ryan1234

What he is getting at here is lateral/directional stability. When an aircraft is rolling into the turn you will have adverse yaw and yaw rotational inertia. The positive stability of the angle of attack of the vertical stabilizer (hence why it's called that) will 'weathervane' away from the disturbing force, in this case inertia and adverse yaw. The rudder helps more efficiently to overcome adverse (side force) during flight.

gesres

You actually had it right. The horizontal component of lift merely sideslips the airplane one way or the other. The changing relative wind on the vertical stabilzer causes the aircraft to yaw in the new direction of movement.

(Note that some people are confusing yaw with sideslip. In a 360 degree turn, perfectly coordinated, the nose will yaw 360 degrees, with no sideslip.)

Cubdriver

First, I went back and changed my earlier post, the one where I said load factor varies with speed. That was incorrect, it varies only with bank angle. Thanks for fixing me on that, shdw. Second, I have to agree with Joe that this thread is way off track despite all the interesting thoughts people have provided. There's nothing like a group of engineers to overanalyze something. Going back to basic physics in 2 dimensions, the acceleration on a particle is:


where
a is acceleration
v is velocity
r is radius

You can't get any simpler than that. Assuming our particle has some mass, if it goes faster it takes more force to hold it in orbit around the center. It takes less force if our particle slows down. Since we are talking about level turns in the air, then this most basic analysis applies for an airplane too. Let's take another look at the first equation I presented on page 1, rearranged a little for clarity:


where
phi is bank angle
v is velocity
r is radius

See how similar they are? The lift forces that are present in a real airplane drop out because they do not matter to this relationship, and I am not showing them here. They were there in the force balance equation, but they do not affect this equation. The equation shows that for a set bank angle, and a set amount of gravity, speed and radius of turn are proportional.

gesres

Just to provide a reference to avoid the "hot air" syndrome, I refer to "Fundamentals of Flight" by Richard S. Shevell, p. 323:This rudder, by the way, is necessary regardless of the existence of adverse yaw.

Actually, though, the aircraft is more than just yawing, it's also pitching throughout the turn in order to keep itself aligned with the relative wind. The greater the bank angle, the more pitching that is occurring with respect to the yawing. The mix of pitching and yawing is contained in these formulae:As you can see, in a flat turn, it's all yaw, no pitch; in a 90 degree banked turn, it would be all pitch, no yaw. Both the yawing moment and the pitching moment are produced by the natural weathercock stability of the airplane.

Cubdriver

Hey this is great- we have at least 4 degreed engineers chiming in on this thread. Never seen so many, makes for an interesting exchange.

Gesres: since you have the Shevell text, you may want to see what I am talking about a few pages earlier in the same section (320-322). That was taken from Shevell as well, great book for introductory engineering topics.

USMCFLYR

Which is why it left me in weeds about 20 posts ago!
This reminds me of HARM school and remembering that I was more interested in how to EMPLOY it than BUILD it

I think this is a good discussion. Keep going!

USMCFLYR

gestrich19

So according to this reference, the aircraft is basically moving around the axis that is in between the vertical and lateral axis?

Most references simplify with "the horizontal component of lift turns the aircraft" without going much further. That is simple enough for what is required by the FAA but I hardly find that satisfying.

Actually, I was very surprised to find how there is a lack of *detailed* information there is for the curious *layperson* on how an aircraft turns. If its not painful obvious, I'm not a engineer of the natural sciences. I am sure I have intellectually dragged the discussion down a notch with the number of engineers and those with experience here, but I am at least glad to participate and thankful for the help in understanding from everyone.

ryan1234

You have not dragged this discussion down, it's caused me to open and reference books that had been long packed up and put away. If I've personally said anything in error, I would appreciate it if someone points it out. I'm still trying to figure if I've said anything contrary to fact.

You really bring up a valuable conversation.

gesres

Hmmm, I had to think about that one, but yes, I think you could invent a new axis for that.

Good for you. The FAA stuff is awful. It's not as wrong as it was 10 years go, but that's mainly because they don't go into as much.

You're right, there's not. The Skip Smith book you have is about the best you can find at that level. It's what I use for my CFI candidates. I might *cautiously* recommend to you the "Flightwise" series. The second book on stability and control actually walks you through how a turn works and some other similar topics. The only reason I hesitate when recommending the book is that the author boasts that he's not going to use math, but he does. And so he gets into stability derivatives in this book, which is really beyond the audience that he claims to be aiming for. However, I think there's enough good stuff in there to make it worthwhile. He tells you how dihedral works, too.

Actually, no, you've been right all along. If you master the Skip Smith book, you'll have a better understanding than 95% of the pilots out there. And if I were you, I wouldn't try to discuss it with any other pilots because they'll just get angry when you tell them the airplane doesn't fly the way they think it does.

ryan1234

The basic things I understand are (and please anyone correct me if I'm wrong):

Turn Radius varies with true airspeed and load factor.

Turn Rate varies with true airspeed and load factor.

A coordinated turn has no sideforce (well realistically almost zero).

A rudder in a coordinated turn is needed (mainly) to overcome yaw rate dampening, which acts in opposition to the established yaw rate (i.e. positive yaw rate for a coordinated turn to the right).

An aircraft can exhibit a yaw rate with zero sideslip.

Yaw vs. Sideslip:

Sideslip is described as the angle generated by the relative wind not being aligned with the geometric longitudinal axis of the aircraft.

Yaw (the angle of yaw) is defined as the angular displacement of the airplane's geometric longitudinal axis in the horizontal plane from some arbitrary direction taken as zero at some instant of time. Yaw can also be used to describe rates and moments.