Nosewheel Flutter: can anyone help me with the physics?

[Bede]

Yeah I think we're saying the same thing.

The more positive the real roots (b<<a,c) of the characteristic equation, the greater the oscillation.

The more negative the real roots (b>>a,c), the more damped.

This is a fascinating discussion. These concepts never really made sense until now. I knew the concept of a characteristic equation for feedback systems (too high a gain results in an unbounded output- ie increasing amplitude oscillations), but there's a lot more practical applications.

I should ask, I've seen e^iωt and e^-iωt show up in a few places. Solutions to forcing functions, Laplace transforms when substituting for iω for s. I'm curious if it shows up anywhere else.

[photofly]

I should ask, I've seen e^iωt and e^-iωt show up in a few places. Solutions to forcing functions, Laplace transforms when substituting for iω for s. I'm curious if it shows up anywhere else.

Well, gosh, yes. They’re everywhere. All trig functions (sin and cosine) are combinations of e^iθ and e^-iθ. Analyze any time dependent system and you’re there.

They are the “special functions” that solve the linear second order linear DE, they describe any kind of periodic motion: simple harmonic motion individually and then literally anything that repeats (which is essentially everything) by way of Fourier series. So that’s waves, including radio waves, light, matter waves (quantum theory) as well rotating and oscillating machinery, you name it.

Then there’s Euler’s identity: e^iπ + 1 = 0. You don’t get a lot cooler than that.

By the way Laplace transforms are different: they don’t have the “i” in the exponent which makes them qualitatively different and not nearly as useful.

[Bede]

Fascinating. I guess it comes back to Euler. You expand the e to the trig functions and thats where you get your oscillations.

[digits_]

Which chapter of From The Ground Up discusses this?

[NotDirty!]

Which chapter of From The Ground Up discusses this?

Your version probably only has real number chapters. You need the complex edition. Chapter cis theta.

[Bede]

Which chapter of From The Ground Up discusses this?

It's the chapter after how lift is produced. lol. (open's can of worms).

[JasonE]

Interesting discussion. One of the tailwheel airplanes I fly often gets a complaint about a shimmy. It has been looked at multiple times, the entire assembly is reasonably new. I've had it happen once to me landing close to gross in the 3 point attitude. I reduced the amount of load (stick pressure) and it went away.

[PilotDAR]

Taildraggers are thread drift, but a worthy discussion. For some, the spring leaves have sagged over the years. I always jack the weight off mine when I tie down, or I park it with the tailwheel swiveled backward if I'm away. The tailwheel steering axis must be "backward" such that the lower end of the steering axis is further forward than the upper end. I know it sounds counter intuitive, but that's what works. I keep the tailwheel shimmy plates in good order, with the recommended 5 pounds steering friction. Sometime people "look in" the Scott tailwheel, but fail to notice that the three pins in the shimmy damper plate are sheared off, they do no good that way. I also keep the tailwheel inflated to the highest permitted pressure. I always wheel land, and hold the tail off as long as possible. Since I have been doing all of that, I have never had a tailwheel shimmy.

[digits_]

Taildraggers are thread drift, but a worthy discussion. For some, the spring leaves have sagged over the years. I always jack the weight off mine when I tie down, or I park it with the tailwheel swiveled backward if I'm away. The tailwheel steering axis must be "backward" such that the lower end of the steering axis is further forward than the upper end. I know it sounds counter intuitive, but that's what works. I keep the tailwheel shimmy plates in good order, with the recommended 5 pounds steering friction. Sometime people "look in" the Scott tailwheel, but fail to notice that the three pins in the shimmy damper plate are sheared off, they do no good that way. I also keep the tailwheel inflated to the highest permitted pressure. I always wheel land, and hold the tail off as long as possible. Since I have been doing all of that, I have never had a tailwheel shimmy.

Are you referring to the principle demonstrated in this picture?



Where are the shimmy plates in that drawing? I can't seem to find what part you are referring to.

[PilotDAR]

Yes, that's the correct picture, and concept. The anti shimmy friction plates are inside the pivot mechanism of the Scott tailwheel. Five small coil springs force a series of plates against each other. three of the five of those spring (I don't know why not all five) are located by pins, which can shear off the one plate. The tailwheel still steers fine, but the anti shimmy properties are no longer effective. I have spent many years getting to know the nuances of my retractable Scott tailwheel, and after a few hundred hours of trouble free operation, I think I have it figured - but I still keep a replacement built up for a quick change, just in case!

[digits_]

Thanks, learned something new today!

[Ruckus]

I think the Grob G115 is a great airplane but I believe that the landing gear, specifically the nose gear is one of the weak points in the aircraft. I have owned one for over 14 years and done a lot of instruction in it. The nose gear is very finicky, and even when it is in perfect condition you need to be careful with your technique. The flight manual states that on takeoff, you need to apply "Nose gear relief" at a MIN. of 32kts, Then there is "Nose gear lift-off" at 54kts.
On landing I keep the weight on the mains as long as possible, with the stick coming back and gently let the nose wheel down as I approach full stick back.
Another issue with the nosegear is that it will turn a full 47 degrees, and I have had students stop for a runup, leaving the nose gear 47 degrees off. They almost have to complete a 360 before they can straighten out the nosewheel when they try to taxi forward again.
There is also a spring connection between the rudder and the ailerons, so if you move the rudder pedals you will also get some movement in the ailerons. I think this might add some play into the nose gear.
Even though I think it is not the best designed nose gear, I think that proper pilot technique will usually prevent shimmy.