Above
and
Beyond
Additional Explorations
How High?
Using Mathematics to Estimate
Rocket Altitude
Students are excited to learn what altitude their
rockets achieve. Altitude tracking is both simple
and tricky. If the rocket goes straight up, it is pretty
easy to get a good estimate of the altitude. The
altitude tracker activity (page 81) provides a simple
instrument and instructions for estimating rocket
altitudes. A baseline is stretched out from the rocket
launch site. The angle to the rocket, just before it
starts its fall back to Earth, is measured.
The tangent of the angle is determined from the
tangent table in the tracker activity. The tangent,
multiplied by the length of the baseline, gives the
altitude.
Single station tracking is easy to do. If you have two
or more students measure the angle, averaging their
estimates can increase accuracy.
Single Station - No Wind
alttitude (a) equals the
tangent of the angle A
times the baseline (b)
Sample Measurement:
Angle A = 40 degrees
Tangent A = .8391
Baseline b = 25 m
a (altitude) = tan A x 25 m
a = 20.97 m
Tracking becomes more challenging when rockets
stray from straight up. Wind will cause the rocket
to drift. Wind pushes the ns away while the nose
cone points towards the wind. This causes the
rocket to nose into the wind, resulting in larger alti-
tude error estimates.
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One method for reducing windy day error is to set
up the baseline perpendicular to the wind direction.
In the diagram, wind causes the rocket to drift to
the right. This stretches the baseline a bit, but the
overall error for the altitude is reduced. Challenge
advanced students to come up with a way of deter-
mining how much the baseline changes when the
rocket drifts to the right.
Wind effects can also be addressed by employ-
ing two tracking stations at opposite ends of the
baseline. The baseline is stretched up and down-
wind. Each station measures the altitude the rocket
achieves. Both stations calculate the altitude (one
result will be higher than the actual altitude and the
other lower) and divide by two.
Single Station - Tracking with Wind
Angle A is reduced, but line b is increased by
the drift of the rocket.
The above picture shows a different method for
estimating altitude that is appropriate for lower
grade students launching rockets that don’t travel
very high (e.g., straw rockets). Tracking students
simply stand back and compare the rocket altitude
to a building, tree, agpole, etc.
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A rough estimate of rocket altitude can also be
made with a stopwatch. Time the total ight of the
rocket and divide the time by 2. This yields the
approximate time it took for the rocket to fall from
its highest point back to the ground. The equation
for falling bodies yields the altitude estimate. This
method won’t work if the rocket has a recovery sys-
tem such as streamers or parachutes to slow its fall.
Sample Measurement:
Total ight time: 6.2 seconds
Falling time/2 = 3.1 seconds
h = 1/2 g t
2
h = 1/2 x 9.8 m x 9.6 (the seconds cancel out)
h = 47.04 m
Here is a method for calculating altitude graphi-
cally. Two tracking stations are placed equidistant
from the launcher. In this example, the stations are
each 12.5 m from the launcher. Both stations mea-
sure the angle. On a piece of graph paper, a scale
drawing of the stations and the launch site is made.
Using the principle of similar triangles, the scale
altitude of the rocket is measured - 14 m.
Provides a rough estimate of the altitude
reached. Air drag on the rocket is a signicant
source of error.
There is a considerably more advanced method
for altitude tracking that also involves two tracking
stations. The method not only requires measuring
the altitude angle of the rocket but also its azimuth,
or compass direction, from the tracking site. These
two measurements from each station provide very
accurate estimates of altitude regardless of how
much the rocket drifts from the vertical. The prob-
lem with the method is that it requires a tracking
device similar to a surveyor transit plus experienced
trackers to take the measurements. Rocket hobby-
ists, especially those that participate in high per-
formance rocketry, use small recording altimeters
inside their rocket payload sections. These rockets
are easily capable of ights of several thousand
meters, and ground tracking stations have a hard
time providing consistent and accurate data. Upon
recovery, the altimeters are read. For more informa-
tion on two-station tracking and altimeters, search
the Internet for “rocket altitude tracking.”
