Tag Archives: Tom Logsdon

GREAT OLD, BIG, HUGE BLACK HOLES

In 1905 Albert Einstein employed one of the most powerful brains on planet Earth to puzzle out an elusive concept called “The Special Theory of Relativity”.  Ten years later he used those same brain cells to develop his even more powerful “General Theory of Relativity”.

Figure 1 highlights his most dramatic proposal for proving – or disproving! – his General Theory of Relativity.  The test he proposed had to take place during a total eclipse of the sun.  For, according to The General Theory of Relativity, light from a more distant star would be bent by about one two-thousandths of a degree when it swept by the edge of the sun.

Four years later (in 1919) the talented British astronomer Arthur Eddington in pursuit of a total eclipse of the sun, ventured to the Crimean Peninsula to perform the test Einstein had proposed based on the idea that “starlight would swerve measurably as it passed through the heavy gravity of the sun, a dimple in the fabric of the universe.”*

A black hole comes into existence when a star converts all of its hydrogen into helium and collapses into a much smaller ball that is so dense nothing can escape from its gravitational pull, not even light.

Capture3

Figure 1:  In 1915, when he finally worked out his General Theory of Relativity, Albert Einstein proposed three clever techniques for testing its validity.  Four years later, in 1919 the British astronomer, Arthur Eddington, took advantage of one of those tests during a total eclipse of the sun to demonstrate that, when a light beam passes near a massive celestial body, it is bent by the local gravitational field as predicted by Einstein’s theory.  This distinctive bending is similar to the manner a baseball headed toward home plate is bent downward by the gravitational pull of the earth.

The existence of black holes was inadvertently predicted by a mathematical relationship Sir Isaac Newton understood and employed in 1687 in developing many of his most powerful scientific predictions, including the rather weird concept of escape velocity.  As Figure 2 indicates, it is called the Vis Viva equation.

Start by solving the Vis Viva equation for the radius Re, then plug in the speed of light, C, as a value for the escape velocity, Ve.  The resulting radius Re is the so-called “event horizon”, which equals the radius at which light cannot escape from an extremely dense sphere of mass, M.  As the calculation on the right-hand side of Figure 2 indicates, if we could somehow compressed the earth down to a radius of 0.35 inches – while preserving its total mass light waves inside the sphere would be unable to escape and, therefore, could not be seen by an observer.  The radius of the event horizon associated with a spherical body of mass, M, is directly proportional to the total mass involved.

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Figure 2:  The Vis Viva equation was developed and applied repeatedly by Isaac Newton when he was evaluating various gravity-induced phenomena.  Properly applied, the Vis Viva equation predicts that sufficiently dense celestial bodies generate such strong gravitational fields that nothing – not even a beam of light – can escape their clutches.  Today’s astronomers are discovering numerous examples of this counterintuitive effect.  Black holes are one result.

As Figure 3 indicates, an enormous black hole 50 million light years from Earth has been discovered to have a mass equal to 2 billion times the mass of our sun.   It is located in the M87 Galaxy in the constellation Virgo.

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Figure 3:  In 1994 the Hubble Space Telescope discovered a huge black hole approximately 300,000,000,000,000,000,000,000 miles from planet Earth nestled among the stars of the M87 galaxy in the Virgo constellation.  Astronomers estimate that it is 2,000,000,ooo times heavier than our son.  That black hole’s event horizon has a radius of 3,700,000,000 miles or about 40 astronomical units. One astronomical unit being the distance from the earth to our sun.The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

See all the ATI open-enrollment course schedule

https://www.aticourses.com/schedule.html

See all the ATI courses on 1 page.

What courses would you like to see scheduled as an open-enrollment or on-site course near your facility?

ATI is planning its schedule of technical training courses and would like your recommendations of courses

that will help your project and/or company.

These courses can also be held on-site at your facility.

http://www.aticourses.com/catalog_of_all_ATI_courses.htm

 

 

DEORBITING SPACE DEBRIS FRAGMENTS USING ONLY EQUIPMENT LOCATED ON THE GROUND

The researchers at NORAD*, which is located under Cheyenne Mountain in Colorado Springs, Colorado, are currently tracking 20,000 objects in space as big as a softball or bigger.  Most of these orbiting objects are space debris fragments that can pose a collision hazard to other orbiting satellites such as the International Space Station.

