Talk:Dihedral

From Wikipedia, the free encyclopedia

	This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.	Physics Portal
???	This article has not yet received a rating on the assessment scale. [FAQ]
???	This article has not yet received an importance rating within physics.
Help with this template Please rate this article, and then leave comments here to explain the ratings and/or to identify the strengths and weaknesses of the article.

[edit] High mount of wings itself does not increase the roll stability

Imagine a plane with high mounted horizontal wings (with no dihedral). This plane flies straight, with no roll. Weight force is hooked at the mass centre and directed vertically down, lift is hooked above the centre and directed vertically up.

Now some random cause rolled the plane, for example, 5 degrees left. If high mounted wings are expected to recover the plane to horizontal position i.e. make a rotation of plane, they MUST apply some torque on it. But what really happens here: weight is still hooked at the centre, thus it doesn't cause any torque (the arm is zero). Lift is hooked at some point which is nearly above the centre, but deviated by 5 degrees left. And lift is directed not vertically up, but 5 degrees left, and actually its direction is exactly the same as the direction of the arm (i.e. vector from the mass centre to hook of lift force). In other words, vector of lift force is parallel to vector of arm, and thus lift doesn't generate any torque, either. Thus, there is still no torque and the plane does not recover!

It's better understandable if drawing is seen, but I don't know how to attach a drawing in the discussion pages.

In fact, if a random left roll occurs, it causes a left sideslip, and the fuselage begins to create a lift force directed to the right. And this lift can generate a torque. The hook of this side lift is usually around the centre of fuselage, and thus lower than the mass centre of the whole plane (mass of the wings raises the mass centre). And thus, it generates a torque which makes even more left roll and worsens the situation!

It's true, however, that high mounted wings increase pitch stability.

--Grzes 23:49, 26 Jan 2005 (UTC)

While I follow your argument, this clearly isn't the case. I haven't done any mathematical analyses, but I have built a couple of simple chuck gliders! It's easy to demonstrate that where there is a lump of mass hanging below the wing the aircraft will fly a lot more stably than if the same mass is added above the wing, all else being equal (and with no dihedral to cloud the picture). In fact the aircraft was so unstable with the mass above it tended to flip over and fly the other way up! This is an example of how aerodynamicists sometimes seem to fall into the trap of not actually looking at things with their own eyes, but to bury themselves in equations. Notably, the infamous assertion that "the bumblebee cannot fly". Yes it can, open your eyes! Therefore the analysis MUST be wrong... Graham 22:47, 27 Jan 2005 (UTC)

How, Graham, can you be sure that the instability is not due to pitch instability as suggested by Grzes? If his analysis is logical, and you claim that he is wrong, where is the discrepancy in his logic? I am a beginner to flight mechanics and I am finding these pages quite confusing.

I don't think the 'analysis' above is logical. It is wrong, though it's hard to be sure since the terms used (e.g. 'hooked at the centre') are not the conventional scientific terms and so my interpretation of what the writer meant might be wrong. If you are learning flight mechanics then I strongly recommend that you don't use Wikipedia as a text book! I believe that the explanation in the article is correct, but I wouldn't stake my degree on it. Incidentally, the statement about a high-mounted wing conferring pitch stability is possibly even more confusing - it's much less obvious to see how that might be the case than with roll - but in any case the 'pendulum effect' will confer stability in all axes where gravity acts normal to the axis, which would be roll and pitch. If you accept that stability is conferred in the pitch axis by the effect, why would you discount it in the (much more obvious) roll axis? What's the difference, from the point of view of gravity acting? Having read through Grzes entry again, just to check, I'm pretty sure he's simply wrong - the centre of mass will be offset horizontally relative to the centre of lift, and this sets up a torque which acts to restore the original position. The sideslip drag (not lift) that the low fuselage position might create is a possible factor, and it would act to further destabilise the position, but its effect must be absolutely tiny, and the pendulum effect easily overcomes it. Finally, remember that the talk pages are not the article. Often things get debated and clarified on the talk pages at great length, especially where some misunderstanding exists. It doesn't mean that the misunderstanding should cast any doubt on what the article itself actually states. Personally I'm happy to take the time to try and clarify people's misunderstandings as far as I am able to do so, but entering into these discussions in itself shouldn't be taken as a sign that the original point is especially worthy. If someone said that roll stability was conferred by the action of invisible fairies pushing on the low wing, then such a view could be easily and quickly put right - but it doesn't mean that that the original idea was worth anything, just because it exists in print on the talk page. Graham 23:29, 19 December 2005 (UTC)

