Rate/Radius of Turn
#41
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.
#42
On Reserve
Joined APC: Jun 2009
Posts: 11
(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.)
Last edited by gesres; 02-12-2010 at 09:26 AM.
#43
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.
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.
#44
On Reserve
Joined APC: Jun 2009
Posts: 11
When the airplane is accelerated sidewise in a turn, the directional or weathercock stability will rotate the airplane about its vertical axis automatically to keep the airplane pointing into the relative wind. Therefore, turns can be made with ailerons only. The airplane always has an angle of sideslip in such a turn to cause the directional correction. This increases the drag, a condition that can be avoided by use of the rudder to yaw the airplane at a rate that keeps the airplane always headed into the relative wind during the "coordinated" turn.
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:
rate of pitch = Ω cos(θ) sin(φ)
rate of yaw = Ω cos(θ) cos(φ)
where Ω (omega) is rate of turn, θ (theta) is pitch angle, and φ (phi) is bank angle.
(source:Elements of Airplane Performance, Ruijgrok, p. 304)
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.
rate of yaw = Ω cos(θ) cos(φ)
where Ω (omega) is rate of turn, θ (theta) is pitch angle, and φ (phi) is bank angle.
(source:Elements of Airplane Performance, Ruijgrok, p. 304)
Last edited by gesres; 02-12-2010 at 04:47 PM.
#45
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.
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.
#46
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.
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.
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
#47
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Joined APC: Dec 2009
Posts: 32
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.
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.
#48
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.
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.
You really bring up a valuable conversation.
#49
On Reserve
Joined APC: Jun 2009
Posts: 11
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.
I am sure I have intellectually dragged the discussion down a notch with the number of engineers and those with experience here
#50
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.
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.
Last edited by ryan1234; 02-12-2010 at 08:04 PM. Reason: adding and formating
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