Physics
HSC Course
Stage 6
Space
Part 3: Lift-off!
Contents
Introduction ............................................................................... 2
Rockets ..................................................................................... 4
Rocket fuel............................................................................................4
A little bit of history ...............................................................................6
Reaction engines..................................................................... 11
Rocket acceleration............................................................................13
Apparent weight and g forces.................................................. 19
Apparent weight .................................................................................19
Acceleration and g forces ..................................................................25
How much is enough? .......................................................................30
The effect of Earth’s motion .................................................... 32
Summary................................................................................. 35
Appendix ................................................................................. 37
Suggested answers................................................................. 43
Exercises – Part 3 ................................................................... 47
Part 3: Lift-off!
1
Introduction
In the last part you began to focus on the issue of escaping the Earth’s
gravitational field. You learned about projectiles, that is, objects that are
projected into the air but are not propelled after launch; and then
continued on to the question of escape velocity. In this part you will
focus on rockets, which are bodies that are propelled after launch by
some on-board fuel source. You will look at what they are, how they
developed and how they can escape the Earth… at least as far as
achieving an orbit around the Earth.
Before beginning this part you should have already studied certain
concepts.
In particular you must be able to describe and calculater weight
r
r
r
(W = mg) , as well as apply Newton’s second law of motion: Â F = ma .
These were covered when you studied the topic Moving about in the
preliminary physics course.
In Part 3 you will be given the opportunities to learn to:
2
•
use the term ‘g forces’ to explain the forces acting on an astronaut
during launch
•
compare the forces acting on an astronaut during launch with what
happens during a roller coaster ride
•
discuss the impact of the Earth’s orbital and its rotational motion on
the launch of a rocket
•
analyse the changing acceleration of a rocket during launch in terms
of the:
–
Law of Conservation of Momentum
–
forces experienced by astronauts.
Space
In Part 3 you will be given the opportunities to:
•
identify data sources, gather and process information from secondary
sources to investigate conditions during launch and use available
evidence to explain why the forces acting on an astronaut increase to
approximately 3W during the initial periods of the launch
•
identify data sources, gather, analyse and present information on the
contribution of Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie,
O’Neill or von Braun to the development of space exploration.
Extract from Physics Stage 6 Syllabus © Board of Studies NSW, 1999. The
original and most up-to-date version of this document can be found on the
Board’s website at http://www.boardofstudies.nsw.edu.au.
Part 3: Lift-off!
3
Rockets
As already mentioned, the essential difference between a projectile and a
rocket is that the rocket continues to be propelled after the launch. Like
a jet engine, a rocket engine carries a fuel source that it burns in order to
produce a backward direction force, called thrust, which propels the
craft forward. Where a rocket engine differs from a jet engine is that it
carries its oxygen supply as well as fuel.
Rocket fuel
Burning fuel means combining it with oxygen, and a jet engine gets its
oxygen from the air through which it is travelling. A rocket engine needs
to have its oxygen for combustion of fuel on board, and this makes rocket
engine ideal for use in space, where there is no atmosphere.
The fuel/oxygen combination can be of two basic types – solid or liquid.
Solid rocket propellant, as it is called, is a dry mixture of fuel and
chemical oxidiser. The mixture is packed into a large cylinder, usually
leaving a hollow core up the middle. The purpose of the hole is to
increase the surface area of the fuel available for burning. This increases
the burning rate and increases the thrust. An electrical igniter is built into
the rocket so that the combustion can be started remotely. Finally, a
nozzle is fitted to the cylinder, so that it looks like the diagram following.
When ignition begins, the combustion produces a large volume of hot
gases very quickly, these are then expelled from the engine. An
important point to note is that once a solid propellant has been ignited its
thrust cannot be easily varied – the fuel will burn at a steady rate until it
has run out.
Liquid rocket propellants are kept separately in tanks within the rocket.
There is a fuel, usually kerosene or liquid hydrogen, and an oxidiser,
usually liquid oxygen. When required, each is pumped from their
separate tank and sprayed into a combustion chamber, where they burn.
4
Space
This produces a large volume of hot gases that are expelled through a
nozzle, just as in a solid propellant rocket. A significant difference
however, is that the pumps can be slowed down, reducing the supply of
fuel and oxidiser, and thereby reducing the thrust. This ‘throttling’
ability allows liquid fuelled rockets greater control over their thrust and
the g forces that arise from it.
liquid
fuel
tank
solid mixture
of fuel and
oxidiser
liquid
oxidiser
tank
hollow core
pumps
combustion
chamber
nozzle
(a) solid propellant
rockets
(b) liquid propellant
rockets
Take a look at the picture of the space shuttle following. The rockets on
either side of it are solid propellant rockets – they provide early thrust
and are exhausted very quickly after lift-off and then jettisoned.
Notice that the orbiter (that’s the part that most people call the ‘space
shuttle’) has three engines of its own. They are liquid propellant rocket
engines, the propellants for these rocket engines are stored in the very
large central, external tank. This tank is carried all the way up to orbit
altitude before it too is empty and then jettisoned, never to be recovered.
There is only enough propellant left on board the orbiter to control its
return to Earth. Because the majority of its thrust comes from these
liquid propellant rocket engines, the space shuttle has the ability to
throttle back in order to minimise the loads experienced by its astronauts
and payloads, restricting these forces to just three times their normal
weight.
Part 3: Lift-off!
5
orbiter
external tank
solid rocket booster
Space shuttle.
A little bit of history
If you look around the world for centres of rocket development you will
find them in Russia, the USA, France, Japan and, at least during World
War II, in Germany. Why is it that these places have been able to
develop rocket industries? To answer that question you need to consider
the early history of modern rocket development.
The early days
Before going further it is worth noting that the first use of rockets was by
the Chinese in the 11th century. They had already discovered gunpowder
and used it to make small rockets that they used as weapons.
The idea was adapted by India in the 16th century, and by the late 17th
century the British had learned of it. They improved the idea of a rocket
as a military weapon, and successfully used it against the French fleet of
Napoleon Bonaparte in 1806.
The lyrics of the USA national anthem tells the story of a British assault
in 1812 upon Fort McHenry (near Baltimore), and refers to the ‘rocket’s
red glare’. Use of rockets continued throughout the 18th century,
however, they were primitive and inaccurate with very little in common
with modern rockets. They were eventually replaced by quicker and
more accurate artillery guns.
6
Space
The true inspiration for modern rocket development came from Jules
Verne who, in the mid 1800s, wrote stories such as From the Earth to the
Moon, that spoke of using a rocket to leave the Earth and travel to the
Moon. These stories were very popular and included some quite
advanced ideas about rockets.
There was a handful of talented individuals around the world who saw
the potential of Verne’s ideas, and were so inspired that they went on to
develop plans for practical rockets that could accomplish the things that
Verne described.
