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If I understand right, when you are trimmed for current speed, let’s say 290 KTAS, does that mean if airspeed increases to 295, the plane will pitch up to slow it back down? And vice versa for the speed falling below 290. The plane would essentially dive on it, to get the speed back? Or am I way off?

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  • $\begingroup$ Pilots often don't really learn how to use trim, because they don't really grasp that pitch is fundamentally a speed control and the trim wheel is basically hands-free speed control dial. $\endgroup$ – John K Dec 5 '19 at 1:06
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    $\begingroup$ @JohnK, this is also not quite correct and is somewhat of a misconception. 'Fundamentally' pitch is pitch. In short-period motion (which is often no less important) it is more related to AoA than to speed. Only in steady state your view (approaches to be) correct. $\endgroup$ – Zeus Dec 5 '19 at 1:18
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The pitch trim setting is based on the angle of attack. The angle of attack is affected by indicated airspeed, center of gravity and any unbalanced forces.

In a steady state aircraft where the airplanes forces are all balanced then we are left with airspeed and center of gravity. Under normal operations where fuel is not being transferred from an aft tank to the wing tanks or vice versa, center of gravity for a certain period of time remains relatively constant. This leaves airspeed as the primary change in angle of attack.

Your analysis would be correct. If you are trimmed for 290 KIAS (not KTAS like you stated) and you increase thrust the following sequence will occur.

  • Airplane will begin to accelerate
  • The lift formula comes into play and additional lift is created on the wings causing the airplane to pitch up and start to climb.
  • The airplane experiences an increase in induced drag which opposed thrust.
  • The airplane will now begin to decelerate while still climbing.
  • The decreased airspeed causes lift and induced drag to decrease.
  • The aircraft will pitch down and start to descend.
  • Aircraft will begin to accelerate as it descends.
  • The cycle continues until the phugoid oscillation dissipates (provided the airplane demonstrates positive dynamic stability)
  • In the end, the airplane will be at a higher pitch attitude (in relation to the horizon), climbing, and at 290 KIAS.

The same type of analysis can be accomplished if airspeed is reduced. The airplane, at the end of the phugoid oscillation, will be at a lower pitch attitude and the same airspeed.

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    $\begingroup$ The sequence is wrong. First, think: in the end, where does the excess added thrust go? Second, why does additional lift due to speed cause the airplane to pitch up? $\endgroup$ – Zeus Dec 5 '19 at 1:27
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    $\begingroup$ Yeah, I think @Zeus is right here. If the airflow at the beginning doesn't produce a pitching moment, then after the airspeed increases, it still won't produce a pitching moment (as long as the angle of attack doesn't change—which it won't right away, if the aircraft is in level flight before and after the power increase.) Instead, the increased speed will cause the wings to produce more lift, which will cause the aircraft to climb, and that will cause the aircraft to pitch up. $\endgroup$ – Terran Swett Dec 5 '19 at 4:13
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    $\begingroup$ Also, you haven't mentioned the fact that while the aircraft is climbing, lift (not just drag) will cause it to slow down, and while it's descending, lift (not just a reduction in drag) will cause it to speed up. I don't know which of the two forces has a greater contribution, but my guess is it's lift. In particular, even a drag-free aircraft would still undergo phugoid cycles. $\endgroup$ – Terran Swett Dec 5 '19 at 4:19
  • $\begingroup$ @wbeard52, you are missing the energy trade between kinetic and potential in the behavior. Without that, no phugoid (but you still have short period). $\endgroup$ – MikeY Dec 5 '19 at 12:11
  • $\begingroup$ @Zeus is right, if you just increase thrust without changing anything else you will end up at 290 Knots as phugoid dies down, but you will be climbing. Climb angle will depend on how much thrust you added. $\endgroup$ – Kolom Dec 5 '19 at 16:59
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You wrote

If I understand right, when you are trimmed for current speed, let’s say 290 KTAS, does that mean if airspeed increases to 295, the plane will pitch up to slow it back down? And vice versa for the speed falling below 290.

You are describing the phugoid mode for longitudinal dynamics. The key is that it trades kinetic and potential energy back and forth.

