Why does NASA need an aircraft model flying over a flat and nonrotating earth?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.