NASA along with Navy, Army, Flight schools all state that assumptions have to be made with aircraft.

Are they assuming the earth is a ball with a 8 inches per mile (or miles squared) ?

Nope! Why not? Because if they did, the pilots would have to constantly dip down to compensate for vertical drop in every direction and crash the aircraft HAHAHHA.

What does assumption mean? a thing that is accepted as true or as certain to happen, without proof. – Oxford Dictionary

General Equations of Motion for Damaged Asymmetric Aircraft


Page 1: “…equations of motions must properly reflect the underlying physics.”


page 2:


“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

Approximate Optimal Guidance for the Advanced Launch System

On page one this document does mention a spherical rotating earth but then states that “…these schemes” (based on a spherical rotating earth) 1) “…are difficult to prove” and 2) “…not suggested to be used as a basis for an online real-time guidance law.”

Page 32 goes on to say:

“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/archive/nasa/casi.ntrs.nasa.gov/19940020279.pdf

SR-71


Page 8 “…nonrotating Earth…”


https://www.nasa.gov/centers/dryden/pdf/88507main_H-2179.pdf

page 14:


/pdf/88072main_H-1259.pdf

NASA Technical Paper 2835

Page 1 Summary:

Flat nonrotating earth

page 126:


“The nonlinear equations of motion used are six-degree-of-freedom equations


sith stationary atmosphere and flat, nonrotating earth”

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

Determination of Angles of Attack and Sideslip from Radar Data and a Roll Stabilized Platform

March 1972

page 2:


“The method is limited, however, to application where a flat, nonrotating earth”

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720012071.pdf

An Aircraft Model for the AIAA Controls Design Challenge

NASA


1991

page 11:


“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”

https://www.nasa.gov/centers/dryden/pdf/88248main_H-1777.pdf

Investigation of Aircraft Landing in Variable Wind Fields

NASA 1973

page14 pdf or 6 on actual report:

a) The earth is flat and non-rotating.

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

A Mathematical Model of the CH-53 Helicopter

NASA

page 17:

“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.pdf8

Atmospheric Oscillations

Georgia Tech April 1965

Prepared for NASA

page 13:


A model frequently used is that of a flat, nonrotating earth.

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

page 19:


These equations assume a rigid vehicle and a flat, nonrotating Earth.


https://www.nasa.gov/centers/dryden/pdf/88733main_H-2465.pdf

Flight Testing a VSTOL Aircraft


NASA 1988


page 9 pdf or 4-5 on actual doc:


“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

Time to Climb

page2:


“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

Russia 1948

Shape of the earth unknown..

https://www.cia.gov/library/readingroom/docs/CIA-RDP80-00809A000600231031-1.pdf

Russian Light Study

“Brightness of the firmament”

Flat earth :

https://drive.google.com/file/d/1KX7_0tlTAzFEWJ1CWOXQ_K2JnUgbfzb8/view

Propagation of Electromagnetic Fields Over Flat Earth

http://www.arl.army.mil/arlreports/2001/ARL-TR-2352.pdf

page 9: based upon the signal having a single bounce on a flat Earth

http://www.arl.army.mil/arlreports/2009/ARL-TR-4998.pdf

page 1:

Trajectory of Spinning Projectiles:

“These equations assume a flat Earth.”

http://www.arl.army.mil/arlreports/2010/ARL-TR-5118.pdf

page 2:

“These equations assume a flat Earth..”

http://www.arl.army.mil/arlreports/2011/ARL-TR-5810.pdf

page 216:

“assuming a flat Earth“

http://tycho.usno.navy.mil/ptti/2007papers/paper21.pdf

Page 1:

“…so that a flat-earth approximation provides the best estimate.”

http://www.arl.army.mil/arlreports/2001/ARL-TN-175.pdf

Page 39:

model works over a flat earth

http://www.arl.army.mil/arlreports/2003/ARL-TR-2696.pdf

page 1:

transmission loss over flat earth

http://www.arl.army.mil/arlreports/2000/ARL-TR-2156.pdf

page 9:

“…input to a flat earth”

http://www.arl.army.mil/arlreports/2003/ARL-MR-563.pdf

page 3:

“The first is the Earth-fixed coordinate system, which is fixed to the Earth with a flat Earth assumption.”

http://www.arl.army.mil/arlreports/2010/ARL-CR-650.pdf

page: 1

flat earth approximation provides the best estimate

http://www.arl.army.mil/arlreports/2002/ARL-TR-2683.pdf

page 32:

This model works well over a flat-earth

http://www.arl.army.mil/arlreports/2000/ARL-TR-1812.pdf

page 168:

equations of flat-earth trigonometry.

http://www.irig106.org/docs/106-17/106-17_Telemetry_Standards.pdf

page 8:

The Earth is flat and nonrotating.

http://www.navair.navy.mil/nawcwd/command/Inplace.aspx/LoadFile/531