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Multidisciplinary
Design, Analysis, and
Optimization Branch
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EDUCATIONAL ACTIVITIES: THE NASA AEROQUIZ
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Week of 11/2/98:
Q:
In 1922, fantasy author Edgar Rice Burroughs wrote At the Earth's Core;
a story of a hollow Earth kingdom called Pellucidar. In the story,
adventurers drilled their way into the Earth. As they went ever deeper, the
force of gravity reversed direction, and they began climbing "up"
into the land of Pellucidar. When they "surfaced," they stood upright inside
the hollow shell of the Earth, held there by the gravity generated by the mass
of Earth directly beneath them. Assuming the Earth really is a hollow shell,
would gravitation work that way?
A:
No. In fact, it can be shown that there is no net force of gravity at all
inside a hollow Earth! The mass of the Earth directly under your feet would
indeed generate a gravitational force on you (as Burroughs surmised), but so
would the mass of Earth far over your head. Although the mass over your head
is far away, there is a lot more of it than the mass under your feet. For a
perfect spherical shell, you can mathematically show that the net force of
gravity is zero. In "reality," there would be small forces acting on you
due to mass concentrations within the Earth's crust, the centrifugal force
of the Earth spinning (about 0.3% of a "gee" at the equator), and because
the Earth is an imperfect sphere. But Burroughs was wrong -- You would float
in Pellucidar!
Congratulations to John D. Winstel.
Week of 11/9/98:
Q:
Last week's question made us realize how the Earth's gravity is often
misunderstood. For
an object in orbit around the Earth, the equations of motion for its trajectory
can be solved analytically if one assumes that the Earth is a "point mass."
That is, an assumption is made that all of the Earth's mass is concentrated at
a single point right at the Earth's center. This simplifies the equations of
motion such that they can be solved on the back of an envelope. This week's
question: how good is the "point mass" assumption?
A:
Luckily, gravity from a spherical mass (like a planet or a star) can be simply
described. The force of attraction on, say a satellite in Earth orbit, is
calculated by starting with the formula for Newton's law of gravitation.
The force from the satellite to the Earth is integrated across all of Earth's
"mass elements" in all directions. Since a sphere is symmetric,
it's easy to visualize that all forces acting normal to lines between the
satellite and the Earth cancel each other. When the simplified
integration is carried out, it is seen that the gravitational attraction
of the Earth is the same as if all of the Earth's mass were concentrated at
a single point! This is not only true of homogeneous spheres, but it's also
true for spheres with spherically symmetric (onion-like) shells of variable
density, like the Earth. Non-spherical objects with distributed mass do
not behave this way, and orbits around them would be very complex and would
require computational methods to describe them. Indeed, even the Earth
is an imperfect sphere with some mass concentrations, and small corrections
to the "point mass" approach are required for very precise calculations.
No one got the correct answer!
- The Aeroquiz Editor.
Week of 11/16/98:
Q:
This week, the Earth will pass through fresh debris left by comet
Tempel-Tuttle, providing viewers with the most intense meteor shower in
33 years. Since the biggest pieces are only the size of sand, the meteors will
easily burn up in the atmosphere and will pose no threat to anyone on Earth.
Experts, however, are very concerned about damage to satellites in Earth orbit.
At more than 150,000 miles per hour, a small grain can carry the destructive
force of a .22-caliber bullet. Although the meteoroids can poke holes in
solar panels, pit lenses, and blast off reflective coatings, experts
are more concerned about another kind of damage. What is it?
A:
The damage that is more harmful is the static electricity
that is discharged when the particles hit the satellite.
It can cause the satellite to lose all electrical power.
Congratulations to Jack Felici.
Given the high velocity of the Leonid meteoroids, their impact is an order of
magnitude larger when compared with typical background sporadic meteoroids.
The impact on orbiting satellites could be both mechanical and electrical.
Electrical damage could occur when meteoroids disintegrate upon impact with
the spacecraft. This could generate a plasma cloud as a result of ionization,
which could lead to electrostatic discharge on adjacent surfaces.
- The Aeroquiz Editor.
Week of 11/23/98:
Q:
When machine guns are used in aviation dogfights, incendiary tracer
bullets are often mixed with the ordinary bullets at regular intervals.
The incendiary coatings (often red phosphorus) ignite at about five hundred
degrees Fahrenheit as the tracers exit the muzzle, allowing the pilot to see
where the bullets are going. However, if the pilot aims exactly at where the
tracers are going, he is guaranteed to miss with the bulk of his ammunition!
Why?
A:
The combustion of the coating alters the surrounding airflow, and the
trajectories of the incendiary bullets are different than the ordinary bullets.
Congratulations to Nicolas Cousinea.
Tracer bullets provide a good example of drag reduction via "base burning."
The red phosphorus combustion effectively pressurizes the flat rear base
of the tracer bullet (an area that would otherwise be a low-pressure
recirculation zone) and greatly reduces its "base drag." The tracer
bullets fly significantly farther than ordinary bullets.
- The Aeroquiz Editor.
Week of 11/30/98:
Q:
In many conceptual designs for hypersonic airbreathing aircraft, the
vehicle's fuel flow rate requirement is often much more than what the engine
can effectively burn. In some flight regimes, it can be several
times the fuel flow rate required for complete combustion. Why?
A:
The fuel is the only heat sink available. The heat loads are huge.
Evaporation is very likely required. So, keep the fuel flowing whether
you need it for propulsion or not, or you will become cooked meat.
Congratulations to Joe Eisenberg.
Hypersonic speeds produce a very hostile flight environment. The friction
of the air on the exterior surface of the vehicle can produce temperatures of
several thousand degrees. In virtually all hypersonic airbreathing aircraft
designs, fuel is used as a heat sink to cool the hot exterior surfaces of the
vehicle and the even more hostile environment around the high-speed engines.
If the flight speed is sufficiently high, the fuel demand for vehicle and
engine cooling is higher than what the engine needs for combustion.
- The Aeroquiz Editor.
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