As you read about each of these men, bear in mind that they were doing
this work in the late 18th century and early 19th century – when
photography had only just been invented, the horseless carriage or motor
car was a novelty and flying machines were just getting off the ground.
In Russia
Konstantin Tsiolkovsky (1857 – 1935) was a mathematics teacher who
took an interest in rocketry after reading From the Earth to the Moon.
He worked alone, but managed to develop accurate calculations for space
flight and the details of many aspects of rocket design and space
exploration. His rocket designs were quite advanced, featuring liquid
fuel with throttling capability and multi-staging.
To find information on Konstatin Tsiolkovsky see pages on the physics
websites page at http://www.lmpc.edu.au/science
Perform some independent research to discover some of Tsiolkovsky’s
other design achievements. List your sources below. (The Internet is
very useful for this type of research.) If you cannot locate any material,
your teacher can assist you.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Tsiolkovsky was a theoretician only and never tried out his ideas, yet his
work inspired and helped others who came after him. One of these was
the famed Russian Chief Controller during the space race years of the
1950s and 60s – Sergei Korolev (1906 – 1966).
Part 3: Lift-off!
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Can you perform independent research to find out some of the
accomplishments of Sergei Korolev? List some of them here. If you
cannot locate any material, your teacher can assist you.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
To find information on Sergi Karolev see pages on the physics websites
page at http://www.lmpc.edu.au/science
In France
Roberts Esnault-Pelterie (1881 - 1957) published two books that proved
to be influential – Astronautics in 1930 and Astronautics Complement in
1934. It was his suggestion that rockets could be used as long-range
ballistic missiles. The French Army thought the idea had potential and
employed him to develop these rockets.
His designs used liquid propellants and he tried out a variety of fuel/
oxidiser combinations, such as liquid oxygen and gasoline, nitrogen
peroxide and benzene, and liquid oxygen and tetranitromethane.
This last combination proved to be extremely volatile and resulted in an
accident in which he suffered a major hand injury.
In Germany
Herman Oberth (1894 – 1992) was a Romanian-born German. Like
Tsiolkovsky, he was inspired by Jules Verne’s writings and was solely a
theoretician. He wrote an unsuccessful doctoral thesis called By
Rocketry to Space that, ironically, proved to be a very popular book and
inspired many other Germans to pursue rocketry. He followed this up
with another book, titled The Road to Space Travel. Germany had a
society for space travel called the VfR, and Oberth was one of its earliest
members.
Wernher Von Braun (1912 - 1977) was one of those inspired by
Oberth’s writings. A member of the VfR, he was enlisted by the German
army in 1932 to work at developing larger and more powerful rockets.
In 1934 they tested a rocket called the A2, which developed a thrust of
16 000 newtons. Under Von Braun’s supervision this was developed into
the A4, with a thrust of 250 000 N and a range of 300 km. This rocket
was renamed the V2 by the German military and used as a weapon
against London in 1944.
8
Space
Von Braun and his team went to America following World War II where
they became integrally involved with the development of the American
space program at NASA. The Mercury-Redstone rocket that put the first
American into space was a modified V2.
warhead/explosive
charge
automatic gyro control
guidebeam and radio
command receivers
container for
alcohol-water
mixture
container for
liquid oxygen
turbopump
rocket motor
German V2 (A4) missile.
The USA
Robert H. Goddard (1882 – 1945) decided as a boy to dedicate his life to
rocketry after reading Jules Verne. It is ironic that the USA relied so
heavily on the contributions of foreign rocket engineers yet during his
lifetime Goddard, the American pioneer, was ridiculed and vilified for
suggesting that people would one day be able to go to the Moon using
rockets. In 1960, the US government bought all of Goddard’s patents for
liquid-fuel engines, and today he is revered as an American national
hero.
Goddard was a college professor with a very pragmatic approach to the
development of rockets. He conceived and patented hundreds of designs,
systematically building, testing and developing them. Examples of his
developments include liquid-fuel valving, and the use of gyroscopes for
directional stability.
Part 3: Lift-off!
9
Perform independent research to discover some more of Goddard’s technical
achievements, and list them below. His list of patents is quite impressive, so
you may need to be selective! You should use the internet for this if it is
available to you.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
You should now attempt Exercises 3.1 and 3.2.
10
Space
Reaction engines
Rockets have been called ‘reaction engines’. This is because their basic
principle of operation is Newton’s third law of motion: for every action
(or force) there is an equal and opposite reaction (or force). In this case
the ‘action’ is the rocket quickly pushing a large volume of gas out
behind itself, and the ‘reaction’ is the gas pushing forward on the rocket,
providing the thrust.
By expressing this relationship in terms of forces it can be written down
as an equation:
r
r
Frocket = –Fgases
r
where Frocket = the force on the rocket
r
Fgases = the force on the gases
Although there are two forces that are equal and opposite, the rocket
experiences just one of them – the forward push that is called thrust.
Note that this works with or without surrounding air.
The forward motion of the rocket can be explained using the Law of
conservation of momentum. In the preliminary course module Moving
about you saw how momentum is conserved in any collision or
‘interaction’.
This also holds true here because the expulsion of exhaust gases from a
rocket is an interaction. This law says that during any interaction in a
closed system the total momentum of the system does not change. In this
case the closed system is the rocket and its exhaust gases. If the law is to
be true, then for any small time period (such as a second) any forward
increase in momentum of the rocket must be equal and opposite to the
change in momentum of the exhaust gases being pushed out of the back.
Part 3: Lift-off!
11
r
Total Dp for closed system = 0
r
r
Dprocket = -Dpgases
r
r
r
r
D(mv)rocket = -D(mv)gases since momentum, p = mv
r
Dp = change in momentum, in kg ms-1
m = mass, in kg
r
v = velocity, ms-1
Notice that the mass of gas ejected from the back of a rocket in one
second is small compared to the mass of the rocket, yet its velocity (and
therefore, change in velocity) must be much greater than the rocket’s for
the above expression to hold true.
force of gases on rocket. T
gravitational force of Earth on rocket, mg
force of rocket on gases
gravitational force of rocket on Earth
Force pairs influencing a rocket after lift-off.
12
Space
Standing at its launch site, a rocket’s mass can be up to 90% fuel. As it
lifts off it begins burning its way through this fuel so that its mass
immediately begins to decrease. At the same time it is accelerating due
to the thrust produced, so that its velocity is increasing. This means that
its momentum is changing as a result of changes in both its mass and its
velocity.
Unfortunately, this complicates the mathematics involved. The
expression above can be used to derive an equation for the velocity of a
rocket, but this expression and its differential equation derivation are
outside the scope of this course. However, what the equation shows is
that the velocity of a rocket increases logarithmically throughout a
launch, which is quite different to the usual type of acceleration that you
have previously dealt with (in fact, the velocity is increasing much
faster). To see why it is so you will need to return to Newton’s second
law of motion.
