I Does an airplane have to nose down in order to follow a curve?

[A.T.]

the plane is NOT taking a curved path.

Yes it is. It is moving on a circle around the planet, which requires a non zero net force.

 

[Dale]

we are in no way talking about any varaibles, gusts of wind, pockets of air, or any other vibrations.

That is silly. Those things are always present. Every airplane engine produces vibration and every atmosphere warmer than 0 K has thermal fluctuations. Equilibrium is always disturbed. Furthermore ...

we are ONLY talking about the adjustments of a plane flying over a flat vs round earth

The perturbations due to changing gravity are also perturbations away from equilibrium, and this perturbation cannot be idealized away since it is inherent to the question. So the question remains, how does the aircraft respond to perturbations from equilibrium in the absence of control? In this case, you are interested in how it responds to perturbations in pitch.

 

[zanick]

Yes it is. It is moving on a circle around the planet, which requires a non zero net force.

yes, its moving in a circle, but its orientation is always level with respect to being perpendicular to the direction to the center of the earth. its flying level, and never changing control, but its also following a curved earth. the non zero force is caused by the curved atmosphere, NOT the planes change of control.

 

[zanick]

That is silly. Those things are always present. Every airplane engine produces vibration and every atmosphere warmer than 0 K has thermal fluctuations. Equilibrium is always disturbed. Furthermore ...

The perturbations due to changing gravity are also perturbations away from equilibrium, and this perturbation cannot be idealized away since it is inherent to the question. So the question remains, how does the aircraft respond to perturbations from equilibrium in the absence of control? In this case, you are interested in how it responds to perturbations in pitch.

Dale, its silly to incorporate those things that can effect the analysis of the question. sure those "things" are always present, but if we remove them, does the plane need to have control inputs to follow the curve of the earth. remove the "noise" from the conditions. there is no change of pitch with level flight, by definition. level flight is a plane flying level with respect to the direction of gravity and at a specific pressure density altitude above the earth.
there is no control adjustment needed for the curve alone of the Earth , just as a plane sitting on the tarmac doesn't need a control force to keep its nose wheel on the ground. it achieves this by the constant balance of force and the direction of that force, on the front nose wheel and the nose wheel against it. the plane rotates 360 over a 24 hour period,but no control is required. same as the plane in flight 1 foot above the ground. it flies level for 24hours and and makes no change to its orientation with any control surface changes as it flies level. think of a helicopter or a balloon. both can hover above the Earth , with an equilibrium of lift vs gravity and never be required to produce a "non zero" force to cause rotation. the Earth's atmosphere causes the force that creates the rotation in space..

 

[Dale]

but if we remove them, does the plane need to have control inputs to follow the curve of the earth

You cannot remove them from the question because they are part of the question. As you go around the curve of the Earth at a minimum (even with all of the thermal and vibrational instabilities removed) the change in the direction of gravity is a perturbation from equilibrium. So the question is specifically, how does this aircraft fly in the face of an upward perturbation in pitch. The answer depends on the stability of the aircraft.

level flight is a plane flying level with respect to the direction of gravity

And if that direction changes then it is a perturbation from equilibrium. Some planes, without control input, will have progressively larger perturbations and others will return back to equilibrium.

just as a plane sitting on the tarmac doesn't need a control force to keep its nose wheel on the ground

That is because the equilibrium is stable. You could easily conceive an unstable tarmac which would require a control force to keep it parked, e.g. an icy tarmac at the top of a hill.

 

[sophiecentaur]

. the plane is NOT taking a curved path.

If that were the case, the plane would surely be aiming out into space. At constant altitude, the plane is following a curve and rotating.
Can't this thread just lay down and die?

 

[A.T.]

the plane is NOT taking a curved path.

yes, its moving in a circle

A circle is a curved path.

the non zero force is caused by the curved atmosphere.

If gravity is the same (as you stated), but the net force is different (straight vs. curved path), then the other forces (aerodynamic & thrust) must be different between your two scenarios (flat Earth vs. round Earth).

 

[sophiecentaur]

The term “level” should not have been allowed on this thread. The geometry forbids it.

