Rigid aircraft of constant mass, flying in a stationary atmosphere over a flat, nonrotating earth.

KorbenDallas

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#1
Ran into this NASA Reference Publication 1207 - Derivation and Definition of a Linear Aircraft Model. After a whole bunch of formulas we have this conclusion stating:
  • This report derives and defines a set of linearized system matrices for a rigid aircraft of constant mass, flying in a stationary atmosphere over a flat, nonrotating earth. Both generalized and standard linear system equations are derived from nonlinear six-degree-of-freedom equations of motion and a large collection of nonlinear observation (measurement) equations. This derivation of a linear model is general and makes no assumptions on either the reference (nominal) trajectory about which the model is linearized or the symmetry of the vehicle mass and aerodynamic properties.
Could somebody explain the meaning of the part 3 Concluding Remarks? Why are they talking about a stationary atmosphere over a flat, nonrotating earth?

flat_plane.png

I understand the nonrotating portion in ref to the atmosphere and the airplane being in the same system. But what happened to the curvature? Why are they talking about flat plane?
 

humanoidlord

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#2
probally to simplify the experiment? its quite hard to replicate a curvature at those conditions
 
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KorbenDallas

KorbenDallas

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#3
probally to simplify the experiment? its quite hard to replicate a curvature at those conditions
They can do whatever during the experiments. When they fly, it is not being done on paper. Airplanes have to physically compensate for the curvature of the Earth. Otherwise they will keep on gaining altitude.

Flat earth curvature airplane.png

Obviously in real life airplanes do not adjust for the curvature. We are told that an airplane is a part of our atmosphere, therefore no corrections are needed. Of course the official explanation is in line with everything else, "Believe us because we say this is the way it works".
The aircraft is usually flown along the density altitude (by pilot or autopilot, as the case may be). As long as the aircraft is flown at a certain altitude, it will be following the earth's curvature (as the atmosphere is attached to the spherical earth and has same properties at same distance from the center, in an ideal case) as the altitude is measured from the surface, which is curved, and not a plane.
There is no adjustment needed as the aircraft will naturally follow the curvature of the earth without any input from the pilot. This is because the aircraft flies through the atmosphere which also follows the curvature of the earth.
Funny how this "atmosphere" thing is the solution for everything which contradicts simple observations. Because of the "atmosphere" we do not need to account for the curvature, or the rotation of the Earth. Funny how it works the exact same way when you fly over a flat nonrotating Earth.

Gyroscope_operation.gif

A gyroscope in operation. Note the freedom of rotation
in all three axes. The rotor will maintain its spin axis
direction regardless of the orientation of the outer frame.


gyroscope_airplane_flat_earth_1.jpg


When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting,
according to the conservation of angular momentum.
So, what forces make the gyroscope follow the curvature of the Earth? Or airplanes are flying in a stationary atmosphere over a flat, nonrotating earth? (as it was noted in the above NASA publication)

Of course I know an official explanation - do not believe your own eyes, some formula will demonstrate how it works.
 

humanoidlord

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#4
They can do whatever during the experiments. When they fly, it is not being done on paper. Airplanes have to physically compensate for the curvature of the Earth. Otherwise they will keep on gaining altitude.


Obviously in real life airplanes do not adjust for the curvature. We are told that an airplane is a part of our atmosphere, therefore no corrections are needed. Of course the official explanation is in line with everything else, "Believe us because we say this is the way it works".


Funny how this "atmosphere" thing is the solution for everything which contradicts simple observations. Because of the "atmosphere" we do not need to account for the curvature, or the rotation of the Earth. Funny how it works the exact same way when you fly over a flat nonrotating Earth.

View attachment 3373
A gyroscope in operation. Note the freedom of rotation
in all three axes. The rotor will maintain its spin axis
direction regardless of the orientation of the outer frame.