Tracking these fragments of debris is complicated and expensive.  Preventing collisions is expensive, too.  So, too, is designing and building space vehicles that can withstand high-speed impacts.  A cheaper alternative may be to sweep some of the debris out of space to minimize its hazard to other orbit-crossing satellites.

When two orbiting objects collide with one another, the energy exchange can be large and destructive.  Two one-pound fragments impacting each other in a solid collision in low-altitude orbits intersecting at a 15-degree incidence angle can create the energy caused by exploding two pounds of TNT!!

One scientific study showed that returning substantial numbers of debris fragments to Earth with a hydrogen-fueled spaceborne tug would cost approximately $3 billion for each percent reduction in the fragment population – which has been increasing by about 12 percent per year, on average.

Fortunately, a powerful, but relatively inexpensive laser on the ground pointing vertically upward can be used to deorbit fragments of space debris traveling around the earth in low-altitude orbits.  The radial velocity increment provided by such a ground-based laser causes the object to reenter the earth’s atmosphere as shown in  the sketch in the upper left-hand corner of Figure 1.

The total required velocity increment can be added in much smaller increments a little at a time over days or weeks.  Drag with the atmosphere was neglected in the case considered in Figure 1, but, in the real world, atmospheric drag would help the object return to Earth.

Radiation pressure created by the assumed 50,000 watt laser beam is equivalent to 40 suns spread over the one square foot cross section of the object.  The total photon pressure equals 1/13th of a pound per square foot.

*  NORAD = North American Aerospace Defense (Command)

Figure1The researchers at NORAD*, which is located under Cheyenne Mountain in Colorado Springs, Colorado, are currently tracking 20,000 objects in space as big as a softball or bigger.  Most of these orbiting objects are space debris fragments that can pose a collision hazard to other orbiting satellites such as the International Space Station.

Tracking these fragments of debris is complicated and expensive.  Preventing collisions is expensive, too.  So, too, is designing and building space vehicles that can withstand high-speed impacts.  A cheaper alternative may be to sweep some of the debris out of space to minimize its hazard to other orbit-crossing satellites.

When two orbiting objects collide with one another, the energy exchange can be large and destructive.  Two one-pound fragments impacting each other in a solid collision in low-altitude orbits intersecting at a 15-degree incidence angle can create the energy caused by exploding two pounds of TNT!!

One scientific study showed that returning substantial numbers of debris fragments to Earth with a hydrogen-fueled spaceborne tug would cost approximately $3 billion for each percent reduction in the fragment population – which has been increasing by about 12 percent per year, on average.

Fortunately, a powerful, but relatively inexpensive laser on the ground pointing vertically upward can be used to deorbit fragments of space debris traveling around the earth in low-altitude orbits.  The radial velocity increment provided by such a ground-based laser causes the object to reenter the earth’s atmosphere as shown in  the sketch in the upper left-hand corner of Figure 1.

The total required velocity increment can be added in much smaller increments a little at a time over days or weeks.  Drag with the atmosphere was neglected in the case considered in Figure 1, but, in the real world, atmospheric drag would help the object return to Earth.

Radiation pressure created by the assumed 50,000 watt laser beam is equivalent to 40 suns spread over the one square foot cross section of the object.  The total photon pressure equals 1/13th of a pound per square foot.

*  NORAD = North American Aerospace Defense (Command)

Figure2

Figure 2:  These engineering calculations show that the 20,000 space debris fragments now circling the earth in low-altitude orbits could, on average, each be deorbited with ground-based lasers for approximately $40,000 worth of electrical power.  Those same ground-based lasers could be used in a different mode to reboost valuable or dangerous payloads in low-altitude orbits or to send those payloads bound for geosynchoronous orbits onto their transfer ellipses.  (SOURCE:  Short course “Fundamentals of Space Exploration”.  Instructor: Tom Logsdon. (Seal Beach, CA)

See all the ATI open-enrollment course schedule

https://www.aticourses.com/schedule.html

See all the ATI courses on 1 page.

What courses would you like to see scheduled as an open-enrollment or on-site course near your facility?

ATI is planning its schedule of technical training courses and would like your recommendations of courses

that will help your project and/or company.

