Discussion
Right,
Following our little chat about aeros in the F1/fighter thread I thought Id contact an old friend of mine and ask him if he would send me his fairly well known text on instability (well Ok, it was after laughing at Mickee Boy). I will leave it to the MODS whether they wish it to remain here or transfer to the Planes section, but as the initial aero discussion was in here I thought it would be best here for a while and get the most views from folks who were reading the thread. If there are any ex or current MESSYBEAST, rec.miscers, sci mil naval or model flyers on here then Im sure you will probably recognise the txt and know exactly who wrote it.
Anyway, enjoy:
If I had a servo for every time I’ve heard someone say “modern fighters are made unstable to make them more agile” I’d have crow-brakes on everything! It seems every single model flyer knows about this, which would be great were it not for the annoyingly inconvenient detail that it isn’t actually true. Which is a shame, given how often it’s said. I’m hoping that in writing this piece people will understand WHY it isn’t true!
The concept that instability leads to high agility is a fallacy that dates back over 40 years to the days when autostabilisers were being developed to address the handling deficiencies of various early American jets and persists to this day. Let's start with the basics:
1. Many modern supersonic jets have a negative Static Margin (ie they have the C of G behind the Neutral Point) which makes them aerodynamically unstable, and they are made controllable by use of a full-authority autostabilisation system. This is true.
2. These modern supersonic jets are designed with inherent instability to give enhanced agility. This is NOT true. Not only is it not the reason why the aircraft are designed in this way, it is also not true that an unstable aeroplane is more agile.
I know this is contrary to the received wisdom, but let's just examine what's going on. Most of the following is grossly oversimplified to avoid the use of mathematics, and is also rather over-generalised, but it is valid and accurate for the purposes of this discussion. Professional aerodynamicists are requested to stop reading this now and pop into the forums to see how Phil is getting on with those wonderful Fw190 and B26 builds.
"Agility" of an aircraft in the pitching plane is determined by how quickly it can apply the lift forces to pull the 'G'. This in turn is dependant on how quickly the angle of attack can be increased - the pitch-plane angular acceleration, or more to the point the INSTANTANEOUS pitch-plane angular acceleration. Now a clever chap called Newton once showed that in any constant mass situation the acceleration of an object was dependant solely on the mass of the object and the sizes of the forces applied to it. The same is just as true for angular accelerations, except that we substitute "moments of inertia" for mass and use the "moments" of the forces as any attentive GCSE science pupil will be able to tell you. You will note that nothing has made reference to the "angular stability" of the object, because it's irrelevant and so we have just demonstrated that instability does NOT increase agility (QED – not that hard, was it?).
Fine, so why DO we bother with all this negative-stability-and-fly-by-wire cockamamie? After all, it would be so much simpler, cheaper and more reliable to simply connect a conventional aircraft hydraulic system (or even a pushrod) between the stick and the control surfaces! The answer is simple - it reduces the supersonic fuel consumption.
[What? Where did that come from? What's this guy been smoking!? I mean one minute I was dozing through a bit about stability and the next thing I know you're blathering on about fuel consumption. How can these be related?? - Ed].
To understand this we need to briefly look at another bit of aerodynamics, the concept of "Trim Drag". We all know that with a stable aeroplane you place the CG in front of the "centre of pressure" (I'd prefer to use "Neutral Point" but let's keep it simple) which makes the aeroplane pitch downwards. We oppose this by having a tailplane to push the tail down or a foreplane to lift the nose up and voila! We have a stable aeroplane.
The actual amount of effort the tailplane/foreplane has to exert to do this depends on how far the CG is from the centre of pressure, and we call this the "Static Margin". Those who have paid a bit of attention, rather than chatting up the totty at the back, will also know that the act of generating lift inherently generates drag. Indeed the more pretentious will point out that it has to because lift and drag are the hydrostatic and the hydrodynamic manifestations of the same phenomenon (at which the rest of us will jeer, throw ink bombs and put sand in their PE kit because we can't STAND a smarty-pants).
