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Navworld
Quarterly Newsletter - The Navigator Winter Solstice December 21, 2001 Seasons Greetings |
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The
Institute of Navigation is holding the following meetings in 2002: 2002
National Technical Meeting
For more details contact www.ion.org
Surely
You’re Joking Mr. Feynman!
(From the book by this name first published by W.W. Norton & Company,
New York 1985) “Surely
You’re Joking Mr. Feynman!”
Feynman, the Noble Prize winner in physics, was so addressed by the
dean’s wife at his first afternoon tea at Princeton where he had entered
graduate school. She had asked him whether he would like cream or lemon in
his tea and he replied, “I’ll have both, thank you,” then he heard
“Heh-heh-heh-heh-heh.” He
learned that he had made a social error. Later in his illustrious career,
his name became legend in physics and soon the rest of the world was
treated to his national bestseller "Surely You're Joking Mr. Feynman!" revealing that humor
and physics were more than compatible.
At Cornell where he taught after a WWII tour at Los Alamos working
on the Manhattan Project, he observed a student in the cafeteria tossing a
plate in the air. Feynman
recalled in his book, which he wrote over thirty years later, that the
Cornell red medallion on the plate was spinning faster than it’s
wobbling. He retired to his office and worked out the physics of the
phenomenon. He recalled that the rotation rate was twice the frequency of
the wobble. He described his
finding to Hans Bethe; the famous atomic physicist, who had helped him get
his job, was not impressed with this diversion.
Undeterred, Feynman continued his studies in wobbles and applied
that knowledge to how electron orbits moved in relativity which he states
led to his winning the Nobel prize. What
is interesting is that he reversed the effect in describing the phenomenon
in his book; in reality the wobble frequency was twice the spin frequency.
A footnote in the book identifies the error that escaped
Feynman’s proof reading. Hidden in this complex motion was such a
stunning riddle. Was Feynman testing the reader to replicate the
experiment? Or had he simply forgotten the relationship through the years.
Feynman looked at the forces or dynamics in action and worked out the
motion of the mass particles and arrived at the two to one ratio.
This phenomenon is portrayed as a problem (with the wobble ratio
correctly stated) for the student to solve in Introduction to Space Dynamics by William Tyrell Thomson
in Chapter 5 Gyro Dynamics. Why do we care about this in navigation?
The tuned rotor gyro used in inertial navigation systems also illustrates
this phenomenon. The spin
frequency of the gyro has harmonics that rectify into a wobble frequency
of twice the spin frequency. If
the twice the frequency harmonic is not compensated for the gyro’s
performance is impaired. Litton Guidance and Control Systems found a
solution to this disturbing effect of twice spin rectification (known as
“2N” ) on the performance of its tuned rotor gyros by attaching
two symmetrical gimbals at right angles between the shaft and rotor which
reduced the heading sensitivity in the
platform to a trivial threshold and provided for excellent
long-term bias stability. Over
the Pole with Nowhere To Go In
a flight to the Pole on an acceptance test of an early generation astro
inertial doppler navigation system several decades ago, some members of
the system design team aboard for the test were challenged when the system
became disabled. The flight had impressively reached the Pole guided by
the astro inertial doppler system. The
systems engineer annoyed by the spinning longitudes that appeared on the
display at ultra high latitudes, temporarily disabled the updating routine
of longitude. When the Pole was reached, the aircraft was directed to its
inbound leg and the systems engineer entered the command to restore the
disabled routine erroneously. The
inertial platform unceremoniously tilted; the values on the displays began
to portray erroneous information. Ground
speeds rose to more than twice their true value.