Rocket acceleration
In the analysis that follows assume that the rockets concerned are
launching straight up (which, they don’t actually do). The previous
figure shows the force pairs influencing a rocket just after the moment of
lift-off.
In addition to the rocket-gas force pair there is a gravitational force pair
between the rocket and the Earth. Noticerthat there are just two forces
acting on the rocket – the upward thrust T of the engines and the
r
downward weight mg .
Its acceleration at this point in time is described by Newton’s second law
of motion:
r
r
r
r ÂF
 F = m a and therefore a = m
r r
r
Since
 F = T - mg
r
r
r T - mg
we can say that a =
m
Look at this expression and consider what will happen as the launch
proceeds. As already mentioned, up to 90% of a rocket’s mass is fuel.
As the fuel is burned the mass m of the rocket decreases, while the thrust
remains essentially constant until burnout.
Part 3: Lift-off!
13
This means that:
r
r
• the term (T – mg) becomes greater, increasing the numerator (the
top of the fraction)
•
•
the value of m decreases, decreasing the denominator (the bottom of
the fraction)
r
r
T – mg
therefore, the expression
becomes greater.
m
In other words, the acceleration of a launching rocket is not uniform, but
increases as the launch proceeds. This makes this type of motion quite
different to uniformly accelerated motion you have studied previously.
One of the consequences is that the velocity of the rocket will not
increase uniformly, but logarithmically (meaning that its velocity
increases at ever faster rates throughout the launch).
As a result of these complications, the acceleration equation above can
only apply at a particular instant in time.
Sample problem 1
A model rocket has a mass of 250.0 g and is able to produce a thrust of
9.70 N. Determine its initial rate of acceleration upon lift-off.
Solution
r
r
r
r  F (T - mg)
a=
=
m
m
(9.70 - 0.250 ¥ 9.8)
=
0.250
-2
= 29 ms
That is, the rocket’s initial rate of acceleration will be 29 ms-2.
1
As a rocket gains velocity through the atmosphere the force of air
resistance can quickly become significant. In fact, it is often relied upon
in the basic design of a rocket to give it stability. Like any other
frictional force, air resistance is a force that opposes the motion of a
rocket. Alter the acceleration
r expression already used above to include
the force of air resistance FR . (Hint: it is part of the sum of forces.)
_____________________________________________________
_____________________________________________________
_____________________________________________________
14
Space
2
When in space, away from the influence of gravity, the acceleration
expression becomes much simpler. Write the form of the expression
that will apply here:
_____________________________________________________
_____________________________________________________
3
By examining the expressions you have written above, determine in
each case whether a rocket’s acceleration will continue to increase
during a burn, as long as the rocket has fuel.
_____________________________________________________
_____________________________________________________
4
Here is a problem for you to solve. A model rocket has a mass of 95
g and is able to produce a thrust of 4.16 N. 37% of its mass is fuel.
Determine its initial rate of acceleration upon lift-off, as well as its
acceleration just before all of the fuel is exhausted.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Check your answers.
Simple model rockets
In this activity you are going to observe the action-reaction behaviour of
rockets using very simple models. The models are so simple that the
exercise may seem trivial at first, however you should persevere with it.
You may even find that it’s fun!
You will need:
•
several balloons
•
drinking straws
•
paper
•
tape.
Diagrams of simple rockets that you will build are shown following.
Part 3: Lift-off!
15
balloon
tape
balloon
6 drinking
straws taped
together
A
B
balloon
balloon
tape
straw
straw
paper fins
folded to
form slight
“pin-wheel”
shape
paper
fins
C
D
As seen already, the behaviour of a rocket can be explained using either
the conservation of momentum, with which we can say that at any given
instant:
negative momentum of gases = positive momentum of rocket
or using Newton’s third law, with which we can say that at any given
instant:
negative force of rocket on gases = positive force of gases on rocket.
A simple way to demonstrate this simple idea is to inflate a balloon and
then let it go, as shown in diagram A. As a free balloon deflates, the
escaping air models the exhaust gases of a rocket. Perform this and then
describe your observations.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
16
Space
You probably saw that the motion of the balloon is very erratic, as is any
rocket without guidance. The simplest method of stabilising the flight of
a rocket is by ensuring that the centre of pressure (or drag, the force of air
resistance) is behind the centre of mass. This can be done just by tying a
lightweight stick to the rocket so that it trails behind. This was the
method used by the original Chinese rockets as well as the Congreve
rockets used by the British in the late 1800s.
As shown in diagram B, you can use this method to improve upon the
first model rocket. However the guide-stick must be long and very light
or its weight will exceed the thrust. Tape several drinking straws
together (five or six work well) to make a guide-stick and tape it to the
side of a new balloon. (The balloons will need to be replaced regularly,
because they become stretched and lose thrust.) Aim the balloon upward
and let it go. Describe your observations.
_________________________________________________________
_________________________________________________________
_________________________________________________________
Later ‘passive’ designs employed fins for stability but with greater
directional control. A way to do this is shown in diagram C. Make a
square of paper from an A4 sheet and fold as shown in the diagram.
Tape this to a straw and tape the straw to a new balloon. The rocket will
perform better than the last model, as the fins introduce considerable
resistance to pitch, yaw and roll motions. Launch this rocket and
describe your observations:
_________________________________________________________
_________________________________________________________
_________________________________________________________
Another passive design variation for stability angles the fins to cause the
rocket to ‘roll’. Rolling or spinning creates stability about the axis of
rotation. The flight path of the last rocket can be made quite straight by
folding the fins slightly as shown in diagram D. This will cause the
rocket to spin or roll, though with a slight loss of peak height. Use a new
balloon, aim upward and release. Describe your observations below.
_________________________________________________________
_________________________________________________________
_________________________________________________________
Modern rockets use ‘active’ systems that employ gyroscopes and
gimballed rocket nozzles to control the flight path.
Part 3: Lift-off!
17
Compare the motions of the model rockets you built.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Is an atmosphere necessary for the gases to push on? See if you can find
a definite answer to this question.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
You should now attempt Exercises 3.3 and 3.4.
18
Space
Apparent weight and g forces
In the first part of this module you learned that a mass within a
gravitational field experiences
a force called weight, and that its
r
r
magnitude is given by W = mg . This is ‘true weight’. Your own body
has a true weight. This is equal to your mass multiplied by the value of
acceleration due to gravity at your particular location, however it is a
force-at-a-distance and delivers no sensation of weight (perhaps because
you are so used to it). In other words, you can’t feel your true weight!
Apparent weight
The weight that you do feel, called your ‘apparent weight’ results from
contact forces acting on your body, usually resisting your true weight.
Examples are the normal reaction force of the floor on your body, or the
thrust of a rocket engine.
In any inertial frame of reference (this means that you are not
accelerating) your apparent weight equals your true weight. Examples of
this are shown in the diagram below. In every case the true weight is
balanced by an equal and opposite reaction force, and so the person feels
an apparent weight equal to their true weight.
