# Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram.

Would an aircraft in such state maintain constant distance to the earth i.e fly concentric to earth surface with constant altitude or will it continue straight 'ahead' with slowly increasing altitude?

In other words, Assuming calm air, flight on ocean (so no flight path change need due to terrain), and no change in aircraft's weight is the pilot required to trim the aircraft continually to maintain the level flight at this constant altitude (15000 feet)?

Would the aircraft fly in trajectory A or B here?

When trying to find an answer to this problem, many people have mentioned that the aircraft will follow a path concentric to the surface of the earth due to 'gravity'. But I cant get my head round this because in level flight all forces including weight/gravity are being counteracted by another force - lift in this case. Can someone please explain the forces at work here in a bit more detail. Thanks.

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I updated my answer. You should edit your question to reflect that you are interested in the constant-weight case. – tpg2114 Dec 27 '12 at 18:02
Actually, the plane is flying in a curve concentric with the earth. The pilot or auto-pilot adjusts everything as necessary to maintain the chosen altitude and, yes, that means the lift is very slightly different from the weight. Keep in mind that the air and surface of the earth at the equator are traveling roughly 1000 mph eastward. – Mike Dunlavey Dec 27 '12 at 18:09

The pilot is required to trim to maintain constant altitude but not because of "flying straight ahead."

Rather, the aircraft is getting lighter as it flies because it is burning fuel. So holding speed constant (and thus lift), if the aircraft is in balance at one point, in the future it will be lighter so unless the pilot trims or reduces thrust (and thus lift), the aircraft will steadily climb.

This is actually desirable. Air is less dense as the aircraft climbs to higher altitudes, meaning the drag decreases and it can fly with less fuel for the same speed. This is called cruise climbing. However, this is problematic for air-traffic controllers. For sanity and safety reasons, aircraft should maintain a constant altitude. So, to compromise, they step climb where the aircraft holds constant altitude for a bit, then is allowed to climb up to a new altitude and hold there, etc.. The aircraft will be slightly less efficient at each phase, but it should average out to be close to the ideal smooth curve.

Neglecting the change in weight, if all forces are in balance then the altitude remains constant without any change required by the pilot. Since gravity always points towards the center of the Earth and since lift is exactly normal to this, if weight doesn't change and lift doesn't change, there is no vertical displacement. So the aircraft would maintain a constant altitude without any additional inputs.

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Thanks tpg2114. Lets assume for the sake of argument that the aircraft is not getting lighter or not burning fuel and still somehow manages to fly. What would happen in that case? When trying to find an answer to this problem, many people have mentioned that the aircraft will follow a path concentric to the surface of the earth due to 'gravity'. But I cant get my head round this because in level flight all forces including weight/gravity are being counteracted by another force - lift in this case. – Imran Ullah Dec 27 '12 at 17:56
@tpg2114 - thanks again. Here is the part I still dont get "all forces are in balance then the altitude remains constant without any change required by the pilot. Since gravity always points towards the center of the Earth and since lift is exactly normal to this, if weight doesn't change and lift doesn't change, there is no vertical displacement" Can this be put alternately as - the aircraft follows a curved trajectory because the direction of gravity is constantly changing. Sorry if im being thick :) – Imran Ullah Dec 27 '12 at 18:30
@ImranUllah the direction of gravity is constant - from the point of view of the plane. It's only constantly changing from the PoV of someone outside the Earth – Martin Beckett Dec 27 '12 at 18:36
I think the fallacy is "lift doesn't change". The force produced by the wings is not automatically normal to gravity. Its direction is dependent on the shape of the wings and the airflow. For analysis, you break up that force into lift and drag components, where the lift is normal to gravity. If you assume everything else is the same for plane A, you'll see that the angle of the wing-generated force has shifted 'backwards' with respect to the gravity vector - you get less lift and more drag. – AShelly Dec 27 '12 at 18:54
@AShelly The original question said it started out in static balance, so it is assumed that thrust balances drag and lift balances weight. And typically the "lift" force is the component of the force generated by the wing normal to the direction of flight -- which is horizontal here -- so the force from the wing can be broken into components aligned with the vertical (lift) and the horizontal (drag). – tpg2114 Dec 27 '12 at 19:00

1. the airplane is in a feedback control system. It does what the pilot wants it to do, continually making small or not so small adjustments in pitch, power, etc. to maintain what the pilot considers straight and level flight although, as you point out, it is actually concentric to the earth. So lift and weight are seldom exactly equal - that's only an approximation.

