Aircraft Stability

[TOPC]

I am looking for an easy to understand analogy of the different stabilities of an aircraft,
What affects these stabilities ?.
What do aircraft designers do to build in/out these stabilities ?

Has anyone done any work on this or perhaps know of an easy to understand sight ?

Thank you

[Milt]

TOPC

Aircraft stability in its multiple dimensions is not an easy subject.

Design engineers often go grey trying to meet present design requirements and Test Pilots are often hard placed to sort out the designers' shortfalls..

The stability we are most familiar with is the steering stability of a car. You have to apply a small force to the steering wheel to make the car depart from its positive stable desire to continue going in a straight line. Adjustments of the stability to be negative can make the car very hard to handle. It will want to depart from the straight line incessantly and you have to fight it all the way. Flying an aircraft with negative pitching stability is almost impossible for any lengthy period. If an aircraft has negative directional stability like the car it will always be trying to turn round to go backwards.

New aircraft designs often go pear shaped when stability effects interact from one dimension to another.

Best way for you to get some comprehension of the subject is to initially narrow your approach to one dimension such as that of an aircraft pitching - called longitudinal stability. There are easy to find websites which will provide you with the basics.

For some it may become addictive and they may be the ones who end up aspiring to become aeronautical engineers.

[Mad (Flt) Scientist]

Originally Posted by Milt

For some it may become addictive and they may be the ones who end up aspiring to become aeronautical engineers.

... if you arrange an intervention quickly enough, though, it may be possible to save them.

One general comment on the original question. Part of the problem is that too much stability is as bad as too little; to take the motoring example, there are times when you'd like to turn corners, and having to fight with the wheel when doing so, whether at speed or when trying to park, is not agreeable.

[Milt]

Mad Scientist

We should all celebrate that you were not diverted from becoming an Aero Eng particularly as you have managed to retain a sense of humour mixed with a desire to contribute your expertise to PPRuNers.

Have you worked to correct any significant aircraft stability problems?

[cwatters]

How easy is easy?

In the pitch axis... I learned quite a lot from reading this page on the design of flying wing model aircraft - because the same issues apply to conventional layouts.

http://www.mh-aerotools.de/airfoils/flywing1.htm

[chornedsnorkack]

Number of stabilities

How many stabilities does a plane have?

Trying to figure out how many degrees of freedom there are...

Two directions of location are necessarily neutrally stable (the third does not have to be, as air density changes with altitude). One heading degree of freedom has to be neutrally stable, too.

[Milt]

Still counting!!

[rhovsquared]

from The Book (HTBJ);
lateral, spiral, oscillatory, static stick free longitudinal and speed as least some of the more important modes of stability.

[Mad (Flt) Scientist]

Stabilities, or modes? Different things:

Usually we think of three 'stabilities' - longitudinal, lateral and directional. Generally most aircraft are positively stable in pitch and yaw, and neutrally stable in roll. So for 'lateral' stability that often means 'dihedral effect' rather than pure lateral stability, which is boringly useless to discuss.

Longitudinal stability is often thought of as the most important - it probably most directly affects the pilot's perception of the ease or otherwise of handling; there's been a hell of a lot of research into the optimum value for this. Affected very strongly by cg position relative to the wing, and tailplane size and location.

Directional stability is a real problem in design (not so much now as once, but still...) because it's the consequence of two competing effects - the tendency of the fuselage to be unstable aerodynamically, such that if disturbed sideways it keeps going - and the fin (vertical tail) which is there to stop that happening. Neither effect is easy to predict, and often the resultant margin of stability is a small difference of two large numbers - a recipe for error. Many, many aircraft had tails resized during development before 'we' got smart about this. Affects things such as crosswind capability and Dutch Roll behaviour - but not always as you'd expect.

Dihedral effect (or dihedral stability if you prefer) relates to the tendency of an aircraft to bank into or away from sideslip. Affected by the inclination of the wings (hence the name, dihedral effect) and also their position on the fuselage. Affects things such as Dutch Roll (especially the roll/yaw relationship)

The usual oscillatory modes for a conventional aircraft are:

Longitudinal (2)
* Short Period Pitch Oscillation : characterised by a (duh) short period, basically a pitching motion of oscillatory nature with little change to the flightpath. Usually quite well damped.
* Phugoid : a much longer period oscillatory motion, essentially an energy-interchange mode between potential and kinetic energy as the aircraft climbs/slows then decends/accelerates. Usually at near-constant angle-of-attack. Often poorly damped, as it is damped in part by drag, which is usually minimized in design for economic reasons.