R
constant
speed
R
R
W
W
W
Apparent weight equals true weight when you are not accelerating.
When an up or down acceleration is involved, however, apparent weight
and true weight have different values.
Part 3: Lift-off!
19
In order to relate these ideas to the forces experienced, the diagram
below compares two more common
examples to an astronaut. In each r
r
r
case there is a weight force W = (mg) down as well as an upward force T
causing the system to accelerate upward.
r
r
In each case we can say that
 F = ma
r
r
r
so that
T - mg = ma
r
r
r
and therefore
T = mg + ma
r r
= m (g + a)
In each case, the apparent weight of the person is the value of the contact
force applied to them (and is resisting their true weight). Therefore, the
r r
apparent weight of the person is given by m(g + a) , which is greater than
their true weight mg. In other words, the person feels heavier than they
really are! Remember the last time you rode in a lift, and as it began to
accelerate upwards you felt a little heavier. Astronauts, too, experience
this increase in apparent weight, except for them it is more severe and
sustained since the accelerations are greater and for longer periods of
time.
The term ‘g force’ is used to express a person’s apparent weight as a
multiple of their normal true weight (that is, weight when standing on the
surface of the Earth).
Hence, g force =
apparent weight
normal true weight
You have already see that for an astronaut in a launching rocket,
r r
apparent weight = m (g + a)
apparent weight
Now we can say, g force =
normal true weight
r r
m (g + a)
=
9.8 m
r r
g+a
Therefore, g force =
9.8
where
r
g = acceleration due to gravity at altitude, in ms-2
m = mass of astronaut, in kg
Notice that the ‘g’ in the apparent weight refers to the value of
acceleration due to gravity at the specific altitude of concern to the
astronaut (and so has been left as ‘g’), whereas the g in the true weight
refers to the value of acceleration due to gravity on the ground (so a
value of 9.8 has been substituted).
20
Space
r
You may recall from Part 1 of this module that the value of g reduces
with altitude, and at the altitude of an orbiting space shuttle it has a value
of approximately 8.8 ms-2.
Sample problem 2
A model rocket has a pre-launch mass of 85 g, of which 25 g is solid
propellant. It is able to deliver a thrust of 3.8 N for a period of 2.8 s.
Assuming that the rocket is fired directly up, determine:
a)
the initial rate of acceleration and g force
b) the final rate of acceleration and g force just prior to exhaustion of
the fuel.
Solution
r
Use g = 9.8 ms-2.
a)
Initial acceleration:
r
r
r
r  F (T - mg)
a=
=
m
m
3.8 - (0.085 ¥ 9.8)
=
0.085
= 35 ms-2
b) Final acceleration:
final mass = 85 - 25 = 60 g
r
r
r
r  F (T - mg)
a=
=
m
m
3.8 - (0.060 ¥ 9.8)
=
0.060
= 54 ms-2
Initial g force:
r r
g+a
g force =
9.8
9.8 + 35
9.8
= 4.6 ms-2
=
Final g force:
r r
g+a
g force =
9.8
9.8 + 54
9.8
= 6.5 ms-2
=
Now it is time for you to try another of these problems yourself. This model
rocket has a pre-launch mass of 150 g, of which 60 g is solid propellant. It
is able to deliver a thrust of 4.5 N. Assuming that the rocket is fired directly
up, determine:
a)
the initial rate of acceleration and g force
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part 3: Lift-off!
21
b) the final rate of acceleration and g force just prior to exhaustion of
the fuel.
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
Check your answers.
Weightlessness
Why is it that an astronaut experiences weightlessness in orbit around the
r
Earth, when it is still well within the Earth’s gravitational field and g
still has a significant value of about 8.8 ms-2? To understand this, recall
the analogy of the lift that was used earlier. If you are riding in a lift that
r r
begins to accelerate down, then your apparent weight will be m(g – a) ,
r
which is less than your true weight mg . What would happen to your
apparent weight if the cable breaks and the lift falls freely?
In this case:
r r
a=g
r r
= m(g – g) = 0
r r
g force = (g – g) / m = 0
Your apparent weight would be zero! Within the confines of the falling
lift you would be apparently weightless. This is precisely what happens
to astronauts between rocket stages (when they have no power and
simple coast along for a few seconds) and when they are in orbit. In both
cases they can be regarded as being in free fall, like the falling lift, but
with considerable horizontal velocity as well.
Why doesn’t the orbiting spacecraft strike the ground if it is freefalling?
A quick answer is that the spacecraft’s high horizontal velocity carries it
around the Earth as it falls, however for a more complete answer to this
question will have to wait for Part four of this module when you will
learn more about circular motion.
22
Space
Away from the Earth
What would be the g forces experienced by an astronaut in an
accelerating spacecraft so far from any planet that gravitational forces
r
could be ignored? In this case there is no true weight at all since g = 0.
However, the astronaut will still experience an apparent weight due to the
thrust (a contact force) experienced by his (or her) body. The
expressions for apparent weight and g force in this case are simpler than
before.
r
r
apparent weight = m (g + a)
r
r
= ma
(since g = 0)
apparent weight
normal true weight
r
ma
=
9.8 m
r
a
Therefore, g force =
9.8
g force =
Also,
A roller coaster ride
A roller coaster ride can also provide variations in the g force felt by its
riders. When the carriage rolls over the top of a crest in the track and
accelerates downhill, the riders are accelerated downward. As a result of
r r
this the g force they experience is (g + g) / 9.8 , which has a value less
than one.
g<1
g=1
g>1
g forces experienced during a roller coaster ride.
Part 3: Lift-off!
23
When the carriage speeds through a valley in the track and curves
upward, the riders are accelerated up. The g force they experience in this
r r
case s (g + g) / 9.8 , which has a value greater than one.
Astronaut training
This idea has been used to train astronauts in a simulated weightless
environment. Included with these notes in the Appendix to this part is a
copy of an article that appeared in the November 1999 issue of
‘Scientific American’. It is titled ‘A taste of weightlessness’ and
describes the experience of a journalist on the plane that NASA use to
simulate weightlessness – a plane they call the ‘vomit comet’. Read the
article in the Appendix and then answer the questions below.
1
What is the ‘vomit comet’, and how did it get its nickname?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
2
What is hypoxia? (You may need to look this up.)
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
3
Describe how the airplane achieves weightlessness.
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
4
Why does this strategy work?
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
24
Space
5
During which parts of the flight is the occupants’ apparent weight
greater than their true weight?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
6
Draw a sketch of the trajectory of the plane. On your sketch
indicate the g forces experienced at the upper and lower parts of the
trajectory.
7
How long do the periods of weightlessness last?
_____________________________________________________
_____________________________________________________
Check your answers.
Acceleration and g forces
When a rocket stands at its launch pad and its engines are started, it will
not move until the thrust has built sufficiently. The point of lift-off
occurs when the thrust just begins to exceed the weight of the rocket.
