Why is yaw damper inop limited to a maximum altitude?
Thread Starter
Join Date: Jun 2010
Location: Canada
Age: 37
Posts: 382
Likes: 0
Received 0 Likes
on
0 Posts
Why is yaw damper inop limited to a maximum altitude?
I understand why there is a maximum airspeed, but why a maximum altitude?
The more detailed and technical the answer, the better!
The more detailed and technical the answer, the better!
Moderator
Yaw damper generally is to provide a moderating influence on Dutch Roll tendencies.
Dutch Roll gets worse with increasing altitude, ergo, no Y/D = height limit if the DR problems warrant.
Similar limitations can exist for aircraft with additional fins included as certification flight test fixes for directional stability.
For instance, having a copy of the Super King Air POH and MMEL on the desk at the moment, that Type runs to FL 350 per the TC but, with Y/D U/S the limit is A050. With Raisbeck mod per STC SA5151NM (aft body strakes - couple of fixed fins under the tail) the A050 limit increases to FL 190. If, for instance, one demoded the aircraft, say, for damage recovery to base considerations, the basic limit of A050 would then apply for the ferry recovery.
Dutch Roll gets worse with increasing altitude, ergo, no Y/D = height limit if the DR problems warrant.
Similar limitations can exist for aircraft with additional fins included as certification flight test fixes for directional stability.
For instance, having a copy of the Super King Air POH and MMEL on the desk at the moment, that Type runs to FL 350 per the TC but, with Y/D U/S the limit is A050. With Raisbeck mod per STC SA5151NM (aft body strakes - couple of fixed fins under the tail) the A050 limit increases to FL 190. If, for instance, one demoded the aircraft, say, for damage recovery to base considerations, the basic limit of A050 would then apply for the ferry recovery.
Thread Starter
Join Date: Jun 2010
Location: Canada
Age: 37
Posts: 382
Likes: 0
Received 0 Likes
on
0 Posts
I understand what a yaw damper is for. I think the main problem I'm mulling over is the difference between pressure and density.
At the same EAS at 35,000' or at SL, the control effectiveness should be the same. But apparently it's not due to the density of the air...?
The pitot (or total) pressure equals the static pressure plus the dynamic pressure (1/2 rho V squared). Rho being the density. So what's the difference between the static pressure and the density (rho) included in dynamic pressure? Obviously there has to be density or else there would be no dynamic pressure, regardless of how fast the object was traveling.
Anyone have equations that explain this?
At the same EAS at 35,000' or at SL, the control effectiveness should be the same. But apparently it's not due to the density of the air...?
The pitot (or total) pressure equals the static pressure plus the dynamic pressure (1/2 rho V squared). Rho being the density. So what's the difference between the static pressure and the density (rho) included in dynamic pressure? Obviously there has to be density or else there would be no dynamic pressure, regardless of how fast the object was traveling.
Anyone have equations that explain this?
At the same EAS at 35,000' or at SL, the control effectiveness should be the same. But apparently it's not due to the density of the air...?
Handling the big jets, pages 162 to 164 explains it nicely. Principle is applicable to any aeroplane requiring yaw damper, it's just more critical on big jets due to their higher speed.
How do I get in contact with John?
Join Date: Mar 2006
Location: Vance, Belgium
Age: 62
Posts: 271
Likes: 0
Received 5 Likes
on
3 Posts
italia458,
you asked
This equation is the equation of damped coupled oscillators.
It is somewhat complex as it is a tensorial equation:
M ḧ(t) + B ḣ(t) + K h(t) = 0
where M, B and K are tensors (read it as square matrices with as many columns or rows as there are oscillators) and ḧ,ḣ and h are matrices of 1 column by the oscillator count number of rows and each element of these h matrices are some function of the time t.
ḧ(t) is the acceleration vector. each row i contains the acceleration of the movement of oscillator i at time (t).
ḣ(t) is the speed vector. each row i contains the speed of the ocillator i at time (t).
h(t) is the displacement vector. each row i contains the displacement of the ocillator i at time (t).
