The Federal Aviation Administration (FAA) assumes a flat earth when training pilots and air traffic controllers using their Target Generation Facility (TGF). The TGF consists of several software programs that control simulation scenarios, using simulated aircraft. The TGF computer simulator drives almost all of the air traffic control laboratories at the FAA William J. Hughes Technical Center. 1 The FAA states: “Our lab has worked closely with the TGF group to have aircraft perform the way air traffic controllers would expect them to behave in the real National Airspace System (NAS). The simulated aircraft in TGF are quite realistic representations of their real-life counterparts.” 2

The software used in the TGF must be accurate in order to properly train pilots and air traffic controllers on the behavior of aircraft in flight. The assumption of a flat earth can be seen in a publication from the FAA, The Engineering Analysis and Design of the Aircraft Dynamics Model For the FAA Target Generation Facility [TGF]. That FAA publication explains the software that is used by the TGF to accurately simulate the behavior of aircraft over the earth.

Specifically, this document discusses the detailed engineering design and software implementation of an Aircraft Dynamics Model (ADM) suitable for incorporation into the FAA TGF simulations at the FAA William J. Hughes Technical Center, Atlantic City, NJ. The model is designed to be implemented on computers located within the facility, and to work in conjunction with software models of radar, data links, and other Air Traffic Management (ATM) equipment to provide realtime simulation of aircraft operating within the National Airspace System (NAS). 3

The FAA publication explains that in order for the software to accurately replicate the behavior of aircraft during flight over the earth, the software running the TGF simulator assumes that the earth is flat.

The observant reader will notice that the aircraft equations of motion were calculated assuming a flat Earth and that we here assume the development frame was the NorthEast-Down frame. This implies necessarily that earth rotation and the variation of the gravity vector with position over the earth were ignored in developing the aircraft equations of motion.

This simplification limits our mathematical model to the flight of aircraft only. The model will not properly handle the flight of sub-orbital craft and spacecraft such as intercontinental ballistic missiles, satellites, or the space shuttle. The model is adequate for all vehicles traveling under Mach 3. 4 (emphasis added)

Notice that the FAA document both assumes a flat earth and ignores the rotation of the earth and gravity. The FAA maintains that the computer model assumes a stationary, flat earth and at the same time remains precise and accurate regarding the flight of aircraft. The only way that a stationary, flat earth can be the basis for a model, and that model still be accurate, is if the earth is in fact flat and stationary. That means that the ignored gravity and rotating, globular earth do not affect the accuracy of the model, because they do not in fact exist in reality.

The proviso in the last sentence that the computer model does not address spacecraft or satellites is meaningless surplusage. The statement that the model is adequate for all vehicles traveling under Mach 3 is also meaningless, since it does not specify that it would be inaccurate for vehicles traveling over Mach 3.

The entire purpose of the TGF simulation is to create as real a simulation of actual aircraft flight over the earth as is possible. The only way to do that is to simulate what is real. That is why the TGF software assumes a flat earth. The TGF is designed to have “high fidelity” to reality. The FAA publication states:

Currently, the aircraft dynamics incorporated in the TGF are based on the first principles of physics and aeronautics. The models provide the performance characteristics needed to support high fidelity simulations. The TGF incorporates fuel burn models environmental (weather) effects. Additionally, the modeled aircraft are representative of commercial air traffic in the US National Air Space (NAS). As future simulations are developed or brought to the Technical Center, higher fidelity will be required to identify NAS operational safety and performance issues. The TGF is prepared to increase its fidelity and operational connectivity required to meet the demands by the other FAA programs and simulators. The goal of this project has been to develop and maintain a high-fidelity simulation capability to meet the needs of the FAA in operating, testing, and evaluating its NAS. 5 (emphasis added)

The reality to which the TGF software is faithful is that the earth is stationary and flat. If the TGF simulator based its model on the false premise of a globular, spinning earth, it would create a safety issue for aircraft. The FAA simply had to assume a flat earth, because that is reality. If the FAA had assumed a spinning, spherical earth model, the pilots and air traffic controllers would be trained improperly and create the messy and embarrassing result of planes crashing with regularity.

Indeed, since safety is paramount, it was necessary for the FAA to verify, with real-life testing, the algorithms in the TGA simulator that assume a flat, stationary earth. The FAA publication states that “[t]he document concludes with a section on verification and validation, the process by which the various features of the simulation are tested and verified.” 6 What did the section on verification reveal? The FAA publication reports that “[t]he testing that was done to verify and validate the TGF simulation gives us a high degree of confidence that the models contained herein have sufficient fidelity for use as a target generating tool.” 7 The models that the testing validated as being faithful to reality to a high degree of confidence assumed a flat, stationary earth. That means that the FAA verified, through actual testing with aircraft, with a high degree of confidence, that the earth is flat and stationary.

