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

[jbriggs444]

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.

To dig down into the noise...

An aircraft flying east will be pitching down more rapidly than an aircraft parked facing the rising sun. Similarly, an aircraft flying west will be pitching up less rapidly than an aircraft parked facing the setting sun.

To say nothing about the discrepancies as roll and yaw change roles for aircraft flying north or south in the temperate zones.

 

[CWatters]

Darn it. You're right.

 

[gary350]

I fly airplanes if you set auto pilot to fly level it will follow the curve of the Earth all the way around the world. There are 2 ways to go down, push the controls forward the tail goes up and the nose does down OR reduce speed and gravity pulls you down. If you want to land the airplane you reduce speed but if your a fighter pilot dropping a bomb dive bomb the target at full speed.

 

[CWatters]

Isnt that because auto pilots maintain a set altitude.

Suppose you were in an infinitly powerfully military jet. If you point the nose up at 45 degrees you will keep going up in a straight line. If you point it upwards at say 20, 10, 5 or 1 degree it will do the same. Point it "up" at 0 degrees and somehow it now doesn't move in a straight line but instead follows the curve of the earth? Not without an auto pilot to maintain altitude.

 

[CWatters]

I think perhaps the answer is power...

To maintain constant height and constant speed an aircraft will require a certain amount of power. If the aircraft were to try to climb (by not following the curvature of the earth) then the additional energy for that would ultimately have to come from the engine. If power is set constant then the aircraft can't climb and must follow the curvature of the earth.

 

[sophiecentaur]

The angle is surely too small to be significant (angle between chord and tangent?). i reckon it will be l/r where l is the length of the plane (say 20m) and r is the Earth's radius (6e6m) is that worth bothering about?

 

[gary350]

Magnet compass makes the airplane follow the setting which is actually a circle around earth. If you set the airplane to fly at 5000 ft it will fly all the way around earth. How is it possible to fly an airplane in a straight line? If you lock controls so they never move no guarantee your flying straight. Even if you could fly in a straight line soon elevation will change and air becomes too thin for lift then airplane can no longer fly straight. Even with the most powerful engine you could not fly straight very long the engine burns fuel & air at high elevation there is no oxygen to burn fuel. Airplanes are not designed to fly in a straight line. Nothing goes in a straight line, cars follow the road, boats follow the ocean, bullets do not shoot straight, sunlight is not a straight line either.

 

[CWatters]

I think the real world issues are understood. We're talking about a hypothetical "ideal" aircraft that can fly in straight lines, no turbulence etc. In such an unrealistic situation would the autopilot have to make a tiny nose down correction to follow the Earth's curvature? I think we've established that any such input ranges from zero to incredibly small but which is it?

 

[OmCheeto]

The angle is surely too small to be significant (angle between chord and tangent?). i reckon it will be l/r where l is the length of the plane (say 20m) and r is the Earth's radius (6e6m) is that worth bothering about?

Not if you have a REALLY big plane.

In which case, I'm not sure if the plane is flying up or down.
I guess it depends on where you are seated.

 

[A.T.]

Going back to the original comparison:

(all other factors remaining constant when comparing a suppose flat Earth vs round Earth set of conditions)

The plane going around a round Earth has a net centripetal force, while the plane going straight has zero net force. So these two conditions are not equal. For example, the amounts of required lift are different. That is the physics.

How the amount of lift can be controlled is another question, and the answer depends on what exactly you mean by "all other factors remaining constant".

 

[CWatters]

Ok so that explains half the problem. Less lift is required on a spherical Earth than a flat Earth due to the need for a centripetal force.

But the aircraft also has to rotate to account for the change in latitude or longitude relative to the starting point. Obviously only a small torque is required. My feeling is that this provided by the same mechanism that provides longitudinal stability?

 

[sophiecentaur]

Not if you have a REALLY big plane.

In which case, I'm not sure if the plane is flying up or down.
I guess it depends on where you are seated.

View attachment 225092

What a great distraction! And you managed to make me think twice about it Grrrr.
But no part of the plane is increasing or decreasing its height above ground so, wherever you are sitting, The centre of the plane is a tiny bit closer than the rest and if the pilot has managed to eliminate all other factors and is concentrating on what we are discussing, no one is going up or down.