The tensor M is the inertial tensor. Multiplied by ḧ(t), it gives the inertial pseudo-force. That is, each value in column i row j gives the inertial response in the degree freedom of oscillator j caused by the acceleration of oscillator i.
The tensor D is the damping tensor. It express the "friction" that damps the oscillation energy. The damping force vector is obtained by multiplication of D with the speed vector.
The tensor K is the stiffness tensor. It express the "reaction" force of the oscillator when multiplied with the displacement vector.
Dutch Roll is indeed a phenomenon of coupled oscillators.
One oscillator is the plane itself oscillating around its CG and pushed back in the relative wind direction by dynamic pressure on the rudder and rudder fin.
The second oscillator is the slip and roll oscillation fed by the slipstream pressure on swept wings or wings with dihedral.
There is much to say to explain why a single oscillator cannot generate a self sustained oscillation (even with energy fed by the dynamic pressure). The self sustained ocillation requires at least two coupled oscillators with different frequencies. But this is too long a story to fit here. If you are interested, please lurk into the links I provide below.
Back to coupled oscillators equation : when one or more of the oscillators are aerodynamic oscillators (at least the stiffness comes from an aerodynamic pressure), the equation becomes:
(Ms + ρπb² Ma) ḧ(t) + (Bs + ρvcπ Qb) ḣ(t) + (Ks + ρv²cπ Qk) h(t) = 0
The tensors Ms, Bs and Ks are just the structural part of the tensor, that is, the part that would exist if the oscillators were mere springs.
The terms ρπb²Ma , ρvcπQb and and ρv²cπQk are the aerodynamic part of these tensors.
ρπb²Ma is the aerodynamic inertia ; it is the mass of an arbitrary cylindar of air (with radius b) that moves with the oscillator movement. ρ is the density of the air.
ρvcπQb is the aerodynamic damping. v is the relative speed of the air flow and c is the width of the airfoil that oscillates (comes from c the chord in case of wing oscillation). Q is a very complex tensor and I shall not detail its contents.
ρv²cπQk is the aerodynamic force developped by the aerodynamic pressure. The factors ρv² is twice the dynamic pressure. cπ comes again from using the vibrating wing as the primary use case and Q is again a very compley tensor. It should be noted that this aerodynamic force depends on some incidence factors that are contained on the displacement vector h(t). The translation from oscillator displacement into a real lift factor is contained in the tensor Q.
Now, lets consider what happens when the altitude is increasing whilst keeping a constant indicated speed, and thus a constant dynamic pressure ρv²/2.
1. Obviously, the stiffness terms stays constant : it varies with ρv².
2. The aerodynamic inertia is going to decrease (ρ is decreasing) and thus the oscillation frequency will increase. However, Ma is usually small compared to Ms which stays constant. The frequency change is thus small.
3. However, the aerodynamic damping ρvcπQb is usually sizeable compared to the structural damping Bs. For dutch roll, the structural damping is insignificant compared to the aerodynamic one. The aerodynamic is proportional to ρv and not ρv². This means that, if ρ decreases and v increases so that ρv² stays constant, then ρv will decrease as the square root of the density decrease.
All in all, aerodynamic damping is decreasing with altitude.
That's why a mechanical damping may be absolutely necessary above a given altitude.
Note: the various flutter oscillations (aileron flutter, wing flutter, etc) are governed by the same equations and their prevention may require a speed or speed per altitude limitation.
Luc
Some links on coupled oscillators and aeroelasticity:
Ltas-aea ::Aeroelasticity Course
http://www.keybridgeti.com/videotrai..._Stability.PDF
http://www.cs.wright.edu/~jslater/SD...ter_banner.pdf
http://aerade.cranfield.ac.uk/ara/arc/rm/3011.pdf
Edit: when reviewing the post, I notice that I have not been very clear as to why the aerodynamic damping has a factor ρv and not ρv² or ρ.
Here it is :
- The aerodynamic pressure can have an effect that is directly opposed to and influenced by the oscillatory movement ; this is the lift on the aerofoil and also the aerodynamic stiffness. It is proportional to the dynamic pressure and is factored by ρv².
