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I was having a discussion with my friend about equilibrium condition in flight:

Scenario: While going in straight and level flight, say I reduced my airspeed by 30 mph. At the same time keeping the airplane's attitude strictly the same as before (doing whatever it takes to keep the nose where it was before).

Reducing the speed means, the aircraft develops less lift: Aircraft is supported by less pounds of lift force (meaning which lift is less than weight)

What happens next? (imagining that pilot does not nose down)

My take: 1. Since weight > lift, aircraft drops attitude and falls like a stone that was dropped in midair unless the nose is down.

My friend says: 2. The airplane finds new lift. This sinking motion creates lift for aircraft. But it will not maintain straight level flight but descends. It will be a steady descent not accelerating descent. (not like a stone falling out of sky). He says this is called power descent

My question is:

1) Who is right here

2) If my friend is right, if aircraft can find lift after it descends (which means it found equilibrium) , why can not it maintain straight and level flight. And what exactly caused it to find new lift? Has angle of attack changed?

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  • $\begingroup$ Maintaining fixed pitch is actually used in the unreliable airspeed procedure. When airspeed indicator fails, the usual procedure is to assume specified attitude (which corresponds to typical attitude during approach) and adjust power to achieve desired rate of descent (which must be no higher than normal approach). $\endgroup$ – Jan Hudec Apr 17 '16 at 11:00
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Neither of you are necessarily right, but you both have some understanding which is accurate.

Let me reiterate what you have stated, for clarity's sake. The scenario starts with the aircraft flying straight and level. Then the airspeed is reduced by 30 mph through a power reduction while the attitude is held constant. Regardless of what else happens we all recognize that this will result in some type of descent.

You are right in that the airplane has lost "lift" from the lost thrust and will thus descend. Depending on the aircraft and the starting airspeed, you might be right that the aircraft might respond with an uncommanded attitude pitch down. If that were the case, it would be due to the scenario resulting in an aerodynamic stall. However, even if the aircraft were to stall it would not drop like a stone (that is, with no lift to oppose gravity), but would descend at what would still be a substantial rate of descent while still producing some lift to oppose gravity. Moreover, considering the possible entry speeds and attitudes, a stall would be unlikely in this scenario.

Your friend is right in that, with sufficient airspeed and no aerodynamic stall—both of which depend on the airspeed at which the maneuver was started—this scenario will result in a descent. It would be accurate to call this a powered descent. Depending on what he means by it, your friend may not be quite right to think that any "new" lift would be produced by the sinking motion itself, but this might be a difference of semantics. Let's explore this further.

Let's consider a Cessna 172 cruising straight and level at 110 mph. We then reduce the power to maintain 80 mph and hold the pitch attitude exactly where we started. In this scenario we have transitioned from cruise speed to something closer to the aircraft's best rate of climb speed. This means that we have transitioned from a high speed, high drag region of flight to a lower speed, lower drag region of flight. At the same time, by holding the aircraft's pitch attitude constant, we have changed from a low angle of attack, low coefficient of lift region of flight to a high angle of attack, high coefficient of lift region of flight. This increase in angle of attack is due to the new angle of the relative wind introduced by the aircraft's descent. The overall amount of lift doesn't change, but the way the lift is created does change. As the speed is reduced the wing's ability to create lift (expressed by the coefficient of lift) increases with the increase in angle of attack. Thus the lift doesn't change, but the lift is now due more to the angle of attack than the airspeed. If this is what your friend means by "new" lift introduced by the sinking motion, then he is right.

However, this "new" lift must be understood to be due to the angle of attack change, not an increase in net speed (kinetic energy). The lift isn't actually changing, merely the way in which it is created—angle of attack as opposed to speed. However, if the scenario were different and we allowed the aircraft to pitch down as we reduced power, the aircraft would pitch down to maintain about 110 mph, and the wing's coefficient of lift would change very little as the airspeed and angle of attack remained relatively constant.