These courses can also be held on-site at your facility.

http://www.aticourses.com/catalog_of_all_ATI_courses.htm

OUR MOON QUIETLY GROWS TO SUPERMOON SIZE

 


Tom Logsdon
“Hi diddle diddle,
The cat and the fiddle,
The cow jumped over the moon.
The little dog laughed,
To see such fun,
And the dish ran away with the spoon.”
My mother taught me that playful English nursery rhyme when I was about nine years old..
Notice how the poet who wrote it couldn’t think of anything more fanciful than having a living,
breathing creature ending up in the vicinity of the moon!
It took 300,000 of us a full decade of very hard work, but we did it! We sent two dozen
astronauts on the adventure of a lifetime and we brought all of them back alive. In 1961
President John F. Kennedy, youthful and exuberant and brimming over with confidence,
announced to the world that America’s scientists and engineers would—within a single decade
—land a man on the moon and return him safely to the earth. No cows need apply. But
potential human astronauts were bigly and hugely enthusiastic about their new opportunity
to fly through space to a different world.
By using the math and physics we had learned in school, we covered hundreds of pages with
with cryptic mathematical symbols to work out the details down to a gnat’s eyebrow.
We ended up hurling 24 American astronauts into the vicinity of the moon!. 12 of them
“kangaroo hopped“ on its surface.
Earlier this month, when the moon grew to its maximum apparent size, we were all reminded of
the excitement we felt during Project Apollo. Of course, the size of the moon did not actually
change, it merely moved up to its point of closest approach.
Systematic perturbations on the moon’s orbit coupled with rhythmic variations in its distance
from the Earth as it traveled around its elliptical orbit resulted in surprisingly large variations
in its apparent size and its brightness as seen from the Earth.
These distance variations, in turn, cause its observed diameter and its brightness to vary by as
much as 15 and 30 percent, respectively. When the moon approaches its maximum apparent
size and brightness, it is characterized as a supermoon. The biggest and brightest supermoons
are spaced out several decades apart.
My son, Chad, who participates in Special Olympics, used his cellphone camera to create the
two photographs that accompany this blog. He took the first picture at the crack of dawn
when the moon reached its maximum diameter at the edge of the parking lot at the Embassy
Suites Hotel in Lexington, Kentucky (population 360,000). He made the second photograph
12 hours later in my hometown of Springfield, Kentucky, ((population 2900). That second
picture was made on a small roadside hill beside the Bardstown Road above the IGA
Supermarket within sight of the yellow blinker light at the edge of town.
Author and short-course instructor, Tom Logsdon, who wrote this article, teaches the Launch
and Orbital Mechanics short course for The Applied Technology Institute. Click here for more
information on that course. He also teaches the GPS and Its International Competitors short
course. Click here for more information.

Super-Moon Photos and Facts

One of the super-moon photos is a humorous hoax. Can you spot it? We knew that ATI’s instructors are world-class experts. They are the best in the business, averaging 25 to 35 years of experience, and are carefully selected for their ability to explain advanced technology in a readily understandable manner. We did not know that many are talented photographers. We challenged them to take some photographs of the November 13-14 super-moon.  See our previous post and then the resulting photographs.

http://www.aticourses.com/blog/index.php/2016/11/13/get-your-camera-ready-super-moon-november-13-14/

Tom Logsdon, who teaches Orbital & Launch Mechanics – Fundamentals provided us some of the orbits key parameters.

Here are the best, most appropriate, average orbital parameters for Earth’s.

perigee radius: 363,300 Km (for the super-moon it was 356,508 Km (or 221,524 miles)

apogee radius: 405,400 Km

Inclination to the ecliptic plane: 5.145 deg

(the plane containing the Earth and the moon)

orbital eccentricity: 0. 0549 (sometimes quoted as 5.49 percent)

recession rate from the Earth: 3.8 cm/yr

Siderial month: 27.3 days

Synodic month: 29.5 days

( the sidereal month is the time it takes for the moon to make one 360 deg trip around the earth;

the synodic month is the month we observe from the spinning earth…it involves a few extra degrees of travel beyond the sidereal month)