- The aerodynamic pressure also can have an effect that is perpendicular to the direction of the oscillatory movement. This is the drag generated by the aerofoil. Perpendicular means that, at first level of approximation, it makes no work on the oscillatory system. However, at higher levels of approximation, it does. And that is the damping.
Consider that ḣ(t) (the speed vector of the oscillatory movement) and v (the speed vector of the relative wind) are perpendicular. They sum up to give the wind speed relative to the oscillating surface. This composite speed is at an angle with the relative wind direction and the tangent of it is ḣ(t)/v.
(the total speed is square root of v²+ḣ(t)² and the sine of the angle is ḣ(t)/sqrt(v²+ḣ(t)²) )
Therefore, the drag force (which is always in the same direction as the relative wind) is also at an angle relative to the oscillating surface and its inclinaison is such that it opposes to the oscillatory movement (therefore the "damping").
The drag force is Fd = Cd.ρv²/2 (in the absence of the oscillatory movement)
and becomes Fd = Cd.ρ.(v²+ḣ(t)²)/2 when adding the oscillation.
The part of it that opposes to the oscillatory movement is given by the sine of the angle.
Damping = ( ḣ(t)/sqrt(v²+ḣ(t)²) ). Cd.ρ.(v²+ḣ(t)²)/2
Damping = Cd.ρ.( ḣ(t).sqrt(v²+ḣ(t)²) )/2
ḣ(t) is normally small compared to v ; therefore sqrt(v²+ḣ(t)²)can be safely simplified into v. We get:
Damping = ρv.ḣ(t).Cd/2
We see that this matches the aerodynamic damping term of the coupled oscillators equation (ρvcπ Qb) ḣ(t) where Cd/2 is replaced by cπ Qb.
you asked
Anyone have equations that explain this?
It is somewhat complex as it is a tensorial equation:
M ḧ(t) + B ḣ(t) + K h(t) = 0
where M, B and K are tensors (read it as square matrices with as many columns or rows as there are oscillators) and ḧ,ḣ and h are matrices of 1 column by the oscillator count number of rows and each element of these h matrices are some function of the time t.
ḧ(t) is the acceleration vector. each row i contains the acceleration of the movement of oscillator i at time (t).
ḣ(t) is the speed vector. each row i contains the speed of the ocillator i at time (t).
h(t) is the displacement vector. each row i contains the displacement of the ocillator i at time (t).
The tensor M is the inertial tensor. Multiplied by ḧ(t), it gives the inertial pseudo-force. That is, each value in column i row j gives the inertial response in the degree freedom of oscillator j caused by the acceleration of oscillator i.
The tensor D is the damping tensor. It express the "friction" that damps the oscillation energy. The damping force vector is obtained by multiplication of D with the speed vector.
The tensor K is the stiffness tensor. It express the "reaction" force of the oscillator when multiplied with the displacement vector.
Dutch Roll is indeed a phenomenon of coupled oscillators.
One oscillator is the plane itself oscillating around its CG and pushed back in the relative wind direction by dynamic pressure on the rudder and rudder fin.
The second oscillator is the slip and roll oscillation fed by the slipstream pressure on swept wings or wings with dihedral.
There is much to say to explain why a single oscillator cannot generate a self sustained oscillation (even with energy fed by the dynamic pressure). The self sustained ocillation requires at least two coupled oscillators with different frequencies. But this is too long a story to fit here. If you are interested, please lurk into the links I provide below.
Back to coupled oscillators equation : when one or more of the oscillators are aerodynamic oscillators (at least the stiffness comes from an aerodynamic pressure), the equation becomes:
(Ms + ρπb² Ma) ḧ(t) + (Bs + ρvcπ Qb) ḣ(t) + (Ks + ρv²cπ Qk) h(t) = 0
The tensors Ms, Bs and Ks are just the structural part of the tensor, that is, the part that would exist if the oscillators were mere springs.
The terms ρπb²Ma , ρvcπQb and and ρv²cπQk are the aerodynamic part of these tensors.