2. Since the plane is flying in a circular arc concentric with the earth, centripetal force is always there, but is usually small enough to ignore. If an airplane is flying over the north or south pole, its speed in that circle is just its airspeed. OTOH if it is flying at the equator, the whole body of air is moving east at about 1500 kilometers per hour, which is added to its airspeed. So if it is flying east it is moving faster than that, and is lighter. If it is flying west, it is slower than that, so it is heavier, and so on. It's no coincidence that satellites are seldom launched in a westerly direction.

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Would an aircraft in such state maintain constant distance to the earth i.e fly concentric to earth surface with constant altitude or will it continue straight 'ahead' with slowly increasing altitude?

In any flight random motions of the air will pitch (and roll and yaw) the airplane to a smaller or bigger extent. You can be flying in an updraft or downdraft. Flying the airplane is that you correct for those random jostlings. So the pilot (or autopilot) is always in the process of keeping the airplane level and at the designated altitude.

A side-effect of that is that the airplane keeps flying along a concentric circle around the Earth's center. Following the Earth's curvature requires no separate input because the corrections for the random jostlings are far bigger anyway.

But yeah, as a thought experiment: in a perfectly motionless atmospere that would allow you to fly dead ahead you will over time gain altitude as the earth curves away from under the airplane.

http://i435.photobucket.com/albums/qq73/TheKinSlayer_1993/Untitled.jpg

The text in the above picture is confusing. To the left it says: 'no gravity'
What is intended, I guess:
On the left side: 'Resultant force of gravity and lift is zero'

Let me make a comparison with an orbiting satellite. In orbit there is only one factor: gravity. For a satellite the curve of the trajectory is due to gravity only. The satellite is falling down, but it has so much velocity component parallel to the Earth's surface that it never reaches the Earth.

For an airplane the altitude comes from the resultant force of gravity and lift. To fly along a circle that is concentric with the Earth the lift force must be slightly less than the gravity, in such a way that the resultant force of the two is just enough to keep the airplane moving along that circle with that velocity.

Imran Ullah has pointed out a subtlety, and I think I should address that.
The initial condition is that the direction of gravity force and the direction of lift force are exactly opposite.

Recapitulating: if the autopilot keeps the orientation of the aircraft the same then the aircraft proceeds on a straight line that is tangent to the surface of the Earth. As the aircraft moves along that line over time the direction of gravity force will no longer be exactly opposite the lift force. As indicated by Imran Ullah, the new resultant force will not be zero: it will point rearward, and slightly upward.

So, if the autopilot is programmed to maintain constant air speed, but to leave the altitude to whatever happens, the prediction is that the flight path will curve up.

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@ Cleonis - If the aircraft was to fly 'dead ahead' or 'straight', wouldn't gravity start acting on it in from slightly behind (off-perpendicular) --\-- direction forcing it to lower altitude i.e force it in a cocentric path over earth? – Imran Ullah Dec 27 '12 at 22:02
@ Imran Ullah - My assumption is that the autopilot is dialed in to maintain a designated airspeed. As you say, flying dead ahead gravity will be increasingly off-perpendicular, which would tend to slow the aircraft down. In response the auto pilot will increase thrust. That is, I describe the thought experiment where the autopilot maintains every variable at the same value, except altitude. – Cleonis Dec 27 '12 at 22:12
Thanks @ Cleonis but im still confused by the two answers. 1). If all forces are in balance then the altitude remains constant without any change required by the pilot. Since gravity always points towards the center of the Earth and since lift is exactly normal to this, if weight doesn't change and lift doesn't change, there is no vertical displacement. So the aircraft would maintain a constant altitude without any additional inputs AND 2) In a perfectly motionless atmospere that would allow you to fly dead ahead you will over time gain altitude as the earth curves away from under the airplane – Imran Ullah Dec 28 '12 at 1:58
@ Imran Ullah - When the resultant force is zero then the motion is along a straight line, with uniform velocity. When an aircraft is flying along a straight line then it is the earth beneath it that drops away, the earth being curved. Again, this issue only exists in a thought experiment. In a real situation the (auto)pilot is flying the aircraft, and the effect you ask about is always swamped. – Cleonis Dec 28 '12 at 21:38