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Science Fiction and the Exploration
of Space
Long before the rst astronauts entered space,
humans dreamed of space travel. Little about the
space environment was known, and it seemed
reasonable that the worlds above would be like
the world below. In imagination, existing forms of
transportation were sufcient to travel through the
heavens. Storytellers, the rst science tion writ-
ers, concocted adventures that carried people
to the Moon on sailing ships and platforms sus-
pended beneath eagles ying to catch legs of
mutton dangled just out of reach by sticks. Giant
spring-propelled sleighs and whirlwinds transported
others. In one story, people traveled to the Moon
on the temporary bridge created by Earth’s shadow
during a lunar eclipse.
During the nineteenth and twentieth centuries,
ctional space explorers began to travel through
space using rockets, cannons, and antigravity sub-
stances. In 1865, Jules Verne’s story, De la terre á
la lune, space explorers traveled to the Moon inside
a cannon shell. In 1901, an H.G. Wells story pro-
pelled a spacecraft to the Moon with an antigravity
substance called “cavorite” in The First Men in the
Moon.
Near the end of the nineteenth century, motion
pictures were invented. Space exploration science
ction (sci-) stories quickly moved to the silver
screen. Sci- became one of the rst movie genres.
In 1902, the 8-minute Le Voyage dans la lune was
released. Loosely based on Jules Verne’s story, the
movie startled audiences with its special effects.
Special effects scene from Le Voyage dans la lune.
Another early effort was Fritz Lang’s 1929 movie Fra
im Mond. It featured a Moon rocket launched from
underwater.
Since the earliest lm efforts, hundreds of space
exploration sci- movies and weekly “cliff-hanger”
serials have been created. They tell fantastic stories
and stretch the viewer’s imagination from Earth orbit
to the deepest reaches of outer space. In the late
1940s, movies were joined by television and began
broadcasing multi-episode space “westerns.”
Today, space exploration sci- is among the most
popular of lm and television genres. Audiences
love the stories, in part because they make almost
anything seem possible. The stories they tell are
often visionary. Long before the Apollo program,
movies took humans to the Moon and Mars. Long
before they were needed, movie and television
makers created spacesuits and space maneuvering
units. Large space stations were erected in imagi-
nary orbits. The rst space stations didn’t reach
Earth orbit until the early 1970s, but they orbited
Earth in 1950s lms. Every few days a new extraso-
lar world is discovered by scientists. Science ction
space explorers have been exploring those worlds
for decades.
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However improbable and however dopey some
of the early special effects may now seem, space
exploration movies and television have much to
offer.
Comparing the science and technology they present
to real space exploration is a fascinating endeavor.
What has turned out to be real and actually hap-
pened? What hasn’t happened yet? What is scien-
tically correct? What is scientically incorrect or
just plain silly?
Regardless of their scientic and technological
authenticity, space exploration movies and televi-
sion energize the imagination. They have excited the
masses and have helped generate popular support
that makes real space exploration possible.
Opportunities for Student Research
Space exploration sci- offers students interesting
and entertaining research lines. Telling the differ-
ence between good and bad science and technol-
ogy requires knowing good science and technology.
Have students select a movie and review it for the
science and technology presented. The following
are a few questions students might try to answer in
their reviews:
• What is the movie’s title?
• When was the movie made?
• What is the plot (story) of the movie?
• How was space travel accomplished?
• Describe the vehicle used. What was its power
source?
• Did the movie employ real science and technol-
ogy? Give some examples.
• Did the movie make science and technology
mistakes? Give some examples.
• Has NASA used similar science and technology
to explore space? Explain.
• Did the movie accurately predict the future?Give
some examples of how.
Here are a few suggested movies for students to
review. All are available on DVDs from rental stores
and online rental stores.
Scene from Fra im Mond.
Rocketship XM (1950)
Engine and fuel problems during ight cause
Rocketship XM to zoom its crew past its original
target, the Moon, and arrive at Mars instead. G
forces and a destroyed Martian civilization are some
of the challenges faced by the crew.
