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

[zanick]

I've been in discussions on another board with a physicist and he contends that a pilot in a plane will need to put a 1 degree downward direction input to the controls to account for the 1 degree of curvature rate at 500mph.
as small as those control inputs are required, he says that the control surfaces need to conform to the shape of the earth.

I disagree

I contend that no control is needed due to the aircraft being in level flight, with gravity pointing straight down. the plane flies level, the atmosphere is curved and no adjustment is ever needed. (all other factors remaining constant when comparing a suppose flat Earth vs round Earth set of conditions)
I equate the condition to that of a control line airplane... the airplane just stays perpendicular to the centripetal force of the string... it follows the circular path naturally with no control input.

can the board here add some color to the example and correct me if I am wrong in my analysis?

thanks!

ps as a side note, our discussion started to talk about the ISS . how does it rotate around the Earth .. does it have a natural rotation about its own axis to match 1 revolution every 90 mins? or is it effectively tidally locked to the Earth via how it was launched?

 

[A.T.]

or is it effectively tidally locked to the Earth via how it was launched?

It is made to rotate once per orbit by the initial lunch and eventually corrected by control rockets. Tidal torque alone is not sufficient for such a small object. Same for a plane.

But a plane with a lift center that is above the gravity center can have an self orienting torque too, similar to the plane on a line that you mentioned.

 

[sophiecentaur]

It is made to rotate once per orbit by the initial lunch

Brilliant typo. You must have been hungry at the time of posting.

 

[sophiecentaur]

.. it follows the circular path naturally with no control input.

The CM of the plane would need to be 'outside' the attachment point to ensure that the angle between plane and line remains constant. The "control input" is passive and built in.

 

[Dale]

But a plane with a lift center that is above the gravity center can have an self orienting torque too,

And a plane with a center of lift below the center of gravity will be unstable and will require control input to avoid crashing even on a flat earth.

 

[zanick]

It is made to rotate once per orbit by the initial lunch and eventually corrected by control rockets. Tidal torque alone is not sufficient for such a small object. Same for a plane.

But a plane with a lift center that is above the gravity center can have an self orienting torque too, similar to the plane on a line that you mentioned.

can you further explain the self orienting "torque"?

what about the comparisons to the ISS in orbit to a plane. does the ISS have a intial rotation that matches its speed around the Earth to remain in a constant orientation, or is that controlled by corrective forces? in space , the ISS is just falling, but is the CM position a factor for its auto orientation?

 

[Dale]

can you further explain the self orienting "torque"?

Take a pencil and hold it vertically by one end, once with the center of mass above your hand and once with the center of mass below your hand. Which feels more stable?

what about the comparisons to the ISS in orbit to a plane.

I don’t think that the comparison is particularly relevant to the question you are asking.

 

[zanick]

I understand the aerodynamics of airplanes and their mass distribution in relation to the center of lift or pressure. Sure, the CG ahead of the CP allows for a stable aircraft when near stall, at the cost of more overall drag and a higher stall speed. However, I'm just trying to see how this is a force that allows for the airplane to follow the curve of the earth. if you had a plane that had its CG very far rearward, it would still fly, be more unstable, but would follow the Earth curve by just flying level (parallel to the relative wind) The nose would never have to be controlled down because the aircraft would always be following a consistent air pressure region. (assuming there are no variables such as air currents, temp change, density changes). i mean, an blimp travels around the Earth , with no "nosing " of the craft downward to follow the curve... nor does a submarine. this is the argument I am trying to fight, and there is a physicist, that seems that he "knows" that the airplanes, have to "nose down" ever so slightly , to follow the Earth curve. again, i disagree and am looking for more logic from the board to either learn if I am wrong or help correct this misconception.

 

[zanick]

A.T. and Dale, are you talking about the CG vs lift cente as far as position aft or rearward, or are you literally talking "above" or "below". the reason i ask is that many low wing airplanes have the center of mass above the lift cener, while high wing cessna's have it above the CM and yes, are very stable because of it. however, how does this relate to a centering torque as an aircraft circles the globe. it seems like it shouldn't matter.