At this point in time the rocket has zero acceleration and the astronaut
inside is experiencing a one g load.
The thrust of the rocket will quickly build to its maximum and then
remain approximately constant for the remainder of the burn (assuming a
solid fuel rocket engine), while the mass will begin to decrease because
fuel is being burned. This means that the acceleration of the rocket will
increase steadily and the astronaut will experience building g force.
Part 3: Lift-off!
25
just prior to lift-off:
T=W
so that
a=0
g=1
lift-off occurs when:
T begins to exceed W
and then
a>0
g>1
Rocket lift-off.
This trend reaches a climax just before the rocket stage has exhausted its
fuel. It is at this point that the mass of the rocket is at minimum value,
even though the thrust is still present. Under this condition the rocket
will have its maximum acceleration and the astronaut will experience
maximum launch g force loads. At this point a single stage rocket begins
a freefall trajectory, just like the trajectory of NASA’s ‘vomit comet’
airplane mentioned in the article. As a result the astronaut within the
rocket experiences weightlessness, until what is left of the rocket begins
to re-enter the atmosphere.
A multistage rocket, however, does something else. The spent stage is
switched off and jettisoned away. While this happens the rocket is
unpowered and simply ‘coasts’ along, accelerating only due to gravity.
This condition will produce a few seconds of weightlessness, until the
rocket engines of the next stage are turned on. The second stage engines
quickly develop the thrust needed to exceed the rocket’s weight, which
then starts to accelerate again. The acceleration of the rocket again
begins from zero and builds, while the g force experienced by the
astronaut again begins at 1 g and builds. The maximum acceleration and
g force achieved by the second stage is usually not as great as those of
the first stage. If there is a third stage then this pattern will be repeated
once more.
Saturn was a huge rocket used for most of the Apollo missions. It was a
three-stage rocket used to get the spacecraft up into orbit and then on its
way to the Moon if required.
26
Space
The first two stages were used to achieve a low orbit altitude, somewhere
around 180 to 200 km, while the third stage was used to speed up to the
velocity required for a stable orbit, approximately 28 000 kmh-1, all the
while following a smoothly curved trajectory.
peak g force occurs
at end of 1st stage
g force
increasing
acceleration
2nd stage rocket
engine quickly builds
to maximum thrust
1
zero g
between stages
subsequent stages
last longer and
have lower peaks
0
0
time - after lift-off
Rocket stages. Time after lift-off vs g force.
1
Describe the changing acceleration of a launching multistage rocket.
_____________________________________________________
_____________________________________________________
_____________________________________________________
2
Describe the changing g force experienced by astronauts inside a
launching multistage rocket.
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Check your answers.
Part 3: Lift-off!
27
Case study: Mercury Redstone 3
The first American in space was Alan Shepard in 1961, completing a
15 min sub-orbital flight, which means that it went high enough to be in
space (said to begin at an altitude of 80 km) but did not achieve an orbit.
Alan Shepard inside the Freedom 7 capsule. Photo credit NASA.
His rocket, shown following, was made up of a small black capsule
(which Shepard named Freedom 7) on top of a Redstone rocket,
developed from the German V-2 wartime rockets. It was of the liquid
propellant type, using alcohol for fuel and liquid oxygen as the oxidiser.
The characteristics of this rocket were as follows:
fueled mass = 28 440 kg
empty mass = 3 125 kg
payload (capsule) mass = 1290 kg
thrust = 350 000 N
burn time = 142 s
Sample problem 3
a)
Determine the rate of acceleration and g force at lift-off.
b) Determine the rate of acceleration and g force just prior to
exhaustion of the fuel.
28
Space
Solution
(a) Assume that the rocket launched directly up.
Initial acceleration:
r
r
r ( T - mg)
a=
m
350000 - (29730 ¥ 9.8)
=
29730
= 1.97 ms-2
g force:
r r
g+a
9.8
9.8 +1.7
=
9.8
= 1.2
g force =
(b) Determine the final accelerations as follows:
r
r
(T - mg)
a =
m
350000 - ( 4415 ¥ 9.8)
=
4415
-2
= 69 ms
Final g force:
r r
g+a
g force =
9.8
9.8 + 69
=
9.8
= 8.0
Bear in mind that we have ignored the drag on the rocket due to air
resistance, so the peak g force calculated here is too high. In fact,
Shepard experienced a peak g force of 6.3 on the upward part of his
journey, which corresponds to a maximum acceleration of approximately
50 ms-2. At this point the velocity of the rocket was 8 200 kmh-1.
Part 3: Lift-off!
29
Mercury-Redstone 3 (MR3) at lift-off in 1961. Photo credit NASA.
The spent Redstone rocket was released from the capsule, which
continued up on a ballistic trajectory. Its velocity would have been
enough to send it higher than the 186 km altitude attained, however the
mission called for Shepard to turn his craft around and fire his retrorocket to slow down and begin re-entry into the atmosphere.
You should now attempt Exercises 3.5, 3.6, 3.7 and 3.8.
To learn more about this and other space missions go to the physics websites
page at: http//:www.lmpc.edu.au/science
30
Space
How much is enough?
All of this information on g forces does raise a question – how much
g force can a person reasonably withstand? It is well known amongst
pilots that many people begin to show load effects at about 4 g – they get
tunnel vision and lose colour perception. However, rocket designers of
the 1950s needed more information than this. In the USA, much of the
research into this question was conducted with rocket-driven impact
sleds, which could produce sudden and massive acceleration and
deceleration forces, with large centrifuges. The centrifuge proved very
relevant to modelling the g forces of space flight.
E R Ballinger conducted a series of experiments, varying the g load
exerted on a subject as well as the duration. He concluded that 8 g was
the maximum safe load for an astronaut, but symptoms such as chest pain
and loss of consciousness could be experienced at this level. He stated
further that 3 g applied across the body was an ‘ideal load’ for a human
body, meaning that 3 g could be safely tolerated.
However, while these limits were suitable for a launch, designers knew
that the g forces of re-entry would be much greater (you’ll find out why
in Part four of this module). The challenge then was to find ways to
increase a person’s tolerance of higher g loads, and a flurry of further
research took place. Some of the findings are listed below.
•
The load should be applied across the body, which meant that the
astronaut should be lying down at take-off rather than or sitting or
standing.
•
The load is easier to tolerate if it is directed ‘eyeballs-in’, rather than
‘eyeballs-out’. This meant that the astronaut should be lying face up
at launch time.
•
Supporting the body fully increases tolerance to loads. This idea led
to the development of a fibreglass couch moulded to the shape of a
human body, much like the seats used in modern formula one racing
cars. Using this couch subjects withstood loads of up to 20 g. This
was the sort of capability that was astronauts were expected to need,
based on then-current spacecraft designs.
