Positive Dynamic Stability

[Dazzler]

This came up in a lesson with a student the other day....

How is positive dynamic stability designed into a fixed wing aircraft?

(I'm expecting the answer will contain the words "horizontal stabilizer" and "damping" somewhere!)

[tgrayson]

Originally Posted by Dazzler

How is positive dynamic stability designed into a fixed wing aircraft?

There is generally no need to add any design features for this behavior; most airplanes, if they exhibit positive static stability, will have positive dynamic stability. However, high moments of inertia around the particular axis in question, or poor damping (such as at high altitude) can result in a normally positive static situation becoming neutral or negative. For instance, take an airplane high enough and they'll all exhibit an unstable dutch roll problem. Only way to fix it is to 1) Add a much larger vertical fin (draggy) or 2) install a yaw damper.

[nosehair]

Originally Posted by Dazzler

How is positive dynamic stability designed into a fixed wing aircraft?

"rolling" stability (around the longitudinal axies) is designed into the airplane by "dihedral". The wings are slanted up slightly. When a gust of air causes a wing to go down, this downwaed motion causes a slight increase in angle of attack which increases lift which brings the wing back up level with the other. Think exagerated. Think of a boat in water. The sides of the hull of the boat are like the dihedral of the wing. Think of a boat or wing at 45 degrees. If the airplane or boat is pushed over, the pressure on the down-going wing or hull against the airplane or boat will push it back towards equalibrium so that the boat or airplane 'floats' upright in the air/water.

"pitching" stability (around the lateral axies) is designed into the airplane by designing the center-of-gravity in front of the center-of-lift. By having a designed nose-heavy airplane, it will always fall nose first when it stalls.

When it is level the CG is pulling the nose down at all times, so the horizontal stabilizer (hmm...horizontal stabilizer..) is designed to produce a down force equal to the down force of the CG. So the center of lift is between the down force of the nose and the down force of the tail. You are balancing this stabilizing force when you trim to the exact nose down weight of the airplane.

These are the two main stabilizing forces; there are others, but this will
satisfy the initial inquiry.

[Dazzler]

Originally Posted by nosehair

"rolling" stability (around the longitudinal axies) is designed into the airplane by "dihedral". The wings are slanted up slightly. When a gust of air causes a wing to go down, this downwaed motion causes a slight increase in angle of attack which increases lift which brings the wing back up level with the other. Think exagerated. Think of a boat in water. The sides of the hull of the boat are like the dihedral of the wing. Think of a boat or wing at 45 degrees. If the airplane or boat is pushed over, the pressure on the down-going wing or hull against the airplane or boat will push it back towards equalibrium so that the boat or airplane 'floats' upright in the air/water.

"pitching" stability (around the lateral axies) is designed into the airplane by designing the center-of-gravity in front of the center-of-lift. By having a designed nose-heavy airplane, it will always fall nose first when it stalls.

When it is level the CG is pulling the nose down at all times, so the horizontal stabilizer (hmm...horizontal stabilizer..) is designed to produce a down force equal to the down force of the CG. So the center of lift is between the down force of the nose and the down force of the tail. You are balancing this stabilizing force when you trim to the exact nose down weight of the airplane.

These are the two main stabilizing forces; there are others, but this will
satisfy the initial inquiry.

Yup - knew that stuff, but how does that make the dynamic stabilty positive, rather than neutral? Something must gradually dampen the oscillations so the aircraft settles back to equalibrium. What provides that damping effect? Is it just that, when an oscillation starts, it gradually loses energy?

[tgrayson]

Originally Posted by Dazzler

Is it just that, when an oscillation starts, it gradually loses energy?

It's true that energy must be removed from the system; a clean airplane is more susceptible to the phugoid than a clean one, but I don't think the normal mathematics looks at it from this perspective; I'll have to take a look to be sure.

One factor is damping due to such things as yaw rate. Consider this:

If I push the right rudder pedal to the floor, the nose swings right, the tail left. If I release the pedal, the tail starts to yaw right and the increasing velocity generates a relative wind that opposes the motion of the tail. As the tail overshoots center, it won't swing quite as far as the previous time and so the oscillations will eventually die. Thinner air or more weight distributed towards the tail will increase the period of the oscillations.

[BobDDuck]

This was all stuff I thought I could leave behind to my college and instruction days. Interestingly enough on my upgrade oral with our POI, he spent about 25% of the entire oral having me talk about Part 25 certification, and mostly how it pertained to high altitude/high airspeed aerodynamics. The point of focus was mach trim and on how worked to keep the airframe dynamically stable around the pitch axis while hand flying.

