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…”

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.”


Page 8 “…nonrotating Earth…”

page 14:


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”

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”

An Aircraft Model for the AIAA Controls Design Challenge



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”

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.

A Mathematical Model of the CH-53 Helicopter


page 17:

“The helicopter equations of motion are given in body axes with respect to

a flat, nonrotating Earth.”

Atmospheric Oscillations

Georgia Tech April 1965

Prepared for NASA

page 13:

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

page 19:

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

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…”

Time to Climb


“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.

Russia 1948

Shape of the earth unknown..

Russian Light Study

“Brightness of the firmament”

Flat earth :

Propagation of Electromagnetic Fields Over Flat Earth

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

page 1:

Trajectory of Spinning Projectiles:

“These equations assume a flat Earth.

page 2:

“These equations assume a flat Earth..”

page 216:

“assuming a flat Earth

Page 1:

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

Page 39:

model works over a flat earth

page 1:

transmission loss over flat earth

page 9:

“…input to a flat earth

page 3:

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

page: 1

flat earth approximation provides the best estimate

page 32:

This model works well over a flat-earth

page 168:

equations of flat-earth trigonometry.

page 8:

The Earth is flat and nonrotating.