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A Quick Explanation of Relaxed Stability

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One of the frustrations of being a child and reading lots and lots of books on combat aircraft was that there would be impressive-sounding technical terms bandied about, but no explanations.  Or if there were explanations I didn't understand them because I was a child.

 

One of the terms that got thrown around a lot was "relaxed stability" or "artificial stability" or even "instability," and this was given as one of the reasons for the F-16's superiority.  Naturally, an explanation of what on earth this was was not forthcoming, but it had something to do with making the F-16 more maneuverable.

 

This is partially true, but relaxed stability doesn't just make a plane more maneuverable.  It makes a plane better in general.

 

Why is this so?  Let's look at a schematic of a typical aircraft:

 

1024px-Longitudinal_aircraft_stability_1

 

There are two points of interest here; the center of lift (CL) and center of gravity (CG).  The CL is the net point through which all aerodynamic forces acting on the aircraft pass.  Various things can cause the CL to shift around in flight, such as the wing stalling or the transition to supersonic flight, but we'll ignore that for now.

 

The CG is the net center of mass of the aircraft.  The downward force of the weight of the aircraft will act through this point, and the aircraft will rotate around this point.

 

The reason that this configuration is stable is that the amount of lift a wing generates is a function of its angle of attack (AOA, or alpha).  AOA is the angle of the moving air relative to the wing.  If the wing is more inclined relative to the air, it generates more lift up until it starts to stall.  The relationship looks like this:

 

936px-Lift_curve.svg.png

Obviously this depends on the exact shape of the wing and the airspeed, but you get the idea.  The lift increases as alpha goes up, but falls off after the wing stalls.

 

This means that in a conventionally stable aircraft in level flight, anything that causes the nose to pitch up will cause the amount of lift to increase, but because the CL is behind the CG, this increased lift will cause a torque on the aircraft that will rotate the nose back down again.  Thus, any disturbances in pitch are self-correcting.  This is important because it means that a human being can fly the aircraft.  If random disturbances were substantially self-magnifying, the plane would begin to tumble through the air.

 

There's a bit of a problem though.  Because the CL is behind the CG, the plane has a tendency to rotate downwards.  So, to keep the plane level the tail has to apply a torque to trim out this tendency to rotate.  The torque that the tail is applying is pushing downward, which means that it's cancelling out part of the lift!  Keeping the tail deflected also increases drag.

 

These problems would go away if the arrangement were reversed, with the CG behind the CL:

 

1024px-Longitudinal_aircraft_stability_0

 

However, this would make the plane unflyable for a human.  But this is the 21st century; we have better than humans.  We have computers.

 

A computer (actually, an at-least-triply-redundant set of computers) and an accelerometer detect and cancel out any divergences in pitch faster and more tirelessly than a human ever could.  The tail downforce becomes tail upforce.  Also (contrary to wikipedia's shitty diagrams), the distance between the CG and CL is closer on unstable designs, so the trim drag of the tail is smaller too.

 

OK, so unstable designs get a slight reduction in drag and a slight increase in lift.  Why is that a big deal?

 

Think of a plane as a set of compromises flying in close formation.  Everything in aerodynamics comes at a cost.  Let's take a look at how this principle can kneecap people trying to be clever.

 

The quicker of you will have no doubt objected to my characterization of stable aircraft losing lift due to tailplane downforce.  "But that doesn't apply if the plane is a canard design!  The CG will be in front of the CL, but still behind the canards, so the canards will generate an upforce to trim the plane out!  No need for fancy computer-flown planes here!"

 

Yeah, they tried that.  But the need for CG/CL relationships ends up screwing you anyhow.  Let's look at a stable canard design (and one of my favorite aircraft), the J7W1 Shinden:

j7w_3view.jpg

 

Note that the wings are swept.  Now, this is a prop-driven plane, so I can guaran-fucking-tee you that the wings aren't swept to increase critical mach number (I don't think the designers even knew about critical mach number at the time).  Instead, the wings are swept for two reasons:

 

1)  To move the CL back so that the plane is stable

 

2)  to move the rudders back so that they're far enough behind the CG that they'll have adequate control authority.

 

There are lots of reasons you don't want swept wings on a prop fighter.  Since the thing is never going to go fast enough to encounter the benefits of them, in fact, the swept wings are almost entirely a negative.  They reduce flap effectiveness and have goony stall characteristics.  If you could get away with not having them, you would.

 

But you can't.  You can't because it's 1945 and the computers are huge and unreliable.  Your clever dual-lifting-surface canard design's advantages are heavily watered down by the disadvantages imposed by the need for stability.

 

That is the big advantage of instability.  The designer has a lot more freedom because there's one less thing they have to worry about.  This can indirectly lead to huge improvements.  Compare a mirage 3 and a mirage 2000.  The mirage 2000 is unstable, which adds some extra lift (nice, especially on takeoff where deltas really hurt for lift), but more than that it allows the designer to move the wings further forward on the fuselage, which allows for better aft-body streamlining and better area ruling.  Instability doesn't allow for better area ruling per se, but it frees the designer enough that the could potentially opt for that.

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When I have more time (HA!) I will have to re-write this; I don't think I did a particularly good job explaining.