Now if we put these two things together we will see that the lift generated by the tailplane/foreplane to stabilise the aeroplane will inherently result in some extra parasitic drag which, since it is the result of trimming the aeroplane, we call "trim drag". The amount of drag generated is proportional to the size of the static margin. This is important, and I’ll be coming back to it in a minute.
Now we need to look at what happens when an aeroplane goes supersonic. When an aeroplane flies at moderate speeds the “aerodynamic centre” can be considered to be at 25% mean aerodynamic chord. It isn’t really, but this assumption works for the purpose of this discussion and where required the differences are corrected for other purposes with what is technically known as “complicated mathematical stuff”. Now if the pilot pushes the throttle into afterburner and leaves it there the aircraft accelerates until it goes supersonic, whereupon something interesting happens; the aerodynamic centre moves back to 50% mean aerodynamic chord. This is why the early attempts at supersonic flight often ended up in ever-steepening dives because there wasn’t enough elevator authority to pull out.
At this point I would be grateful if any professional aerodynamicists who didn’t pop over to the forums would do so now (that B26 really IS worth looking at) or perhaps go off and make themselves a coffee. Have they gone? Good! Now as far as the rest of you are concerned, the aerodynamic centre can be considered to be bolted to the “centre of pressure” via a short piece of carbon-fibre rod and a pair of high quality metal clevises, so that when the AC moves aft the CP moves with it – got that? Great! Oh here they come – nice coffee? No, you haven’t missed anything; we were just talking about transonic AC shift.
Now we can start to put it all together. The AC shifts aft, and increases the static margin so the tailplane/foreplane has to produce more lift to hold the aircraft level, and this substantially increases the trim drag. So when the aircraft is trying to fly as fast as possible there’s an inherent and unwelcome increase in drag, which increases the supersonic fuel consumption and limits the cruise speed. This is technically referred to as a “bad thing”(tm) so there are a number of techniques used to overcome it, and this is where we get back to where we started.
If you design the aeroplane so that the static margin is just sufficient for stability when the aircraft is supersonic you significantly reduce the supersonic trim drag and thus get lower fuel consumption, longer range and higher cruising speeds. Unfortunately when you slow down again the AC moves forwards and ends up in front of the CG, so the static margin is actually negative and the aeroplane is unstable. This is unpopular with the pilots because they’re essentially pretty lazy types who don’t like to work for a living, so the aircraft manufacturer reluctantly installs an expensive and complex autostabilisation system to allow the pilots to catch up on their sleep. And so there you have it, without so much as a whiff of an agility pixie. Pitch instability isn’t the only issue incidently - as the AC moves aft it affects directional stability as well, which is why supersonic aircraft have such vast fins (and often more than one).
Negative stability isn’t the only solution, there are others. Concord pumps fuel around to keep the static margin under control, and you could in principle use variable geometry, although this would require the wings to be moved forwards at supersonic speeds and you have trouble keeping the structure inside the Mach cone. A particularly elegant variable geometry solution was used on the cancelled XB-70 Valkyrie supersonic bomber project, which drooped its outer wing panels through 60 degrees at supersonic speeds. This did three things:
• It provided a “tunnel” to trap the shock-lift at speeds above mach 2
• It reduced the wing area behind the CG, moving the AC forwards and overcoming the supersonic trim drag issue
• It substantially increased the fin area when supersonic, overcoming the directional stability problems due to the AC shift.
Much more than anyone really wanted to know, I’m sure. But hopefully this note might go some way towards dispelling the myth that negative stability is used to increase agility. As professional control system designers will tell you, agility is controlled by agility pixies. But that is a subject for another day.
Following our little chat about aeros in the F1/fighter thread I thought Id contact an old friend of mine and ask him if he would send me his fairly well known text on instability (well Ok, it was after laughing at Mickee Boy). I will leave it to the MODS whether they wish it to remain here or transfer to the Planes section, but as the initial aero discussion was in here I thought it would be best here for a while and get the most views from folks who were reading the thread. If there are any ex or current MESSYBEAST, rec.miscers, sci mil naval or model flyers on here then Im sure you will probably recognise the txt and know exactly who wrote it.
