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On the NASA Technical Reports Server (NTRS) there's an article titled Derivation and definition of a linear aircraft model:

Abstract

A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.

direct PDF link

Authors

  • Duke, Eugene L. (NASA Hugh L. Dryden Flight Research Center, Edwards, CA, United States);

  • Antoniewicz, Robert F. (NASA Hugh L. Dryden Flight Research Center, Edwards, CA, United States);

  • Krambeer, Keith D. (NASA Hugh L. Dryden Flight Research Center, Edwards, CA, United States)

I cannot understand why NASA has an aircraft flying over a non-rotational flat earth, this doesn`t make any sense to me.

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    $\begingroup$ But why do they mention a flat earth and not a globe? I can't understand this. Your answer does not satisfy my questions. Why is the aircraft designed over a flat, non-rotating earth ! If the earth rotates why do the test over a non-rotating, flat earth ? Can you see why I am confused, this just doesn't make any sense unless the earth is flat, which is absurd...I think ?? $\endgroup$ – janner1952 Mar 19 '17 at 11:12
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    $\begingroup$ Why a flat earth though and not a globe, and how does this make the equation easier ?? Surely the equation would be wrong if they tested it on a flat plane instead of a sphere, and if the earth is spinning at 1,040 mph I would say this is hardly negligible, seems pretty fast to me. I am not looking for an argument, I just came across this as I am interested in aerodynamics and I am totally baffled by it. $\endgroup$ – janner1952 Mar 19 '17 at 11:24
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    $\begingroup$ No, it's not significant. Where are you now - can you feel the earth rotating at 1040 mph? Does the floor look curved? If you look out the window you migth see some hills or mountains, but even at sea basically up to about 25 miles away it looks flat. How many aircraft are even 1 mile across? $\endgroup$ – JMLCarter Mar 19 '17 at 11:31
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    $\begingroup$ @janner1952 I am aware that, to a non-scientist, at first glace things like this appear to suggest this is how the world is believed to be. However it is just an assumption based on what the experimenter believes is a contributing factor. For example I've yet to see a nuclear model which takes gravity into account but I'm sure you're aware that this doesn't imply a belief that there is no gravity - the effects are just insignificant. This paper has merely stated its assumptions because it is important in case anyone attempts to apply their results to a point where rotation does come into play. $\endgroup$ – Lio Elbammalf Mar 19 '17 at 12:35
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    $\begingroup$ Why change the subject ? I was talking about why they use a flat ,stationary earth model instead of a spinning sphere which would be correct for testing the aircraft, according to scientism, not gravity which may or may not exist as we cannot prove it exists. Answer the question please. $\endgroup$ – janner1952 Mar 19 '17 at 15:12
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All models are wrong. Some are useful.

These days there's a popular trend when simulating things to simulate every possible mechanism we can imagine. Those who think that way would agree with you. Why would you ever make a flat Earth model when everything is eventually going to make its first flight on a real rotating spherical-ish Earth?

This approach works great until you come across real development or computational limits. The cited paper is from 1988. Computers were much weaker back then. For perspective, the Cray Y-MP was sold that year. Its peak performance was 333 megaflops. She cost \$15 million dollars. Contrast that to today. A Geforce GTX 1070 is capable of 6,500,000 megaflops (6.5 teraflops) and has a price tag of around \$400.

In those days, you didn't waste computational power on frivolities. It turns out that for a vast array of aeronautical problems, the effects of a flat earth vs. round are minimal (much less the effects of rotating vs. not). If you're shooting a shell 15km, and need it to land with pinpoint precision, you need all that extra complexity. However, many aero problems include a guidance unit which would address any error due to Coriolis effects or the spherical ground the same way it would handle any other errors. It'd simply see it wasn't on the right path and make a correction. The other sources of error here, such as winds, play a far larger effect in deviations from a flight plan, so all the rotating and spherical effects can just get lost in the noise.

Even today, we still make flat Earth models. The reason is not computation time, like it was in 1988, but development time. The more things you model, the more things you need to develop, verify, and maintain. If a particular problem does not call for advanced models, why waste budget developing and maintaining them?

A real life example of this shows up in geoids. Quite often we can do all the modeling we need with a spherical Earth. However, sometimes we find that we need to model the Earth with its proper oblate shape, so we them switch to the WGS84 geoid, or any one of its brethren. The price: all sorts of fun complexities. When I say I have a "forward/right/down" body rotation matrix, is the "down" vector towards the center of the earth, or is it perpendicular to the geoid? On a sphere, they're the same. On an oblate spheroid, I have to take the time to figure out which one was intended. If I don't take the time, then I might as well have just used a sphere.