 

Another consequence of relaxed stability, which is important for fighters, is that a relaxed stability aircraft will have greater available lift during a turn.

 

ec56900364e71e857f5f31dd32395e6d.jpg

 

This is the F-15; big, beautiful, and freaking expensive.  Like the MiG-29, it has all the gadgets you'd expect on a fourth-generation fighter except for relaxed stability and fly by wire; both being the last fighter designs from their respective countries to use conventional hydraulic, pilot-actuated controls.

 

As you can tell from the afterburners and wing contrails, this eagle is pulling serious Gs.    

 

Note the position of the horizontal stabilizers.  The leading edges are tipped downwards, which means that they are producing downforce.  Because the horizontal stabs are behind the CG of the eagle, this rotates the nose up.  This increases the AOA of the wings, which increases the amount of lift they generate.  This lift pulls the eagle into a tight, banked turn; ideally one that vectors the nose in the direction of wicked reprobates so that they can be smote from the earth with any of a variety of exciting ordnance.

 

Just one problem; in addition to generating torque that's pitching the aircraft, those horizontal stabilizers are generating downforce.  That downforce is partially cancelling out the lift from the wings, which is wasteful.  However, the horizontal stabilizers need to stay deflected throughout the maneuver because the eagle is a stable aircraft.  If the horizontal stabilizers go parallel with the airframe, the AOA will return to neutral.

 

DSC_2394-630x417.jpg

 

This is the F-16; medium-sized, beautiful and (less) freaking expensive.  Like the Sukhoi SU-27, it was the first fighter aircraft from its respective country to be completely computer-stabilized all the time (several aircraft, e.g. F-111 had limited computer stability assistance in certain parts of the performance envelope, but could fly without it).

 

This F-16 is also pulling Gs.  Note, however, that the horizontal stabilizers are basically not deflected.  They don't need to be.  Because the F-16 is unstable, any pitch changes self-amplify.  The horizontal stabilizers only need to pitch down at the beginning of the maneuver in order to initiate it, and the instability will take over from there.  The horizontal stabilizers will reverse, briefly, at the end of the maneuver in order to return the AOA to neutral, and the computers will then instruct the fly-by-wire system to make constant, subtle adjustments several times per second to keep the plane level.

 

This means that during a pitch-up maneuver the horizontal stabilizers are not subtracting lift except during the very beginning when they tilt down to initiate the maneuver.  In fact, since the center of gravity is to the rear, the horizontal stabilizers provide lift during the turn just as they do in level flight.

 

This improves lift to drag ratio during maneuver and is part of why the flanker and viper have such excellent speed retention during turns.

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Addendum:

 

 

Not all aircraft designed to be unstable are actually unstable in all flight regimes.  For example, the F-16 is stable in supersonic flight due to the center of lift movement that occurs at those flight speeds.  This is the case with most unstable aircraft.  Some sources claim that the SU-27 is stable with a full internal fuel load, as the weight of fuel in the large forward fuselage tank moves the center of gravity forward of the center of lift.

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An interesting problem in unstable aircraft is what in the hell you do when the hydraulic system loses power.  If the engines in an unstable aircraft die, it won't be able to glide.  Without the constant corrections sent from the computer to the flight control surfaces, unstable aircraft don't coast, they tumble.

 

This problem is much more worrisome in a single-engined aircraft, as it is reasonably unlikely that both engines in a twin engined aircraft will lose power at the same time.

 

In the event that the engine can no longer supply power to the hydraulics, the F-16 has an Emergency Power Unit:

 

ajj.jpg?m=1371916699

 

This compact little generator is powered by hydrazine from a tank in the right strake of the F-16:

 

f16-bay2.jpg

 

Hydrazine is really, really toxic, but as a mono-propellant it has fool-proof ignition reliability.  The tank can supply the EPU for about ten minutes.

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I was 90% sure he was saying something like that, and 10% unsure that he might be drunk again.

 

No ram air turbine on the viper, but that's another possible approach.

 

Yet another possibility, and I believe the gripen does this, is that on an unstable canard design you can feather the canards so the COL shifts backwards and the plane becomes stable.  Sort of the opposite of the trick the YE-8 was doing.

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ja-37_zpsd97b314a-1.jpg

 

A JA-37 with a whole mess of weapons.

 

7j1W43C.jpg

 

A mirage 5 with a whole mess of bombs.

 

This shows one of the weaknesses of stable canard configured aircraft.

 

Delta wings, being short span and long chord length, are quite stiff and make an excellent place to hang heavy weapons from.  But the mirage V hangs them all over the wings, often in drag-reducing tandem, while the viggen has the weapon stations only at the front of the wings, even when carrying huge weapons like the BK 90 candy submunition dispenser:

 

NZSL4tY.jpg

 

 

 

It's because of the canards.

 

The canards, being lift-generating and being in front of the main wing, move the center of lift further forward relative to the wing than it is in the mirage.  In a stable aircraft the center of gravity must be kept in front of the center of lift, which means that the viggen cannot have the weapons mounted vary far back or they will destabilize the aircraft.

 

The unstable gripen has much more leeway in hanging enormous ordnance loads all over the bottom of the plane:

 

rQfTmJE.jpg

 

Which it can then drop on enemies up to five miles away.

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