High wing anhedral
The lift vector though is relevant. Lift is derived at 90 degrees to the lifting surface. With dihedral, the more horizontal wing's vector gives more force upwards, hence more lift, whereas the vector of the wing pointing up is more sideways, so less lift upwards. The imbalance causes a restoring force.
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The lift vector though is relevant.
Without slip, there is no lateral stability. With slip, an- and di-hedral function correctly whether the aircraft is erect, inverted, or anywhere in between. Granted, the different "vertical-ness" of the lift vectors may make the aircraft climb or descend, but this has nothing to do with rolling couples.
Consider a model aircraft that is tied to fly along a taut wire. It can roll but it cannot slip. Will dihedral tend to restore it to wings level, if disturbed in bank? For answer, consider that for every force that you note on the more horizontal wing, there will be an exactly equal force, providing an exactly equal rolling moment, on the other wing.
Last edited by Oktas8; 20th May 2013 at 12:04.
Consider a model aircraft that is tied to fly along a taut wire. It can roll but it cannot slip. Will dihedral tend to restore it to wings level, if disturbed in bank? For answer, consider that for every force that you note on the more horizontal wing, there will be an exactly equal force, providing an exactly equal rolling moment, on the other wing.
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The wire is overcoming weight. It has no effect on roll, so if your explanation is correct, the model should be laterally stable despite there being no slip. Do not confuse TOTAL lift (acting in the vicinity of the CG to overcome weight) with LIFT ASYMMETRY (ignore weight, just focus on rotation in any axis about the CG.
Here's another example, FWIW.
Consider an aircraft at 70* angle of bank in a steady turn. With skilful rudder application, the pilot perfectly prevents slip. The aircraft has dihedral, so the lowered wing's lift vector has a greater vertical component than the raised wing's lift vector. Will the aircraft roll wings level without aileron input? No, there is no slip, therefore no asymmetric lift, therefore no rolling moment about the CG.
(Yes, the raised wing is travelling faster in this case, but we shall say the aircraft is descending slightly also, putting the lowered wing at greater AoA. So each wing is generating precisely the same total lift - in this example!)
Here's another example, FWIW.
Consider an aircraft at 70* angle of bank in a steady turn. With skilful rudder application, the pilot perfectly prevents slip. The aircraft has dihedral, so the lowered wing's lift vector has a greater vertical component than the raised wing's lift vector. Will the aircraft roll wings level without aileron input? No, there is no slip, therefore no asymmetric lift, therefore no rolling moment about the CG.
(Yes, the raised wing is travelling faster in this case, but we shall say the aircraft is descending slightly also, putting the lowered wing at greater AoA. So each wing is generating precisely the same total lift - in this example!)
Yes, your turn example makes sense. I am just debating whether to go and dig out my books.....
Anhedral and dihedral have no effect unless the aircraft is slipping.
With anhedral, the point of application of the combined lift vector is lower. Presumably closer to the CG, thus contributing to the reduction of lateral stability.
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I must respectfully disagree Balsa.
If you are not slipping, then there is no lift asymmetry, and there will be no restoring tendency in the rolling sense.
But what about the pendulum effect, you ask? If you are not slipping (ball centred in the turn) then there is no pendulum effect, and the aircraft will not tend to return to wings level of its own accord.
After the slip develops, yes, what you say is correct.
If you are not slipping, then there is no lift asymmetry, and there will be no restoring tendency in the rolling sense.
But what about the pendulum effect, you ask? If you are not slipping (ball centred in the turn) then there is no pendulum effect, and the aircraft will not tend to return to wings level of its own accord.
After the slip develops, yes, what you say is correct.