Anyway, enjoy:
If I had a servo for every time I’ve heard someone say “modern fighters are made unstable to make them more agile” I’d have crow-brakes on everything! It seems every single model flyer knows about this, which would be great were it not for the annoyingly inconvenient detail that it isn’t actually true. Which is a shame, given how often it’s said. I’m hoping that in writing this piece people will understand WHY it isn’t true!
The concept that instability leads to high agility is a fallacy that dates back over 40 years to the days when autostabilisers were being developed to address the handling deficiencies of various early American jets and persists to this day. Let's start with the basics:
1. Many modern supersonic jets have a negative Static Margin (ie they have the C of G behind the Neutral Point) which makes them aerodynamically unstable, and they are made controllable by use of a full-authority autostabilisation system. This is true.
2. These modern supersonic jets are designed with inherent instability to give enhanced agility. This is NOT true. Not only is it not the reason why the aircraft are designed in this way, it is also not true that an unstable aeroplane is more agile.
I know this is contrary to the received wisdom, but let's just examine what's going on. Most of the following is grossly oversimplified to avoid the use of mathematics, and is also rather over-generalised, but it is valid and accurate for the purposes of this discussion. Professional aerodynamicists are requested to stop reading this now and pop into the forums to see how Phil is getting on with those wonderful Fw190 and B26 builds.
"Agility" of an aircraft in the pitching plane is determined by how quickly it can apply the lift forces to pull the 'G'. This in turn is dependant on how quickly the angle of attack can be increased - the pitch-plane angular acceleration, or more to the point the INSTANTANEOUS pitch-plane angular acceleration. Now a clever chap called Newton once showed that in any constant mass situation the acceleration of an object was dependant solely on the mass of the object and the sizes of the forces applied to it. The same is just as true for angular accelerations, except that we substitute "moments of inertia" for mass and use the "moments" of the forces as any attentive GCSE science pupil will be able to tell you. You will note that nothing has made reference to the "angular stability" of the object, because it's irrelevant and so we have just demonstrated that instability does NOT increase agility (QED – not that hard, was it?).
Fine, so why DO we bother with all this negative-stability-and-fly-by-wire cockamamie? After all, it would be so much simpler, cheaper and more reliable to simply connect a conventional aircraft hydraulic system (or even a pushrod) between the stick and the control surfaces! The answer is simple - it reduces the supersonic fuel consumption.
[What? Where did that come from? What's this guy been smoking!? I mean one minute I was dozing through a bit about stability and the next thing I know you're blathering on about fuel consumption. How can these be related?? - Ed].
To understand this we need to briefly look at another bit of aerodynamics, the concept of "Trim Drag". We all know that with a stable aeroplane you place the CG in front of the "centre of pressure" (I'd prefer to use "Neutral Point" but let's keep it simple) which makes the aeroplane pitch downwards. We oppose this by having a tailplane to push the tail down or a foreplane to lift the nose up and voila! We have a stable aeroplane.
The actual amount of effort the tailplane/foreplane has to exert to do this depends on how far the CG is from the centre of pressure, and we call this the "Static Margin". Those who have paid a bit of attention, rather than chatting up the totty at the back, will also know that the act of generating lift inherently generates drag. Indeed the more pretentious will point out that it has to because lift and drag are the hydrostatic and the hydrodynamic manifestations of the same phenomenon (at which the rest of us will jeer, throw ink bombs and put sand in their PE kit because we can't STAND a smarty-pants).
Now if we put these two things together we will see that the lift generated by the tailplane/foreplane to stabilise the aeroplane will inherently result in some extra parasitic drag which, since it is the result of trimming the aeroplane, we call "trim drag". The amount of drag generated is proportional to the size of the static margin. This is important, and I’ll be coming back to it in a minute.