 

[zanick]

Here is a response to me by the physicist on a discussion of the topic. This seems incorrect, but I am basing my view on the fact that the atmosphere is curved around the Earth and the force of gravity which is perpendicular to the flight direction, should naturally follow the curve with no adjustment. he disagrees , adamantly the video he refers to is by a pilot. also i think he has it wrong. however, he has a video that shows the pendulous vanes compensating for Earth curvature at a rate of 20 degrees over 8 mins, much faster than a 500mph plane flying around the Earth which only would require 1 degree change (correction) every 8 mins.


>>>>>>>>>>>>>>>>>>>>>>I have re-viewed Wolfie's video: "Do aircraft change attitude to follow the curvature of the Earth?" and I find absolutely nothing wrong with his analysis. No, his autopilot really is incorporating a tiny correction for sphericity into the normal trim changes for correction for other variants. It has to. It doesn't know it's flying around a globe, it is set to correct barometric altitude, and as that barometric reading changes as the plane flies into higher, lower pressure air, it must adjust trim slightly downwards, even though it is a much tinier component of trim than any others. Planes have inertia of forward motion, they do not magically stay at a specific altitude or magically bend their path. they are NOT buoyant and the atmosphere doesn't hold them up. The autopilot finds itself, due to travel around the earth, in an inadvertent climb, and adjusts to correct it by trimming down. You see, an autopilot, or any pilot for that matter, changes trim periodically, not continuously. This makes the plane's path through the air a series of successive straight line paths that only approximate a circle around the earth. IF you could adjust trim perfectly, you would NOT need to keep adjusting it, but that is a pipe dream. The inertia of motion of an aircraft is in one direction, not a curved direction. It is NOT in orbit where everything is balanced. It is flying an orbit within the atmosphere, if you will, by brute force. This means it has to steer downward as the Earth falls out from under it due to travel. The autopilot/pilot does not know it/he is supposed to fly an always down-curving path. It is simply told to keep the barometer steady with what it can control, the trim tabs. And it doesn't respond continuously, but periodically, which makes the circular flight around the Earth into geometric approximations of a circle, using straight paths. If you graphed the motion of the trim you would find a train of semi-sinusoidal deviations up and down to correct for flight, but you would find they were riding on an inclined step-wise straight line ascending to the right that accomplishes the change in direction over the sphere segment traveled. This graph for a flat Earth would find that inclined supporting component to have zero slope.

 

[Dale]

it would still fly, be more unstable, but would follow the Earth curve by just flying level (parallel to the relative wind) The nose would never have to be controlled down

If it is unstable then it always needs to be actively controlled to do anything . That is essentially what it means to be unstable. It doesn’t make sense to do the thought experiment with an unstable aircraft. An unstable aircraft, when uncontrolled, doesn’t neatly follow the curve of the earth, it veers off randomly and crashes!

With a stable aircraft there is a natural torque that makes it nose down as needed to follow the curve without control.

are you literally talking "above" or "below".

I am literally talking about above and below, in the vertical direction. Stability in all directions is important, but here we are talking about stability in the pitch axis. Yes, unstable aircraft exist, but they must be actively controlled anyway. To ask about following the curve of the Earth without control you have to have an aircraft that can fly long distances without control. That requires a very stable design, including a center of gravity below the center of lift.

 

[David Lewis]

And a plane with a center of lift below the center of gravity will be unstable...

That will be a destabilizing influence. Stabilizing forces in pitch are greater than destabilizing ones in a correctly designed and trimmed airplane.

 

[zanick]

If it is unstable then it always needs to be actively controlled to do anything . That is essentially what it means to be unstable. It doesn’t make sense to do the thought experiment with an unstable aircraft. An unstable aircraft, when uncontrolled, doesn’t neatly follow the curve of the earth, it veers off randomly and crashes!

With a stable aircraft there is a natural torque that makes it nose down as needed to follow the curve without control.

I am literally talking about above and below, in the vertical direction. Stability in all directions is important, but here we are talking about stability in the pitch axis. Yes, unstable aircraft exist, but they must be actively controlled anyway. To ask about following the curve of the Earth without control you have to have an aircraft that can fly long distances without control. That requires a very stable design, including a center of gravity below the center of lift.

unstable is different than conditionally unstable. a aircraft with its cg at its center of pressure, or even behind it, can be very stable at normal flyiing speeds. infact have less drag as well. But, near stall, can be much more unstable and unpredictable. I don't think we are talking about that..