The U.S. Government implicitly acknowledged the reality of the flat, stationary earth in another official publication. In NASA’s 1988 publication (#1207) titled Derivation and Definition of a Linear Aircraft Model, it states that the generally accepted linear aircraft model is based upon “a rigid aircraft of constant mass flying over a flat, nonrotating earth.” 8

The U.S. Air Force is also on record implicitly admitting that the earth is flat. The Systems Engineering Branch, Flight Determination Laboratory of the United States Air Force prepared a technical memorandum in 1953 titled: Atmospheric Refraction Errors for Optical Instrumentation, Preliminary Report, Technical Memorandum, No. 104. That technical memorandum, which has since been declassified and posted on the U.S. Department of Defense Technical Information Center website, contains the following warning:

This document contains information affecting the National Defense of the United States within the meaning of the Espionage Laws, Title 18, U. S. C., Sections 793 and 794. Its transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law. 9

What is so secret about atmospheric refraction that revelation would be a national security concern? The technical memorandum was written to provide technical information for the design of guided missiles. It is required to be accurate, as the missiles must be able to precisely hit their targets. Notably, the formulae in the technical memorandum were constructed assuming the validity of a flat Earth. Indeed, the assumption of a flat earth was the foundational premise for the atmospheric refraction formulae. 10 It makes perfect sense to assume a flat earth, because that is the actual environment in which the guided missiles will be deployed. With that in mind, the technical memorandum begins with the following passage:

II. VALIDITY OF FLAT EARTH ASSUMPTION FOR ATMOSPHERIC CALCULATIONS

The relative mass of the atmosphere at any elevation angle is given approximately by the cosecant of the elevation angle. This relationship is correct for a flat earth and a flat atmosphere. 11 (bold emphasis added)

In a footnote to the above passage there is mention of the fact that a formula is also given for a spherical earth, but that no account is given for the curved path that the spherical earth is supposed to present. “In the present comparison of the relative air masses at various elevation angles for flat and spheroid earth, no account is taken of the slightly curved path followed by radiation arriving at a given angle.” 12 Why would the publication present two different formulae, one for the flat earth another for a spherical earth, and then disregard the spherical earth formula? Because the spherical earth formula does not comport with reality. It is simply cover language to suggest that the earth is a sphere and thus hide the reality of the flat earth.

Throughout the technical memorandum, the military scientists repeatedly reaffirmed the validity of their assumption of a flat earth. For example on page 5 of the memorandum, it states that “[a] flat earth assumption, then, may be safely used for total angular refraction down to about 7° elevation.” 13 When it really counts, as when designing missiles, the military assumes that the earth is flat.

In March 2010, a research memorandum was published from the U.S. Army Research Laboratory on the issue of six-degree-of-freedom (6-DOF) projectile flight dynamic modeling. That esoteric topic simply means that the research memorandum outlines a model to predict the effect of liquid payloads on the trajectories of projectiles. The memorandum is talking about lethal bombs, and so the predictive model must be precise. The research memorandum states at the outset that “[t]hese equations assume a flat Earth.” 14 Again, when precision is required in calculations, it is necessary for the U.S. Army to assume the reality of a flat earth.

A 2001 report from the U.S. Army Research Laboratory was titled: Electromagnetic Fields Over Flat Earth. 15 And sure enough, the U.S. Army Research Laboratory “assumed that the transmitting antenna and the target (or receiver) are located above, but near the surface of a flat idealized earth.” 16

In a research project on atmospheric oscillations conducted for NASA by the Georgia Institute of Technology, the researchers acknowledged that a flat, nonrotating earth is a common model used by scientists. “A model frequently used is that of a flat, nonrotating earth. … The most one can profitably simplify the problem is to consider an isothermal atmosphere, plane level surfaces, and a nonrotating earth.” 17 That is a secret that not expounded in the classroom; but it is freely shared with NASA.

In a 253 page Master of Science thesis paper published by the Massachusetts Institute of Technology (MIT) Department of Aeronautics and Astronautics, about targeting systems, “[t]hree targeting methods were considered: assuming a flat Earth.” 18 What is significant about the research paper is that it addresses precision guided munitions targeting. The military strike must be pinpoint accurate to be effective. It states that “small changes in elevation can lead to drastic errors due to the orientation of the camera.” 19 Precision guidance requires that the targeting system in the unmanned aerial vehicle (UAV) have a correct model of the earth, because it must have precise data about its elevation and orientation above the earth and the elevation of the target. That is why the paper assumes the reality of a flat earth.