Lateral-Directional (3)
* Dutch Roll : a combined rolling and yawing motion, oscillatory in nature, driven mainly by cross-coupling between the aerodynamic forces in roll and yaw (a sideslipped aircraft wishes to roll as well as yaw; a rolling aircraft reacts in yaw as well as in bank). Often poorly damped. Many aircraft have 'yaw dampers' fitted which control rudder inputs to augment damping. Ironically, it's often easier for a human to damp with roll controls, due to lag/timing issues.
* Spiral Mode : a first order mode, invariably unstable, that will if unattended cause a slowly increasing divergence in roll and yaw.
* Roll Mode : another first order mode, closely related to the roll damping of the aircraft. Usually stable.

Those 5 are the ones generally worried about most. (Unless you're dealing with active control/FBW, in which case all bets are off....)

In addition to those, as someone mentioned the actual POSITION of the aircraft wrt Earth forms another system of equations. In particular, heading is a neutral mode - aircraft aren't like compasses, and have no desire to point any specific direction.

What do deesigners do?

An important question! If I ever find out .... ok, sorry.

Well, the first thing to note is that the stability and control design aspects are rarely primary for a design, and certainly not for a transport category aircraft. Unlike, say, a fighter or aerobatic machine, the degree to which an airliner 'flies nice' is secondary to the economics. So in many ways the S&C designer is picking up the crumbs - unless the handling problem that some other aspect of the design causes is a complete project-killer, you'll be working around it.

The first stage will be to estimate sizes of the major control and stabilizing surfaces. Given a general layout - defined from lift or drag considerations, usually - you'll work out the required sizes of tailplane, fin, ailerons, etc. Usually you'll have some rules of thumb - previous projects, other companies' aircraft - to keep you on the right track. Those may be simple geometric rules - like tailplane volume coefficient, say - or may be more academic/analytical, things like 'control aniticpation parameter' in the pitch axis. At some stage in the process you'll usually get a math model (simulation) up and running so you can start to check dynamic responses. And, again at some stage, your early ESDU/DATCOM guesstimates for the aerodynamic forces and moments will be refined by CFD or wind tunnel data.

As the data behind your modelling becomes more reliable, you'll start looking at more detailed problems. Is the rudder big enough to provide a yawing moment to counter the engine-out cases? What about a growth engine - design for growth or not? Don't forget roll control either. And so on.

You'll also start looking for non-linear behaviour, trying to design it out or get around it ( non linearities are almost ALWAYS bad news). Does the wind tunnel data sow the directional stability - plot of yawing moment versus sideslip - changing slope? Becoming less stable? Is the fin starting to stall, perhaps? try adding a dorsal strake to re-energise the fin flow at high beta. Or maybe it only happens at high AoA, where the fin is being blanked by the fuselage flow - time for some ventral fins perhaps.

Often you don't find details until flight test; then its often a case that the simplest fix wins, even if it isnt most elegant - time on a test programme being money. Maybe it'll be simpler to restrict the range of rudder inputs available to the crew than to add extra surfaces at that stage. Maybe a simple stall strip will cure the handling problems at low speed in one go. If the economics of the aircraft aren't affected, then give it a try.

[rhovsquared]

Very imformative Mad(flt)Scientist makes all of that stuff a little clearer for me
from the physical perspective

[balsa model]

speaking of...

I've got a question about stability for you experts.
(I don't mean to hijack the thread but hope that the original poster might find the answers equally interesting, instructive and related.)

How did they handle stability issues with "swing-wing" (variable geometry) designs? I've read somewhere that some of the original proof-of-concept planes were moving the wing root forward as well as pivoting the wing. Then came along F111 with a single pivot and no problems. No FBW or anything fancy to help with anticipated stability issues.

Is there some kind of an aerodynamic trick? Or am I paranoid about CG and center of lift? But wouldn't fully swept configuration be almost impossible to pitch? Was there variable pitch assist?

If someone could spare some time and shed some light onto this matter, I'd be grateful. Thanks in advance.

[Mad (Flt) Scientist]

Indeed, as you mentioned, some early swing-wing concepts had a complex mechanism that translated the root forwards, the idea being to keep the 'mean aerodynamic chord' (i.e. the chord at about 40% semi-span) roughly fixed relative to the aircraft. The concern was as much control as it was stability, but it was indeed related to movement of the aerodynamic centre relative to the cg.