So, with a stable or aircraft with its CG at its center of pressure, why would it have a "natural torque"? that makes it nose down? this is the part i was looking to understand. it seems to me, if the plane is flying level. (not straight due to the Earth curve), and there is no active control to follow the curve. But, in reality, the plane is rotating about its axis, so is it the atmosphere that causes this rotation?

 

[A.T.]

does the ISS have a intial rotation that matches its speed around the Earth to remain in a constant orientation, or is that controlled by corrective forces?

Both. You make it spin at the desired rate and then correct if there is any drift.

in space , the ISS is just falling, but is the CM position a factor for its auto orientation?

There is no "auto orientation", by gravity only, because the tidal torque is too small.

 

[A.T.]

But, in reality, the plane is rotating about its axis, so is it the atmosphere that causes this rotation?

The combination of aerodynamics and thrust orients the plane.

 

[sophiecentaur]

but is the CM position a factor for its auto orientation?

Once it (ISS or whatever) has been set rotating at the orbit angular frequency, it would tend to keep going. In a vacuum, there will be no other forces to create a torque so it should stay 'facing' along a radius. However, the solar panels need to be rotated to face the Sun and the bearing and motor friction could produce a torque back on the craft. The parallel with an aircraft situation is pretty remote in the same way that the Coriolis force acting on a plane doesn't count either - but just look at the 'Coriolis effect' on a Polar orbiting satellite! It's so extreme that I don't even think it is given that name.

 

[Dale]

So, with a stable or aircraft with its CG at its center of pressure, why would it have a "natural torque"?

I am not aware of the existence of such aircraft so I cannot comment on their operating mechanism. How would such a craft be stable?

 

[russ_watters]

To be honest, it doesn't look to me like any of the posts in this thread are addressing the question being asked in the OP. The question has nothing to do with aircraft stability and performance, but only to do with direction of flight. And it has an obvious answer:

I've been in discussions on another board with a physicist and he contends that a pilot in a plane will need to put a 1 degree downward direction input to the controls to account for the 1 degree of curvature rate at 500mph.
as small as those control inputs are required, he says that the control surfaces need to conform to the shape of the earth.

I disagree

You are correct. The direction of motion of an object moving around a circle is always tangential to the circle (the direction of flight is always level with the ground). This is basic geometry.

The answer of "1 degree of curvature rate at 500mph" doesn't even make any sense: 1 degree of downward angle is not a "curvature rate". If we want to use rectangular coordinates and express the change in angle as a rate, then the rate for 500mph at the equator would be 7.2 degrees per hour.

 

[zanick]

Sorry , i miss quoted him and someone else that bought up that point. yes, i think we rounded it to 8 degrees per hour at 500mph (not 1 degree )
Thanks for the clarification. seems like it is a simple problem, but its been a while since my engineering days, and he touted himself as a physicist, so i started to second guess what i thought would be more likely. that the airplane flies perpendicular to the ground at all times,, no input is needed, and the aircraft will curve around the Earth with no "control" input because the angle of the direction of gravity follows your every move. ;)

 

[zanick]

I am not aware of the existence of such aircraft so I cannot comment on their operating mechanism. How would such a craft be stable?

many aircraft can operate this way. a misplace of passengers and luggage can match CG with center of pressure in a light airplane.
an F16 is conditionally unstable by the way. again, it might be perfectly stable during flight, but would be much more risky to land due to instability at slower speeds.
However, i don't think this has anything to do with controlling in an around the Earth voyage. even an "unstable" aircraft would control the plane to make sure it was always level with respect to the surface of the Earth below... but curving due to the atmosphere curving, and the force of gravity always remaining perpendicular.

 

[CWatters]

8 degrees per hour is tiny. Typically elevator movements can produce pitch rates of several degrees per second, for example at take off. So the elevator deflection required for 8 degrees per hour will be tiny, might be less than the backlash in the controls?

Yes the aircraft does have to nose down to follow the curvature of the earth, and some control input is required to achieve that, but i think the magnitude required will be hidden in the noise.

 

[A.T.]

