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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 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 inward and outward pressing
forces are balanced. When the nozzle is released, air escapes through it
and the balloon is propelled in the opposite direction.
When we think of rockets, we rarely
think of balloons. Instead, our attention is drawn to the giant vehicles
that carry satellites into orbit and spacecraft to the Moon and planets.
Nevertheless, there is a strong similarity between the two. The only significant
difference is the way the pressurized gas is produced. With space rockets,
the gas is produced by burning propellants that can be solid or liquid
in form or a combination of the two.
One of the interesting facts about
the historical development of rockets is that while rockets and rocket-powered
devices have been in use for more than two thousand years, it has been
only in the last three hundred years that experimenters have had a scientific
basis for understanding how they work.
The science
of rocketry began with the publishing of a book in 1687 by the great English
scientist Sir Isaac Newton. His book, entitled
Philosophiae Naturalis Principia Mathematica, described physical principles
in nature. Today, Newton's work is usually just called the Principia. In
the Principia, Newton stated three important scientific principles that
govern the motion of all objects, whether on Earth or in space. Knowing
these principles, now called Newton's Laws of Motion, rocketeers have been
able to construct the modern giant rockets of the 20th century such as
the Saturn V and the Space Shuttle. Here now, in simple form, are Newton's
Laws of Motion.
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Objects at rest will stay at rest and
objects in motion will stay in motion in a straight line unless acted upon
by an unbalanced force.
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Force is equal to mass times acceleration.
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For every action there is always an
opposite and equal reaction.
As will be explained shortly, all three
laws are really simple statements of how things move. But with them, precise
determinations of rocket performance can be made.
Newton's First
Law
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.
Rest and motion can be thought of
as being opposite to each other. Rest is the state of an object when it
is not changing position in relation to its surroundings. If you are sitting
still in a chair, you can be said to be at rest. This term, however, is
relative. Your chair may actually be one of many seats on a speeding airplane.
The important thing to remember here is that you are not moving in relation
to your immediate surroundings. If rest were defined as a total absence
of motion, it would not exist in nature. Even if you were sitting in your
chair at home, you would still be moving, because your chair is actually
sitting on the surface of a spinning planet that is orbiting a star. The
star is moving through a rotating galaxy that is, itself, moving through
the universe. While sitting "still," you are, in fact, traveling at a speed
of hundreds of kilometers per second.
Motion is also a relative term. All
matter in the universe is moving all the time, but in the first law, motion
here means changing position in relation to surroundings. A ball is at
rest if it is sitting on the ground. The ball is in motion if it is rolling.
A rolling ball changes its position in relation to its surroundings. When
you are sitting on a chair in an airplane, you are at rest, but if you
get up and walk down the aisle, you are in motion. A rocket blasting off
the launch pad changes from a state of rest to a state of motion.
The third term important to understanding
this law is unbalanced force. If you hold a ball in your hand and keep
it still, the ball is at rest. All the time the ball is held there though,
it is being acted upon by forces. The force of gravity is trying to pull
the ball downward, while at the same time your hand is pushing against
the ball to hold it up. The forces acting on the ball are balanced. Let
the ball go, or move your hand upward, and the forces become unbalanced.
The ball then changes from a state of rest to a state of motion.
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.
Objects in space also react to forces.
A spacecraft moving through the solar system is in constant motion. The
spacecraft will travel in a straight line if the forces on it are in balance.
This happens only when the spacecraft is very far from any large gravity
source such as Earth or the other planets and their moons. If the spacecraft
comes near a large body in space, the gravity of that body will unbalance
the forces and curve the path of the spacecraft. This happens, in particular,
when a satellite is sent by a rocket on a path that is parallel to Earth's
surface. If the rocket shoots the spacecraft fast enough, the spacecraft
will orbit Earth. As long as another unbalanced force, such as friction
with gas molecules in orbit or the firing of a rocket engine in the opposite
direction from its movement, does not slow the spacecraft, it will orbit
Earth forever.
Now that the three major terms of
this first law have been explained, it is possible to restate this law.
If an object, such as a rocket, is at rest, it takes an unbalanced force
to make it move. If the object is already moving, it takes an unbalanced
force, to stop it, change its direction from a straight line path, or alter
its speed.
Newton's Third
Law
For the time being, we will skip the
second law and go directly to the third. This law states that 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.
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. The whole process is very
similar to riding a skateboard. Imagine that a skateboard and rider are
in a state of rest (not moving). The rider jumps off the skateboard. In
the third law, the jumping is called an action. The skateboard responds
to that action by traveling some distance in the opposite direction. The
skateboard's opposite motion is called a reaction. When the distance traveled
by the rider and the skateboard are compared, it would appear that the
skateboard has had a much greater reaction than the action of the rider.
This is not the case. The reason the skateboard has traveled farther is
that it has less mass than the rider. This concept will be better explained
in a discussion of the second law.
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.
One of the most commonly asked questions
about rockets is how they can work in space where there is no air for them
to push against. The answer to this question comes from the third law.
Imagine the skateboard again. On the ground, the only part air plays in
the motions of the rider and the skateboard is to slow them down. Moving
through the air causes friction, or as scientists call it, drag. The surrounding
air impedes the action-reaction.
As a result rockets actually work
better in space than they do in air. As the exhaust gas leaves the rocket
engine it must push away the surrounding air; this uses up some of the
energy of the rocket. In space, the exhaust gases can escape freely.
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
By using simple algebra, we can also
write the eauation two other ways:
a = f/m
m = f/a
The first version of the equation is
the one most commonly referred to when talking about Newton's second law.
It reads: force equals mass times acceleration. To explain this law, we
will use an old style cannon as an example.
When the cannon is fired, an explosion
propels a cannon ball out the open end of the barrel. It flies a kilometer
or two to its target. At the same time the cannon itself is pushed backward
a meter or two. This is action and reaction at work (third law). The force
acting on the cannon and the ball is the same. What happens to the cannon
and the ball is determined by the second law. Look at the two equations
below.
f = m(cannon) * a(cannon)
f = m(ball) * a(ball)
The first equation refers to the cannon
and the second to the cannon ball. In the first equation, the mass is the
cannon itself and the acceleration is the movement of the cannon. In the
second equation the mass is the cannon ball and the acceleration is its
movement. Because the force (exploding gun powder) is the same for the
two equations, the equations can be combined and rewritten below.
m(cannon) * a(cannon) = m(ball) * a(ball)
In order to keep the two sides of the
equations equal, the accelerations vary with mass. In other words, the
cannon has a large mass and a small acceleration. The cannon ball has a
small mass and a large acceleration.
Let's apply this principle to a rocket.
Replace the mass of the cannon ball with the mass of the gases being ejected
out of the rocket engine. Replace the mass of the cannon with the mass
of the rocket moving in the other direction. Force is the pressure created
by the controlled explosion taking place inside the rocket's engines. That
pressure accelerates the gas one way and the rocket the other.
Some interesting things happen with
rockets that don't happen with the cannon and ball in this example. With
the cannon and cannon ball, the thrust lasts for just a moment. The thrust
for the rocket continues as long as its engines are firing. Furthermore,
the mass of the rocket changes during flight. Its mass is the sum of all
its parts. Rocket parts includes engines, propellant tanks, payload, control
system, and propellants. By far, the largest part of the rocket's mass
is its propellants. But that amount constantly changes as the engines fire.
That means that the rocket's mass gets 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. To enable a rocket
to climb into low Earth orbit, it is necessary to 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 action force 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. Ways of doing this will be described
in the next chapter, practical rocketry.
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
thrust of the rocket.
Putting Newton's
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).
Next
page > Practical Rocketry
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