 

[sophiecentaur]

Obviously only a small torque is required.

I would say that the only torque needed is to compensate for the aerodynamic forces. If there were no air (sky hooks) the plane would keep rotating at the correct rate, once the pilot had got it right - as in the ISS and other satellites. I will tear my hair out if someone brings up the possible effect of the Earth's magnetic field.

 

[A.T.]

Ok so that explains half the problem. Less lift is required on a spherical Earth than a flat Earth due to the need for a centripetal force.

And one way to achieve less lift, is to reduce the pitch of the nose. So that is one possible way to correct for the curvature of the Earth.

But the aircraft also has to rotate to account for the change in latitude or longitude relative to the starting point. Obviously only a small torque is required. My feeling is that this provided by the same mechanism that provides longitudinal stability?

The stabilization of the orientation can be passive or active, as discussed on page 1.

 

[sophiecentaur]

Obviously only a small torque is required.

What is "obvious" about needing any torque to compensate for this effect?

 

[CWatters]

The starting position (on the ground) isn't rotating. I made that mistake above.

At least it's not rotating at the required rate.

 

[jbriggs444]

The starting position (on the ground) isn't rotating. I made that mistake above.

At least it's not rotating at the required rate.

But the torque needed to correct that situation is a one time input. Once you're cruising, no net torque is required to maintain the appropriate pitch rate -- whatever that pitch rate turns out to be.

 

[hutchphd]

But the torque needed to correct that situation is a one time input. Once you're cruising, no net torque is required to maintain the appropriate pitch rate -- whatever that pitch rate turns out to be.

If the plane is stable, the center of gravity is "forward" of the center of lift. The pilot "levels off" by choosing an engine speed (and elevator setting) that results in no altitude change. It is a perfect negative feedback system and no further input is required .
Suppose instead the Earth is flat. Do the same flight inputs (speed/elevator) produce level flight? I think equivalence argues yes. Tthe feedback responses might be different slightly.because of gradients.
Am I missing something?

 

[zanick]

I guess you have to clarify your frame of refernce. yes, going eastward from the perspective from the sun, the plane rotates faster than if it was going eastward. from the perspective of someone on earth, they would rotate the same. regardless , there is no control inputs from either case that would need to be made to produce this rotation, just as there is no inputs needed to make this rotation as the plane sits on the ground.

To dig down into the noise...

An aircraft flying east will be pitching down more rapidly than an aircraft parked facing the rising sun. Similarly, an aircraft flying west will be pitching up less rapidly than an aircraft parked facing the setting sun.

To say nothing about the discrepancies as roll and yaw change roles for aircraft flying north or south in the temperate zones.

 

[zanick]

If the plane is stable, the center of gravity is "forward" of the center of lift. The pilot "levels off" by choosing an engine speed (and elevator setting) that results in no altitude change. It is a perfect negative feedback system and no further input is required .
Suppose instead the Earth is flat. Do the same flight inputs (speed/elevator) produce level flight? I think equivalence argues yes. Tthe feedback responses might be different slightly.because of gradients.
Am I missing something?

exactly right as i see it too. you are flying level, but not straight. the curve of the Earth , curves the atmosphere, and by flying at a set pressure altitude, the plane rotates with the path around the earth, but no controls are needed to do this

 

[zanick]

But the torque needed to correct that situation is a one time input. Once you're cruising, no net torque is required to maintain the appropriate pitch rate -- whatever that pitch rate turns out to be.

there is no pitch rate .you are flying perfectly level, but not straight. (cuved path) .. any change in pitch would require an unbalanced force on the lifting surfaces and this doesn't happen. if the Earth was suddenly flat, the plane would continue to fly straight and level. the only change would be the atmosphere was not curved anymore.

 

[zanick]

Darn it. You're right.

right about what? yes, the rotation is faster when flying east vs west, but there is no difference in the contol inputs in either case when flying level.
the plane could be flying level and traveling east, and make a huge u turn (now flying west) and those same exact control settings would create the same level flight . However there would be ONE major difference. due to the difference in centripetal force, the eastward plane would be effectively heavier and might need to set level flight with a little more elevator input. Eovtos effect.

 

[zanick]

I think perhaps the answer is power...