However, i don't think this has anything to do with controlling in an around the Earth voyage. even an "unstable" aircraft would control the plane to make sure it was always level with respect to the surface of the Earth below... but curving due to the atmosphere curving, and the force of gravity always remaining perpendicular.

If you control to stay level with respect to the surface of the Earth below, then you automatically also control to follow the curvature of the Earth.

 

[A.T.]

...but i think the magnitude required will be hidden in the noise.

That's why the whole approach to understand the orbital mechanics of the ISS, through the much more messy and complex mechanics of airplanes seems rather absurd to me.

 

[CWatters]

Thought about this a bit more while out for a walk. An aircraft sitting stationary on the ground is already rotating at the required rate. So is the air that it's flying in so no control input is required to account for the curvature of the earth.

 

[Tom Kunich]

Take a pencil and hold it vertically by one end, once with the center of mass above your hand and once with the center of mass below your hand. Which feels more stable?

I don’t think that the comparison is particularly relevant to the question you are asking.

The center of mass is usually above the center of lift but that center is so wide that it is self balancing. That is - the center of lift is not a point but a plane.

 

[Dale]

The center of mass is usually above the center of lift but that center is so wide that it is self balancing. That is - the center of lift is not a point but a plane.

That makes a lot of sense, thanks!

 

[zanick]

To be honest, it doesn't look to me like any of the posts in this thread are addressing the question being asked in the OP. The question has nothing to do with aircraft stability and performance, but only to do with direction of flight. And it has an obvious answer:

You are correct. The direction of motion of an object moving around a circle is always tangential to the circle (the direction of flight is always level with the ground). This is basic geometry.

The answer of "1 degree of curvature rate at 500mph" doesn't even make any sense: 1 degree of downward angle is not a "curvature rate". If we want to use rectangular coordinates and express the change in angle as a rate, then the rate for 500mph at the equator would be 7.2 degrees per hour.

Russ, i was reading your reply again and wanted to clarify one small but important point. is the "direction of motion always tangential to the circle"?? or does the path , follow the circle meaning that its orientation is tangential to the circle? i would think that the travel path is a pure arc, not a set of tangents, no matter how small they are broken up into sections. Just making sure I am very clear on the terminology and the representation of what is actually happening. as you will see, others will think the plane is making very small adjustments to follow the curve and that i don't believe is true

 

[zanick]

8 degrees per hour is tiny. Typically elevator movements can produce pitch rates of several degrees per second, for example at take off. So the elevator deflection required for 8 degrees per hour will be tiny, might be less than the backlash in the controls?

Yes the aircraft does have to nose down to follow the curvature of the earth, and some control input is required to achieve that, but i think the magnitude required will be hidden in the noise.

yes, 8 degrees per hour is tiny, but that's a strawman for a reason of why it happens, right? yes, the noise of flight forces, is far greater, but if we eliminate them all and just say, what if the plane has a set level course.. will it fly around the Earth with no input? the answer is yes, because level flight, doesn't equal straight flight. in order to fly straight (which would be a tangent and mean you would fly off into space) the plane has to gain altitude above the Earth and that requires increases of energy. since the plane flys in a equilibrium of differential pressure to maintain level flight, the plane just follows the curve of the atmosphere , which follows the curve of the earth.

 

[russ_watters]

I have re-viewed Wolfie's video: "Do aircraft change attitude to follow the curvature of the Earth?" and I find absolutely nothing wrong with his analysis.

I do:
He describes the rate of change of orientation as being below the threshold needed to detect motion. This is wrong. The change in orientation is continuous and the g-force constant, which means there is nothing to feel at all. No threshold needed! About the only quibble one could make is that due to the motion around the Earth you have a slightly lower than normal, but constant apparent weight traveling one way and slightly higher apparent weight travling the other.

Russ, i was reading your reply again and wanted to clarify one small but important point. is the "direction of motion always tangential to the circle"??

Yes, if we don't include the constant fluctuations and control inputs needed to maintain level flight in unstable air.

or does the path , follow the circle meaning that its orientation is tangential to the circle?

I don't see how this question differs from the previous, but may have an idea:

i would think that the travel path is a pure arc, not a set of tangents, no matter how small they are broken up into sections.

