Is a trimmed flight not always an unstable system?

Question

As soon as I am flying in trimmed flight condition, my pitching moment around the center of gravity becomes zero. So my center of pressure has to be located in the center of gravity, so that there is no resulting turning moment.

But assume, there comes a wind gust, and the angle of attack will increase. This causes the center of pressure to move forward in front of my gravity location. So the aircraft will become instable because the angle of attack will further increase (nose up). The only thing the pilot could do is to use the elevator to trim in pitch.

So in the end, as long as I want to use the principle of "trimmed flight" , I will always have to use control surfaces to counteract the unstable flight condition. So why to care about stability, in trimmed flight it will always come to an unstable flight condition as long as I do not use the elevators?

Can you follow me? Is this true?

Answer 1

But assume, there comes a wind gust, and the angle of attack will increase. This causes the center of pressure to move forward in front of my gravity location. So the aircraft will become instable because the angle of attack will further increase (nose up). The only thing the pilot could do is to use the elevator to trim in pitch.

This is not accurate. Are you familiar with "free-flight" model airplanes? Some of them are stable enough to be flown in the middle of the afternoon when the atmosphere is full of thermal updrafts and downdrafts, with no input from a pilot whatsoever, and no automatic control system (autopilot etc).

You are correct that if some disturbance increases the angle-of-attack of the wing, with a conventional airfoil with no "reflex", the center of lift and center of pressure of the wing will move forward, which is destabilizing.

But the tail is also seeing an increase in angle-of-attack, or if the tail is set to fly at a negative angle-of-attack in normal flight, then the angle-of-attack of the tail becomes either less negative or somewhat positive due to the disturbance. Regardless of which of these is the case in any given instance, the change in angle-of-attack of the tail, which is far from the CG and therefore exerts lots of leverage, causes the center of lift and center of pressure of the whole aircraft to move aft of the CG. So the aircraft noses down to a lower angle-of-attack, where the center of lift and center of pressure are again co-located with the CG. That's how pitch stability works.

For more, see this section of John Denker's "See How It Flies" website.

Note-- for simplicity, I'm assuming that the only forces we need to consider are the "upward" or "downward" ones. I.e., that the "center of lift" and the "center of pressure" are one and the same. This is not exactly true. For example, if the thrust line were way above the CG, then it would still be true that the center of pressure (including the effect of the thrust vector) was co-located with the CG when the aircraft was at equilibrium, but the center of lift would have to be a bit ahead of the CG. If you find this simplification to be objectionable, then just (mentally) strike out "center of lift" from my answer and just leave "center of pressure".

In my answer here, I'm assuming that some sort of disturbance, such as a sudden updraft, has increased the angle-of-attack of the aircraft. However, there's actually an additional question embedded in your question, which is "will a purely horizontal gust of wind cause a change in the angle-of-attack of an aircraft that is flying horizontally?" That's a whole other "can of worms" that we may not really need to get into right now, but let's at least "lift the lid" and take a peek. The answer to that appears to be that the sequence of events is as follows: gust of wind from front -> increased lift -> upward curvature of flight path (which may temporarily decrease the angle-of-attack slightly) -> nose-up change in pitch attitude to conform to new direction of flight path -> continued upward curvature of flight path and continued nose-up pitch rotation. All assuming that the aircraft has not yet come to equilibrium with the new velocity of the surrounding airmass at any given point in the chain of events. It's not obvious that the angle-of-attack is ever increased above the original angle-of-attack.

Answer 2

I think you misunderstand how it works, and how you would respond to changes in wind. Increases in airspeed impact all flight surfaces, including the elevator, so a change in airspeed due to a gust isn't going to create large changes in pitch. There will be some change, however typically the changes in pitch would balance out with the fluctuations. It's rare to get really sudden significant changes in airspeed.

Maybe you are asking is why it's worth trimming an airplane if you'll still be having to make control inputs. Trimming reduces pilot workload and the strength needed for control inputs. If you don't trim you will always be fighting a pitch up or pitch down tendency, which takes energy and concentration. Your priorities are to aviate, navigate and communicate, trimming reduces the amount of effort you put into flying the plane so you can concentrate on the other two. Over a long flight, or a shorter flight in challenging conditions conserving your own energy is important, so it's well worth getting into the habit of trimming.

In calm conditions a trimmed airplane can fly with very little input from the pilot, so you can look at charts or plates, have a drink or just relax while you keep a good visual lookout.

Windy or turbulent conditions are more demanding, and you can't fly 'hands off' as much, trimming is still important because it makes the aircraft easier and less work to control.

Answer 3

Don't overthink it too much. Simplify in your mind. Trim is used to pre-set hands-off angle of attack. Static stability forces will focus on regaining the trimmed angle of attack if the plane is displaced from its trim state.

Since pilots use airspeed as a proxy for angle of attack, trim sets hands-off airspeed, as far as the pilot is concerned. The best way to conceptualize trim in flying is to think of it as a hands-free speed setting dial.

If a plane is disturbed from trim, it will be disturbed from trimed AOA and ultimately speed, and its static stability creates restorative moments that pitch the plane in search of the original trim state. So if below trim speed/above trim AOA, the plane pitches down, and if above trim speed/below trim AOA, it pitches up.

So the thing to keep in mind is, if the plane is disturbed by a gust, and you make no changes to power or configuration, it will naturally seek to regain the AOA/Speed it was at before it was disturbed. You can let it go and hands-free, it will seek that trim state on its own, but will take its sweet time, and oscillate about the trim AOA in smaller and smaller excursions until back at trim AOA/speed.

