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

[A.T.]

since gravity is much like the centripetal force of the string.

No it's not. The string force adjusts to whatever is needed to limit the radial distance, while effective gravity has to be exactly balanced to achieve level flight. The lift in your string scenario is indeterminate.

 

[zanick]

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

why do you say this?? if i was flying westward at 1038mph the there would be no centripetal force of the spinning earth, (it would be a condition so that the lift to keep the plane aloft would be equal to, the force of gravity) so, the force of gravity = the force of lift. since the force of gravity is not changing for curved or flat earth, then the lift required would not change. the thrust and drag would be equal too. this is the same reason the plane doesn't need weigh any more or less sitting on the runway on a flat vs curved earth.

 

[zanick]

No it's not. The string force adjusts to whatever is needed to limit the radial distance, while effective gravity has to be exactly balanced to achieve level flight. The lift in your string scenario is indeterminate.

Actually, it is... gravity is balanced with lift to achieve level flight... this would be the same with the "string" we would assume that force that was created by the rotation would only be able to equal a force that was predetermined. hence, that same force of gravity, paired with the force of lift, would be at parity for a given altitude, level flight and of course , thrust and drag would be matched as well to achieve the constant speed. there would be NO change in KE.
therefore, you wouldn't need to adjust anything on the plane for flying on a flat vs round Earth with the control settings. in both cases the same gravitational pull would be present, there for the lift would be the same, therefore the thrust would be the same , therefore the drag would be the same. this is because the plane's direction, in both cases would be"parellel" to the relative wind. (same distance to ground / the center of the Earth )

 

[zanick]

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?

It is a non factor, due to the fact that the tail of the plane and nose of the plane will always be the same distance to the ground... you have to wrap your head about the angles due to the Earth 's curvature and the force of gravity.

 

[zanick]

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?

So, no... the pilot would NOT have to make any adjustments due to an equilibrium of the 4 forces. drag , thrust, gravity and lift. any change of any of the forces would give a change in energy state, and this wouldn't happen. there would be no pilot adjustments needed, not even small ones due to the equilibrium of forces.

 

[jbriggs444]

since the force of gravity is not changing for curved or flat earth

What exactly is being held constant? The apparent force of gravity for a plane parked on the tarmac, the apparent force of gravity for a plane flying 1038 mph east, or the apparent force of gravity for a plane flying 1038 mph west. You cannot hold them all constant at the same time.

 

[Dale]

We're talking about a hypothetical "ideal" aircraft that can fly in straight lines, no turbulence etc.

I think that goes along the lines of the stability from my earlier comments. What you mean by “ideal” is what I meant by “stable”. Such an aircraft must have a natural restorative torque, whether that is due to a center of lift above the center of gravity or a distributed and stable plane of lift below.

 

[zanick]

What exactly is being held constant? The apparent force of gravity for a plane parked on the tarmac, the apparent force of gravity for a plane flying 1038 mph east, or the apparent force of gravity for a plane flying 1038 mph west. You cannot hold them all constant at the same time.

its a simple answer... if we accept that the force of gravity is equal for a flat Earth vs round earth, then THAT is what is being held constant. the magnitude, however the direction is not. the direction would be straight down on a flat Earth and straight to the core on a round earth. comparing different conditions is not how how you keep the variables consistent for comparisons in question. if you want the round Earth to move 1038mph, then the flat Earth would have to be moving as well. if you want to compare one to the other and narrow down the controlled variables, then just compare a plane flying west at 1038mph vs a plane flying over a motionless flat earth. why introduce variables that cloud the question?

 

[zanick]

I think that goes along the lines of the stability from my earlier comments. What you mean by “ideal” is what I meant by “stable”. Such an aircraft must have a natural restorative torque, whether that is due to a center of lift above the center of gravity or a distributed and stable plane of lift below.

there is no restorative forces needed. the atmosphere is curved, so it aerodynamically, is just following a gradient of pressure equilibrium-s.. this is regardless of its CG vs CoL. Even a conditionally unstable plane flying level, will stay level until acted by another force. it doesn't need to dip its nose down, or have a restorative force based on balance of CG and CoL.
i never said "ideal " that was your term for the plane that would have to ONLY deal with the curvature. and that makes sense, because we want to eliminate all the other variables. So, saying stable or ideal. that's fine... whatever it takes to factor out any unrelated factors. once completed, the answer to your question is that there is NO nosing of the plane to follow the Earth's curve. it happens naturally due to the curve of the atmosphere and the angular following of the direction of gravity. CG would never change, CoP would never change, CoL would never change, as well as thrust to drag or lift to gravity.. so , it follows the Earth curve, but no changes are needed to do that to the controls.

