# Explained: NASA documents stating a flat Earth??? Linear Aircraft Models

#### FlightMuj

##### Active Member
Hello again!!!
A man states without reading any of the part of the NASA document here: https://www.nasa.gov/centers/dryden/pdf/88104main_H-1391.pdf
Although I have not read it myself because of College (vacations are over), and also, it involves a lot of advanced Math.

The summary page in the beginning does assume a "flat, nonrotating Earth" but the introduction page says,
"The need for linear models of aircraft for the analysis of vehicle dynamics and control law design is well known. These models are widely used, not only for computer applications but also for quick approximations and desk calculations. Whereas the use of these models is well understood and well documented, their derivation is not. The lack of documentation and, occasionally, understanding of the derivation of linear models is a hindrance to communication, training, and application."
Also this:"Whereas it is common to assume symmetric aerodynamics and mass distribution, or a straight and level trajectory, or both (Clancy, 1975; Dommasch and others, 1967; Etkin, 1972; McRuer and others, 1973; Northrop Aircraft, 1952; Thelander, 1965), these assumptions limit the generality of the linear model."
So, I just sort of debunked the claim, but I am not convinced as to what can they gain to assume a flat Earth, I mean the model will be a lot simple but still why assume it??? Teaching for the purpose to understand the influences of flight should be rigorous.

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#### Rory

##### Senior Member.
Flat earthers are claiming that NASA said the earth is flat?

Why would they believe NASA?!?

#### imprus

##### New Member
Flat earthers are claiming that NASA said the earth is flat?

Why would they believe NASA?!?

NASA lies to ordinary people, but pilots need to know the truth.

For flatearthers from russian comrades. In old soviet books "Соловьев М. П., Арбузов А. И. Основы бомбометания" (basics of bombing?) you can find (google translate):

"In what follows we consider only the motion of the center of mass of the bobma, and we take:
A) the earth is stationary and its surface is flat, ...".

I'm sure there are also similar books in English.

Соловьев М. П., Арбузов А. И. Основы бомбометания. — М.: Военное издательство НКО СССР, 1940.

http://amyat.narod.ru/theory/osnovy_bombometaniya/index.htm

page3

p3 by Евгений Усов, on Flickr

Yellow highlighted:
В дальнейшем рассмотрим только движение центра массы бомбы, причем примем:
а) земля неподвижна и поверхность ее плоская;

Full page translation:
Fieldset:
Глава I
ОСНОВНЫЕ СВЕДЕНИЯ ИЗ БАЛЛИСТИКИ
1. Общие сведения о движении бомбы
Движение бомбы после отделения ее от самолета
определяется системой шести дифференциальных уравнений:
три уравнения определяют движение центра масс бомбы и три
уравнения - колебания бомбы вокруг центра массы.

Силы, действующие на бомбу в полете, полностью не
изучены, и до настоящего времени задача одновременного
интегрирования всех шести уравнений не решена. Обычно
система шести уравнений разбивается на две отдельные системы,
по три уравнения в каждой. Одна система определяет движение
центра массы при условии, что ось бомбы совпадает с
касательной к траектории. Другая система определяет колебания
бомбы вокруг центра массы при условии, что движение центра
массы известно из решения первой системы.

В дальнейшем рассмотрим только движение центра массы бомбы, причем примем:
а) земля неподвижна и поверхность ее плоская;
б) сила тяжести постоянна по величине и направлению;
в) атмосфера неподвижна относительно земли;
г) сила сопротивления направлена по касательной к траектории
центра массы в сторону, противоположную скорости.
Начнем с простейшего случая - движения центра массы бомбы в пустоте.

2. Движение центра массы бомбы в пустоте
При движении бомбы в пустоте на бомбу действует только
сила тяжести.
Напишем уравнения движения центра массы. Возьмем прямоугольную
левую систему координат и начало ее расположим
в той точке, в которой сбрасывается бомба (рис. 1).
Оси направим следующим образом: ось x - горизонтально
в сторону полета самолета; ось y - вертикально вниз; ось
z - горизонтально, перпендикулярно к направлению полета. и т.д.

Chapter I
BASIC INFORMATION FROM BALLISTICS
1. General information on the movement of a bomb
The movement of the bomb after separating it from the airplane
Is determined by a system of six differential equations:
Three equations determine the motion of the center of mass of the bomb and three
Equations are the oscillations of a bomb around the center of mass.

Forces acting on a bomb in flight are not completely
Have been studied, and up to now the problem of simultaneous
Integration of all six equations is not solved. Usually
The system of six equations is divided into two separate systems,
Three equations in each. One system determines the movement
Center of mass provided that the axis of the bomb coincides with
Tangent to the trajectory. Another system determines the fluctuations
Bombs around the center of mass provided that the movement of the center
Mass is known from the solution of the first system.

In what follows we consider only the motion of the center of the mass of a bomb, and we take:
A) the land is still and its surface is flat;
B) the force of gravity is constant in magnitude and direction;
C) the atmosphere is stationary relative to the ground;
D) the resistance force is directed along the tangent to the trajectory
Center of mass in the opposite direction to the speed.
Let's start with the simplest case - the motion of the center of the mass of the bomb in the void.

2. The motion of the center of the bomb mass in the void
When a bomb moves in a void on a bomb, only
gravity.
Write the equations of motion of the center of mass. Take a rectangular
Left coordinate system and start position it
At the point at which the bomb is dropped (Figure 1).
The axes are directed as follows: the x axis is horizontal
Towards the flight of the aircraft; The y axis is vertically down; axis
Z - horizontally, perpendicular to the direction of flight. etc.

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#### Hevach

##### Senior Member.
It's an educational document. You gain the same thing that you gain having cars be cubes and weightless ropes and spherical cows in a vacuum and all the normal assumptions that are made in physics education: every equation loses several terms and a ton of stuff switches from high degree polynomials to quadratic or even linear equational.

#### deirdre

##### Senior Member.
but I am not convinced as to what can they gain to assume a flat Earth, I mean the model will be a lot simple but still why assume it???
i googled your question ( why do linear aircraft models assume a flat earth )and there are some answers on this site: (although i cant tell you if they are accurate

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#### Henk001

##### Senior Member.
It describes a model with three sets of reference frames. These are interconnected and to avoid overcomplicated math (it is already very complicated as it is) the three frames are taken to be euclidic ("traditional" x,y,z-frames). This is applicable for movements within a limited space range. It is a bit like assuming local thermodynamic equilibrium in star models, or free fall calculations assuming "no air friction"; both are not really true but they can give good approximate results for some domains of application.

#### FlightMuj

##### Active Member
Flat earthers are claiming that NASA said the earth is flat?

Why would they believe NASA?!?

Well, someone is trying to sneak past NASA and tell us the "truth" that the agency apparently wants to hide . Wake up people!!!

#### FlightMuj

##### Active Member
Good resources, I should have googled!!! Thanks everybody!!!

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