Now we need to look at what happens when an aeroplane goes supersonic. When an aeroplane flies at moderate speeds the “aerodynamic centre” can be considered to be at 25% mean aerodynamic chord. It isn’t really, but this assumption works for the purpose of this discussion and where required the differences are corrected for other purposes with what is technically known as “complicated mathematical stuff”. Now if the pilot pushes the throttle into afterburner and leaves it there the aircraft accelerates until it goes supersonic, whereupon something interesting happens; the aerodynamic centre moves back to 50% mean aerodynamic chord. This is why the early attempts at supersonic flight often ended up in ever-steepening dives because there wasn’t enough elevator authority to pull out.
At this point I would be grateful if any professional aerodynamicists who didn’t pop over to the forums would do so now (that B26 really IS worth looking at) or perhaps go off and make themselves a coffee. Have they gone? Good! Now as far as the rest of you are concerned, the aerodynamic centre can be considered to be bolted to the “centre of pressure” via a short piece of carbon-fibre rod and a pair of high quality metal clevises, so that when the AC moves aft the CP moves with it – got that? Great! Oh here they come – nice coffee? No, you haven’t missed anything; we were just talking about transonic AC shift.
Now we can start to put it all together. The AC shifts aft, and increases the static margin so the tailplane/foreplane has to produce more lift to hold the aircraft level, and this substantially increases the trim drag. So when the aircraft is trying to fly as fast as possible there’s an inherent and unwelcome increase in drag, which increases the supersonic fuel consumption and limits the cruise speed. This is technically referred to as a “bad thing”(tm) so there are a number of techniques used to overcome it, and this is where we get back to where we started.
If you design the aeroplane so that the static margin is just sufficient for stability when the aircraft is supersonic you significantly reduce the supersonic trim drag and thus get lower fuel consumption, longer range and higher cruising speeds. Unfortunately when you slow down again the AC moves forwards and ends up in front of the CG, so the static margin is actually negative and the aeroplane is unstable. This is unpopular with the pilots because they’re essentially pretty lazy types who don’t like to work for a living, so the aircraft manufacturer reluctantly installs an expensive and complex autostabilisation system to allow the pilots to catch up on their sleep. And so there you have it, without so much as a whiff of an agility pixie. Pitch instability isn’t the only issue incidently - as the AC moves aft it affects directional stability as well, which is why supersonic aircraft have such vast fins (and often more than one).
Negative stability isn’t the only solution, there are others. Concord pumps fuel around to keep the static margin under control, and you could in principle use variable geometry, although this would require the wings to be moved forwards at supersonic speeds and you have trouble keeping the structure inside the Mach cone. A particularly elegant variable geometry solution was used on the cancelled XB-70 Valkyrie supersonic bomber project, which drooped its outer wing panels through 60 degrees at supersonic speeds. This did three things:
• It provided a “tunnel” to trap the shock-lift at speeds above mach 2
• It reduced the wing area behind the CG, moving the AC forwards and overcoming the supersonic trim drag issue
• It substantially increased the fin area when supersonic, overcoming the directional stability problems due to the AC shift.
Much more than anyone really wanted to know, I’m sure. But hopefully this note might go some way towards dispelling the myth that negative stability is used to increase agility. As professional control system designers will tell you, agility is controlled by agility pixies. But that is a subject for another day.
mikee boy said:
Interesting. Could you copy something off the internet about Whales.
Alas, not copied off the internet, but written by an esteemed gentleman and now saved as a text file on his desktop. It was originally written as a reply to a post on a forum several years ago and is now kept as a permanent file such is the frequency with which it needs to be used due to the misunderstanding he was writing about. He is also a car guy and an all round good bloke. He knows a thing or two about Harriers and UAV aswell
But anyway, I thought it would be a humerous and interesting read for a few folks.
I'm no control engineer, nor am I a flight dynamics engineer (which this post is really about), but I read with some skepticism.
For example, take dihedral and anhedral wing geometry. Ignoring all other factors like sweep etc...
