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.”
“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…”
NASA Technical Paper 2835
Page 1 Summary:
Flat nonrotating earth
“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
“The method is limited, however, to application where a flat, nonrotating earth”
An Aircraft Model for the AIAA Controls Design Challenge
“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
page14 pdf or 6 on actual report:
a) The earth is flat and non-rotating.
A Mathematical Model of the CH-53 Helicopter
“The helicopter equations of motion are given in body axes with respect to
a flat, nonrotating Earth.”
Georgia Tech April 1965
Prepared for NASA
A model frequently used is that of a flat, nonrotating earth.
These equations assume a rigid vehicle and a flat, nonrotating Earth.
Flight Testing a VSTOL Aircraft
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.
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
Trajectory of Spinning Projectiles:
“These equations assume a flat Earth.”
“These equations assume a flat Earth..”
“assuming a flat Earth“
“…so that a flat-earth approximation provides the best estimate.”
model works over a flat earth
transmission loss over flat earth
“…input to a flat earth”
“The first is the Earth-fixed coordinate system, which is fixed to the Earth with a flat Earth assumption.”
flat earth approximation provides the best estimate
This model works well over a flat-earth
equations of flat-earth trigonometry.
The Earth is flat and nonrotating.