Conquest of Space (1956)
A space crew onboard a spinning wheel space
station uses a space taxi during space walks to
prepare their ship for launch. On its way to Mars,
the crew dodges a aming asteroid and deals with
emotional problems.
Forbidden Planet (1956)
Humans travel by ying saucer to a distant world
and meet their inner selves.
First Men in the Moon (1964)
An H. G. Wells story adaptation carries two acci-
dental space travelers and an eccentric scientist to
the Moon in an antigravity-propelled space sphere.
2001 A Space Odyssey (1968), 2010 (1984)
In a series of slow-moving visual experiences,
humans travel to the Moon and Jupiter to follow
mysterious alien signs. The lm predicts space
hotels and multi-year space missions.
Star Wars, Episodes I - VII ( 1977 - 2005)
Rebel forces battle an evil empire across a gal-
axy far, far away. A wide range of space vehicles,
robots, and alien life sustain the action.
Star Trek (1979 - 2002)
In a series of movies Captains Kirk and Picard save
Earth and strive for peace in the galaxy. Using warp
drive and transporters, they boldly go where no
humans have gone before.
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The Art of Spaceight
Space art has long been a key part of the explora-
tion of space. In the 1950s, space artists such as
Chesley Bonestell illustrated space exploration con-
cepts for books and magazine articles. At the same
time, animation artists at Disney Studios, working
with space experts such as Dr. Wernher von Braun,
showed what the rst missions to space, the Moon,
and beyond might look like. The American public
was enchanted by dreams of spaceight, and the
American effort to explore outer space was born.
Space art continues to support the exploration of
space. Besides promoting mission concepts with
decision makers and the public, space art also
provides scientists, engineers, and technicians a
concept picture of what they are trying to do. They
see what the systems they are working on look like
when assembled together. Furthermore, space art
excites and motivates students to pursue careers in
science, technology, engineering, and mathematics.
Early space art was created using traditional materi-
als and techniques. Many space artists still portray
their dreams this way, but computer graphics has
also found a place in space art. Spacecraft can
be created using 3D technology that permits them
to be rotated, enlarged or reduced, and brought
forward or backward and layered on one of many
backgrounds.
The three pictures on the right show how forced
perspective is accomplished. The top picture is a
space art conception of the 1999 Terra Spacecraft
launched on an Atlas II rocket. The middle picture
shows the relationship between horizon line and the
vanishing point. The bottom picture shows a sketch
based on the original but with a few lines added to
emphasize motion.
Vanishing Point Horizon Line
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To create excitement, space artists often take
advantage of forced perspective. For example, see-
ing a rocket launched from above provides a unique
and exciting experience for the viewer. To create
such a view, a horizon line and a vanishing point are
laid out on the canvas or screen. Lines merging into
the vanishing point provide guides for the 3D effect.
Rockets, drawn within the lines, appear to go into or
out of the picture.
Invite students to create their own space art. Space
art begins with a mission. Students should rst
decide where they want their spacecraft to go. If the
destination is Mars, what will the Mars spacecraft
require for the mission? The length of time required
to reach Mars will necessitate a larger vehicle than
a vehicle for going to the Moon. More supplies and
more crew will be needed, etc.
Space art is something that students of all ages can
do. Young students can create an animated space
launch with a simple paper fold trick.
Make two folds in a strip of paper. Draw a launch
platform on the lower segment. Draw a rocket
launching on the upper two segments.
Fold the paper to prepare the rocket for launch.
Pull on the top and bottom of the paper to open the
folds and launch the rocket.
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Rocket Glossary
Action - A force (push or pull) acting on an object.
See Reaction.
Altitude - The height above Earth achieved by a rocket
or other vehicle.
Artemis Program - NASA’s new lunar exploration
program, which includes sending the rst woman and the
next man to the Moon.
Attitude Control Rockets - Small rockets that are
used as active controls to change the direction (attitude)
a rocket is facing in space.
