Aircraft 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.