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methinks the plot is being lost......
a wing does not have to be slipping for dihedral to have effect. what do you think corrects for the off centre pilot weight in a two seater aircraft?
the left wing is slightly more level than the right wing, has a longer effective span and generates just a tad more lift and thus makes the aeroplane fly straight(ish)
dihedral also has the effect of changing the angle of attack of each wing in a slip that is self correcting.
ligetti wrote that about 6 degrees of sweep back was equal to about a degree of dihedral. so in the BAE146 the anhedral is to reduce the stability.
not to kill an argument with facts entirely why do tailplanes occasionally have dihedral? :-)
a wing does not have to be slipping for dihedral to have effect. what do you think corrects for the off centre pilot weight in a two seater aircraft?
the left wing is slightly more level than the right wing, has a longer effective span and generates just a tad more lift and thus makes the aeroplane fly straight(ish)
dihedral also has the effect of changing the angle of attack of each wing in a slip that is self correcting.
ligetti wrote that about 6 degrees of sweep back was equal to about a degree of dihedral. so in the BAE146 the anhedral is to reduce the stability.
not to kill an argument with facts entirely why do tailplanes occasionally have dihedral? :-)
You just need to think about the lift vectors when rolling a bit left or right.
With anhedral, the 'opposing' wing's Lift vector component in vertical direction will increase (Lift x cos(dihedral - roll)), whereas on the 'supporting' side it will decrease Lift x cos (dihedral + roll).
You get a self righting moment of the wing's lift. Then you need to consider the leverage of this stabilising force against the CG. If the CG is higher than the combined vertical position of where the lift is produced, these two moments will act against each other. If the postion where the Lift is applied is above the Cg the two moments will complement each other.
If you have anhedral, the effect will be inverse.
Therefore for a low wing aircraft you want to have rather dihedral if you don't want to go too aerobatic. With a low wing and no dihedral the aircraft will constantly try to roll off.
In a high wing design the leverage between Cg and the point where the Lift is applied will already cause a stabilising moment. This leads to increased aileron forces if you want to bank.
In order to avoid excessive self righting and thus excessive aileron forces for turning (which would increase drag and structural loads) high wing aircraft often get anhedral, especially bigger ones where the mentioned factors become significant.
Last edited by henra; 30th May 2013 at 09:57.
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Well, there are some misconceptions going on here!
Lateral stability summary:
- Wing sweep, high wing, dihedral and the vertical tail are stabilising influences
- Low wing, anhedral and keel area are destabilising influences
- A laterally stable aircraft ALWAYS rolls away from sideslip
Lateral stability will only come into effect when there is sideslip present. This will happen whenever the lift force is not directly aligned with (and opposite to) the resultant of the weight force and any centrifugal force present. Weight ALWAYS acts vertically down, regardless of aircraft attitude, but lift will roll and pitch with the aircraft. Therefore if the aircraft has a non-zero roll angle, the lift force will be at an angle to the weight force and thus there will be a sideways component of lift. This causes the aircraft to fly slightly sideways as well as forwards, leading to sideslip.
Sideslip will cause the wing on that side to experience a higher AOA than the other wing, leading to a difference in lift that rolls the aircraft level.
Lateral stability summary:
- Wing sweep, high wing, dihedral and the vertical tail are stabilising influences
- Low wing, anhedral and keel area are destabilising influences
- A laterally stable aircraft ALWAYS rolls away from sideslip
Lateral stability will only come into effect when there is sideslip present. This will happen whenever the lift force is not directly aligned with (and opposite to) the resultant of the weight force and any centrifugal force present. Weight ALWAYS acts vertically down, regardless of aircraft attitude, but lift will roll and pitch with the aircraft. Therefore if the aircraft has a non-zero roll angle, the lift force will be at an angle to the weight force and thus there will be a sideways component of lift. This causes the aircraft to fly slightly sideways as well as forwards, leading to sideslip.
Sideslip will cause the wing on that side to experience a higher AOA than the other wing, leading to a difference in lift that rolls the aircraft level.
How about a hypothetical situation:
Dark night. The aircraft is not loaded symmetrically, so it WANTS to roll. We loose all gyros. We have a glider style slip indicator (a string on the centerline of the windshield, in the slipstream) and we religiously keep the string centered with rudder. So no sideslip. No lateral inputs (since we have no gyros). Are we going into a spiral, or does it depend on our anhedral / dihedral setup?