Soon after this work, the Mercury rocket program commenced,
employing all of these ideas. As already mentioned, on his first flight,
Alan Shepard experienced 6.3 g during the lift-off and tolerated this load
well. Later missions were kinder to their passengers and cargo - Apollo
astronauts experienced maximum lift-off loads of 4 g while space shuttle
astronauts experience just 3 g, a gentle ride by comparison.
During his descent, Alan Shepard talked all the way through the
maximum g load period, repeating the words ‘I’m OK… I’m OK…
Part 3: Lift-off!
31
I’m OK…’ just to let the ground crew know that he had not blacked out.
The reason? His maximum re-entry load was 11.6 g!
Draw a number line and on it indicate values from zero to twenty five.
On the number line indicate the g force that correspond to:
•
weightlessness
•
normal weight
•
safe lift-off load
•
the g force at which most people begin to show effects;
•
Ballinger’s maximum safe limit;
•
Shepard’s lift-off and re-entry loads;
•
maximum load endured by occupants of the contoured couch in a
centrifuge.
Check your answers.
32
Space
The effect of Earth’s motion
If you were to throw a ball while riding a bicycle, would the ball go
faster than if you threw it while just standing on the ground. Of course,
it would. The reason is that the velocity of the bike relative to the ground
will add to the velocity of the ball relative to the bike to give a greater
velocity of the ball relative to the ground.
Earth
(looking from above
north pole)
Earth’s
rotation
north
pole
rocket launches
to east and receives
a velocity boost
The Earth’s rotation affects rocket launch.
Space mission planners can use this same idea in two different ways.
•
Part 3: Lift-off!
The Earth is rotating on its axis once per day. A point on the ground
near the equator is travelling the full circumference of the Earth
(about 40 000 km) in 24 hours, which works out to a velocity
relative to the Sun of approximately 1 700 kmh-1.
33
In order to reach a stable low Earth orbit a rocket must reach an
orbital speed of about 30 000 kmh-1. If it launches in the direction of
the Earth’s rotation then it will receive a 1 700 kmh-1 boost towards
its target speed, just as in the ball-bike analogy mentioned earlier.
Launching in the direction of the Earth’s rotation means launching
towards the east.
•
The Earth is revolving once around the Sun per year, giving it a
velocity of approximately 107 000 kmh-1 relative to the Sun.
A rocket intended to head out of orbit and further into space can be
manoeuvred to take advantage of this relative motion too. Mission
planners will wait until the Earth’s own motion is in the direction
desired. Only then is the rocket placed into orbit around the Earth.
It is allowed to circulate around its orbit until it is heading in the
same direction as the Earth and then its rockets are fired, moving
ahead of the Earth, just like the ball in the analogy used earlier.
By doing this, the velocity of the Earth relative to the Sun adds to the
velocity of the rocket relative to the Earth to give a greater velocity
of the rocket relative to the Sun.
Earth’s
orbital
motion
around
Sun
rocket
heads off
in direction
of Earth’s
velocity to
receive a
velocity boost
Sun
Earth
The revolution of the Earth affects rocket launch.
Planning of this sort means that certain times of the year are better than
others for launching space missions. These favoured periods of time are
called ‘launch windows’.
34
Space
You should now attempt Exercises 3.9 and 3.10.
In this part you have learned about the nature and development of rockets
and the issues associated with launching a rocket up to an orbit. In
addition you have learned about apparent weight and g force. In the next
part, you will learn about the orbital motion of satellites as well as the
problems associated with returning to the Earth from space.
Part 3: Lift-off!
35
Summary
•
Unlike a projectile, a rocket continues to be propelled after it is
launched.
•
Unlike a jet, a rocket carries its own oxygen supply on board for the
purpose of burning its fuel.
•
Rockets can use solid or liquid fuels. Liquid-fuel rocket engines can
be throttled to minimise g forces.
•
A rocket is a reaction engine – its behaviour can be explained using
Newton’s third law of motion, as well as by the conservation of
momentum.
r
r
The acceleration of a rocket obeys Newton’s second law: Â F = ma
•
36
•
The term ‘g force’ is used to describe apparent weight as a multiple
of normal true weight.
•
During a launch, a rocket’s acceleration and g forces begin low and
build steadily due to the decrease in mass as fuel is burned.
•
Common devices that can produce variations in apparent weight and
g force are lifts and roller coasters.
•
Apparent weightlessness is experienced in frames of reference that
are accelerating due to gravity. Examples are inside a falling lift or
airplane, or inside an orbiting spacecraft.
•
The orbital motion (around the Sun) and rotational motion (on its
axis) of the Earth can be exploited to provide a rocket with speed
boost.
Space
Appendix
The following extract is from Scientific American website:
http://www.sciam.com/1999/1199issue/1199scicit3.html.
It was downloaded 14 September 2000.
A taste of weightlessness
‘Our reporter flies on NASA's zero-g-simulating "Vomit Comet"
Flush and excited in Houston's late-summer heat, some of the visiting
collegians are dreaming of becoming astronauts, and others are bent
on publishing their first scientific paper. Almost all of them are
quietly hoping they won't throw up. In a few days, they will get to do
something most people do only in their dreams: float in midair,
unchained from gravity's anchor.
The buoyant interlude will occur in the cargo bay of the National
Aeronautics and Space Administration's world-renowned Vomit
Comet, a KC-135A aircraft that is flown so as to provide
weightlessness in 25-second snippets. Although best known for its
role in astronaut training, about 80 percent of the plane's flights are
actually conducted in support of research or engineering. And a Ph.D.
isn't required: under a program administered by the Texas Space Grant
Consortium, the space agency makes the plane available for a couple
of weeks each year to undergraduate researchers. Up to four students
from each team get a taste (perhaps literally) of weightlessness, along
with a journalist-observer who carries out the all-important publicrelations mission.
The team I have been assigned to, consisting of five earnest
mechanical engineering majors from the University of Alabama at
Birmingham (UAL), will study heat convection in artificial gravity.
They have built a spinning assembly that produces centrifugal force in
a test cell. If all goes well, thermoelectric devices will heat and cool
air in the cell, while temperature sensors record how the heat is
conducted through it. The other student experiments encompass such
subjects as suturing skin (on pigs' feet), the miscibility of fluids with
different viscosities and the damping of vibrations in solids.
Part 3: Lift-off!
37
Am I Blue?
Before we can fly, though, we'll have to make it through a day of
lectures, physiological training and testing. We'll have to pass a
written test covering gas laws, atmospheric science, physiological
principles of balance and motion sickness, and aircraft emergency
equipment. The training highlight is a soirée of sorts in NASA's big
hypobaric chamber, in which 15 of us and two NASA technicians are
rapidly decompressed to a pressure equivalent to that at an altitude of
25,000 feet (7,620 meters). Besides acquainting us with the
emergency breathing equipment and with the symptoms of hypoxia,
NASA officials are making sure we would be able to cope if the
aircraft cabin suddenly lost pressure.