In practice, the complexity hasn't been needed on any swing-wing I'm aware of, mainly because:

1. There is some corresponding aftwards cg motion when the wings sweep aft, which helps a bit.
2. There are changes to the downwash flowfield around the tail as a result of the wing sweeping closer to the tailplane. IIRC the Tornado tail was positioned quite carefully to take advantage of this.
3. The relative tail contribution to stability is actually reduced - if you think of the tailplane volume design coefficient:

VT = tail area * tail arm to wing AC / (wing chord * wing area)

you'll note that the tail arm decreases as the wing sweeps back, and the wing chord (streamwise) increases.

Since the overall aircraft stability is a combination of the wing-body and tailplane contributions, some reduction in the latter offsets the increase due to the aft motion of the wings.
4. the wing also becomes less efficient when swept in terms of generating lift, so while the AC is moved back, it's nothing like as bad as if the forward-swept wing were translated aft
and finally (though there are no doubt others)
5. the tail may be sized for low speed trim requirements (e.g. Tornado's very complex and powerful flap system no doubt requires a lot of trim authority at the tail) - in which case you may have tail power to spare at high speed.

Obviously it makes the design more complex - more configurations to worry about, especially if you have some kind of autosweep and dont have fixed positions. But it's not really much different to the design process than having a lot of flap positions - just another bunch of design points, another bunch of lines on the sizing diagrams, etc. It just so happens that designers, using some or all of the above factors, have managed to get a solution that didn't require forward translation of the root.

(As an aside, IIRC the F-14 wing gloves were supposed to be for AC position control, but were found to be unnecessary and were locked in for later operations)

[balsa model]

Thank you very much. This puts some order into my thinking. And gives me food for more. Thanks again.

[chornedsnorkack]

Originally Posted by Mad (Flt) Scientist

The usual oscillatory modes for a conventional aircraft are:

Longitudinal (2)
* Short Period Pitch Oscillation : characterised by a (duh) short period, basically a pitching motion of oscillatory nature with little change to the flightpath. Usually quite well damped.
* Phugoid : a much longer period oscillatory motion, essentially an energy-interchange mode between potential and kinetic energy as the aircraft climbs/slows then decends/accelerates. Usually at near-constant angle-of-attack. Often poorly damped, as it is damped in part by drag, which is usually minimized in design for economic reasons.

Lateral-Directional (3)
* Dutch Roll : a combined rolling and yawing motion, oscillatory in nature, driven mainly by cross-coupling between the aerodynamic forces in roll and yaw (a sideslipped aircraft wishes to roll as well as yaw; a rolling aircraft reacts in yaw as well as in bank). Often poorly damped. Many aircraft have 'yaw dampers' fitted which control rudder inputs to augment damping. Ironically, it's often easier for a human to damp with roll controls, due to lag/timing issues.
* Spiral Mode : a first order mode, invariably unstable, that will if unattended cause a slowly increasing divergence in roll and yaw.
* Roll Mode : another first order mode, closely related to the roll damping of the aircraft. Usually stable.

Those 5 are the ones generally worried about most. (Unless you're dealing with active control/FBW, in which case all bets are off....)

YouŽd expect the spiral mode to be the worst, because it is the one with negative stability, and therefore the mode that will fly the craft into ground...

Originally Posted by Mad (Flt) Scientist

What do deesigners do?

An important question! If I ever find out .... ok, sorry.

Well, the first thing to note is that the stability and control design aspects are rarely primary for a design, and certainly not for a transport category aircraft. Unlike, say, a fighter or aerobatic machine, the degree to which an airliner 'flies nice' is secondary to the economics.

Hm... wouldnŽt there be important economics points about stability?

Pitch stability defines the CoG range - move CoG too far to the rear, and the tailplane AoA equals that of main wing, so that the pitch stability vanishes; move CoG too far forward and the tailplane has inverted stall and the plane falls nose over.

How do you add CoG range to a plane? I suspect it would require enlarging the tailplane - with economic penalty in form of trim drag.

[Mad (Flt) Scientist]

Originally Posted by chornedsnorkack

YouŽd expect the spiral mode to be the worst, because it is the one with negative stability, and therefore the mode that will fly the craft into ground...

In fact, no. Negative spiral stability and weakly damped Phugoids are both quite flyable - they add to workload, of course, but a simple autopilot can easily accomodate both of these. This is because both have relatively long periods (usually) and so it's relatively simple for a human or an artificial system to compensate.

The Dutch Roll and SPPO are much more serious impacts on handling qualities because they are higher frequency modes, at or about the natural human response frequencies. Therefore they get excited by normal human behaviour, and are hard to damp manually sometimes. Most 'Pilot Induced Oscillations' are interactions between the human and one of the higher frequency modes.
Because the frequencies are higher, it's relatively harder to design compensation systems, too.