 

[zanick]

A circle is a curved path.If gravity is the same (as you stated), but the net force is different (straight vs. curved path), then the other forces (aerodynamic & thrust) must be different between your two scenarios (flat Earth vs. round Earth).

I agree, the plane is taking a curved path. i couldn't edit my post as i meant to write, "level" not "curved" path. .so, now you are saying when flying on a round earth, there is no input required, as on a flat earth, BUT, the comparative settings might be different? I would think this is only possible due to the differences (as subtle as it is) of the air flow over the wings in a curved atmosphere vs flat atmosphere.

 

[jbriggs444]

I agree, the plane is taking a curved path. i couldn't edit my post as i meant to write, "level" not "curved" path. .so, now you are saying when flying on a round earth, there is no input required, as on a flat earth, BUT, the comparative settings might be different? I would think this is only possible due to the differences (as subtle as it is) of the air flow over the wings in a curved atmosphere vs flat atmosphere.

Has your understanding of the problem been that it asks whether continual control corrections are needed for a properly trimmed and stable aircraft set to fly at constant altitude around a spherical Earth but not for a properly trimmed and stable aircraft set to fly at a constant altitude above a flat earth?

I have understood the problem to ask whether the initial control settings would be different for the two environments, not whether stability is adversely affected.

 

[zanick]

A circle is a curved path.If gravity is the same (as you stated), but the net force is different (straight vs. curved path), then the other forces (aerodynamic & thrust) must be different between your two scenarios (flat Earth vs. round Earth).

So, if a plane flys west at 1038mph, the plane will not rotate because it would remain in the same position in space .its still following the curve of the earth, not requiring any control inputs to fly level, but is NOT rotating in space.would the forces in all directions be the same as if the plane was flying on a flat earth? there would be no need for control inputs to follow the curve because the plane would be flying in a equilibrium of atmospheric pressure, with equibrium of drag va thrust for the given velocity, and lift vs gravity. AND, the plane would not be rotating in space.

 

[zanick]

Has your understanding of the problem been that it asks whether continual control corrections are needed for a properly trimmed and stable aircraft set to fly at constant altitude around a spherical Earth but not for a properly trimmed and stable aircraft set to fly at a constant altitude above a flat earth?

I have understood the problem to ask whether the initial control settings would be different for the two environments, not whether stability is adversely affected.

i think the question has morphed into two, maybe 3 , unintentionally.
1. does a properly trimmed and conditionally stable aircraft require additional control inputs to follow the Earth's curve at a set altitude and speed.
2. does this properly trimmed aircraft , also fly on a flat Earth with no changes to the control settings from the round earth.
2a. above but with the aircraft being conditionally unstable.

 

[zanick]

You cannot remove them from the question because they are part of the question. As you go around the curve of the Earth at a minimum (even with all of the thermal and vibrational instabilities removed) the change in the direction of gravity is a perturbation from equilibrium. So the question is specifically, how does this aircraft fly in the face of an upward perturbation in pitch. The answer depends on the stability of the aircraft.

And if that direction changes then it is a perturbation from equilibrium. Some planes, without control input, will have progressively larger perturbations and others will return back to equilibrium.

That is because the equilibrium is stable. You could easily conceive an unstable tarmac which would require a control force to keep it parked, e.g. an icy tarmac at the top of a hill.

That makes more sense. however to your last point and set of conditions for an unstable equilibrium . Would the force required to keep the nose down during Earth rotation, upset the plane's orientation?

 

[jbriggs444]

Would the force required to keep the nose down during Earth rotation, upset the plane's orientation?

What force? How much torque is required to produce zero angular acceleration?

 

[Dale]

Would the force required to keep the nose down during Earth rotation, upset the plane's orientation?

Are you asking about on the tarmac or during flight?

 

[rcgldr]

For a normal plane with positive pitch stability, then the throttle and (elevator) trim settings will hold an altitude (technically fly about a specific density of air). So there will be some fluctuation over time, but it will stay at the same "altitude" with respect to effective density of the air, and will follow the curvature of the Earth in the same manner that the atmosphere does, without any adjustment. As fuel is consumed, the plane will get lighter, and this will affect the overall "trim", but the plane will just hold a slightly different altitude depending on fuel consumed.

 

[A.T.]