ρπb²Ma is the aerodynamic inertia ; it is the mass of an arbitrary cylindar of air (with radius b) that moves with the oscillator movement. ρ is the density of the air.
ρvcπQb is the aerodynamic damping. v is the relative speed of the air flow and c is the width of the airfoil that oscillates (comes from c the chord in case of wing oscillation). Q is a very complex tensor and I shall not detail its contents.
ρv²cπQk is the aerodynamic force developped by the aerodynamic pressure. The factors ρv² is twice the dynamic pressure. cπ comes again from using the vibrating wing as the primary use case and Q is again a very compley tensor. It should be noted that this aerodynamic force depends on some incidence factors that are contained on the displacement vector h(t). The translation from oscillator displacement into a real lift factor is contained in the tensor Q.
Now, lets consider what happens when the altitude is increasing whilst keeping a constant indicated speed, and thus a constant dynamic pressure ρv²/2.
1. Obviously, the stiffness terms stays constant : it varies with ρv².
2. The aerodynamic inertia is going to decrease (ρ is decreasing) and thus the oscillation frequency will increase. However, Ma is usually small compared to Ms which stays constant. The frequency change is thus small.
3. However, the aerodynamic damping ρvcπQb is usually sizeable compared to the structural damping Bs. For dutch roll, the structural damping is insignificant compared to the aerodynamic one. The aerodynamic is proportional to ρv and not ρv². This means that, if ρ decreases and v increases so that ρv² stays constant, then ρv will decrease as the square root of the density decrease.
All in all, aerodynamic damping is decreasing with altitude.
That's why a mechanical damping may be absolutely necessary above a given altitude.
Note: the various flutter oscillations (aileron flutter, wing flutter, etc) are governed by the same equations and their prevention may require a speed or speed per altitude limitation.
Luc
Some links on coupled oscillators and aeroelasticity:
Ltas-aea ::Aeroelasticity Course
http://www.keybridgeti.com/videotrai..._Stability.PDF
http://www.cs.wright.edu/~jslater/SD...ter_banner.pdf
http://aerade.cranfield.ac.uk/ara/arc/rm/3011.pdf
Edit: when reviewing the post, I notice that I have not been very clear as to why the aerodynamic damping has a factor ρv and not ρv² or ρ.
Here it is :
- The aerodynamic pressure can have an effect that is directly opposed to and influenced by the oscillatory movement ; this is the lift on the aerofoil and also the aerodynamic stiffness. It is proportional to the dynamic pressure and is factored by ρv².
- The aerodynamic pressure also can have an effect that is perpendicular to the direction of the oscillatory movement. This is the drag generated by the aerofoil. Perpendicular means that, at first level of approximation, it makes no work on the oscillatory system. However, at higher levels of approximation, it does. And that is the damping.
Consider that ḣ(t) (the speed vector of the oscillatory movement) and v (the speed vector of the relative wind) are perpendicular. They sum up to give the wind speed relative to the oscillating surface. This composite speed is at an angle with the relative wind direction and the tangent of it is ḣ(t)/v.
(the total speed is square root of v²+ḣ(t)² and the sine of the angle is ḣ(t)/sqrt(v²+ḣ(t)²) )
Therefore, the drag force (which is always in the same direction as the relative wind) is also at an angle relative to the oscillating surface and its inclinaison is such that it opposes to the oscillatory movement (therefore the "damping").
The drag force is Fd = Cd.ρv²/2 (in the absence of the oscillatory movement)
and becomes Fd = Cd.ρ.(v²+ḣ(t)²)/2 when adding the oscillation.
The part of it that opposes to the oscillatory movement is given by the sine of the angle.
Damping = ( ḣ(t)/sqrt(v²+ḣ(t)²) ). Cd.ρ.(v²+ḣ(t)²)/2
Damping = Cd.ρ.( ḣ(t).sqrt(v²+ḣ(t)²) )/2
ḣ(t) is normally small compared to v ; therefore sqrt(v²+ḣ(t)²)can be safely simplified into v. We get:
Damping = ρv.ḣ(t).Cd/2
We see that this matches the aerodynamic damping term of the coupled oscillators equation (ρvcπ Qb) ḣ(t) where Cd/2 is replaced by cπ Qb.
