# Observations/Flat and Nonrotating

## Flat and Nonrotating

Below are research papers and technical memos that describe how aircrafts, helicopters, or unguided missiles lift off, fly above, and land upon the Earth. In each case, the aeronautical engineers assume the **Earth to be flat and non rotating**. So where is the paper that assumes earth to be round and rotating? Good luck ..

### Publications

#### Army Research Laboratory - Spinning Projectiles

A 6-DOF rigid projectile model is employed to predict the dynamics of a projectile in flight. These equations assume a flat Earth. The 6-DOF comprises the three translational components describing the position of the projectile’s center of mass and the three Euler angles describing the orientation of the projectile with respect to the Earth. Figures 1 and 2 provide a visualization of the degrees of freedom. File:Army_Research_Labratory_ADA519118.pdf

#### American Institute of Aeronautics and Astronautics

General Equations of Motion for a Damaged Asymmetric Aircraft (Page 2, Section II) ... “In this paper, the rigid body equations of motion over a flat non-rotating earth are developed…”

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070030307.pdf

#### NASA Technical Note: Optimal Nonlinear Systems

A Method for Reducing The Sensitivity of Optimal Nonlinear Systems to Parameter Uncertainty (Page 12 Problem Statement) ... "(2) A flat, nonrotating Earth"

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710018599.pdf

#### NASA Technical Paper: 2835

User's Manual for LINEAR, a FORTRAN Program to Derive Linear Aircraft Models (Page 1, Summary) AND (Page 126 , Report Documentation Page, Section 16) "The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions."

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890007066.pdf

#### NASA Contractor Report: 3073

Investigation of Aircraft Landing in Variable Wind Fields (Page 6, Chapter II - Aircraft Landing Model) ... "The Aircraft trajectory model employed in this study was derived based on the following assumptions: a) The Earth is flat and non-rotating. "

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790005472.pdf

#### NASA Technical Memorandum: 81238

A Mathematical Model of the CH-53 Helicopter (Page 17, Equations of Motion) .. "The helicopter equations of motion are given in body axes with respect to a flat, nonrotating Earth."

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19810003557.pdf

#### Engineering Experiment Station:Atmospheric Oscillations

Georgia Institute of Technology, Prepared for NASA; Atmospheric Oscillations (Page 10) ... "A model frequently used is that of a flat, nonrotating earth." ... (next paragraph) .. "The most one can profitably simplify the problem is to consider an isothermal atmosphere, plane level surface, and a nonrotating Earth."

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650015408.pdf

#### NASA Technical Memorandum: 100996

Flight Testing a VSTOL Aircraft to Identify a Full-Envelope Aerodynamic Model (Pages 4-5, State Estimation) ... “For aircraft problems, the state and measurement models together represent the kinematics of a rigid body for describing motion over a flat, nonrotating Earth…”

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880014378.pdf

#### NASA Ames Research Center

Singular Arc Time-Optimal Climb Trajectory of Aircraft in a Two-Dimensional Wind Field (Page 2, Section II. Singular Arc Optimal Control) ... “In our minimum time-to-climb problem, the aircraft is modeled as a point mass and the flight trajectory is strictly confined in a vertical plane on a non-rotating, flat Earth."

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20060053337.pdf

#### Determination of angles of attack and sideslip from radar data and a roll-stabilized platform

"The method is limited, however, to application where a flat, nonrotating earth may be assumed."

https://ntrs.nasa.gov/api/citations/19720012071/downloads/19720012071.pdf

#### NASA Technical Note: Unguided Rockets

Calculation of Wind Compensation for Launching of Unguided Rockets (Page 8 Trajectory Simulation, 2nd Paragraph) ..."this simulation assumes ... the missile position in space is computed relative to a flat nonrotating Earth"

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040008097.pdf

#### Novel Levenberg–Marquardt based learning algorithm for unmanned aerial vehicles

Section snippets: considered inertial under the hypothesis of flat and nonrotating Earth

https://www.sciencedirect.com/science/article/abs/pii/S0020025517308393

#### Approximate optimal guidance for the advanced launch system

"Lastly, the equations of motion for the zeroth-order problem of flight in a vacuum over a flat Earth are presented." https://ntrs.nasa.gov/citations/19940020279

#### NASA's Reference Publication: 1207

Derivation and Definition of a Linear Aircraft Model (Introduction -- 2nd paragraph, Concluding Remarks - Page 30, Report Document Page - Page 102, Section 16) ... "This report documents the derivation and definition of a linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating Earth."

#### NASA Technical Memorandum: 104330

Predicted Performance of a Thrust-Enhanced SR-71 Aircraft with an External Payload (Page 8 - Digital Performance Simulation Description) "The DPS equations of motion use four assumptions ... a nonrotating Earth."

#### NASA Technical Paper: 2768

User's Manual for LINEAR, a FORTRAN Program to Derive Linear Aircraft Models (Page 12, Program Overview) ... “Within the program, the nonlinear equations of motion include 12 states representing a rigid aircraft flying in a stationary atmosphere over a flat nonrotating Earth”

#### NASA Technical Memorandum

Determination of Angles of Attack and Sideslip from Radar Data and a Roll Stabilized Platform (Page 2, Section 16.) “The method is limited, however, to application where a flat, nonrotating earth may be assumed.”

#### NASA Contractor Report: 186019

An Aircraft Model for the AIAA Controls Design Challenge (Page 11, Equation of Motion and Atmospheric Model) ... “The nonlinear equations of motion used in this model are general six-degree-of-freedom equations representing the flight dynamics of a rigid aircraft flying in a stationary atmosphere over a flat nonrotating Earth.”

#### NASA Technical Paper: 2002-210718

Stability and Control Estimation Flight Test Results for the SR-71 Aircraft With Externally Mounted Experiments (Pages 10-11 Equations of Motion) ... "These equations assume a rigid vehicle and a flat, nonrotating Earth."