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  • $\begingroup$ The lift would be the same, regardless of speed. In the low-speed case the airplane still weighs as much as in the high-speed case, so lift must be the same. Only in the transition between states it will change a little. $\endgroup$ – Peter Kämpf Apr 16 '16 at 14:24
  • $\begingroup$ @PeterKämpf There, is that better? The coefficient of lift increases with the increase in angle of attack. $\endgroup$ – J Walters Apr 16 '16 at 14:42
  • $\begingroup$ Let the upvote be my answer. $\endgroup$ – Peter Kämpf Apr 16 '16 at 14:48
  • $\begingroup$ so what I understand is that when the aircraft descends maintaining same attitude, it increases angle of attack since the relative wind is meeting the wind from below and we are not pitching down. As a result of higher angle of attack, aircraft regains its lift and establishes its equilibrium. What I am not clear is that since there is 'some' thrust available, why does the aircraft keeps descending. Why can not it maintain level flight with this 'new' lift? Sorry if I missed this from your answer. $\endgroup$ – user2927392 Apr 16 '16 at 16:29
  • $\begingroup$ @user2927392 The issue is that by maintaining the same attitude throughout the maneuver you eliminate the option of increasing lift. If we were to instead pitch up beyond the initial pitch attitude we could increase our angle of attack sufficiently to increase lift to make up for the lost thrust. $\endgroup$ – J Walters Apr 16 '16 at 16:35
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Note: This answer refers to the initial question as asked by user2927392.

Who is right depends on the initial speed.

Lift is determined by two parameters as long as the wing geometry stays unchanged, angle of attack and dynamic pressure (which is the product of air density and speed squared). The slower plane will initially develop less lift and start to descend, which in turn will increase the angle of attack such that the initial lift is regained. Since you want to maintain the attitude of the aircraft, its sinking motion will mean that the airflow comes in more from below. Note that we speak of very small angle changes - just a few degrees normally.

Now much depends on how close the aircraft was to its minimum speed. As angle of attack increases, the flow will have trouble to follow the steeper contour of the wings and start to separate. If this separation grows, it will limit the lift the wings can produce. Now we have two cases:

  1. If the initial airspeed was higher than minimum airspeed + 30 mph, your friend is right. The aircraft will settle at a new angle of attack and will compensate the missing thrust with a gradual altitude loss, just as in SMSvonderTann's answer. Like a glider, the airplane will glide down to the ground. I assume you intend to keep the nose up by pulling on the stick: This will trim the aircraft to the lower speed and a higher angle of attack where it settles at the new equilibrium.
  2. If the initial airspeed was lower than minimum airspeed + 30 mph, you are partially right. The aircraft will stall, lift will not suffice to find a new equilibrium, and the airplane will pitch down to pick up the missing speed, no matter how hard you pull. If you still insist on lowering the speed, you will now pull out of the dive and repeat this maneuver all over again, until the ground interfers. Note that the resulting motion is not a continuing dive, but a sequence of "J"-shaped curves when seen by an outside observer. The dive is less a vertical plummeting than a steep glide, similar to a rollercoaster.

To answer your second question: Drag will slow down the aircraft unless some energy is continuously furnished by reducing altitude. Please read this answer which has a detailed explanation, albeit for paper aircraft, including some fancy math.

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  • $\begingroup$ Are you worried that someone will change the question? I rolled the edit back to match the original question. I didn't change the question. $\endgroup$ – J Walters Apr 16 '16 at 14:47
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  1. Your friend is right. The airplane is basically a glider in that scenario and gliders still fly even though they are mostly unpowered of themselves, motor-gliders excepted.

  2. The airplane can find lift as it descends because of the gravitational potential energy it has. However, the lift produced is less than the weight of the aircraft, due to drag and the Laws of Thermodynamics (The First and Second if I am not mistaken) so the airplane starts to descend. The lift is caused by the airspeed as the potential energy of the "dropping" plane converts to kinetic energy and thus airspeed and lift along with it. You could find net positive lift by flying into a rising thermal like a glider does to bring it higher.

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  • $\begingroup$ Hey, downvoter! This answer is not wrong, just incomplete. No need to downvote it! $\endgroup$ – Peter Kämpf Apr 16 '16 at 14:17
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Let's generalized where the airspeed is any X, where X >> 30 kts and that X << Mach 1.

If you were level and you reduce the power and touch nothing else, the aircraft will descend and accelerate until it reaches roughly X again; the point of equilibrium between angle of attack and airspeed. The aircraft will descend with roughly the same airspeed as what you started with.

This effect is critical in landing. Adding power reduces the descent and reducing power increases the descent; without significantly and over the long term changing the airspeed.

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  • $\begingroup$ The question stipulates maintaining attitude. $\endgroup$ – J Walters Apr 16 '16 at 14:48
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I think you (and some of the answerers) are making this way more complicated than it needs to be. These are the facts:

(1) If you are in level flight and you reduce power, you will descend. This is the normal way to descend.

(2) If you are in level flight and you push the yoke forwards, you will go faster.

(3) If you are in level flight and you pull the yoke back, you will slow down.

That is all there is to it. Don't make it too complicated.

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