The phugoid behavior occurs at approximately a constant angle of attack, or coefficient of lift $c_{L}$. The lift is just a function of speed.

Faster = more lift, and when the lift exceeds weight, the aircraft pulls up. As it goes up, it trades kinetic for potential and slows down. Slower = less lift, and when the lift is less than the weight, the plane arcs over the top and heads back down, trading potential for kinetic.

There are other physics going on, but that is the core of it.

If you were to try this in a huge space station with no gravity, you wouldn't see the phugoid. The energy trade is a key part of the behavior. You would only see the short period.

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Yes, in practice the airplane will do "whatever" (as you describe) to maintain its "trim speed". The airplanes are, in fact, reqired to do this. So if you are a pilot and practical considerations is all that matters, this is enough to know. (Perhaps though, you will also be interested in the dynamics of this process and how to control it better).

However, if you are interested to know why the airplanes do this and understand the fundamentals, read on.

First thing to note is what the trim actually does. There are different mechanisms, from aerodynamic tabs to direct stick force control, but what they all do is setting the elevator (or the whole stabiliser) at a certain angle with respect to the wing when no force is applied to the controls.

Now it is ieasy to show that the airplane is trimmed not for speed but for an angle of attack (AoA).

basic forces

In a level steady flight, we have both the force and moment balance: $L + L_t + mg = 0, Lx_{CP} + Lx_{L_t} = 0$ ($x$ is the arm with respect to centre of gravity CG; all forces are vectors). If we simply change speed, none of the points will move (until we get close to the speed of sound). All the aerodynamic forces will change proportionally (as square of speed). It follows that the moment remains balanced. This can be verified in a wind tunnel: a hinged model will remain at the same angle if we change airspeed.(*)

If we change the stabiliser angle ('trim' it), only $L_t$ will initially change. This will change the pitch balance, and the airplane will start to pitch - until it finds another balance angle. Here, CP will move and $L$ will change, but in the end $Lx_{CP}$ will again be equal in magnitude to $Lx_{L_t}$. This will be the new 'trimmed' angle of attack.

On all 'normal' aircraft (that is, human-sized), this AoA change will happen a lot quicker than speed or altitude change. The aicraft will settle on the new AoA, and only then the rest will happen. Namely, with new lift (at the new AoA) comes vertical acceleration, and also new drag. This all combines into changed trajectory and speed.

As you see, the traditional pilots' belief that trim sets speed isn't entirely correct. A pre-requisite to stabilising on a new speed is that the airplane stabilises on a new AoA. This is why by 'static longitudinal stability' engineers understand AoA stability rather than speed stability. If the airplane is unstable in AoA, it will not live to see 'speed stability', or anything else for that matter.

But what actually happens to a nicely trimmed airplane when only speed changes? Well, by definition, initially it does not involve AoA change, and so the process is relatively slow. As I explained above, the moment balance does not change, so there is no tendency to pitch. However, changed lift will cause vertical acceleration (let's say, for simplicity of explanation, that speed and thus lift increased). This causes two consequences:

  • The energy for moving up must come from somewhere, and the airplane will start to decelerate - unless it increases thrust.
  • Vertical speed will change AoA: now we have a vertical airspeed component. This component is equal for both the wing and the tail, so the absolute AoA change is equal (say, -2°). Now the usual thing will happen: since we haven't re-trimmed, the airplane will tend to restore its trimmed AoA, which means pitching up by the same amount (+2°). And this will happen rather quickly: the airplane will 'track' AoA according to the current vertical (and horizontal) speed.

The ability to track (stabilise) AoA means that the equilibrium can only be restored if speed is restored to its previous value. This will eventually happen, but this will happen slowly because it involves exchange of potential and kinetic energy. There will likely be an oscillatory process (known as phugoid motion), where the initial rise and pitch up sets the airplane for climb, it loses speed more than it should, loses lift, starts to descend, and the process reverses. But once again, AoA stability is the driving factor here.

It is possible to make an aircraft which will be statically stable in AoA but unstable in speed. For example, by having strong positive dependency of thrust on speed (turbojet engines are like that at certain speed ranges). But because speed changes are slow, such aircraft can still be flown by a human - unlike AoA-unstable aircraft.


