Tag Archives: Tom Logsdon


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.

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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/