[edit] Center of lift vs. center of gravity

I have read several explanations of how dihedral produced roll stability and this is the first time I've heard anything about this sideslip theory. The theory has merit and may be part of the picture but is not the generally-accepted theory. If this is a personal theory and not an established one it should not be put forth as the actual explanation. I think this requires some discussion and possibly changing the article.

The mistake most people make is assuming that movement around the roll axis somehow affects how much lift a wing produces. It doesn't; it can't. In the absence of gravity an aircraft will fly the same way no matter what roll angle it is at. The other thing people don't take into account is that, like any other force that is spread over an area, all of the lift produced by the entire airframe acts as if it were concentrated at a single point--the center of lift.

If the center of lift is above the center of gravity the aircraft will act as if it were hanging from a string. If the aircraft rolls, barring any other external forces, it will swing like a pendulum back to the position where the center of lift is directly over the center of gravity. If the center of lift is below the center of gravity the aircraft will act is if it were siting on a pin, clearly an unstable position. This is why a high-wing aircraft, like a Cessna 172, has very little dihedral. It doesn't need it. The center of lift is above the center of gravity by virtue of having the whole wing above the center of gravity. A low-wing aircraft, unless it is designed for maneuverability (i.e. aerobatics or dog fighting), will usually have more dihedral than a high-wing aircraft. The extra dihedral is required to raise the center of lift. This is why a high-wing aircraft is inherently more stable than a low wing aircraft. Rsduhamel 17:38, 22 Mar 2005 (UTC)

Two points. The pendulum effect is definitely very real - that is, I think, what my earlier comments (and actual experiment) were meant to demonstrate. The whole torque-couple argument stated at the top of this page is erroneous (there is a torque-couple formed because the centre of gravity is offset to one side by the roll). The second point is that the sideslip theory seems to be the now commonly accepted one by all serious works on the topic. By serious works I mean books such as A.C Kermode's "Mechanics of Flight", and PPL training manuals, etc. Many other laymans' guides still get it wrong. Roll by itself cannot change the amount of lift, as you correctly state - so any argument that is based on this idea is wrong by definition. However, a sideslip CAN create additional lift, since a small lateral airspeed results which sees the dihedral as an angle of attack. Your argument about raising the centre of lift makes sense, but I believe it is not really the purpose of dihedral. Many low-wing aircraft do not have sufficient dihedral to place the centre of lift above the centre of gravity - to do this would require a very extreme amount of dihedral which you just do not see in practice. The sideslip theory explains the roll stability much more elegantly since it only requires a small dihedral angle, as seen in practice.

To add to my point, I'll quote from 'Mechanics of Flight". If you have an interest in aerodynamics but don't need screeds of equations, this book is a highly readable introduction, and very well respected. Recommended.

"Mechanics of Flight", 10th edition quotes from page 280+: First it dismisses the erroneous "horizontal aspect" explanation in a couple of paras. "What then, is the real explanation as to why dihedral angle is an aid to lateral stability? When the wings are both equally inclined [straight and level] the resultant lift on the wings is vertically upwards and will exactly balance the weight. If, however, one wing becomes lower than the other, then the resultant lift force will be inclined to the vertical, while the weight will of course remain vertical. Therefore the two forces will not balance and there will be a small resultant force acting in a sideways and downwards direction. This force is temporarily unbalanced and therefore the aeroplane will move in the direction of this force - i.e. it will sideslip - and this will cause a flow of air in the opposite direction to the slip. This has the effect of increasing the angle of attack of the lower plane and decreasing that of the upper plane. The lower plane will therefore produce more lift and a restoring moment will result." It goes on to discuss the variation of the centre of pressure ALONG the wing in this case. Following this there is a further section titled "High wing and low centre of gravity": "If the wings are placed in a high position and the centre of gravity correspondingly low, the lateral stibility can be enhanced." Curiously, it explains this in terms of a lateral drag force arising from the sideslip forming a couple with the centre of gravity acting to right the plane. This seems novel, but in fact it's much what you're saying, since this drag force appears as a slight skewing of the lift force. The book then goes on to dicuss other factors affecting lateral stability - sweepback, fin area, etc. etc.