Dr. Peter Zipfel Shalimar, Florida

  Dr. Peter Zipfel

Six Degree of Freedom Modeling of Missile and Aircraft Simulations

Aerospace Simulations In C++

  James  Jenkins, Riva, MD

Sonar Signal Processing

 Matt Moran, Windsor, Ontario, Canada

Engineering Systems Modeling with Excel / VBA

Thermal & Fluid Systems Modeling

  Matt Moran, Windsor, Ontario, Canada

Richard Carande, Denver, CO

Fundamentals of Synthetic Aperture Radar

Advanced Synthetic Aperture Radar

Richard Carande, Denver, CO

The photos that beat them all! Taken by the wife or Matt Moran

ELON MUSK AND COLLEAQGUES RESURRECTING THE GIANT TELEDESIC S CONSTELLATION

Elon Musk in SpaceX in Hawthorne, California, seems to become enamored by a new grandiose idea every week or so. And this week was no exception. This time he and his well-heeled colleagues are trying to find a way to serve the 3 billion earthlings hunkering down at scattered locations around the globe lacking service by modern cellphones or conventional telephones.

The solution? Launch a giant swarm of broadband communication satellites into low-altitude circular orbits flying in a tight formation with one another as they circle around the globe. It is called OneWeb.

300-pound satellites are to be launched into 18 orbit planes with 40 satellites following one another in single file around each plane. Ku-band transmitters will provide satellite-based cellphone services to remote and underserved users everywhere in the world. Mass production techniques and the economies of scale should help keep the cost of each individual satellite in the $500,000 range. Recently the OneWeb satellites passed their preliminary design review at the famous satellite design center in Toulouse, France. OneWeb’s total network cost, including a widely dispersed network of gateway Earth stations, is expected to come in at about $3.5 billion, provided the cost-conscious satellite-makers in Exploration Park, Florida, can come in within their target budget. Company spokesmen ha ve indicated that, so far, their team members are on schedule and within 5% of their estimated costs.

About 15-percent of the $3.5 billion has been raised and has been funding about 300 full-time experts. Present schedules call for initial money-raising services to being in 2019. Some industry experts have been calling the concept the O3b “other three billion”, for the three billion widely distributed individuals unserved by mobile or hard-wired telephones.

Elon Musk is famous for turning wild ideas into practical reality and squeezed out impressive profits along the way. Many of his ideas have been floating around for some time when he decides to take a shot at turning them into reality. An earlier version of OneWeb was touted by Edward Tucks in the 1970’s. It was called Teledesic.

The Teledesic concept sprang to life because Tucks read that “40 million people (were) on the waiting list for telephone services around the world.” He quietly sketched up the plans for an 840-satellite constellation of communication satellites flitting through space in 435-mile orbits.

Launch costs were a big barrier then. But Elon Musk can now put a big dent in that problem with his surprisingly inexpensive Falcon boosters.

Tom Logsdon, the author of this blog teaches short courses for the Applied Technology Institute in Riva, Maryland. He will be discussing, in detail, the rapidly evolving OneWeb plans as they are springing from the drawing boards in the following short courses:

The author of this article, Tom Logsdon, teaches short courses, on a regular basis, for the Applied Technology Institute in Riva, Maryland. Here is his upcoming schedule of courses:

GPS and International Competitors Dec 5-8, 2016 Colorado Springs, CO
GPS and International Competitors Apr 17-20, 2017 Columbia,MD
Orbital & Launch Mechanics – Fundamentals Jan 23-26, 2017 Albuquerque, NM
Orbital & Launch Mechanics – Fundamentals Feb 28-Mar 3, 2017 Columbia, MD

Click here for further information: ATIcourses, Tom Logsdon

Eric Clapton, Tom Logsdon, & the Kitchen Stove: A Tiny Tale of Creativity & Innovation

Last week when a customer had questions I talked with Tom Logsdon about the 6 methods of training used in his

Creativity & Innovation course. The six methods are spelled out in his book Six Simple Creative Solutions that

Shook the World. Tom is a mathematician and rocket scientist by training (and he teaches courses on GPS and

Orbital & Launch Mechanics in his spare time) who teaches creativity paired with discipline.

Yesterday, my husband called to alert me to a minor crisis at home. Our 2 year old gas stove, both burners and

oven, had ceased to heat. It was fine at breakfast and not at lunch. Although fueled by gas it has electric igniters.