Balanced Force - A force that is counterbalanced by
an opposing force, resulting in no change in motion.
Canards - Small movable ns located towards the nose
cone of a rocket.
Case - The body of a solid propellant rocket that holds
the propellant.
Center of Mass - The point in an object about which
the object’s mass is centered.
Center of Pressure - The point on the surface of an
object about which the object’s surface area is
centered.
Combustion Chamber - A cavity inside a rocket where
propellants burn.
Compressed - Material that is forced into a
smaller space than normal.
Drag - Friction forces in the atmosphere that “drag” on a
rocket to slow its ight.
Exploration Ground Systems (EGS) - NASA’s
program to develop and operate the systems and
facilities necessary to process and launch rockets and
spacecraft.
Fins - Arrow-like wings at the lower end of a rocket that
stabilize the rocket in ight.
Gimbaled Nozzles - Tiltable rocket nozzles used for
active ight control.
Igniter - A device that ignites a rocket’s engines.
Liquid Propellant - Rocket propellants in liquid form.
Mass - The amount of matter contained in an object.
Mass Fraction - The mass of propellants in a rocket
divided by the rocket’s total mass.
Microgravity - An environment that imparts to an object
a net acceleration that is small compared to what is pro-
duced by Earth at its surface.
Motion - Movement of an object in relation to its
surroundings.
Movable Fins - Rocket ns that can move to stabilize a
rocket’s ight.
Newton’s Laws of Motion - Laws governing all
motion and in particular rocket ight.
Nose Cone - The cone-shaped front end of a rocket.
Nozzle - A bell-shaped opening at the lower end of a
rocket engine through which a stream of hot gases is
directed.
Orion - NASA’s new spacecraft to carry humans on deep
space missions.
Oxidizer - A chemical containing oxygen compounds
that permit rocket fuel to burn in the atmosphere and
space.
Passive Controls - Stationary devices, such as xed
ns, that stabilize a rocket in ight.
Payload - The cargo carried by a rocket.
Propellant - A mixture of fuel and oxidizer that burns to
produce rocket thrust.
Reaction - A movement in the opposite direction from
the imposition of an action. See Action.
Rest - The absence of movement of an object in
relation to its surroundings.
Solid Propellant - Rocket fuel and oxidizer in solid
form.
Space Launch System (SLS) - NASA’s new
super heavy-lift launch vehicle.
Space Station - An Earth orbiting space laboratory and
testing ground for technologies needed for missions into
the solar system.
Stability - A measure of the smoothness of the ight of
the rocket.
Stages - Two or more rockets stacked on top of each
other in order to reach a higher altitude or have a
greater payload capacity.
Throat - The narrow opening of a rocket nozzle.
Thrust - The force from a rocket engine that
propels it.
Unbalanced Force - A force that is not countered by
another force in the opposite direction.
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NASA Resources
The National Aeronautics and Space Administration (NASA) has an amazing collection of resources for the
classroom. Educator guides, fact sheets, activity booklets, and lithographs, just to name a few, have been
developed and are free to download. Photo galleries, a video database, and a YouTube channel are also
available. Information about programs, projects, and current & future missions can be found on NASA’s
portal. To speed you and your students on your way to your space exploration adventure, a few useful links
are highlighted below.
NASA Portal – www.nasa.gov
Artemis Program – www.nasa.gov/specials/artemis/
Space Launch System – www.nasa.gov/sls
Orion – www.nasa.gov/orion
Exploration Ground Systems – www.nasa.gov/egs
STEM Engagement – www.nasa.gov/stem
Social Media – www.nasa.gov/socialmedia
Image Galleries – www.nasa.gov/multimedia/imagegallery/index.html
Videos – www.nasa.gov/multimedia/videogallery/index.html
YouTube Channel – www.youtube.com/user/NASAtelevision
NASA Centers – www.nasa.gov/about/sites/index.html
History – www.nasa.gov/topics/history/index.html
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