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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 9/4/00:
The 2000 Olympics are here! Second in a series of Olympian quiz questions!
Q:
In many events, track and field athletes can take advantage of low aerodynamic
drag. The reduced drag that occurs on hot days and high altitudes, for example,
has been attributed to helping U.S. athlete Bob Beamon break, in Mexico City
in 1968, what was then the world long jump record by almost two feet.
Would an airplane also experience better performance trying to take off from
a high altitude field on a hot day?
A:
Ever hear about hot and high takeoffs? First, the lift generated by a
wing is a function of the mass of air flowing around it. So, as both
altitude and heat decrease the air density, a wing traveling in air such as
Mexico City's is much less effective. Second, the power output of a jet
engine is, in part, a function of the difference in temperature between
the inlet and the turbine entry. More air will be burned in a cooler
atmosphere.
Congratulations to Nicholas Cousineau.
Although drag is indeed less on a hot day at high altitude, so is lift!
Jet engine thrust also suffers substantially. The low-density air results in a
reduced flow rate through the engine. So, thanks to Newton, we know the
force of thrust is penalized. The nozzles also have less enthalpy difference
to work with, and, for you thermodynamic cycle analysis fans out there,
the engine's integral of TdS is smaller!
- The Aeroquiz Editor
Week of 9/11/00:
The 2000 Olympics are here! Third in a series of Olympian quiz questions!
Q:
The discus throw was known in the days of the Greek poet Homer,
who mentioned it repeatedly, and it was one of the five events included
in the pentathlon in the ancient Olympic Games. The discus throw was
introduced as an event in the first modern Olympic Games at Athens in 1896.
In the discus throw, the athlete makes about one and a half quick,
graceful turns and slings the discus away while imparting a certain
amount of spin to it. A portion of the total force applied to the discus
during the throw must be expended in order to spin it. Would a discus
thrower be better off if all of the force could be applied to propelling
the discus forward rather than expending some of the force to spin it?
A:
A discus, when thrown without any spin, would behave like an unconstrained
low aspect ratio wing. The pitching moment would quickly tumble the discus,
presenting the full planform area to the freestream flow: not good for range!
Essentially a highly loaded frisbee, the discus gains stability from the
spin. The aerodynamically-induced gyroscopic precession loads acting to
tip it sideways are small compared to the rotational inertia of the discus.
Congratulations to Andrew White.
Spinning has long been known to stabilize
objects that are otherwise unstable. Even with
spin, a discus is difficult to properly stabilize. One of the skills a
beginning discus thrower needs to develop is to spin the discus nearly
perfectly about the principal axis that passes through the center and
perpendicular to the disc. Unless thrown with precision, the discus
can easily become unstable in flight and wobble erratically.
- The Aeroquiz Editor
Week of 9/18/00:
The 2000 Olympics are here! Fourth in a series of Olympian quiz questions!
Q:
In some racing events, the lines that separate individual race lanes
have helped to improve athletes' times. How could this be?
A:
In swimming, the line barriers help the racers by reducing the drag
caused by those in the next lane.
Congratulations to Jesse Newman.
Jesse figured out that the events I had in mind are for swimming,
not track! "Lanelines" are the dividers
used to separate individual swim lanes in a competitive pool. They
are made of small finned disks strung on a cable. Each disk is designed
to rotate independently of the others. The disks rotate on the cable
when hit by a wave and absorb and dissipate wave energy within the
channel of each lane. This wave reduction reduces hydrodynamic drag
on the swimmers and helps to improve their times.
- The Aeroquiz Editor
Week of 9/25/00:
The 2000 Olympics are here! Fifth in a series of Olympian quiz questions!
Q:
Many Olympic events, such as the ten meter platform dive and
several of the gymnastic events, involve athletes spinning in
free fall conditions. In the physics of dynamics, the principal
axes of a symmetrically-shaped rigid object are defined as
the set of axes going through the object's lines of symmetry. Let's
assume that a diver falling from a platform could hold his body in a
symmetrical rigid position. Would it be a good idea for him to
spin about his principal axis with the intermediate moment of inertia?
That is, not the axis with either the largest or smallest moment of
inertia, but rather the one with the "in between" moment of inertia.
This is a tough question! Hint: Check out Euler's equations of motion!
A:
Okay, so this was a pretty obtuse question and no one got the correct answer.
Here's what I was trying to get at:
A symmetric rigid body spinning about its principal axis with
the "in between" moment of inertia is unstable! And unstable spinning
certainly wouldn't impress the judges. This is an interesting
problem that is usually covered in advanced engineering dynamics classes.
The unforced Euler equations for rigid body motion can be reduced and
analyzed as a really cool eigenvalue problem. Note that I type the phrase
"really cool eigenvalue problem" at my own peril. You can see this
for yourself. Take a board or a hardcover book and tape it closed.
You will be able to easily spin it without tumble about two of the axes
(see Quicktime movies
"Axis 1" (497 kB) and
"Axis 2" (383 kB) ),
but it will tumble about the third axis
(
"Axis 3" (673 kB) ).
- The Aeroquiz Editor
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