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

1. Apr 29, 2018

### 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?

2. Apr 29, 2018

### A.T.

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.

3. Apr 29, 2018

### sophiecentaur

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

4. Apr 29, 2018

### sophiecentaur

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.

5. Apr 29, 2018

### Staff: Mentor

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.

6. Apr 29, 2018

### zanick

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?

7. Apr 29, 2018

### Staff: Mentor

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.

8. Apr 29, 2018

### 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 im 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 im wrong or help correct this misconception.

9. Apr 29, 2018

### 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 shouldnt matter.

10. Apr 29, 2018

### zanick

Here is a response to me by the physicist on a discussion of the topic. This seems incorrect, but im 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.

11. Apr 29, 2018

### Staff: Mentor

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.

Last edited: Apr 29, 2018
12. Apr 29, 2018

### David Lewis

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

13. Apr 30, 2018

### zanick

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 dont 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?

14. Apr 30, 2018

### A.T.

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

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

15. Apr 30, 2018

### A.T.

The combination of aerodynamics and thrust orients the plane.

16. Apr 30, 2018

### sophiecentaur

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.

17. Apr 30, 2018

### Staff: Mentor

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?

Last edited: Apr 30, 2018
18. Apr 30, 2018

### Staff: Mentor

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.

19. Apr 30, 2018

### 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. ;)

20. Apr 30, 2018

### zanick

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.