The fun starts when we take off the breathing masks to experience
hypoxia firsthand. Most people can stay conscious for three to five
minutes, and for the first couple minutes I figure I'll be able to go the
distance. After three minutes, however, I start sliding into a drunken,
groggy torpor. At about three and a half, NASA medical specialist
Mike Fox calls everyone's attention to the lovely purplish-blue hue of
my lips. At four minutes, I feel consciousness slipping away like a
thief in the night. A NASA technician helps me put my mask back on,
and sharp-edged sobriety comes flooding back. Oh well. At least I
didn't tap dance or try to take my clothes off--behaviors Fox swears he
has seen in the chamber.
During the lectures, as might be expected, we're never too far from the
issue of vomiting. It comes up again and again. The airplane is aptly
nicknamed: "Of three first-time flyers, one gets violently sick, one
gets mildly sick, and a third doesn't get sick at all," explains John
Yaniec, who as lead test director has logged a total of 353 flights.
Thus, crew members and instructors have developed a rich
epistemology of motion sickness that in depth and complexity rivals a
geologist's knowledge of volcanoes.
In her lecture, Sharon Sands of NASA's manned test support group
describes the three stages of motion sickness that precede vomiting.
We are advised to have the bag out and ready at stage three (in which,
for some, crankiness accompanies the increasingly terminal sick
feeling) and to get to the back of the plane if possible, to avoid turning
fellow fliers into hurlers. Charles Shannon, another speaker, leaves us
with this advice: "If someone seems sick, get away from him. If
they've been holding it in and holding it in, you could have an
explosive force of vomitus, and in zero-g it sprays real well." No one
laughs.
By the break, the students and journalists are swapping scuttlebutt and
strategies about what to breakfast on before the flights, which take off
promptly at 9:30 a.m. "I've heard canned peaches are the way to go,"
declares Brian Bliss, a member of the huge Purdue contingent. "I've
heard bananas, because they don't taste so bad when they come up,"
counters Peter W. Yost, news editor of the aviation Web site AvWeb.
38
Space
There is even bizarrely pervasive folklore about cherry Lifesavers,
which are said to help ward off nausea during the flight.
Finally, we're told not to feel bad if we become "casualties." "It's not
a macho thing," contends Charles Ross, a veteran NASA flight
surgeon who has also logged numerous flights. "We have astronauts
with their own little issues with the Vomit Comet." Sands notes,
"Your body will be going through some stuff it's never gone through
before. Your visual system is saying you're not moving but your
vestibular system is out in left field."
The Ultimate Roller Coaster
It is the trajectory of the aircraft, like a huge roller coaster in the sky,
that throws the vestibular system for a loop. The plane flies a series of
parabolas, with weightlessness (technically, "microgravity") induced
for about 25 seconds around the top of each. Peaking at around 34,000
feet, the airplane then dives about 10,000 feet, its fuselage pitched
down at 40 degrees. If that fact does not seem impressive, bear in
mind that the KC-135A is just over 136 feet long; it is the military
version of Boeing's 707 airliner. Surprisingly, the KC-135A was so
well built that it required no special structural improvements to fly the
parabolas. Only the hydraulic system of NASA's aircraft was
modified, to keep it from losing pressure during the weightless
periods.
When the airplane comes out of the dive and begins its next ascent-the part of the flightpath known as the "pullout"--the plane pitches
upward at about 50 degrees and passengers and craft are subjected to
forces up to 1.8 times that of gravity.
Typically, the pilot flies 30 parabolas that provide weightlessness, and
then one that simulates lunar gravity (one sixth that of Earth's) and
one for Martian gravity (one third that of Earth's). It is especially
important not to move your head during the pullouts, we are told.
"The name of the game is not stimulating your semicircular canals,"
Shannon emphasizes. By all accounts, the weightless part of the first
parabola is unforgettable, to put it mildly. "The first time it happens
it's going to freak you out," Sands says. "For about three seconds it
feels like you are falling. You've got to force yourself to relax, even if
it takes every ounce of your psyche."
Finally my flight day arrives. For breakfast I settle on half a large
mango, a banana and some ginger snaps. In my hotel room shortly
before dawn, I peel the banana and wonder if I'll see it again. At the
preflight briefing, I sit with the two UAB student researchers I will be
accompanying on the flight: team leader Michael Bell and Richard
Shunnarah. The flight surgeon distributes the motion-sickness pills-an industrial-strength concoction of scopolamine and Dexedrine. All
but three first-time flyers decide to take it. Then we are ready to board
the plane.
Part 3: Lift-off!
39
As we climb out over the blue Gulf of Mexico, my teammates fiddle
with their experimental setup, which is contained within a squat,
metal-framed, clear-plastic box. I chat with Eric Santos, an orthopedic
surgeon and avid scuba diver who crews from time to time on the
Vomit Comet because he can't get enough of that floating feeling.
After we talk for a while, Santos looks me in the eye and says, "You'll
be fine." I wonder how he can be so sure. "Two minutes!" Yaniec
yells.
The Ape Man Falls
We go into weightlessness, and suddenly five million years of
evolution go down the drain and I am an ape losing his balance in a
tree. For about three seconds, and just as Sands promised, panic and
terror mingle in my brain. But by the time a rational thought enters my
head--dismay that terror might be the overriding sensation for me
throughout all the weightless periods--the fear is gone, replaced by
euphoria. My brain has somehow decided that I am floating, not
falling. To call the perceptual shift strange wouldn't do it justice.
Elsewhere in the plane, scattered shrieks and squeals suggest mine
isn't the only perceptual shift going on.
By the fifth or sixth parabola, I am not experiencing any initial flash
of panic at all, just joy. I snap pictures of my teammates. Shunnarah
seems to have a permanent grin as he writes numbers on a clipboard.
Other students float around, doing their best to concentrate on their
experiments. Some time after parabola 10, however, motion sickness
begins claiming some fliers, who strap themselves into seats in the
rear of the aircraft.
Around parabola 26, I finally accept the fact that I am not going to get
sick, and I celebrate with a few backflips and other gyrations. About
22 seconds into each weightless period, Yaniec's cry of "feet down,
coming out!" means that I have about three seconds to figure out
where the padded floor is and to make sure my head isn't pointing
toward it--or worse, toward one of the students' experiments. During
parabola 30, with Yaniec's permission, I bounce and float through the
plane to take in the view from the cockpit during the last two
parabolas.
Through the airplane's windshield I see blue sky as we climb. Then, in
simulated lunar gravity near the top of the parabola, I watch the
grinning flight engineer drop his pen repeatedly to the little shelf in
front of him. The shiny writing instrument falls in surreal slow
motion. Through the cockpit glass I see clouds and horizon shoot
upward as we nose over the top of the parabola. Then I see the deeper
blue of the Gulf of Mexico as we nosedive toward it. On the altimeter,
a hand is literally spinning as we plunge oceanward. For sheer
exhilaration, not much can compare to it.