 

[Dale]

there is no restorative forces needed.

I think there are. Without restorative forces then the plane crashes.

 

[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

i was thinking a lot about your picture, and you need to change it. the nose and tale are same distances respectively to the ground, regardless if we are talking flat or round earth. the way you drew the picture, the distance of the nose and tail to the ground increases, but it is the distance to the ground on route to the Earth center on a round earth. the distances would be the same...round or flat.

 

[zanick]

I think there are. Without restorative forces then the plane crashes.

what is your logic to determine that outcome? why would you need restorative forces, when the plane is flying in an equilibrium state ?
does a plane crash while sitting on the runway too? same thing. does a blimp crash?

 

[A.T.]

if you want the round Earth to move 1038mph, then the flat Earth would have to be moving as well.

But even when round Earth and flat Earth are both static, you still need different net forces, and thus have to make adjustments.

 

[zanick]

But even when round Earth and flat Earth are both static, you still need different net forces, and thus have to make adjustments.

why would you need net forces to be different. the distance of the front of the wing to the ground is the same round vs flat. so is the rear of the plane vs the ground (flat or round). Because the distance and pressure gradients are the same flat or round, i would think that both set ups would fly level, regardless of the flat or round earth.

what do you mean , " and thus have to make adjustments"? to nose the plane down to follow the curve, or change the set up when comparing the same plane flying on round vs flat earth?

So, we maybe we agree, that once both are flying , there is NO adjustment needed for curve.. correct? but you are arguing that the round set up, might not fly level on the flat environment?

 

[A.T.]

why would you need net forces to be different.

Because moving along a circle requires a different net force than moving along a straight line.

what do you mean , " and thus have to make adjustments"?

Whatever it takes to change the net force. But you cannot keep all controls settings exactly the same, if the net force is to be different.

 

[Dale]

what is your logic to determine that outcome? why would you need restorative forces, when the plane is flying in an equilibrium state ?

Because without restorative forces it will not stay in an equilibrium state. There are always perturbations that take a system out of equilibrium and to return to equilibrium requires a restorative force. If the equilibrium is stable then the restorative forces are part of the system, and if the equilibrium is unstable then the forces must come from external control.

 

[zanick]

Because without restorative forces it will not stay in an equilibrium state. There are always perturbations that take a system out of equilibrium and to return to equilibrium requires a restorative force. If the equilibrium is stable then the restorative forces are part of the system, and if the equilibrium is unstable then the forces must come from external control.

only if the equilibrium state is disrupted, and i contend that it wouldn't be.
we have to distill the problem to eliminate external variable forces.

 

[zanick]

Because moving along a circle requires a different net force than moving along a straight line.Whatever it takes to change the net force. But you cannot keep all controls settings exactly the same, if the net force is to be different.

what is the net force that allows a plane on the ground to move along a circle.. i contend those forces are the same as the plane in flight in an equilibrium state of level flight.

there is no net force because there is no work done, just like the plane on the ground rotates and 0 work is done. no work, no net force required.
the controls all can be fixed for level flight, and never change because there is no net force required .

look at the problem from the opposite perspective. what would the plane do if no pilot input ( control input) was made? then, look at the equilibrium of forces for level flight... what would change as a plane goes around the Earth flying through a curved atmosphere.

does a control line airplane need to "dip its nose" (if tied to the axis of rotation via its belly or top CG point) ? Gravity acts much like the centripetal force of the string .

 

[A.T.]

there is no net force because there is no work done.

This is just wrong. No work done does not imply no net force.

 

[Dale]

only if the equilibrium state is disrupted, and i contend that it wouldn't be.

