust (Favg).
This number is useful in making approximations of burnout velocity and maximum altitude
of a given vehicle, and is also used in the designation of motor types (see next section).
Since no rocket motor has constant thrust throughout its burn time,
average thrust is computed by dividing total impulse by burn time (Favg = I / t).

### Specific Impulse

Propellant efficiency of a rocket propulsion system is measured by specific impulse (Isp).
Put simply, specific impulse is the total impulse obtainable per unit weight of
propellant. This means that the higher the Isp, the less fuel mass required
for a desired total impulse. Specific impulse is expressed by the equation:

Isp = I / mp g

where

Isp is the Specific Impulse, measured in seconds (s),
I is the Total Impulse, in newton-seconds (Ns),
mp is the Propellant Mass, (kg), and
g is the acceleration of Gravity at the surface of the earth,
(roughly 9.81 m/s2).

The next section will describe how these terms are used in the designation and
classification of commercial hobby rocket motors.

## Rocket Motor Designation

Rocket motor manufacturers designate each of their motors with standardized letter
and number codes which approximate total impulse and average thrust. This allows
motors built by different manufacturers, possibly having different propellant types
and weights, to be classified by their total impulse.

Each motor will have a code similar to the following:

C6-7

The first letter of the code indicates the Total Impulse category. In this case,
the letter “C” indicates that this motor has a total impulse between 5.01 and 10.00 Ns.
Each successive letter indicates twice the impulse of the previous category (e.g., a “D”
motor has an upper limit of 20.00 Ns.)

The next number indicates the Average Thrust of the motor throughout its burn time. In
our example, the number “6” indicates that the average thrust of this motor is roughly 6 N.
[Note: Motors of equal impulse will often have different average thrust values. Assuming equal
total impulse (e.g. two “C” motors), a greater average thrust value will produce greater
acceleration over a shorter burn time. This is helpful for getting heavy rockets off the

The number following the dash (-) is not always present, as it represents the
Delay, in seconds, between motor burnout and the recovery system ejection charge. Here, the
number “7” indicates a seven-second delay between motor burnout and chute deployment.
Longer delays allow a longer coast phase between burnout and apogee. [Note: Many
high-power motors (“G” impulse and higher) will have no built-in delay, allowing
the user to tailor the delay length to vehicle mass and predicted coast time,
either with a modular delay charge or a flight computer. A motor with a -0 designation
is intended for use as a first stage motor on vehicles with multiple stages.]

The following table lists standardized impulse categories by their alphabetic designator. Specific
information on each motor type, including thrust curves, can be found at the
NAR Certified Motors page.

 Total Impulse (Ns) Engine Type 1.26 – 2.50 A 2.51 – 5.00 B 5.01 – 10.00 C 10.01 – 20.00 D 20.01 – 40.00 E 40.01 – 80.00 F 80.01 – 160.00 G 160.01 – 320.00 H 320.01 – 640.00 I 640.01 – 1280.00 J 1280.01 – 2560.00 K 2560.01 – 5120.00 L 5120.01 – 10,240.00 M 10,240.01 – 20,480.00 N

## Model Rocket Flight Profile

Diagram credit
NASA Glenn Research Center
.