Last edited by Luc Lion; 21st Nov 2011 at 11:37. Reason: typos
Join Date: Jan 1997
Location: UK
Posts: 7,737
Likes: 0
Received 0 Likes
on
0 Posts
Trainers, tech pilots and safety people should be aware that Boeing will be releasing a major document on rudder control, input reversals, slideslip and structural integrity today, 18th November 2011.
It is a Flight Ops Tech Bulletin across all Boeing supported swept wing jets and therefore includes DC and MD series aircraft.
It reviews handling, certification, and training for operational flying in the light of the A300 accident over Queens and the resulting NTSB recommendations.
It's 16 pages long and, in essence, points out reversal of rudder input outside the 'normal' environment of single engine, crosswinds and so on can potentially lead to severe control and structural problems whether vertical fins are traditional or composite. The regulatory framework ensures all normal use of rudder to it's limits - 150% of load - it is the total reversal of direction in the rudder travel and ensuing, increasing sideslip forces generated which is the problem described and effectively illustrated.
Additionally guidance on rudder use in stall and unusual attitude recovery is given along with specific warnings regarding carry over of techniques from other types of aircraft and flying being extremely unsuitable for commercial, swept wing airliners.
The report also touches on the inadvisability of some of the mooted manoeuvring suggested by some in a hijack situation.
Rob
It is a Flight Ops Tech Bulletin across all Boeing supported swept wing jets and therefore includes DC and MD series aircraft.
It reviews handling, certification, and training for operational flying in the light of the A300 accident over Queens and the resulting NTSB recommendations.
It's 16 pages long and, in essence, points out reversal of rudder input outside the 'normal' environment of single engine, crosswinds and so on can potentially lead to severe control and structural problems whether vertical fins are traditional or composite. The regulatory framework ensures all normal use of rudder to it's limits - 150% of load - it is the total reversal of direction in the rudder travel and ensuing, increasing sideslip forces generated which is the problem described and effectively illustrated.
Additionally guidance on rudder use in stall and unusual attitude recovery is given along with specific warnings regarding carry over of techniques from other types of aircraft and flying being extremely unsuitable for commercial, swept wing airliners.
The report also touches on the inadvisability of some of the mooted manoeuvring suggested by some in a hijack situation.
Rob
Join Date: Jan 1997
Location: UK
Posts: 7,737
Likes: 0
Received 0 Likes
on
0 Posts
It's actually been around along time Aterpster but seems utterly forgotten since 2002 when Boeing and Airbus both issued significant analysis, warnings and advice.
This thread seemed an ideal time to to highlight this latest revision to it because significant points within don't seem to have percolated through to the glass face over the course of a mere 9 years.
Search on "Use of rudder on transport category airplanes" to get to a current version. No url offered because the same search criteria will lead Airbus folks to their own version.
Rob
This thread seemed an ideal time to to highlight this latest revision to it because significant points within don't seem to have percolated through to the glass face over the course of a mere 9 years.
Search on "Use of rudder on transport category airplanes" to get to a current version. No url offered because the same search criteria will lead Airbus folks to their own version.
Rob
Thread Starter
Join Date: Jun 2010
Location: Canada
Age: 37
Posts: 382
Likes: 0
Received 0 Likes
on
0 Posts
Luc Lion... I appreciate the extensive write up and links you provided. I'll have to take some time one of these days to delve into all of this material and try to understand it better.
Join Date: Aug 2009
Location: UK
Posts: 18
Likes: 0
Received 0 Likes
on
0 Posts
A non-mathematical explanation as to why yaw damping decreases with altitude:
Imagine sitting, facing forward, on the tail of an aircraft that is yawing (i.e. the yaw angle is increasing steadily) to the right. If the aircraft is otherwise stationary on a still day, you will feel a faint wind on your left cheek. This wind will appear to come directly from your left. Now imagine that, at the instant we are considering, there is also a light wind blowing from straight ahead. There will now also be a component of wind from straight ahead and you will feel the resultant wind to originate from somewhere forward and left. The fin will experience this same wind and generate a side-force that acts to oppose the yaw rate.