The inertial platform was now useless. The design team became
deeply concerned over their plight. Would they find themselves and safely
return to their lower latitude base? What to do? they worried. At very
high latitudes, it was not feasible to realign the inertial navigation
system as the horizontal component of earth rate was too weak to be
useful. The team's navigator,
with former Air Force experience, was conditioned not to abort a mission
and thought he had a remedy. He engaged the periscopic sextant and
extended it to its celestial landscape. He selected one of the available
navigational stars and swung the periscopic sextant to its azimuth. He
then was able to read the true heading of the aircraft to within 0.5
degrees. He gave the reading
to the systems engineer and established the aircraft's approximate
position from the craggy icy land mass portrayed on the map and matched
with its radar image. The best he could judge the aircraft's position was
within five miles accuracy. The
systems engineer now had two of the three essential inputs for this
airborne re-alignment of the inertial navigation system using the
coordinates and true heading given to him. He obtained the third input,
velocity, from the doppler. By then the aircraft was over 200 nmi. south
of the Pole. The team was hopeful that they had resolved their difficult
dilemma. When they landed
several hours later with an error comparable to the heading uncertainty at
realignment, they were all relieved; the customer was impressed. The team
had successfully salvaged the mission and achieved what they believed was
the highest latitude airborne inertial alignment on record at that time
decades ago. Good
navigation requires not only constant vigilance but flexibility as well. When
a young navy lieutenant hitched a ride with an Air Force crew, which had
to fly just to the east of Italy, he was challenged by an avionics
failure. The ADF went out and the crew became disoriented. The lieutenant
volunteered his services and asked the crew if they had any nav equipment
on board--they did not. He then took a nav chart and matched buoy lights
flashing off a large landmass to the east. The land mass was Yugoslavia
and they were not very friendly at the time having shot down a C-47 a few
weeks earlier. It was growing dark, a thick cloud mass was below the C-47,
but the lieutenant managed to DR the C-47 over an Italian Air Force Base,
Travisio, just at the foot of a mountain range. The C-47 let down through
the soup, lo and behold Travisio was just below the plane, and the crew
and lieutenant spent the night as guests of the Italian Air Force. Ted
Graser tells his favorite Nav story, which can be, appreciated best by
another nav in a flight he had from Tokyo to Midway. "Shortly after
take off we lost almost all of our electronics; the boss (a brigadier
general who wanted to get home) said lets press on. I then was left with
only the radar and pressure altimeters, a sextant, the sun and the
temperature gauge as we headed for Midway Island.
Soon sun lines gave me my ground speed when I crossed them with my
pressure pattern derived line of position. All that remained was to watch
the temperature and the altimeter to make sure we were in the jet stream,
which reached 150 knots. We slid into Midway within two minutes of my ETA.
The boss and the pilots were really impressed but only another nav would
know how easy it was. For the non navigators, the difference between the
radar and pressure altimeter readings (adjusted by a constant) divided by
the elapsed air distance (from the last fix) provided me with the
crosswind component of the geotropic wind. This component was displaced
normal to the air path (to the left when flying into a high) to provide
the pressure line of position." Websightings Navworld
under the link Navworlds features the 12 Earthshapes each endowed with its
own attributes. The Wegeneroidal world depicts the Earth as envisioned by
the German geologist Alfred Wegener who in 1915 promulgated his theory of
continental drift on how the continents were once joined and then drifted
apart. Wegener found paleontological correlations on either side of the
southern Atlantic Ocean. His
theory met considerable resistance until 1960. For a more esoteric
treatment of the theory visit: http://www.gps.caltech.edu/~devans/iitpw/science.html Animal
navigation and migration are intriguing subjects that are developed in the
"The Secret of the Swallows" appearing under the link
Navcerebrations showing that both the daily solar shadow tip path and the
swallow's circadian mechanism (internal clock) play a role toward
triggering the annual return of the swallows of San Juan Capistrano.
Professor D. Gibo advances several theories on the navigation and
migration capabilities of the Monarch butterfly: Great Circle,
Magnetic-Latitude and Magnetocline hypotheses at http://www.erin.utoronto.ca/~w3gibo/index.htm. The theories
hinge on his belief that the butterflies can sense the Earth's magnetic
field. One
Long Hop "One
Long Hop" is an article by Capt. Eugene P. Rankin USN (Ret.) that
describes the flight of the P2V-1 Truculent Turtle one of earliest of this
series of Navy patrol planes just off the Lockheed Aircraft Corporation
production line in Burbank, CA. Its
planned itinerary was Perth Australia to Washington, DC., the longest
non-stop piston driven flight in history. The P2V-1 was named the Neptune
and was designed to fulfill the role of an ASW/Sea surveillance aircraft.