To maintain constant height and constant speed an aircraft will require a certain amount of power. If the aircraft were to try to climb (by not following the curvature of the earth) then the additional energy for that would ultimately have to come from the engine. If power is set constant then the aircraft can't climb and must follow the curvature of the earth.

yes, in order to fly "straight" instead following the curve, an airplane must gain potential energy and it has to come from somewhere. it would work against gravity to get to a higher distance from the Earth and take a certain amount of energy to do this, which means.. more power! :)

 

[russ_watters]

Ok so that explains half the problem. Less lift is required on a spherical Earth than a flat earth...

Related to @jbriggs444 's point yesterday, it is less flying east and more flying west. Remember, our baseline isn't a stationary Earth, it is a rotating Earth (and therefore moving plane). Flying east you increase that speed and flying west you decrease it.

 

[russ_watters]

But the torque needed to correct that situation is a one time input. Once you're cruising, no net torque is required to maintain the appropriate pitch rate -- whatever that pitch rate turns out to be.

I like this combined with your point yesterday best: when you take off you change your tangential speed which changes both your apparent g and rotation rate. But after achieving cruise, both are constant until you start heading down again (other caveats); no further input needed.

 

[jbriggs444]

there is no pitch rate .you are flying perfectly level, but not straight. (cuved path)

Fair enough. "absolute rotation rate about the pitch axis" captures the relevant notion better, perhaps.

 

[jbriggs444]

yes, in order to fly "straight" instead following the curve, an airplane must gain potential energy and it has to come from somewhere.

For instance from the lessened induced drag when flying east with less lift required. Better throttle back.

 

[A.T.]

However there would be ONE major difference. due to the difference in centripetal force, the eastward plane would be effectively heavier...

Lighter. And the same applies to your comparison of round Earth vs flat Earth.

... and might need to set level flight with a little more elevator input.

Different lift requires different thrust. So I wouldn't say that no control inputs are needed to account for the curvature of the Earth.

 

[sophiecentaur]

The starting position (on the ground) isn't rotating. I made that mistake above.

At least it's not rotating at the required rate.

It is rotating - once a day, which is almost enough for a conventional passenger aircraft.

 

[zanick]

Lighter. And the same applies to your comparison of round Earth vs flat Earth.Different lift requires different thrust. So I wouldn't say that no control inputs are needed to account for the curvature of the Earth.

i didnt say "differnet lift" i said, different elevator setting ... the plane would be lighter due to the spin of the earth, so it basically would weigh more going west vs east. so, for just a direction change, some elevator input would have to be done to change this equilibrium force of lift = gravity to stay at a given altitude.

 

[zanick]

For instance from the lessened induced drag when flying east with less lift required. Better throttle back.

lessen induced drag? to to lift of the aircraft being effectively heavier flying west? yes, throttle back a little . ;)

 

[zanick]

Not if you have a REALLY big plane.

In which case, I'm not sure if the plane is flying up or down.
I guess it depends on where you are seated.

View attachment 225092

thats a great diagram.. I was explaining it that way to my pilot father and we both scratched our heads. obviously, its the reason there is NO adjustments to the controls once level flight is established. BUT, if the world suddenly became flat, would the forces be the same on the aircraft ? can the relative wind be curved? and if so, with a straight wing, if the wind straightened, what would this oversized plane do?

 

[zanick]

So, the oversized plane is a great thought experiment. think of this plane, instead of circling the Earth with gravity, it is on a string to its center of gravity. (string represents gravity, since gravity is much like the centripetal force of the string. suddenly the plane breaks free. and suddenly it flys onto a plane with. does it fly straight with its current control settings? (assuming it flys off to a flat Earth with gravity pointing straight down_)

 

[OCR]

...think of this plane, (snip) , it is on a string...

Oh, my God!... for a moment there, I thought you were going to post:

"think of this plane, it is on a conveyor" ... .

Carry on...

 

[A.T.]

i didnt say "differnet lift" .

But you do need different amounts of lift for flying straight on a flat Earth vs. flying on a circle around a spherical Earth.

different elevator setting ..

If that's how you achieve different net lift, fine. But you will likely need to adjust thrust was well. In any case, you have to adjust something between these two cases.