If we now progressively increase the headwind, the resultant wind will appear to come more and more from ahead. So the apparent wind angle seen by the fin decreases with forward speed. The important aspect, as far as yaw damping is concerned, is that the relevant forward speed is the true rather than the indicated air speed.
Note that I am ignoring any apparent wind angle due to the actual yaw angle. The argument applies only to the angle induced by the rate of yaw.
Now imagine two identical aircraft, one at sea level and one up in the flight levels. If both are flying at the same equivalent airspeed and yawing at the same rate, the fins of both will see the same equivalent wind speed. But the fin of the higher aircraft will see the wind as coming nearer from straight ahead, due to its higher true airspeed. Its fin therefore generates less side-force to oppose the yaw rate.
So, the higher you fly, the lower the yaw damping.
Imagine sitting, facing forward, on the tail of an aircraft that is yawing (i.e. the yaw angle is increasing steadily) to the right. If the aircraft is otherwise stationary on a still day, you will feel a faint wind on your left cheek. This wind will appear to come directly from your left. Now imagine that, at the instant we are considering, there is also a light wind blowing from straight ahead. There will now also be a component of wind from straight ahead and you will feel the resultant wind to originate from somewhere forward and left. The fin will experience this same wind and generate a side-force that acts to oppose the yaw rate.
If we now progressively increase the headwind, the resultant wind will appear to come more and more from ahead. So the apparent wind angle seen by the fin decreases with forward speed. The important aspect, as far as yaw damping is concerned, is that the relevant forward speed is the true rather than the indicated air speed.
Note that I am ignoring any apparent wind angle due to the actual yaw angle. The argument applies only to the angle induced by the rate of yaw.
Now imagine two identical aircraft, one at sea level and one up in the flight levels. If both are flying at the same equivalent airspeed and yawing at the same rate, the fins of both will see the same equivalent wind speed. But the fin of the higher aircraft will see the wind as coming nearer from straight ahead, due to its higher true airspeed. Its fin therefore generates less side-force to oppose the yaw rate.
So, the higher you fly, the lower the yaw damping.
Last edited by Flash131; 12th Mar 2012 at 21:10. Reason: "equivalent" added to last paragraph.
Join Date: Mar 2012
Location: Earth
Posts: 6
Likes: 0
Received 0 Likes
on
0 Posts
You guys got it all wrong.
Raisbeck King Air 300/350 Performance Systems
Look the increased Yaw damp limitation, consider the certification reasons..yada, yada, and it should be clear..
Raisbeck King Air 300/350 Performance Systems
Look the increased Yaw damp limitation, consider the certification reasons..yada, yada, and it should be clear..
Thread Starter
Join Date: Jun 2010
Location: Canada
Age: 37
Posts: 382
Likes: 0
Received 0 Likes
on
0 Posts
You guys got it all wrong.
Raisbeck King Air 300/350 Performance Systems
Look the increased Yaw damp limitation, consider the certification reasons..yada, yada, and it should be clear..
Raisbeck King Air 300/350 Performance Systems
Look the increased Yaw damp limitation, consider the certification reasons..yada, yada, and it should be clear..
Flash... I believe in your last paragraph equivalent airspeed, not indicated, would be the correct term. It's important to make that distinction when operating at high altitude.
Last edited by italia458; 12th Mar 2012 at 19:41.
Join Date: Aug 2009
Location: UK
Posts: 18
Likes: 0
Received 0 Likes
on
0 Posts
Italia: Well caught, my terminology was less than rigorous. But then again, if we include compressibility effects, we should also take into account such things as the change in the fin lift curve slope.
Edit to original post now made.
Edit to original post now made.
Thread Starter
Join Date: Jun 2010
Location: Canada
Age: 37
Posts: 382
Likes: 0
Received 0 Likes
on
0 Posts
Italia: Well caught, my terminology was less than rigorous. But then again, if we include compressibility effects, we should also take into account such things as the change in the fin lift curve slope.