During the phone call we took a scientific approach.

Six Simple Creative Solutions that Shook the World #1: Break your problem apart & put it back together:

we concluded that since the burners could be started with a lighter that the problem was not in the gas

feed. Additionally, the digital clock didn’t work. Everything pointed to something electric. However, the

circuit breaker was fine.

Later, when I came home we pulled the stove out and

6SCStStW #2: Take a fresh look at the interfaces. The electric connection appeared secure on both ends

and it didn’t work with an alternate outlet.

By this time -in a too-crowded kitchen with a malfunctioning appliance- the (wall) clock was ticking, no food was

being prepared and my husband and mother were chomping at the bit. I reached for the iPod, plugged it in to the

speaker and turned on some vintage Eric Clapton Unplugged….and nothing…..happened. Zero sound. Then the

Eureka moment occurred! Or

6SCStStW #6. Happy Serendipity. Believe me, I needed those mellow acoustic notes. That is when I

realized that the outlet circuit had tripped. I hit the reset button and Voila! Eric Clapton strummed the

guitar and Chuck Leavell dazzled on the piano.

Electricity was restored to the stove and dinner was prepared and served. Thank you Tom Logsdon & Eric Clapton!

Note: Tom Logsdon’s Creativity & Innovation course is available for training at your facility.

APPLIED TECHNOLOGY INSTITUTE INSTRUCTOR, TOM LOGSDON, HELPS INTERNATIONAL SURVEYORS MASTER THEIR CRAFT

Instructor Tom Logsdon, turquoise shirt at front center, poses with some of his students at the United Nations Humanitarian Center located on the heel of the boot in Brindisi, Italy. Over a period of five days, the students learned how to use the GPS-based radio navigation system to survey their countries with extreme precision. The students and their instructors were flown into Brindisi by the United Nations from various other countries around the globe.

In June 2014 while on assignment for the Applied Technology Institute in Riva, Maryland,

Logsdon and his professional colleague, Dr. Moha El-Ayachi, a professor at Rabat, Morocco,

taught a group of international students who were flown into the United Nations Humanitarian

Services Center in Brindisi, Italy. The students came in from such far-flung locales as Haiti,

Liberia, Georgia, Western Sahara, the South Sudan, Germany, and Senegal to learn how to

better survey land parcels in their various countries. Studies have shown that if clear,

unequivocal boundaries defining property ownership can be assured to the citizens of a Third-

World Country, financial prosperity inevitably follows. By mastering modern space-age

surveying techniques using Trimble Navigation’s highly precise equipment modules, the

international students were able to achieve quarter-inch (1 centimeter) accuracy levels for

precise benchmarks situated all over the globe.

This was Logsdon’s second year of teaching the course in Brindisi and the Applied Technology

Institute has already been invited to submit bids for another, similar course with the same two

instructors for the spring of 2015. The students who converged on Brindisi were all fluent in

English and well-versed in American culture. Their special skills were especially helpful to their

instructors, Tom and Moha, who trained them to use the precisely timed navigation signals

streaming down from the 31 GPS satellites circling the Earth 12,500 miles high.

The DOD’s Request for Proposal for the GPS navigation system was released in 1973.

Rockwell International won that contract to build 12 satellites with the total contract value of

$330 million. Over the next dozen years, the company was awarded a total of $3 billion in

contracts to build more than 40 GPS navigation satellites. Today 1 billion GPS navigation

receivers are serving satisfied users all around the globe. The course taught by Tom and Moha

covered a variety of topics of interest to specialized GPS users: What is the GPS? How does it

work? What is the best way to build or select a GPS receiver? How is the GPS serving its user

base? And how can specialize users find clever new ways accentuate its performance?