(BTW: I don't think pitch matters here.)
So I think I agree that all roll disturbance recovery and final stable equilibrium will involve some sideslip. I don't know whether this helped the OP, but it got me straightened out a bit. Thanks.
And to answer my own prior dilemma about 1st / 2nd order influence of relative position of center of lift w.r.t. CG: it must be 2nd order. The moment of unbalanced lift (in a slip) must be a much larger effect, considering typical wing spans.
Dark night. The aircraft is not loaded symmetrically, so it WANTS to roll. We loose all gyros. We have a glider style slip indicator (a string on the centerline of the windshield, in the slipstream) and we religiously keep the string centered with rudder. So no sideslip. No lateral inputs (since we have no gyros). Are we going into a spiral, or does it depend on our anhedral / dihedral setup?
(BTW: I don't think pitch matters here.)
So I think I agree that all roll disturbance recovery and final stable equilibrium will involve some sideslip. I don't know whether this helped the OP, but it got me straightened out a bit. Thanks.
And to answer my own prior dilemma about 1st / 2nd order influence of relative position of center of lift w.r.t. CG: it must be 2nd order. The moment of unbalanced lift (in a slip) must be a much larger effect, considering typical wing spans.
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Had a long think about Balsa's scenario:
If you maintain zero sideslip with rudder, the relative airflow will always come from straight on. However, the laeral mass imbalance will cause a wing to drop because he weight vector and lift vector will have a lateral distace between them, causing a couple which will roll the aircraft.
So you are now rolling but keeping sideslip zero, which will prevent the dihedral effect from happening. As you roll, the lift vector will point away from vertical, which should cause sideslip except you are using rudder to point the nose back into the relative airflow. Therefore as the roll continues, the nose points more and more into the turn.
This would lead to a spiral dive with increasing roll angle, eventually ending up with a near vertical dive. Not a nice thing to happen at night if you have lost your AI!
Following this thought experiment, my thinking is that if you lose gyros at night, it is essential to let sideslip do what it wants to do. that way a lateral mass imbalance would lead simply to a steady heading sideslip, which is way more manageable than a spiral dive!
If you maintain zero sideslip with rudder, the relative airflow will always come from straight on. However, the laeral mass imbalance will cause a wing to drop because he weight vector and lift vector will have a lateral distace between them, causing a couple which will roll the aircraft.
So you are now rolling but keeping sideslip zero, which will prevent the dihedral effect from happening. As you roll, the lift vector will point away from vertical, which should cause sideslip except you are using rudder to point the nose back into the relative airflow. Therefore as the roll continues, the nose points more and more into the turn.
This would lead to a spiral dive with increasing roll angle, eventually ending up with a near vertical dive. Not a nice thing to happen at night if you have lost your AI!
Following this thought experiment, my thinking is that if you lose gyros at night, it is essential to let sideslip do what it wants to do. that way a lateral mass imbalance would lead simply to a steady heading sideslip, which is way more manageable than a spiral dive!
Last edited by WeekendFlyer; 5th Jun 2013 at 10:42.
Well, just for my own revision I went and dug out my ATPL notes and, yes it does say that dihedral works because a roll causes a side slip which changes the AoA vectors which increases the lift on the lower wing.
I find that hard to visualize, which is why I think of the correcting roll coming from the difference in the vertical lift vector between the two wings - because in the real airplane in the real air, we are after all talking about overcoming weight. My (incorrect) theory assumes a vertical movement of the aircraft to provide the correcting roll whereas the actual restoring force is created by a sideways movement.
Okta's thought experiment with the wire prevented sideways and vertical movement of the aircraft, which then stops the dihedral working.
Cheers!
