Nathan Roberts thins that government documents admit the earth is flat. He even has a list of 44 documents that he thinks admit this. I review them here.

- Dissertations Defended in the Scientific Council of the Institute of Physics of the Earth
- Pages: 19, 20
- https://www.cia.gov/library/readingroom/docs/CIA-RDP86-00513R001343720008-3.pdf
- This is a document from the USSR. It is a dissertation defense predicting light dispersion in the atmosphere based on a model. This model assumes a flat earth to made simplify calculations. Modeling is common in engineering to eliminate things that increase complexity without adding significant value to the output. This model also only calculated first-order scattering. This does not mean there is no scattering other that first-order, it means it was not included in the model.
- Page 25 of this document has a different dissertation titled “Determination of the Gravity Forces on the Sea by the Pendulum Method”. This is an admission that gravity exists.
- If the earth were flat and stationary, it would collapse into a sphere due to gravity.
- “If both energy and angular momentum are exported efficiently, the object (if large enough) will collapse into a sphere.”
- Page 2: https://arxiv.org/pdf/1004.1091.pdf

- Propagation of Electromagnetic Fields Over Flat Earth
- Pages: Cover Page, 7, 17, 18, 28, 35
- https://www.arl.army.mil/arlreports/2001/ARL-TR-2352.pdf
- Page 7: “It is assumed that the transmitting antenna and the target (or receiver) are located above, but near the surface of a flat idealized earth (constant permittivity, ε, and conductivity, σ) ground.”
- This assumption has three parts:
- flat earth
- constant permittivity
- constant conductivity

- Is the government in a global conspiracy to hide the fact that the earth has constant permittivity and conductivity? No, this is a model. Specifically, this model is exploring reflections over a topographically flat surface, thus “flat earth”, but not a perfectly conducting surface.
- Page 8: “The problems of calculating the reflection of uniform plane wave fields from a homogeneous boundary and calculating the fields from a finite source local to a perfectly conducting boundary are relatively straightforward. However, when the source is local to a general homogeneous plane boundary, it is found that the solution cannot be expressed in closed form.”

- An Energy Budget Model to Calculate the Low Atmosphere Profiles of Effective Sound Speed at Night
- Pages: 10, 16
- https://www.arl.army.mil/arlreports/2003/ARL-MR-563.pdf
- Page 10: Nathan thinks a not-to-scale diagram somehow suggests the earth is flat? Surely you can’t be serious.
- Page 16: “To briefly examine short range acoustic attenuation at night, we use the low atmosphere profiles of wind speed, temperature, and relative humidity (shown before) as input to a flat earth, non-turbulent acoustic propagation model called the Windows (version) Scanning Fast Field Program (WSCAFFIP).”
- This very clearly states they are modeling to calculate short-range acoustic attenuation. They are using profiles to model wind, temperature, and humidity as well as topographically flat terrain. Modeling is an engineering tradeoff to reduce complexities, particularly ones that have trivially small effects on the output.

- Computationally Efficient Algorithms for Estimating the Angle of Arrival of Helicopters Using Acoustic Arrays
- https://www.arl.army.mil/arlreports/2010/ARL-TR-5118.pdf
- Page 4 refers to GPS as “global positioning system”.
- Page 17, 30, 31, 35 This document deals with a model for using acoustic signals to ascertain information about helicopters. This includes bouncing the sound off a “flat earth”. This is referring to the topography of the surface of the earth, it is not suggesting anything about the shape of the earth as a whole. It’s important to understand this document is about modeling how sound waves propagate. It’s clear Nathan simply searched this document for the word flat and did nothing more than noting the page numbers. He didn’t even read the full sentence like this for example: “The assumptions of straight-line propagation, constant reflection coefficient, or reflection off a flat earth may not be valid.” Of course, this is not referring to a flat earth model in regard to the entire world either, just the accuracy of the model within the scope this document is exploring.

- Adding Liquid Payloads Effects to the 6-DOF Trajectory of Spinning Projectiles
- Page: 7
- https://www.arl.army.mil/arlreports/2011/ARL-TR-5810.pdf
- This document models spinning projectiles with a liquid payload. This is compared to a model for spinning projectiles that are solid. These models are compared and then compared to real observations.
- The model assumes a flat earth to simplify calculations. Modeling is common in engineering to eliminate things that increase complexity without adding significant value to the output. In particular, this is about not including the topography of the land in the calculations. This is not about the earth’s shape as a whole.

- Trajectory Prediction of Spin-Stabilized Projectiles With a Steady Liquid Payload
- Page: 10
- https://www.arl.army.mil/arlreports/2011/ARL-TR-5810.pdf
- This is an updated version of document #5 from the same author. It’s still about modeling liquid-filled projectiles over flat earth or topography.