Originally Posted by chornedsnorkack

Hm... wouldnŽt there be important economics points about stability?

Not really. Stability and Control - usually the two are considered together - have generally minor impacts on the operating economics of an aircraft. They can affect the design, and if bad enough make the design uncertifiable (and hence by default uneconomic) but assuming you get the aircraft certified there are only a few areas where the S&C affects the operations, and those are really more 'control' than 'stability' issues. Examples might be:
1. Crosswind landing and takeoff capability may restrict operations if control power is poor.
2. Minimum control speeds may impact operations at lighter weights
3. Poor handling in (usually high altitude or high speed) areas of the flight envelope may restrict operational use, especially for dispatch with failures.

But, compared to the huge impact of Performance (the 'other' aerodynamic discipline) these are generally minor effects on the economics of operating the aircraft.

Originally Posted by chornedsnorkack

Pitch stability defines the CoG range - move CoG too far to the rear, and the tailplane AoA equals that of main wing, so that the pitch stability vanishes; move CoG too far forward and the tailplane has inverted stall and the plane falls nose over.
How do you add CoG range to a plane? I suspect it would require enlarging the tailplane - with economic penalty in form of trim drag.

Ah, have to correct you there. Pitch stability doesn't define the cg range, or certainly not alone. There are a number of factors which define the cg range, some are related to stability, some to controllability and some to other factors, and the way they are usually designed (in the traditional sense) is with a graph relating the various different limits to tailplane area. Not sure if it has an official name, but let's call it a tailplane sizing diagram.

On it one plots cg along the horizontal axis, and tailplane area on the vertical. Once you have a general layout and an idea of the aerodynamic characteristics you can start to express various design constraints as a function of tail area verus cg.

So, for example, with no tailplane, I may find that my most aft allowable cg while reatining adequate stability is 20% mac. If the tail is 100 sq ft I calculate I can go to 30% mac cg.

I also calculate that for trimming at stall speed with the landing flap, with no tailplane I cannot be further forward than 25% mac, but with 100 sq ft I can be as far forward as 10% mac.

Having worked out these - and many more - constraints (which will include considerations of things like a minimum weight on the nosegear statically to ensure the plane doesn't tip over when parked!) I end up with a whole bunch of lines, some of which constrain aft cg, some forward.

I now decide how much cg range I NEED for the aircraft - which will be based on predictions of fuel and cargo variations - and that defines how large my tail must be.

For the case above, assume I decide I need 10% cg range (not very much).

At 0 sq ft my aft limit is 20%, my forward limit 25% - obviously, this plane needs a tail! (-5% cg range)

At 100 sq ft my aft limit is 30%, my forward limit is 10% - 20% cg range, more than I need. (20% cg range)

By simple interpolation I can work out that to meet those requirements and a 10% cg range, I need a 60 sq ft tail (16% to 26% will be the limits).

So, yes, adding cg range usually means a bigger tail. But it's not a trim drag problem - it's a profile drag problem, and a weight issue. The trim lift on the tail stays the same for the same conditions, whatever size the tail is.

Also, the items you mention for the forward and aft limits are not really accurate.
For the forward limit, you're close (no-one designs for tail stall; we design for a margin under tail stall for forward trim, and that may not be the limiting forward cg factor. Often its a loads issue at forward cg).
For the aft limit, Im afraid that tail AoA and wing AoA being the same has absolutely no effect on stability. Moving the cg aft does indeed lead to instability, but what matters primarily are the relative slopes of pitching moment and lift with angle of attack (for the wing) and the tailplane lift curve slope and its area and position. Stability is all about small changes and the relative change in forces and moments - in essence, gradients, or DERIVATIVES - and much less to do with values of parameters themselves.

[Unhinged]

Top thread team - Love all the good info !!
Without wanting to hijack it at all ... Every day on the way to work I drive past a gaggle (?) of light twins; Some have dihedral on the horizontal stabilizer and some don't.
On the wings it makes sense, but can anyone tell me the reason for dihedral on the horizontal stabilizer ? or at least give me a more rational guess than I've heard from the local not-very-experts !
Thanks ...

[Mad (Flt) Scientist]

Reasons can include:

1. getting the tail into the 'right' area of the downwash field behind the wing while respecting structural constraints over the attachment at the root (e.g. Hawk/harrier)

2. reducing loads under sideslip conditions (applies rather more to T tails)

3. local effects similar to wing dihedral concerns i.e. adjusting the flow in sideslip to perhaps 'protect' fin effectiveness

[Unhinged]

Originally Posted by Mad (Flt) Scientist

Reasons can include: ...

Thanks - That makes sense at last !!