The GPS constellation currently consists of 31 satellites. That specialized constellation provides

at least six-fold coverage to users everywhere in the world. Each of the GPS satellites transmits

precisely timed electromagnetic pulses down to the ground, that require about one 11th of a

second to make that quick journey. The electronic circuits inside the GPS receiver measure the

signal travel time and multiply it by the speed of light to obtain the line-of-sight range to that

particular satellite. When it has made at least four ranging measurements to a comparable

number of satellites, the receiver employees a four-dimensional analogy of the Pythagorean

theorem to determine its exact position and the exact time. This solution utilizes four equations

in four unknowns: the receiver’s three position coordinates and the current time. The GPS

system must keep track of time intervals to an astonishing level of precision. A radio wave

moving through a vacuum travels a foot in a billionth of a second. So an accurate and effective

GPS system must be able to keep track of time to within a few billionths of a second. This is

accomplished by designing and building satellite clocks that are so accurate and reliable they

would lose or gain only one second every 300,000 years. These amazingly accurate clocks are

based on esoteric, but well-understood principles, from quantum mechanics. Despite their

amazing accuracy, the clocks on board the GPS satellites must be re-synchronized using

hardware modules situated on the ground three times each and every day.

The timing measurements for the GPS system are so accurate and precise Einstein’s two

famous Theories of Relativity come into play. The GPS receivers located on or near the ground

are in a one-g environment and they are essentially stationary compared the satellites whizzing

overhead. A GPS satellite travels around its orbit at a speed of 8600 miles per hour and the

gravity at its 12,500-mile altitude above the earth is only six percent as strong as the gravity

being experienced by a GPS receiver situated on or near the ground. The difference in speed

creates a systematic distortion in time due to Einstein’s Special Theory of Relativity. And the

difference in gravitational attraction creates a systematic (and predictable) time distortion due to

Einstein’s General Theory Of Relativity. If the designers of the GPS navigation system did not

understand and compensate for these relativistic time-dilation effects, the GPS radionavigation

system would, on average, be in error by about 7 miles. Fortunately, today’s scientists and

engineers have gradually developed a firm grasp of the mathematics associated with relativity

so they are able to make extremely accurate compensations to all of the GPS navigation

solutions. The positions provided by the GPS, for rapidly moving users such as race cars and

military airplanes, are typically accurate to within 15 or 20 feet. For the stationary benchmarks of

interest to professional surveyors, the positioning solutions can be accurate to within one

quarter of an inch, or about one centimeter.

Tom Logsdon has been teaching short courses for the Applied Technology Institute

(www.ATIcourses.com) for more than 20 years. During that interval, he has taught nearly 300

short courses, most of which have spanned 3 to 5 days. His specialties include “Orbital and

Launch Mechanics”, “GPS Technology”, “Team-Based Problem Solving”, and “Strapped-

Down Inertial Navigation Systems”.

Logsdon has written and sold 1.8 million words including 33 nonfiction books. These have

included The Robot Revolution (Simon and Schuster), Striking It Rich in Space (Random

House), The Navstar Global Positioning System (Van Nostrand Reinhold), Mobile

Communications Satellites (McGraw-Hill), and Orbital Mechanics (John Wiley & Sons). All of

his books have sold well, but his best-selling work has been Programming in Basic, a college

textbook that, over nine printings, has sold 130,000 copies. Logsdon also, on occasion, writes

magazine articles and newspaper stories and, over the years, he has written 18,000 words for

Encyclopaedia Britannica. In addition, he has applied for a patent, help design an exhibit for

the Smithsonian Institution, and helped write the text and design the illustrations for four full-

color ads that appeared in the Reader’s Digest.

In 1973 Tom Logsdon received his first assignment on the GPS when he was asked to figure

out how many GPS satellites would be required to provide at least fourfold coverage at all times

to any receiver located anywhere on planet Earth. What a wonderful assignment for a budding

young mathematician! Working in Technicolor— with colored pencils and colored marking pens

on oversize quad-pad sheets four times as big as a standard sheet of paper— Logsdon used

his hard-won knowledge of three-dimensional geometry, graphical techniques, and integral

calculus to puzzle out the salient characteristics of the smallest constellation that would provide

the necessary fourfold coverage. He accomplish this in three days— without using any

computers! And the constellation he devised was the one that appeared in the winning

proposal that brought in $330 million in revenues for Rockwell International.

Even as a young boy growing up wild and free in the Bluegrass Region of Kentucky, Tom

Logsdon always seemed to have an intuitive understanding of and subtle mathematical

relationships of the type that proved to be so useful in the early days of the American space

program. His family had always been “gravel-driveway poor.” At age 18 he had never eaten in a

restaurant; he had never stayed in a hotel; he had never visited a museum. But, somehow, he

managed to work his way through Eastern Kentucky University as a math-physics major while

serving as the office assistant to Dr. Smith Park, head of the mathematics department. He also

worked as the editor of the campus newspaper, at a noisy Del Monte Cannery in Markesan,

Wisconsin, and as a student trainee at the Naval Ordnance Laboratory in Silver Spring,

Maryland.