- Derivation and Definition of a Linear Aircraft Model
- Pages: 6, 35, 55, 102
- Nathan’s link: https://www.nasa.gov/centers/dryden/pdf/88104main_H-1391.pdf
- Link with searchable text: http://hdl.handle.net/2060/19890005752
- The searchable document includes blank pages from the original document so the page numbers diverge throughout the document. I will use page numbers based on Nathan’s unsearchable document.
- This document is modeling aircraft flight. There are many simplifications used to make the calculations more manageable. :
- The aircraft is assumed to be rigid. This is clearly never the case. Wings flex depending on lift. The body of the plane will twist slightly under different forces. However, these flexes have a nominal impact on the flight so can be ignored.
- The aircraft is assumed to have a constant mass. Since airplanes use fuel, this is not possible. However, the varying mass doesn’t affect the outcome enough to require inclusion so is ignored.
- The air is considered to be stationary, that is there is no wind taken into account. We all are aware there is wind, but it is left out of these calculations.
- The surface of the earth is calculated as if it is flat. Obviously, there is topography over land. This document is, in no way, suggesting hills and mountains don’t exist, they are left out of the calculations for simplicity. This is not making any reference to the earth’s shape as a whole.

- Pages 7, 8, 24 acknowledge gravity. See note on document #1.

- General Equations of Motion for a Damaged Asymmetric Aircraft
- Page: 2
- https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070030307.pdf
- This document models a damaged aircraft’s flight. Being this is a model many simplifications are assumed. None of these assumed items are being claimes to be true in general:
- rigid aircraft
- flat non-rotating earth

- In contrast to several other aircraft models, this one specifically calculates the changes based on the non-symmetric weight distribution. This is an excellent example of engineering’s ability to isolate things while modeling and apply them to a larger solution. Regular airplane flight models are used in conjunction with the information in this document to provide a broader model of a damaged aircraft.
- Pages 3, 6, and 7 acknowledge gravity. See note on document #1.

- Predicted Performance of a ThrustEnhanced SR-71 Aircraft with an External Payload
- Page: 10
- https://www.nasa.gov/centers/dryden/pdf/88507main_H-2179.pdf
- “The DPS equations of motion use four assumptions that simplify the program while maintaining its fidelity for most maneuvers and applications: point-mass modeling, nonturbulent atmosphere, zero side forces, and a nonrotating Earth.”
- It seems Nathan didn’t read anything more than just the words “nonrotating Earth”. It’s very clearly stated that these assumptions are to simplify the program.
- If someone thinks this suggests anything about the shape of the earth, would it also suggest that airplanes are actually point-masses? Would it also suggest there is no turbulence in the atmosphere? No.

- Derivation of a Point-Mass Aircraft Model used for Fast-Time Simulation
- On Nathan’s web page he has the title mislabeled.
- Page: 7
- https://www.mitre.org/sites/default/files/publications/pr_15-1318-derivation-of-point-mass-aircraft-model-used-for-fast-time-simulation.pdf
- This document describes a model for aircraft flight and testing avionics systems.
- Here is the quote from page 7: “Assuming a flat, non-rotating Earth, an inertial reference frame N is defined with the n1 axis aligned with east, the n2 axis aligned with north, and the n3 axis pointing up from the Earth.”
- This is an example of real-world engineering happening. Trade-offs are made in engineering to simplify things and reduce time and costs. Notice in the title of the document where it says “Point-Mass Aircraft”. This means the engineering has simplified all the mass of an airplane into a single point. Is this an admission that airplanes actually have all their mass concentrated in one point? Of course not, this is standard engineering.

- (16) U.S. Standard Atmosphere (1962)
- https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19630003300.pdf
- Page 22: “For the accuracy required in this document, it suffices to treat the surface Φ = 0 as an ellipsoid whose flattening (ellipticity) is f = 1-(b/a) = 1/298.32 where b is the semiminor axis, or polar radius.”
- In Nathan’s cherry-picking exposition he got so excited that he read this sentence without attempting to understand what it meant. The flattening of the earth or its ellipticity refers to the difference of the major and minor semi-axes of a sphere.
- Further, this document has many mentions and tables concerning gravity. Way too many to list here. See gravity note on Document 1.
- Notably, starting on page 78 is a table labeled “ACCELERATION DUE TO GRAVITY, SPECIFIC WEIGHT, PRESSURE SCALE HEIGHT, NUMBER DENSITY, PARTICLE SPEED, COLLISION FREOUENCY, MEAN FREE PATH, AND MOLECULAR WEIGHT”
- Further, this document mentions rotation and centrifugal force due to earth’s rotation:
- Page 8: “Under the influence of gravitational and centrifugal forces this line OP will bend polewards as it rises except along the axis of rotation of the earth and along an equatorial radius extended.”
- Page 21: “The force of gravity is the resultant (vector sum) of two forces: (a) the gravitational attraction, in accordance with Newton’s universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference.”
- Page 21: “The centrifugal potential Φc can be expressed as [equation omitted for brevity] where Ω the angular velocity of the earth and r cos Ψ is the distance, measured perpendicularly to the earth’s axis, from this axis to the point (r,Φ,Ψ;).”
- Page 22: “The spherical coordinates r, Φ, and Ψ are, respectively, the radial distance from the earth’s center, the longitude, and the geocentric latitude (the angle that the radius vector makes with the equatorial plane of the earth).”

- Thank you, Nathan, for including this document that admits the earth is a rotating sphere under the influence of gravity. A globe with the necessary ellipticity for a rotating sphere as Newton proved in his Principia.