The flight took place from September 29 to October 2, 1946 with
Cdr. Tom Davies as pilot and Cdr. Eugene Rankin as co-pilot.
The aircraft was stripped of non-essential equipment and in
addition to the bomb bay tank, tanks were added to the outer wing panels,
wing tips, nose, rear fuselage, sonobuoy chute and with the inclusion of
the fuel network the fuel capacity was increased to 8592 gallons or 5,000
gallons greater than normal. The normal range for the P2V-1 of 4,000
statute miles was now extended dramatically. The Truculent Turtle’s gross weight at takeoff was 85,575
lbs with the 50,000 lbs. of fuel aboard.
The heavily laden Truculent Turtle took off from the 6,000-foot
runway aided by four JATO (jet-assisted takeoff) bottles that increased
the thrust by 25 percent for about 10 seconds. The nighttime take-off took
advantage of cooler air to gain altitude and the flight benefited from the
summer seasonal stronger tail winds aloft.
As the Turtle reached the US, freezing rain, snow and ice froze on
the wings and power had to be increased to 80% barely enough to sustain
flight. It became evident to
the crew that Columbus, Ohio was as far as the Turtle could reach. After
flying a distance of 11,235.6 statute miles for 55 hours and 17 minutes,
the Turtle landed. It had broken a previous held record of 7916 statute
miles for a non-stop B-29 flight from Guam to Washington, DC. The
Truculent Turtle record demonstrated that the P2V-1 had an extraordinary
global range and significantly increased ASW/Sea surveillance capability.
Cdr. Rankin was my battalion commander during my plebe year at the Naval
Academy. At the time, it was rumored that the crew of the Truculent Turtle
was unaware that the fuel manifest was in imperial gallons that would
increase their perceived fuel load by 20 percent. If we give credence to
this rumor, it is conceivable that the Truculent Turtle could reach its
original destination of Washington, D.C. But did the imperial gallon
manifest matter if the crew was relying solely on fuel gauge readings? I
also became acquainted with Captain Davies through ION activities but
failed to broach the subject of the imperial gallon gaff with either
Davies or Rankin. Solubility
of GPS Tested Christmas 1998 A
soggy Christmas was in store for a German couple who were relying on their
luxury car's GPS ended their drive in the Havel River six miles from
Berlin. The darkness of the
night and the absence of a warning cue from the GPS left the couple
unprepared for their watery encounter. Instead of an expected bridge, an
unannounced ferry crossing surprised the couple. Even electronic maps can
be misleading. Making
a Mountain Out of a Molehill In
the early Eighties I was intrigued by an interview conducted on PBS with
an atomic scientist who stated that there is a way to determine the
maximum theoretical height of a mountain on the Earth. The scientist
offered no further elaboration. I searched many libraries, bookstore
shelves and used web site search engines seeking the solution.
I finally found the topic included in the book The Cosmological Anthropic Principle by John Barrow and Frank Tipler.
I was elated with the simplicity of the explanation. The concept
became the ponderable "How High the Mountain" in the book Portney's
Ponderables. Dr. John
Barrow graciously furnished his derivation for the book. Since
then I have read more books on cosmology. I have found Paul Davies' book The
Accidental Universe (Cambridge University Press, 1982) to be
exceptionally good. The book
is suited for the reader with scientific inquisitiveness who has been
exposed to algebra and rudimentary physics. Davies also discusses the
maximum height for a mountain. The table for atomic fundamental constants
and derived quantities (which aids in following the derivation) is
furnished as well as a table listing the steps in the structural hierarchy
that builds our physical world. Davies explains that if a "bump"
(mountain) of a given height develops on a planet, it will impose a
pressure at its base and if sufficiently strong will melt the supporting
base material and permit the mountain to sink. If the potential energy of
the mountain becomes an appreciable fraction of the molecular binding
energy of the base material, then liquefaction will take place. This book
probes questions such as: Is our universe an accident? What is the meaning
of the anthropic principle? Are humans intimately locked into the
structure of the universe on all scales?
How does the very early universe relate of the cosmos of today?
Davies derives the equation for the theoretically highest mountain
for any planet that yields as the solution:
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