40
Space
Filing off the plane after we land, some of the passengers are perky,
others considerably less so. It turns out that 10 of 21 became
physically ill (Yaniec won the crew's pool by guessing the correct
number). Unfortunately, one of the afflicted, a good-natured young
cinematographer from California, goes into shock and must be carried
off the plane on a pallet. Almost an hour after we land, he is hunched
over on a seat, motionless, sweaty and pale, in the flight-suit storage
room. Such a reaction is uncommon, a NASA crew member says, and
usually treated by administering fluids intravenously.
Although my teammates were fine, their experimental setup has
unaccountably failed to record any intelligible data from the thermal
sensors. Undeterred, Bell hopes to identify and solve the problem and
have another go next year. Even with the garbled data the flight was
still "a dream come true," Bell says. Adds Shunnarah: "If I could do it
again tomorrow and the day after, I would."
Glenn Zorpette in Houston
Part 3: Lift-off!
41
42
Space
Suggested answers
Rocket acceleration
1
2
r
Including air resistance: a =
r
r
r
r
 F = (T - mg - F
m
r
r
F T
Â
Away from the Earth: a =
=
m
m
air
)
m
3
In each case a rocket’s acceleration will continue to increase
throughout a burn since the mass m will be decreasing.
4
Model rocket problem:
Initially
Finally
r
r
r
r
r  F (T - mg)
r  F (T - mg)
=
a=
=
a=
m
m
m
m
(4.16 - 0.095 ¥ 9.8)
(4.16 - 0.06 ¥ 9.8)
=
=
0.095
0.06
–2
-2
= 60 ms
= 34 ms
______________
Apparent weight and g forces
a) Initial acceleration:
r
r
r
r  F ( T – mg)
a=
=
m
m
4.5 – (0.150 ¥ 9.8)
=
0.150
= 3.0 ms-2
Initial g force:
r r
g+a
g force =
9.8
9.8 + 3.0
=
9.8
= 1.3
Part 3: Lift-off!
43
b) Final acceleration:
final mass = 150 - 60 = 90 g
r
r
r  F (T - mg)
=
a=
m
m
4.5 - (0.090 ¥ 9.8)
=
0.090
= 40 ms-2
Final g force:
r r
g+a
g force =
9.8
9.8 + 40
=
9.8
= 5.1
Astronaut training
1
A KC-135A aircraft flown on a trajectory that provides
weightlessness to the passengers for the purpose of experimental
research.
2
A physiological state where there is insufficient supply of oxygen to
the body or tissues.
3
The trajectory of the aircraft flight path ius in the form of parabolas
in the sky and is like that of a huge roller coaster induced by the
plane climbing to 34000 feet and diving 10000 feet at an angle of
40∞. This induces weightlessness for around 25 s.
4
The plane is actually approaching the surface of the Earth at the
acceleration due to gravity creating a weightless environment.
5
During the beginning of the upward trajectory of the parabolic path
the passengers are subjected to 1.8 g forces.
50∞
6
7
44
40∞
25 s
Space
Acceleration and g forces
1
Acceleration of a multistage rocket. At lift-off, acceleration is
slightly greater than one, but continues to rise throughout the firststage burn. This is mainly because the as of the rocket is decreasing
as fuel is burned. At the end of the stage, thrust ceases and the
acceleration of the rocket engine disappears, leaving only the
acceleration due to gravity. As the second stage fires, the
acceleration quickly begins to rise again, repeating the pattern.
2
g forces of a multistage rocket. g = 1 at lift-off and continues to
increase throughout the first stage burn, as acceleration increases.
When stage is finished, g = 0 as temporary weightlessness sets in.
When second stage fires up, g approaches a value of one again and
then continues to rise, repeating the pattern but not as severe.
0
Part 3: Lift-off!
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4
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10
maximum endured
in contoured couch
Shepard’s re-entry load
Ballinger’s safe limit
Shepard’s lift-off load
effects begin to show
safe lift-off load
normal weight
weightlessness
How much is enough?
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Space
Exercises – Part 3
Exercises 3.1 to 3.10
Name: _________________________________
Exercise 3.1
a) Describe the basic structure of a solid-propellant rocket.
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b) Describe the basic structure of a liquid-propellant rocket.
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c) What is the important operational difference between these two types
of rocket engines?
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Part 3: Lift-off!
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Exercise 3.2
Write a paragraph on the contribution to the development of space
exploration of either Tsiokovsky or Goddard. Ensure that your writing
goes further than the information provided in this work unit.
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Exercise 3.3
acceleration
On the diagram below, draw the force pair that results in thrust being
experienced by a rocket.
0
time
0
(a)
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(b)
Space
a)
On the axes provided in the diagram, draw a graph of the
acceleration of a rocket, assuming that it is only a single-stage
rocket.
b) Given that the thrust is essentially constant, use Newton’s second
law of motion to explain why the acceleration is not uniform.
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Exercise 3.4
Does a rocket carry a fuel/oxidiser mix work in a vacuum? Explain your
answer.
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Exercise 3.5
a)
What is apparent weight?
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b) Describe two situations when your apparent weight and your true
weight are identical.
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c)
Describe two situations when your apparent weight is different to
your true weight.
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Part 3: Lift-off!
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Exercise 3.6
a)
Define the term ‘g force’.
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b) Describe the changes in g force experienced by an astronaut during a
launch. Assume that it is a two-stage rocket used to achieve a low
orbit.
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c)
Show these changes in graph form using the axes below.
g force
0
0
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time
Space
Exercise 3.7
Complete the following table to compare the g forces of a launch to those
experienced on a roller coaster ride.
g force
Period during rocket
launch that produces these
g forces
Period during roller coaster
ride that produces these
g forces
<1g
1g
>1g
Exercise 3.8
The model rocket has a pre-launch mass of 250 g, of which 175 g is solid
propellant. This gives it a ‘mass fraction’ of 0.7, meaning that the fuel is
70% of the total launch mass. It is able to deliver a thrust of 4.0 N.
Assuming that the rocket is fired directly up, determine:
a)
the initial rate of acceleration and g force
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b) the final rate of acceleration and g force just prior to exhaustion of
the fuel.
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Part 3: Lift-off!
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Exercise 3.9
a)
What is the maximum g force that a properly supported human can
withstand?
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b) At what g force do most people begin to show effects of the load?
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c)
What maximum lift-off g forces were experienced by:
i)
Mercury astronauts: __________________________________
ii) Apollo astronauts: ___________________________________
iii) Space shuttle astronauts: ______________________________
d) How is the space shuttle able to minimise g forces in this way?
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Exercise 3.10
a)
Explain how an astronautical engineer can plan to use the Earth’s
rotation (on its axis) to help a launched rocket better achieve the
velocity required for a stable orbit.
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b) Explain how an astronautical engineer can plan to use the Earth’s
orbital motion (revolution around the Sun) help a spacecraft achieve
a higher velocity as it heads further out into space.
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Space