I find that hard to visualize, which is why I think of the correcting roll coming from the difference in the vertical lift vector between the two wings - because in the real airplane in the real air, we are after all talking about overcoming weight. My (incorrect) theory assumes a vertical movement of the aircraft to provide the correcting roll whereas the actual restoring force is created by a sideways movement.
Okta's thought experiment with the wire prevented sideways and vertical movement of the aircraft, which then stops the dihedral working.
Cheers!
Last edited by Uplinker; 5th Jun 2013 at 12:25.
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A completely different reason
Benny Howard, the hero of the 1935 National Air Races, related this story to me in 1969. His production high-wing cabin aircraft (DGA-8 thru DGA-12, all similar save for the engine choice) had no dihedral and had no need for it - EXCEPT for an optical illusion that made the semi-elliptical wings appear drooped when viewed from behind. He thought this was unattractive and might have hurt sales.
So when he revised the design to accommodate another pax, designated DGA-15, he lengthened the wing struts a few mm to raise the wingtips maybe 2 cm. This made the wing LOOK straight, although it had no effect on flying qualities.
PS - probably the worst-kept secret of the day was that his DGA designation stood for "Damned Good Airplane"
So when he revised the design to accommodate another pax, designated DGA-15, he lengthened the wing struts a few mm to raise the wingtips maybe 2 cm. This made the wing LOOK straight, although it had no effect on flying qualities.
PS - probably the worst-kept secret of the day was that his DGA designation stood for "Damned Good Airplane"
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Dan,
like the photo and the "?". A picture speaks a thousand words.
Explanation:
You can see clearly the slight anhedral (which is laterally destabilising). However, remember that aircraft also has:
- T-tail
- Rear side-mounted engines
- Swept wing
all of which are laterally stabilising design features. If you added dihedral as well you would either have an aircraft with a roll-rate that would make a Cessna 152 look like a world-class aerobatic aircraft, or you would need massive ailerons and probably roll spoilers as well, neither of which are particularly desirable design outcomes in a commercial jet...
like the photo and the "?". A picture speaks a thousand words.
Explanation:
You can see clearly the slight anhedral (which is laterally destabilising). However, remember that aircraft also has:
- T-tail
- Rear side-mounted engines
- Swept wing
all of which are laterally stabilising design features. If you added dihedral as well you would either have an aircraft with a roll-rate that would make a Cessna 152 look like a world-class aerobatic aircraft, or you would need massive ailerons and probably roll spoilers as well, neither of which are particularly desirable design outcomes in a commercial jet...
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"Reducing lateral stability makes the airplane more maneuverable,etc (good thing) but if you reduce it too much w.r.t. directional stability the airplane will become spiral-prone (bad thing). I suspect C172 designers felt they had enough maneuverability without adding an anhedral and an extra risk of spinning"
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Cessna 170/172
A note about dihedral on this series: The original "ragwing" Cessna 170 had no dihedral - nor did the 2-place 140 that preceded it. The first metal-wing-skin model, the 170A, also had no dihedral.
But the 170B - which introduced the Fowler "barn door" flaps - also introduced the dihedral seen on all subsequent 172 models. (It may be that it was the flaps that led Cessna to add dihedral, but that's speculation on my part.)
A personal note as an old CFI: If a student receives his initial training in a 172, he is likely to be a bit spoiled by the excellent stability of the ship, and may have a bit of trouble when first flying the 150/152; overcontrolling can be an issue. Conversely, if he starts in a 152, he'll have less problem transitioning to the 172.
But the 170B - which introduced the Fowler "barn door" flaps - also introduced the dihedral seen on all subsequent 172 models. (It may be that it was the flaps that led Cessna to add dihedral, but that's speculation on my part.)
A personal note as an old CFI: If a student receives his initial training in a 172, he is likely to be a bit spoiled by the excellent stability of the ship, and may have a bit of trouble when first flying the 150/152; overcontrolling can be an issue. Conversely, if he starts in a 152, he'll have less problem transitioning to the 172.
