Tag Archives: Tom Logsdon



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.

Rating 3.00 out of 5

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.


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

Rating 4.00 out of 5


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

Rating 3.00 out of 5

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.

Rating 3.00 out of 5


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,


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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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.

View course sampler

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Today virtually every large liquid rocket that flies into space takes advantage of the performance-enhancement techniques we pioneered in conjunction with the Apollo moon flights. NASA’s reusable space shuttle, for example, employs modern versions of optimal fuel biasing and postflight trajectory reconstruction. However, more of the critical steps are accomplished automatically by the computer.

Russia’s huge tripropellant rocket, which was designed to burn kerosene-oxygen early in its flight, the switch to hydrogen-oxygen for the last part, yields important performance gains for precisely the same reason the Programmed Mixture Ratio scheme did. In short, the fundamental ideas we pioneered are still providing a rich legacy for today’s mathematicians and rocket scientists most of whom have no idea how it all crystallized more that 40 years ago.

Illustration 1. below summarizes the performance gains and a sampling of the mathematical procedures we used in figuring out how to send 4700 extra pounds of payload to the moon on each of the manned Apollo missions. We achieved these performance gains by using a number of advanced mathematical techniques, nine of which are listed on the chart. No costly hardware changes were necessary. We did it all with pure mathematics!

In those days each pound of payload was estimated to be worth five times its weight in 24-karat gold. As the calculations in the box in the lower right-hand corner of Illustration 1. indicate, the total saving per mission amounted to $280 million, measured in 2009 dollars. And, since we flew nine manned missions from the earth to the moon, the total savings amounted to $2.5 billion in today’s purchasing power!

We achieved these savings by using advanced calculus, partial differential equations, numerical analysis, Newtonian mechanics, probability and statistics, the calculus of variations, non linear least squares hunting procedures, and matrix algebra. These were the same branches of mathematics that had confused us, separately and together, only a few years earlier at Eastern Kentucky University, the University of Kentucky, UCLA, and USC.


Illustration 1. Over a period of two years or so a small team of rocket scientists and mathematics used at least nine branches of advanced mathematics to increase the performance capabilities of the Saturn V moon rocket by more than 4700 pounds of translunar payload. As the calculations in the lower right-hand corner of this figure indicate, the net overall savings associated with the nine manned missions we flew to the moon totaled $2,500,000,000 in today’s purchasing power. These impressive performance gains were achieved with pure mathematical manipulations. No hardware modifications at all were required.

Read the full article here

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ATICourses Announces A New Course: Fundamentals Of Understanding Space

New ATI Course Bolsters President’s Anticipated Robust Funding of Human Space Flight Program

The Applied Technology Institute (ATIcourses.com) has introduced a new two-day short-course, Understanding Space  scheduled September 28-29 in Beltsville, MD and October 22-23 in Albuquerque, NM. The timely new course will facilitate training for aerospace professionals to support the significant growth expected in the industry.

Last month, Next Step in Space Coalition announced that President Obama’s Review of U.S. Human Space Flight Plans Committee will be recommending an appropriation of 2.5 billion in funding over four years starting in FY2011 to support development of commercial human space transport and capabilities. The review panel’s announcement echoes a declaration earlier in August by NASA that they will invest $50 million of Recovery Act funds to develop a commercial crew program. The funding of these programs is projected to greatly bolster engineering, analysis, design and research jobs.

Tom Logsdon is a top industry expert, author of 29 non-fiction books, and instructor for Understanding Space. He specifically designed the course to provide today’s busy professionals with all the skills they will need to assure themselves a bright, shining future serving tomorrow’s satellites and the astronauts living and working along the space frontier. Examining the status quo, he finds it,  “…rather amazing that our country, the world’s preeminent space power, is currently forced to rely on Russian rockets to carry our American astronauts up to the International Space Station; so I was delighted to read that President Obama’s review panel is so strongly focused on developing new and improved American rockets to supply the station in future years.”  His recent article, Striking it Rich in Space, reflects back on Space Industrialist Expert, Art Dula’s 1980’s prediction – so vehemently criticized at the time – of massive space industry growth in the beginning of the twenty-first century.

Logsdon has long advocated inexpensive access to space, remarking in a recent interview, “ I help my students find clever new ways to gain access to space.  My approach includes conventional chemical rockets with more pizzazz as well as practical alternatives to chemical rockets.”  He tells his students, “There is nothing wrong with the space program that the elimination of chemical rockets won’t cure.”

 The Applied Technology Institute (ATI) specializes in professional development seminars in the technical areas of space, communications, defense, sonar, radar, and signal processing. For over twenty-five years, ATI has presented leading-edge technical training to defense and NASA facilities, as well as DOD and aerospace contractors. Their courses provide a clear understanding of the fundamental principles and a working knowledge of current technology and applications. ATI has the unique capability to schedule and deliver courses in a matter of weeks. They  provide customized on-site training at your facility anywhere in the United States as well as internationally and offer over 200 annual public courses in dozens of locations. World-class design experts lead courses.  To register for a course or request an on-site quote, call (410) 956-8805 or (888) 501-2100 or visit  http://www.aticourses.com/

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