[tgrayson]

Originally Posted by BobDDuck

mach trim and on how worked to keep the airframe dynamically stable around the pitch axis while hand flying.

The usual problem is too much static stability at high speeds, because the aerodynamic center shifts rearward. The aircraft wants to nose over.

[BobDDuck]

Originally Posted by tgrayson

The usual problem is too much static stability at high speeds, because the aerodynamic center shifts rearward. The aircraft wants to nose over.

Right, but that doesn't have anything to do with dynamic stability. The dynamic part is it coming back to level. As far as the mach trim goes, it trims the nose up a bit as the speed increases so *if* the plane noses over (due to turbulence or the captain falling asleep on the yoke), it will be more likely to come back to level through the process of dynamic stability. Hence it being required per part 25 and why our MEL book says that if the mach trim is out we are limited to hand flying no faster then 250 knots.

[tgrayson]

Originally Posted by BobDDuck

As far as the mach trim goes, it trims the nose up a bit as the speed increases so *if* the plane noses over (due to turbulence or the captain falling asleep on the yoke), it will be more likely to come back to level through the process of dynamic stability. Hence it being required per part 25 and why our MEL book says that if the mach trim is out we are limited to hand flying no faster then 250 knots.

According to the books I have, a mach trimmer is merely a trimming device that alleviates the heavy control forces required at high speed flight. Assuming that trim is all it does, it wouldn't have any effect on the stability characteristics of the aircraft, static or dynamic. Do you have any documentation that this device behaves differently?

As for being a required item it may be the control forces involved, or just that the regs require [and they do] that a push force is required to go faster, but mach tuck would mean that a pull force was required.

Yes, I would like a chance to debate your POI on the subject.

[BobDDuck]

Originally Posted by tgrayson

Yes, I would like a chance to debate your POI on the subject.

I wouldn't. The less I talk to the FAA the better.

The documentation on the RJ Mach trim is pretty weak. Best I can make of it is that it trims the nose up as the speed increases irregardless of control input when the autopilot servo is NOT engaged. So in other words, it just makes it so LESS back force is required on the yoke to get a certain amount of pitch up. It trims using the same mechanics that the stabilizer trim uses, but it is NOT linked to the stab trim switches or the autopilot servo. That's just how I understand it though.

[tgrayson]

Originally Posted by BobDDuck

Best I can make of it is that it trims the nose up as the speed increases irregardless of control input when the autopilot servo is NOT engaged.

That fits in with my impressions. You see a lot of pilot literature talking about mach tuck being an "instability" issue, when it's really a "too much stability" issue. But along with that extra stability is a trim change, which is what the trimmer is designed to compensate for.

One of the guys over at PPrune posted the following, and I know the poster to be very knowledgeable:

A Mach trim system will, as the aircraft accelerates, progressively input a aircraft nose-up trim input (whether stab or elevator, stab is easier to visualise).

Suppose you start at M0.80, stab 0 degs, elevator 0 degs (just for simplicity) - column neutral.

Now, push the throttles to the detent and wait.

If the aircraft has good, natural, static stability, it should start to pitch up as you accelerate, which will force the pilot to push the column more and more to keep the aircraft in level flight as it accelerates.

If the aircraft has bad static stability it won't do so as strongly. If it has NO static stability (easiest case to visualise) the aircraft will remain in trim as it accelerates.

We want the first case, not the second. So, if our aircraft is like the second one, you have to find a way to induce the pilot to apply forward column as the aircraft speeds up. One way (typical Mach Trim operation) is to feed in a stab trim motion proportional to the speed increase. The stab is moved to induce a nose-UP motion (stab T/E UP; if it were an elevator it would be elevator T/E UP also). In order to counter that, the pilot pushes forward on the column to get a elevator angle to cancel out the Mach trim stab input. The total lift force on the tail is the same as when we have no Mach Trim, but now it's one force due to the stab, and another opposite force due to the elevator. So it looks like the aircraft requires forward column when it accelerates, and everyone is happy, and the regulations are met.

So in one sense, the mach trimmer does increase the static stability, when you measure it by the control forces needed to get a change in airspeed. And that's the way the regulations DO measure it, which is why the guy referred to "regulations are met."

[BobDDuck]

Ok, I'll buy that.

I really should read the tech forums at pprune more.