Have you taken calculus yet? A basic purpose of calculus is to eliminate the distinction between a bunch of independent segments and a continuous arc. By making the segments smaller and smaller without limit, the result *is* a continuous arc.

Moreover, @CWatters point is well taken and can be applied here: if the segments were separated, the plane would need to start and stop rotating over and over again. It's easier to model it as a continuous rotation that is there before the plane even takes off and never changes.

 

[zanick]

Thought about this a bit more while out for a walk. An aircraft sitting stationary on the ground is already rotating at the required rate. So is the air that it's flying in so no control input is required to account for the curvature of the earth.

Yes, and that's a great perspective to look at the problem through. so, sitting on the ground, the Earth provides the small force to rotate the plane, as does the atmosphere.
Ive always explained it by using the analogy of a control line airplane. its orientation is always perpendicular to the center of rotation, the string represents centripetal force and the plane always flies perpendicular to this force.
where i start to get confused is when you think about the control surface orientation for the control line example. the atmosphere is curved, so the plane flys in an equal pressure region... but what if the Earth suddenly became flat (and the gravitational force and direction was not changed). would the the control orientation still provide level flight? the relative wind faces the direction of travel, and i suppose the wings hit the air mass perpendicular to ground, but does the tail section as its hitting the air mass that is ever so slightly lower in altitude. when on a flat earth, the plane might have a slight tendency to rise or fall now. this would imply that on a round Earth flight path, the curvature is already set into the control settings. true?

However, all this is over and above the original question, and i think we have the answer. regardless of the last thought here... once the controls are set for level flight, no adjustment is needed . the plane is flying level with respect to the Earth below. Just as CW commented ,the plane rotates the Earth when on the ground sitting flat and level .

 

[zanick]

I do:
He describes the rate of change of orientation as being below the threshold needed to detect motion. This is wrong. The change in orientation is continuous and the g-force constant, which means there is nothing to feel at all. No threshold needed! About the only quibble one could make is that due to the motion around the Earth you have a slightly lower than normal, but constant apparent weight traveling one way and slightly higher apparent weight travling the other.

Yes, if we don't include the constant fluctuations and control inputs needed to maintain level flight in unstable air.

I don't see how this question differs from the previous, but may have an idea:

Have you taken calculus yet? A basic purpose of calculus is to eliminate the distinction between a bunch of independent segments and a continuous arc. By making the segments smaller and smaller without limit, the result *is* a continuous arc.

Moreover, @CWatters point is well taken and can be applied here: if the segments were separated, the plane would need to start and stop rotating over and over again. It's easier to model it as a continuous rotation that is there before the plane even takes off and never changes.

yes, calculus! you are right! thanks for the reminder prompt (I've forgotten way too much , if not all of the calculus i took in school. I'm just left with feelings now ;) )

 

[RandyD123]

To be honest, it doesn't look to me like any of the posts in this thread are addressing the question being asked in the OP. The question has nothing to do with aircraft stability and performance, but only to do with direction of flight. And it has an obvious answer:

Funny how you can't get a simple answer. I know 2 pilots and I have asked them both your question. The answer is NO.

 

[russ_watters]

Funny how you can't get a simple answer. I know 2 pilots and I have asked them both your question. The answer is NO.

My question? No to what? I thought I gave a pretty simple answer...

 

[RandyD123]

My question? No to what? I thought I gave a pretty simple answer...

Sorry, the answer to the OP's question is that he is correct. The plane will travel around the Earth at perfect level flight without pointing the nose down.

I was quoting you as in I'm agreeing with what you are saying. Your answer was simple!

 

[RandyD123]

I've been in discussions on another board with a physicist and he contends that a pilot in a plane will need to put a 1 degree downward direction input to the controls to account for the 1 degree of curvature rate at 500mph.
as small as those control inputs are required, he says that the control surfaces need to conform to the shape of the earth.

I disagree

I contend that no control is needed due to the aircraft being in level flight, with gravity pointing straight down. the plane flies level, the atmosphere is curved and no adjustment is ever needed. (all other factors remaining constant when comparing a suppose flat Earth vs round Earth set of conditions)
I equate the condition to that of a control line airplane... the airplane just stays perpendicular to the centripetal force of the string... it follows the circular path naturally with no control input.

You are correct.