Later he earned a Master’s Degree in Mathematics from the University of Kentucky where he

wrote a regular column for the campus newspaper, played ping-pong with the number 9

competitor in the America, and specialized in a highly abstract branch of mathematics called

combinatorial topology. In his 92-page thesis, jam-packed with highly abstract mathematical

symbols, he evaluated the connectivity and orientation properties of simplicial and cell

complexes and various multidimensional analogies of Veblin’s Theorem.

Soon after he finished his thesis, Logsdon accepted a position as a trajectory and orbital

mechanics expert at Douglas Aircraft in Santa Monica, California. His most famous projects

there included the giant 135 foot-in-diameter Echo Balloon, the six Transit Navigation Satellites,

the Thor-Delta booster, and the third stage of the Saturn V moon rocket. A few years later, he

moved on to Rockwell International in Downey, California, where he worked his mathematical

magic on the second stage of the Saturn V, the four manned Skylab missions, the 24-satellite

constellation of GPS radionavigation satellites, the manned Mars mission of 2016, various

unmanned asteroid and comet probes, and the solar-power satellite project which, if it had

reached fruition, would have incorporated at least 100 geosynchronous satellites each with a

surface area equal to that of Manhattan Island (about 20 square miles).

Among his proudest accomplishments at Rockwell International was the clever utilization of nine

different branches of advanced mathematics, in partnership with his friend, Bob Africano, to

increase the performance capabilities of the Saturn V moon rocket by 4700 extra pounds of

payload bound for the moon — each pound of which was worth five times its weight in 24 karat

gold! These important performance gains were accomplished without changing any of the

hardware elements on the rocket. Logsdon and Africano, instead, employed their highly

specialized knowledge of mathematics and physics to work out ways to operate the mighty

Saturn V more efficiently. This involved shaping the trajectories of the rocket for maximum

propulsive efficiency, shifting the burning mixture ratio in mid flight in an optimal manner, and

analyzing their six-degree-of-freedom post-flight trajectory simulations to minimize the heavy

reserve propellants necessary to assure completion of the mission. These powerful

breakthroughs in math and physics led to a saving of $3.5 billion for NASA – an amount equal to

the lifetime earnings of 2000 average American workers!

Currently, Logsdon and his wife, Cyndy, live in Seal Beach, California. Logsdon is now retired

from Rockwell International, but he is still writing books, acting as an expert witness in a variety

of aerospace-related legal cases, lecturing professionally at big conventions, and teaching

short courses on rocket science, orbital mechanics, and GPS technology at major universities,

NASA bases, military installations, and at a variety of international locations. Prior to his recent

trips to Italy, Logsdon delivered two lectures at Hong Kong University in southern China and

taught two short courses at Stellenbach University near Cape Town, South Africa. Over the past

30 years or so he has taught and lectured at 31 different countries scattered across six

continents. At the International Platform Association meetings in Washington, DC, two of his

presentations in successive years placed in the top 10 among the 45 professional platform

lecturers making presentations there. Colleges and Universities that have sponsored his

presentations have included Johns Hopkins, Berkeley, USC, Oxford, North Texas University,

the International Space University in Strasbourg, France, Saddleback.


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DR. ROBERT NELSON: AN EXCELLENT SHORT COURSE INSTRUCTOR, WILL BE SORELY MISSED

The tribute below was written by Mr. Tom Logsdon, a long standing instructor for ATI Courses.

Dr. Robert Nelson, friend and colleague, will be sorely missed.  He lost his battle with cancer after a long and illustrious career serving his students and those who enjoyed interacting with him and reading his lucid prose.

Bob taught down the hall from my various scattered classrooms several times.  And, when time permitted, I always snatched the opportunity to sit in on his exceptional lectures.  He was always clear and logical and well organized.  And interesting ideas and concepts seemed to spill out of his mouth with remarkable ease.  He wrote in the same manner he spoke – always exhibiting strong rapport with his many enthusiastic students hanging on every word.