View attachment 3375

When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting,
according to the conservation of angular momentum.
So, what forces make the gyroscope follow the curvature of the Earth? Or airplanes are flying in a stationary atmosphere over a flat, nonrotating earth? (as it was noted in the above NASA publication)

Of course I know an official explanation - do not believe your own eyes, some formula will demonstrate how it works.
its not only the plane following the atmosphere but also the gravity acting on the plane
 
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KorbenDallas

KorbenDallas

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#5
It does not work like that. Besides no gravity would officially affect the gyroscope.
 

ISeenItFirst

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#8
I think there are some misconceptions here. I'm no aircraft engineer, but I have looked into this in the past. Aircraft gyros have a mechanism built in to orient the axis of the inertial plane towards the pull of gravity. In the old ones, that were vacuum driven, they would have holes covered by pendulums. When the inertial plane gets out of whack, the pendulum opens the hole, which are arranged to cause the necessary precession towards the correct orientation. Not sure how they do it with the electric ones, but the effect is the same.

An aircraft gyro will constantly attempt to correct towards the pull of gravity.

A good video explaining the physics of gyroscopic precession. Gyros

I am not a flat earth guy, just not convinced one way or the other. The most compelling evidence I ever saw was the experiment done in the deep mines in north america with pendulums. It was done multiple times, and did not give the results that anyone expected. If i can find the documentation, maybe Ill do a thread on it.
 
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KorbenDallas

KorbenDallas

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#9
Apologies if I was not clear enough. I was not talking about a gyroscope incorporated into a flight instrument. I was talking about a stand alone gyroscope started by a hypothetical passenger at take off from let's Miami and spinning its way all the way to New York. What position is it gonna land in?
 

ISeenItFirst

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#10
Should be just like your picture above. Except the gyro would be rotating (precessing), as the new angle would have a portion of gravity acting in a lateral direction causing the precession. Off the top of my head.
 
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KorbenDallas

KorbenDallas

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#11
A traditional Gyro does indeed tend to maintain it’s orientation relative to it’s beginning orientation, so as we fly from one location to another it’s vertical axis remains unchanged. So a 1200 Nautical mile journey would produce a tilt of 20 degrees ( 1 degree per 60 nautical miles). As a result early simple gyroscopic attitude and heading indicators needed regular corrections input thru an adjustment knob on the face of the instrument. - Why does an aircraft gyroscope remain level when you're flying a fixed altitude above a curved earth?

My understanding is they are saying that a traditional gyro would tilt. There are plenty of simple powered gyro designs out there. I'm supposed to be on a plane in a few months. Will be a very good way to see if there will be a tilt. I'm wondering what formula is gonna be produced if there will be no tilt :)

Of course I doubt they will allow me to take such a gyro onboard.
 

ISeenItFirst

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#12
Most of the people on the plane have am electronic gyro in their pocket. If your smart phone has a gyro, (electronic type), there is likely an app to read it directly. That would be your best bet.

Otherwise You would need to make an enclosure that allowed full movement of the gyro within. Otherwise it would be difficult to hold the thing without imparting force on it while it is precessing.
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Friction and inertia would affect the outcome to a point. I doubt the result would be conclusive with any mechanical gyro you could hold in your hand.
We could always do the shadow test. We each erect a pole, and measure the angle of the shadow at the same time at different locations. Then simple trig to find the curvature. I believe it was Galileo who first described such an experiment.

By the way, I hate the wording that guy used, saying the orientation would remain relative to its orientation. We know what he means but tautological statements bother me. It would maintain its orientation with respect to the universe.
This was helpful for Einstein in creating his relativity equations. If you stand on the earth axis, you are spinning, but the stars are not, and you feel no inertia. If you spin yourself, the stars spin and now you feel the inertia, as your arms raise and extend outward. Interesting.

Again, I'm no physicist, and I very well may have been born yesterday, but I stayed up all night.
 