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For the purposes of the equations governing the aerodynamic properties of aeroplanes, a whole lot of things can be ignored because they don't make the slightest bit of difference. Such as the curvature of the earth, its rotation, the earth's orbit around the sun, the sun's orbit around the galactic center etc.

For much the same reason, if I want to calculate the path taken by a ball I drop in my lounge, I don't need to worry about those things either.

Sometimes they do matter: if I want to fire a modern artillery gun over a range of 10km or more, then both the curvature of the earth and its rotation do matter because they make a difference to the trajectory at the level of precision I am interested in.

A key skill in physics is in understanding what factors need to be taken into account and what can be ignored, at the level of precision you care about.

As far as aerodynamic models of planes go, the curvature of the earth only matter to the extent that the earth deviates from being flat over the size of the aircraft. Likewise the rotation: if the rotation speed of the earth varies significantly over the span of the aircraft it might matter. But since aeroplanes aren't tens of kilometers in size, it really makes no difference, because we are not doing calculations precise enough for those things to matter (as in dropping a ball in my lounge: if I was worrying about nanometer precision, then maybe the rotation of the earth would matter after all, bit so do a vast number of other things)

If, on the other hand, you are interested in the trajectory of a plane flying thousands of kilometers, these things start to matter, but that's another thing entirely than what the quoted piece is taking about.

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    $\begingroup$ Thank you Phill, yes I am a layman as far as science goes, but I am not talking about the curvature of the earth. I am talking about why they use a flat earth model that is stationary instead of a sphere which is moving to test the airplane, I cannot understand this dynamic, why do they do this ? $\endgroup$ – janner1952 Mar 19 '17 at 13:44
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    $\begingroup$ @janner1952: calm down, reread the answer, and then ask more specifically about what you don't understand. No one is claiming that the Earth is actually flat; the point is that for this experiment it doesn't make any difference. $\endgroup$ – Javier Mar 19 '17 at 19:01
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    $\begingroup$ @janner1952 unless you're paying people for answers, it's difficult to motivate their time when you are being incredibly rude and narrow-minded. For example, you don't seem to be following that "ignoring the curvature of the earth" is the same as using a flat model. PhillS's answer also addresses the rotation issue, yet you keep asking the same question... Rudely. Please take a look at this relevant help page. $\endgroup$ – DilithiumMatrix Mar 19 '17 at 19:31
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    $\begingroup$ Sorry, I did not set out to be intentionally " rude" as you put it. Nor did I intend to have a debate about anything but the question I asked. I simply asked a question about why NASA used a stationary flat earth model to show a derivation and defined linear aircraft design instead of a globe model. I do take exception however, to say I am paying people for answers to my questions. So please don`t be so rude and condescending to suggest this. So how dare YOU be so rude. $\endgroup$ – janner1952 Mar 20 '17 at 0:47
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    $\begingroup$ Also my question has been answered by Cort Ammon clearly and without condescending remarks. Stating exactly what I wished to know. So with that I say goodbye , and to you DilithiumMatrix I suggest you practice what you preach without any derogatory remarks..adieu $\endgroup$ – janner1952 Mar 20 '17 at 1:33
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You have missed the point of the report. Every introductory book and web site on the aerodynamics of flight, and every course on pilot training, makes exactly the same assumptions as this report.

But most of the other literature doesn't bother to state what assumptions it is making, except for vague notions like "common sense" and "drawing some diagrams that are obviously correct". The point of the NASA report is that it carefully derives the relevant equations explicitly, without any further simplifications - for example it doesn't assume the aircraft is symmetrical, even though most real aircraft look symmetrical - but that might not be true if the fuel tanks are full in one wing and empty in the other, or one engine has failed on a twin-engine plane, for example.

As other answers said, there is no sense in including things in a model which are not needed to make it a useful model. Sure, if you really wanted to, you could construct a model of aircraft dynamics that included quantum field theory and the cosmological expansion of the whole universe - but there is no practical reason to do that.

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    $\begingroup$ Cort Ammon,Thank you for answering my question in a precise and understandable way. That`s all I wanted to know, I am not an aeronautical engineer as these other people seem to think, but an ordinary person who is inquisitive about our world and how things work and why they work. I understand that these designs are very old and there are simpler ways to do things now in this technological age.Thank you for making this clear to me. $\endgroup$ – janner1952 Mar 20 '17 at 1:07

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