He will be sorely missed by his students, his colleagues and his many friends.

Read more about Bob’s remarkable career.


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The Bumpy Road to Space

The recent abort, and eventual successful launch, of the Space-X mission to resupply the space station is one of many bumps in the road to commercial space.  One should not expect the road to be smooth, or that replacing a Russian supply system with over a half century and almost 1,000 missions in its heritage will be easy.  While we all hope that the commercial efforts of such companies as Space-X and Orbital Science Corporation will succeed, we also know many problems will arise.

According to Ed Keith, an ATI teacher of rocket and missile design and technology, the NASA commercial space road is a major step in the right direction.  On the other hand, he sees many bumps along that same road.  Historically, American launch vehicles have been developed and operated with large government budgets.  New commercial ventures have an incentive to do the same type of missions at much lower cost.  This means that some short cuts are made, some new risks are accepted, and new ways of doing business are employed.

In Mr. Keith’s three day class on Fundamentals of Rockets and Missiles, the questions of commercial versus government design standards are compared.  The apparent effect is that a commercial rocket DDT&E (Design, Development, Test & Evaluation) effort, like the Space-X Falcon, should cost about one-fifth of what a government DDT&E program costs for a comparable sized rocket.  This cost difference is documented in some cost models or Cost Estimation Relationships (CER).  These same cost models fail to explain why any but commercials should be chosen.  Mr. Keith’s explanation is that the shortcuts have one major impact; lower initial reliability.  Indeed, the first three launch attempts of the Space-X Falcon-1 launch vehicles all failed.  Since then, there have been two successful launches of the Falcon-1 and three successful launches of the much larger Falcon-9.  Commercial space ventures have the opportunity to take calculated risk short cuts that government programs are mandated to avoid, and the business incentive to make wiser trade-offs and choices.

This does not mean that the road to commercial space will be smooth from here on in.  A more realistic expectation is for the road to be bumpy.  Space-X has had five successful launches in a row, but their proven historical reliability is five successes in eight tries, or 62.5% reliability. The best we can say regarding the Falcon-9 rocket is that we can be confident it is at least 75% reliable at this time.  If, or when, a Falcon-9 rocket fails in the future, it should be considered a bump on the way to commercial space, not a failure of this new way of doing business.

Even this latest successful launch cannot be counted as a victory for commercial space until the Dragon Space Capsule successfully docks with the Space Station.  While the launch is the most risky six minutes of the mission, Space-X still must get the craft safely to a docking port with all the cargo intact.  The difficulty and risks of rendezvous and docking of a spacecraft to the Space Station should not be underestimated.

There will always be critics of commercial space who will look for negative occurrences to undermine commercial style ventures.  There is also a high probability that a number of future commercial space missions will include embarrassing failures.  The criteria for success in commercial space should not be whether the road is bumpy with occasional failures.  The success criteria should be whether access to space is better, faster and cheaper using commercial methods and incentives than is practical with the type of government bureaucratic methods and incentives that have dominated the final frontier for the past half century.

Dr. Tom Logsdon teaches Orbital Mechanics and Global Positioning Satellite technology classes for ATI.  His colleague, Edward L Keith, teaches Fundamentals of Rockets and Missiles, Space Mission Analysis and Design and other rocket related classes for ATI. These instructors are available to reporters who need more information. Contact ATI at 410-956-8805.


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ATI’s GPS Technology – Solutions for Earth & Space Course is to be presented in Laurel, MD on March 14-17, 2011

ATI is scheduled to present GPS Technology – Solutions for Earth & Space Course is to be presented in Laurel, MD on March 14-17, 2011.  This course will be taught by legendary instructor, Mr. Tom Logsdon, who taught short courses and lectured in 31 different countries. He has written and published 40 technical papers and journal articles, a dozen of which have dealt with military and civilian radionavigation techniques. He is also the author of 29 technical books on various engineering and scientific subjects.

In this popular four-day short course, GPS expert Tom Logsdon will describe in detail how those precise radionavigation systems work and review the many practical benefits they provide to military and civilian users in space and around the globe.

Each student will receive a new personal GPS Navigator with a multi-channel capability.

Through practical demonstration you will learn how the receiver works, how to operate it in various situations, and how to interpret the positioning solutions it provides.

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