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KorbenDallas

KorbenDallas

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#14
Friction and inertia would affect the outcome to a point. I doubt the result would be conclusive with any mechanical gyro you could hold in your hand.

We could always do the shadow test. We each erect a pole, and measure the angle of the shadow at the same time at different locations. Then simple trig to find the curvature. I believe it was Galileo who first described such an experiment.
Agree. Running a mechanical gyroscope on a commercial airplane is logistically hard. Smart phone gyro is not really a gyroscope. I think there are plenty of these on youtube proving and debunking each other.

Pretty sure it was like Eratosthenes some 300-400 before Christ. The question I have is how they coirdinated it back then being like 400 miles apart.

The main problem with Eratosthenes’s experiment is an assumption that the Sun is super far, and that the planet is spherical.
 

ISeenItFirst

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#15
A smart phone accelerometer is not a gyro. Not all have a gyro. While they work on different principles, there is no reason an electronic gyro should not give an accurate result. They work very well in my RC helicopters. An accelerometer, while very similar would not give the results we would want.

You are probably correct about the shadow experiment origins. I wish I could remember the details from when I was taught about it. I remember being told that the experiment had been described long before being able to be done, and the real trick was synchonizing the timing, but I don't remember how.

Funny, I've spent more time on this thread when it is probaly the least interesting to me, of all the incredible work you've done here. Actually that makes sense, because if I cared more about it, I would do more research and be more formal in my style.
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Had to think on this part a bit. The distance to the Sun is immaterial, except that we need to assume the rays of the sun are essentially parallel. Of course we could do the reverse, and calculate the difference in angle of the rays of the sun to accommodate the results based on a flat earth. Doing this from multiple locations would prove interesting. Seems there should be a way to prove whether the photons from the sun are essentially parallel or not. Something to look into.
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Having now read about the Erasto guy, that is definitely not the story I was taught. The past seems to be always changing.
 
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KorbenDallas

KorbenDallas

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#16
I think the distance to the Sun plays a major role. Just like you said, those rays will either be parallel if the Sun is real far like they say, or at an angle if the Sun is just a thousand miles away.

angular_sunrays_through_clouds.jpg

Of course the above crepuscular rays are parallel, according to the conventional science. We just see everything wrong. Essentially we need to know the true shape of our planet, and the distance to the sun to calculate what we want. ))
 

ISeenItFirst

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#17
Well, I have seen crepuscular rays reconvene on the opposite horizon, which would give credence to the idea that they are essentially parallel, and it is a matter of perspective.

Most of these things do not have one solution, and without assumptions, hell, even with assumptions it is very very hard to isolate any one variable.
 
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KorbenDallas

KorbenDallas

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#18
Agree. If the Sun was that much closer, we would have other supporting evidence. It appears there is a tonne of it. Of course there would be an explanation formulated for everything. Like for this sun hotspot below.

F771CA14-8E1D-43E7-BD98-A7C53561C3C4.jpeg
The issue with too many coincidences got me thinking that at some point those stop being just coincidences. At some point coincidences start looking straight up weird. And after personal observations fall in line with ancient symbology, and legends, you just get more questions.

Yin and yang_flat_Earth.jpg
 

WildFire2000

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#19
KD, why does the sun/moon image there work the way it works, matching the Yin-Yang? Or is that just an artistic representation of what we are to believe? Just curious here, given you posted it.

I'm with ISeenItFirst here. I, of course, was raised with the spherical Earth (that they admit isn't entirely spherical, more oblong-y and bulgy in the middle) but am open to the idea of a different shape. As I posed in another thread, here or in Reddit, I have to ask 'Why?' WHY go through all of this trouble to convince everyone it's a 'ball'? Why lie about space? What, and WHO, are benefiting from it? So far no one has given me a good answer for that. The most common I get is that 'Space is created to disprove God and make you feel insignificant'. So... Do you have any insight to pass on? Maybe PM it if you don't want to post it on the forum yet?
 
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