Generally you don't want to wait that long, so it's more efficient to help the natural stability forces along, with elevator inputs, to short-circuit the oscillations. To do this effectively, you need a handy proxy for AOA that can be used, in the moment, as a target to shoot for with your elevator inputs. For this we use pitch attitude relative to the horizon.

So you are flying along nicely trimmed, the plane is flying along hands free minding its own business, pitch attitude set, and a something changes AOA and speed. Pitch attitude will also have changed. Your objective is to get the airplane back to its trimmed AOA/speed. Instead of letting it hunt up and down and eventually get back to its trimmed state, you make subtle elevator inputs to regain the original pitch attitude, thereby getting back to trim AOA as soon as possible. Once you have regained the original airspeed, the plane should be back to and holding the original pitch attitude, and you're back to where you started.

You should be in the habit of using trim to set a hands-free speed for the plane to fly for any stabilized speed you want to fly at (for more than, say, 30 seconds). If you want to fly at 70kts on approach, don't leave it trimmed at 90 kts and hold elevator pressure; trim away the pressure until it will fly at 70kts hands free. Same for any other speed condition that is more than a short-term transient condition; shoot for the target speed by pitching to a target pitch attitude, and when on-speed, trim away the stick forces so that speed is held hands-free. This is how to fly with minimum work load, by letting the plane's inherent stability do most of the work.

Answer 4

The main purpose of the tail surface is to prevent the pitch instability of the wing from affecting the whole aeroplane. This is why it is often called the horizontal stabilizer.

In the simplest case, the stabilizer exerts no lift force when the plane is in trim. If the nose lifts, the tail AoA increases and it starts to generate lift. The design is arranged so that the pitching moment of this lift is greater than the pitching moment caused by the wing's CP shift. The tail rises and returns the plane to the trim attitude.

There are many complications which can be introduced, but that is the basic physics of how stability works.

Answer 5

I think most answers has missed phugoid oscillation which is a key word here.

Most general aviation airplanes are designed to be more or less stable in flight once trimmed for the actual situation. This means that if the flight is disturbed somehow, the plane most often returs to a new stable situtation. This goes for all the three inputs: roll, yaw and pitch. In the plane you can try this by giving a short measured input on the controls, letting go and wait out the response.

This stability generally comes at a cost of lower performance. So in high performance airplanes the "natural" stability might be intentionally lower: witness as example the extreme case of jet fighters where modern ones often cannot fly without the computer continously counter effecting the instability.

But back to "naturally" stable planes which most often shows a specific pattern called "phugoid osciallation" in the longitudual or pitch direction. This is one of several oscillation modes a plane can have, but one that is most easy to observe in a GA plane. If the plane gets a disturbance in either speed or pitch the following happens (I assume a traditional tail design + starting pitch down):

1. The plane pitches down below "steady horizontal".

• the speed will now increase
• as the speed increases, the down force of the tail will increase and start pitching the plane up (the tail is a wing that pushes down in steady flight, as the plane is pitched down, the attack angle of wind will change and the speed of air over it will increase, giving more "down lift").

2. The plane will now pitch up, often a bit above "horisontal".

• the speed will now decrease
• as the speed the decreases, the down force of tail will decrease and start pitching the plane down

3. Start from 1. again.

This will lead to an oscillation. In GA planes a typical period may be around 30 seconds. (There can actually be several periods concurrently). And this now continues with three possible outcomes:

1. The phugoid oscillation will decrease and gradually stop
2. The oscillation may decrease and continue at a constant amplitude. Often this is the desired state when designing airplanes, as totally stable migth cost to much performance.
3. The oscillation is to extreme to be comfortable or over time increases and leads to extreme pitch changes and you as pilot need to take action.

Over time the trim has to be changed as fuel is consumed and changing balance or the engine changes the output due to air temperature and so on. But for an interval, sometimes 30 minutes in my experience the plane simply flyes itself.

Answer 6

I think you have a major misconception about stability. Trim and stability are related but they are not the same thing. A stable aircraft will always seek its equilibrium or trimmed state if disturbed. In a well designed aircraft, the equilibrium is reached by the aircraft automatically without pilot input whatsoever. That is the neatness of it.

In your question, you have not considered from where the stability comes from. It is important to note that in most airplanes, the Center of pressure (CP) should never go ahead of its Center of gravity (CG). This is because most airplanes have a horizontal stabilizer that generates a downward force. If the CP were to go ahead of CG and with a tail producing a net downforce, the aircraft will remain unstable. However, such an aircraft can be stabilized by having a stabilizer that produces a net pitch up moment. With such a system, the larger moment arm of the stabilizer can generate an up force strong enough to stabilize the aircraft.

So, how does an aircraft with a CP behind CG stabilize after a pitch disturbance. It is simple really. The CP as you hava said will move forward (but not ahead of CG). As the horizontal stabilizer is designed for negative lift this increase of wing angle of attack will reduce the negative angle of attack on the stabilizer. Thus, the down force on the stabilizer will reduce and keep in mind the CP is behind the CG. This will reduce the any upward moments and the aircraft will try to return to its trimmed state.

I would like you to give it a try the next time you go for a flight. For this simple excercise trim the aircraft at a particular speed and angle of attack. Then you pull the nose up and leave the controls and see how the aircraft behaves. A stable aircraft will immediately push the nose down to attain its trimmed state. The amount of time it takes to return to trimmed state can vary ofcourse. This will show how dynamically stable the aircraft is. It is highly affected by the amount of damping in the system. For instance, at higher altitudes the aircraft will have lower dynamic stability due to the reduced aerodynamic damping. Thus, it will take more time or oscillations for the aircraft to attain equilibrium. In a stable aircraft the oscillations should die out in time in what we call subsidence.

The video below demonstrates longitudinal stability.