Dihedral wings in general (ala commercial aircraft) are aerodynamically stable because when a plane rolls, a restoring moment is produced (due to added lift on the downwardly rolled wing compared with the upwardly rolled wing), which without touching the controls will restore the plane to equilibrium.
Anhedral wings in general (ala fighters) do the opposite; they do not produce a restoring moment, they produce a moment in the direction of roll which produces greater roll rates and hence greater maneuverability.
Interestingly your friend only mentions longitudinal (pitching) stability, and not lateral/roll stability. Static margin is only applicable to longitudinal dynamics...
When control systems go wrong... this was purely control systems error I beleive, the pilot (who survived) was just a passenger:
http://www.youtube.com/watch?v=QVF9qQUPqTw
Seems like this thread should be in the planes section
For example, take dihedral and anhedral wing geometry. Ignoring all other factors like sweep etc...
Dihedral wings in general (ala commercial aircraft) are aerodynamically stable because when a plane rolls, a restoring moment is produced (due to added lift on the downwardly rolled wing compared with the upwardly rolled wing), which without touching the controls will restore the plane to equilibrium.
Anhedral wings in general (ala fighters) do the opposite; they do not produce a restoring moment, they produce a moment in the direction of roll which produces greater roll rates and hence greater maneuverability.
Interestingly your friend only mentions longitudinal (pitching) stability, and not lateral/roll stability. Static margin is only applicable to longitudinal dynamics...
When control systems go wrong... this was purely control systems error I beleive, the pilot (who survived) was just a passenger:
http://www.youtube.com/watch?v=QVF9qQUPqTw
Seems like this thread should be in the planes section
Edited by navier_stokes on Wednesday 20th May 18:35
dr_gn said:
navier_stokes said:
due to added lift on the downwardly rolled wing compared with the upwardly rolled wing
How does that work then?Edited by navier_stokes on Wednesday 20th May 18:35
I thought it was a good article.
Cheers,
Nicely illustrated here by NASA:
http://www.centennialofflight.gov/essay/Theories_o...
Edited to add, the content of the piece is correct, but IMO not the conclusion he/she is drawing as they haven't considered roll dynamics.
Edited by navier_stokes on Wednesday 20th May 20:13
navier_stokes said:
dr_gn said:
navier_stokes said:
due to added lift on the downwardly rolled wing compared with the upwardly rolled wing
How does that work then?Edited by navier_stokes on Wednesday 20th May 18:35
I thought it was a good article.
Cheers,
Nicely illustrated here by NASA:
http://www.centennialofflight.gov/essay/Theories_o...
Edited to add, the content of the piece is correct, but IMO not the conclusion he/she is drawing as they haven't considered roll dynamics.
Edited by navier_stokes on Wednesday 20th May 20:13
Cheers,
dr_gn said:
navier_stokes said:
dr_gn said:
navier_stokes said:
due to added lift on the downwardly rolled wing compared with the upwardly rolled wing
How does that work then?Edited by navier_stokes on Wednesday 20th May 18:35
I thought it was a good article.
Cheers,
Nicely illustrated here by NASA:
http://www.centennialofflight.gov/essay/Theories_o...
Edited to add, the content of the piece is correct, but IMO not the conclusion he/she is drawing as they haven't considered roll dynamics.
Edited by navier_stokes on Wednesday 20th May 20:13
Cheers,
Try this, under "effect of wing dihedral".
The lowered wing has its lift increased by v*sin(Gamma) and the upper wing lift decreased by the same amount, where Gamma is the dihedral angle.
navier_stokes said:
dr_gn said:
navier_stokes said:
dr_gn said:
navier_stokes said:
due to added lift on the downwardly rolled wing compared with the upwardly rolled wing
How does that work then?Edited by navier_stokes on Wednesday 20th May 18:35
I thought it was a good article.
Cheers,
Nicely illustrated here by NASA:
http://www.centennialofflight.gov/essay/Theories_o...
Edited to add, the content of the piece is correct, but IMO not the conclusion he/she is drawing as they haven't considered roll dynamics.