I hope this isn't labouring the point too much, but I also took a look at "The Air Pilot's Manual" by Trevor Thom, Volume 4, page 69. This book is the standard training manual for the PPL in the UK. It too puts forward the sideslip theory for dihedral. "As the aircraft sideslips, the lower wing, due to its dihedral, will meet the upcoming relative airflow at a greater angle of attack and will produce increased lift. [...] The rolling moment so produced will tend to return the aircraft to its original wings-level position".

While these references are not the last word on aerodynamics, they are both well-respected. I hope it corrects your impression that the sideslip theory "is not the generally-accepted theory". As far as I can tell it is the generally accepted theory.Graham 01:18, 23 Mar 2005 (UTC)

[edit] Erroneous explanation of stability

Guys, I'm adding the cleanup tag because the explanation of the stability effect in this article is simply wrong. It's not about the amount of aerodynamic force, it's the direction that matters. When an aircraft with dihedral rolls, the wing that's closer to horizontal will generate the same lift as the other wing, but the lift vector is closer to vertical, opposing gravity more directly than that of the other wing. It's not related to the angle of attack, or any sideslip. The stabilizing effect is there as soon as the wingtips aren't at the same height relative to the horizon. I'll come up with some corrected diagrams and fix the text as well.

Sorry, but you are simply wrong. Any authoritive book on the subject will use the sideslip/AoA explanation, and be at great pains to point out that the explanation you're proposing is incorrect. Dihedral in itself doesn't change the lift vector angle from being exactly vertical. Also, you have not signed your comment. I will remove the cleanup tag - feel free to discuss this further if you wish, but please refer to a decent textbook on the topic before making yourself look foolish. (One I recommend is "Mechanics of Flight" by A.C. Kermode, which is a very accessible and well respected textbook on the topic). Graham 11:29, 12 April 2006 (UTC)

The difference in angle of attack due to sideslip causes a rolling moment which tends to roll the body to point the lift vector so as to oppose the sideslip. The fundamental purpose of dihedral is the cancellation of sideslip. It is therefore nonsense to claim that sideslip has no effect. Dihedral does not control the inertial roll angle, but tends to keep the plane of incidence in the plane of symmetry of the aircraft, Much of the above discussion confuses inertial roll with aerodynamic roll. In analysing the stability of aircraft, the reference point is taken as the centre of gravity, so that all gravitational moments are identically zero. Shifting the cg changes all the values of stability derivatives used in the analysis. With stick fixed the lateral modes consist of roll subsidence, Dutch roll and spiral instability, and dihedral is important for the latter two. I suggest reading Arthur Babister's Aircraft Dynamic Stability and Response. Elsever 1980, ISBN 0080247687. Gordon Vigurs 19:50, 27 June 2006 (UTC)

The problem with dihedral is, it has more than one effect. Sideslip results in side force, yaw and roll torques due to dihedral. The side force effect is of second order, but dihedral tends to roll the aircraft to cancel sideslip, and is significant in stabilising the spiral mode, but has a de-stabilising effect on the Dutch roll. It is usually difficult to make both stable. High wing aircraft generate a dihedral effect because the body modifies the local angle of attack, and this effect is modified by sideslip. There is a further dihedral effect arising from wing sweep, to the extent that anhedral is required for a stable Dutch roll on highly swept fighter configurations.Gordon Vigurs 09:39, 7 August 2006 (UTC)