.so, now you are saying when flying on a round earth, there is no input required, as on a flat earth, BUT, the comparative settings might be different?

The question of input vs. setting seems like a matter of pilot convenience, not a matter of physics. All you can say in general is that you will need different net forces for the two cases.

 

[sophiecentaur]

The effect we are discussing is probably a lot less than the effect on the aircraft trim when a member of the cabin staff walks from the galley to the rearmost seat.
[Edit: probably more like a mouse]

 

[OmCheeto]

The effect we are discussing is probably a lot less than the effect on the aircraft trim when a member of the cabin staff walks from the galley to the rearmost seat.
[Edit: probably more like a mouse]

I actually worked that out.
Part of the way, at least.
I got up to the point where the torque exhibited by a child(25kg) produced an angular acceleration(α = 0.000012 s^-2) walking the distance(10 m) to the lou and found that it would take longer than a second(from Δθ = ω0t + 1/2αt^2) to shift a 747(70 m long, 300000 kg) about its center of gravity(35 m), based on its moment of inertia (1,470,000,000 kg m^2), by an angle(0.000006 radians) that yielded the desired matching earth-747 nose to COG height defect(≈ 1/10 mm).
And then I looked at all of the equations to get there, and decided I didn't feel like finishing the problem.

hmmmm... Sounds like a grand problem, for a maths textbook.

 

[sophiecentaur]

And then I looked at all of the equations to get there, and decided I didn't feel like finishing the problem.

Mea culpa too.
But any answer you came up with would have been just as irrelevant to the price of fish and most of the rest of this thread. The whole topic could be dealt with in a single paragraph, imo.

 

[OmCheeto]

Mea culpa too.
But any answer you came up with would have been just as irrelevant to the price of fish and most of the rest of this thread. The whole topic could be dealt with in a single paragraph, imo.

Well, that all depends on if you mean a paragraph of maths, or a paragraph of words.

No amount of words can answer this, IMHO.

ps. When Greg asks for upgrade ideas to the forum next time, please remind me to post that such problems should be sent to the "homework" section, where I'm pretty sure it would have died a quick, and merciful death.

 

[olivermsun]

i think the question has morphed into two, maybe 3 , unintentionally.
1. does a properly trimmed and conditionally stable aircraft require additional control inputs to follow the Earth's curve at a set altitude and speed.
2. does this properly trimmed aircraft , also fly on a flat Earth with no changes to the control settings from the round earth.
2a. above but with the aircraft being conditionally unstable.

“Properly trimmed” includes everything that affects the (desired) flight characteristics of the plane: the speed and weight balance of the plane, the pressure and density of the air outside, the wind, etc. If the pilot notices the plane slowly gaining pitch and altitude, whether because of the earth’s curvature or some other reason, the trim can be corrected. In principle the same plane would then seem to be out of trim for flight in the exact same conditions except over a flat earth. That should answer 1 & 2. 2b shouldn’t change anything except that being out of trim is self-reinforcing.

 

[rcgldr]

“Properly trimmed” includes everything that affects the (desired) flight characteristics of the plane: the speed and weight balance of the plane, the pressure and density of the air outside, the wind, etc. If the pilot notices the plane slowly gaining pitch and altitude, whether because of the earth’s curvature or some other reason, the trim can be corrected. In principle the same plane would then seem to be out of trim for flight in the exact same conditions except over a flat earth. That should answer 1 & 2. 2b shouldn’t change anything except that being out of trim is self-reinforcing.

As mentioned in post #116, assume a normal plane with a center of mass slightly in front of the center of lift, and some up elevator (this is the elevator "trim") to generate aerodynamic downforce at the tail which compensates for the center of gravitational force being in front of the aerodynamic lift force. If "properly trimmed", the plane self corrects. If the plane pitches up, it slows down, reducing the downforce at the elevator, and the plane will pitch down and speed up. If the plane pitches down, it will speed up, increasing the downforce at the elevator, and the plane will pitch up and slow down. If due to curvature of the atmosphere about the earth, the plane travels into lower density air due to the curved atmosphere, the lift on the main wing decreases (and typically power from the engine also decreases), so the plane will tend to follow the curvature of the atmosphere around the Earth since the plane is trimmed to fly "level" at a certain speed and air density.