Edited by navier_stokes on Wednesday 20th May 20:13
Cheers,
Try this, under "effect of wing dihedral".
The lowered wing has its lift increased by v*sin(Gamma) and the upper wing lift decreased by the same amount, where Gamma is the dihedral angle.
Unless they mean angle of attack in the sideslip direction, then its pretty obvious.
Edited by dr_gn on Wednesday 20th May 22:30
Dihedral is very simple, think of a wing and how it works, in order to create maximum upwards lift in the y axis, it needs to be at 90deg to it, in other words, it needs to be flat.
Imagine a glider with 5deg dihedral, when it banks to the left or right by 5deg, the lower wing is then at 0deg and the upper wing is at 10deg. The lower wing is generating more lift and the upper wing less, making the aircraft bank in the opposite direction thus righting the aircaft.
I once designed and built a model glider from scratch (apart from a couple of templates for wing sections etc). I decided to give the tailplane dihedral as well as the main wings, unfortunately, the angles on the wings and tailplane were not completely identical. The result was a very interesting glide, also very difficult to describe, a sort of gentle bobbing motion in pitch and roll IIRC.
I think the tailplane and wings were in conflict when it came to correcting the roll, I'm sure an aerodynamicist could explain it.
Imagine a glider with 5deg dihedral, when it banks to the left or right by 5deg, the lower wing is then at 0deg and the upper wing is at 10deg. The lower wing is generating more lift and the upper wing less, making the aircraft bank in the opposite direction thus righting the aircaft.
I once designed and built a model glider from scratch (apart from a couple of templates for wing sections etc). I decided to give the tailplane dihedral as well as the main wings, unfortunately, the angles on the wings and tailplane were not completely identical. The result was a very interesting glide, also very difficult to describe, a sort of gentle bobbing motion in pitch and roll IIRC.
I think the tailplane and wings were in conflict when it came to correcting the roll, I'm sure an aerodynamicist could explain it.
navier_stokes said:
Anhedral wings in general (ala fighters) do the opposite; they do not produce a restoring moment, they produce a moment in the direction of roll which produces greater roll rates and hence greater maneuverability.
But isn't this offset, at least in part, by the fact that anhedral fighters are high wings, and the high wing configuration itself adds a restoring force due to the centre of lift being higher than the centre of gravity.navier_stokes also said:
Seems like this thread should be in the planes section
agreedSlipStream77 said:
Imagine a glider with 5deg dihedral, when it banks to the left or right by 5deg, the lower wing is then at 0deg and the upper wing is at 10deg. The lower wing is generating more lift and the upper wing less, making the aircraft bank in the opposite direction thus righting the aircaft.
That's a commonly stated, but incorrect description of how dihedral stabilises an aircraft. In the scenario you describe, both wings are still producing the same 'lift', just in a different direction. One wing won't suddenly start producing more (or less) lift depending on the roll angle of the aircraft. In fact, in a rudder-elevator controlled aircraft it is this rotation of the lift vector which causes the aircraft to turn.To give stability you have to somehow increase the angle of attack of the downgoing wing. It is a combination of weight shift and sideslipping, but the exact mechanism I have never fully understood. I seem to think there must be some mechanism by which as the aircraft sideslips towards the lower wing, there is also a yaw component which effectively increases the AoA of the downgoing wing.
If anyone can explain this I'd be grateful. The diagrams in the previously cited references don't seem to show yaw, just a head-on view of the rolled aircraft.
Cheers,
profstoff said:
navier_stokes said:
Anhedral wings in general (ala fighters) do the opposite; they do not produce a restoring moment, they produce a moment in the direction of roll which produces greater roll rates and hence greater maneuverability.
But isn't this offset, at least in part, by the fact that anhedral fighters are high wings, and the high wing configuration itself adds a restoring force due to the centre of lift being higher than the centre of gravity.navier_stokes also said:
Seems like this thread should be in the planes section
agreedCheers,
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