(*) Strictrly speaking, if we increase speed substantially (and instantly), AoA will reduce a bit. But AoA stability, as explained below, will quickly restore AoA, and we'll be left with just changed forces.

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Yes airplanes trim to a speed. The airplane is "in trim" when the tail downforce balances the nose down pitching moment about the airplane's neutral point and it is not accelerating or decelerating. Left on its own (no control input), it will pitch to seek its trim speed when displaced from that speed for whatever reason. If actual speed is below trim speed, the airplane will pitch down because tail downforce is below the "balance value" (and vice versa if it's above).

So if you are below trim speed for some reason, if you just leave the airplane to itself, no hands on the controls, the airplane starts to dive due to too little downforce, and accelerate. It shoots past its original trim speed in the dive, where it now has too much elevator downforce, which makes it start to pitch back up. It will then overshoot going the other way, ending up in a decellerating climb, but a bit less than the initial time. It ends up too slow and starts to dive again on its hunt. Each of these Phugoid oscillations gets less and less and eventually the airplane finds its original trim speed again, more or less.

All this is happening with your hands on your lap. You can short circuit the whole process with timely elevator inputs if you want.

This is "static longitudinal stability". FAR 25.173 requires a minimum level of this "speed seeking" in response to displacement from trim speed and specifies a minimum ability to return to trim speed once displaced (within 7.5% in cruise flight). The airplane will be trimmed for some speed, say 250kt, then slowed down or sped up without any trim change, then left by itself with no input, has to be able to find its way back to trim speed within x knots tolerance, preferably with a relatively small number of Phugoid oscillations as it dives and climbs on its hunt for trim speed. Too slow, it should dive by itself (gently), too fast, it should climb.

In cert testing they will push the nose over with an elevator input, forcing it to dive and accelerate to say trim speed +50kt (or climb and decelerate to go the other way), then let go and watch what happens. It should slowly climb and dive, climb and dive, less and less each cycle, until it settles down to hopefully a few knots from the original speed with nicely damped, diminishing oscillations as it does so.

Trim speed is also affected by changes to the balance of pitching moments and forces, like adding or reducing thrust where the thrust line makes the nose pitch up or down. But for this case we are talking about steady state conditions.

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    $\begingroup$ No. Like StephenS (please see my comment to his answer), you are missing a vital link between speed and picth changes. "If you are below trim speed", you will have less downforce, but you will also have less wing lift and moment to compensate with this downforce. The pitch balance doesn't change at this point. Also, "static longitudinal stability" is a different thing; technically, it relates to response to AoA disturbances. It is related, in turn, to speed stability you are talking about, but they are not the same thing. (This relation is the actual answer to the question). $\endgroup$ – Zeus Dec 5 '19 at 1:56
  • $\begingroup$ Yes the wing's lift decreases along with the tail's downforce but the net result is that the downforce is insufficient and the nose down pitching moment about the neutral point is able to overcome down force and the nose drops. FAR 125.73 which describes the speed seeking behaviour requirements I described is TITLED "static longitudinal stability". But, whatever; go argue with the FAA. Dynamic Stability describes how well the system is damped when displacements occur per FAR 23.181 risingup.com/fars/info/part23-181-FAR.shtml $\endgroup$ – John K Dec 5 '19 at 4:03
  • $\begingroup$ @Zeus I don't know what the fuss is. Static longitudinal stability = speed stability. $\endgroup$ – JZYL Dec 6 '19 at 3:32
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    $\begingroup$ @JZYL, not quite. This is a secondary effect. I had to write an answer to explain. $\endgroup$ – Zeus Dec 9 '19 at 2:09
  • $\begingroup$ @Zeus You're redefining a term that has been defined already. In both industry (airplane certification) and academia (see references on Etkins), static speed stability and static longitudinal stability are exactly equivalent. Your answer is correct in that AOA stability and speed stability are not exactly the same. But the term, static long stab, is used exclusively by any certification agency to mean speed stability. $\endgroup$ – JZYL Dec 9 '19 at 2:15

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