The equilibrium state is always disturbed. In this case it could be small gusts of wind, little pockets of air with different densities or humidity, sound vibrations, thermal fluctuations, even tidal forces or variations in gravity.

 

[jbriggs444]

its a simple answer... if we accept that the force of gravity is equal for a flat Earth vs round earth, then THAT is what is being held constant.

In that case, the required lift is not constant.

if you want the round Earth to move 1038mph, then the flat Earth would have to be moving as well.

You are aware that a moving flat Earth is silly -- Galilean invariance makes such movement irrelevant,.

if you want to compare one to the other and narrow down the controlled variables, then just compare a plane flying west at 1038mph vs a plane flying over a motionless flat earth. why introduce variables that cloud the question?

To figure out what the question is.

 

[zanick]

This is just wrong. No work done does not imply no net force.

if there is a net force, there has to be work done. do you not agree? and if not, please explain.

 

[zanick]

The equilibrium state is always disturbed. In this case it could be small gusts of wind, little pockets of air with different densities or humidity, sound vibrations, thermal fluctuations, even tidal forces or variations in gravity.

we are in no way talking about any varaibles, gusts of wind, pockets of air, or any other vibrations. we are ONLY talking about the adjustments of a plane flying over a flat vs round Earth and whether the pilot needs to make any corrections for curvature. I think it was agreed that there would be no need for any adjustments to flight control from level flight settings . (other than those that might be made for those variables you mention)

 

[zanick]

In that case, the required lift is not constant.

You are aware that a moving flat Earth is silly -- Galilean invariance makes such movement irrelevant,.

To figure out what the question is.

the question is the topic of the thread. "does a plane have to nose down to follow a curved earth" and the answer is "no". do you not agree?
as far as flat Earth "moving" that was in response to factoring out your implication that flying eastward, with eotvos forces, of about .3% less gravitational forces vs a flat Earth , would require slightly different aircraft control settings if transplanted magically to a flat Earth . ;)

so, why would " the required lift " not be constant, if the gravity was the same on a flat vs round earth. both would have the same lift to gravity balance. both wold have the same thrust to drag balance. the only difference would be that the aircraft on a flat earth, would be flying in a straight line and the aircraft on a curved Earth would be flying in a curved atmosphere.

 

[A.T.]

if there is a net force, there has to be work done. do you not agree?

No.

and if not, please explain.

If the net force is perpendicular to velocity then no work is being done.

 

[A.T.]

if the gravity was the same on a flat vs round earth. both would have the same lift to gravity balance.
both wold have the same thrust to drag balance.

You cannot follow a curved path around a planet, if all the forces balance. You need a centripetal net force for that.

the only difference would be that the aircraft on a flat earth, would be flying in a straight line and the aircraft on a curved Earth would be flying in a curved atmosphere.

Curved path vs. straight path is a crucial difference:
https://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton's_second_law

 

[zanick]

No.If the net force is perpendicular to velocity then no work is being done.

Good, so, you would agree that level flight is a net force perpendicular to velocity and direction of travel is parallel to the relative wind would result in altitude change above the earth.
I know your wheels are turning, but the reason the there is rotational acceleration is due to the atmosphere . again , it is no different than the plane sitting on the ground. is there a net force acting on the plane when it is on the ground? does the planes nose need to be tied to the ground to keep it from raising up?

 

[zanick]

You cannot follow a curved path around a planet, if all the forces balance. You need a centripetal net force for that. Curved path vs. straight path is a crucial difference:
https://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton's_second_law

And gravity provides the centripetal net force. gravity is considered a form of centripetal force

 

[A.T.]

And gravity provides the centripetal net force.

"Net force" is the sum of all forces. 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).

 

[zanick]

No. "Net force" is the sum of all forces. 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).

you are forgetting the atmosphere is curved. the plane is NOT taking a curved path. it is at the same altitude always, and this doesn't change, so no changes to control inputs are needed to follow the Earth's curve because it is always level, at the same distance above the Earth with the force of gravity pulling it straight down. again, consider a control line airplane or a blimp. the blimp for example doesn't need to make any changes to its flight path or orientation, all it needs to do is add thrust to move forward and that thrust equaling the drag at a given speed will fly level at that speed with no changes to the controls. the atmosphere is curved.

 

[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.