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Aeroplanes flying upside-down
By Ed Tolputt (M274) on Tuesday, January 11, 2000 - 11:35 pm:

How do display aeroplanes achieve lift when flying upside-down?
Ed

By Richard Dwight (Rpd25) on Wednesday, January 12, 2000 - 09:26 pm:

Hi Ed,

This is a good question. Here's my take on it. The shape of an aerofoil (or aeroplane wing is (very) roughly symmetric, as you can see below, taking a typical aerofoil shape and inverting it (and rotating a little; which of course the stunt pilot can do by angling his plane up or down) gives something that looks approximately like an aerofoil the right way up. Furthermore it is the case that while the shape of an aerofoil is fairly important to it's lift generating ability it is much less important than the angle the aerofoil makes to the oncoming air, commonly called the angle of attack, (in fact the reason an aerofoil has the shape it has is more to do with making the wings of a plane aerodynamic and reducing the drag on them than providing lift). The pilot can adjust the angle of attack also by pointing the nose of his plane higher or lower and so angling the wings. He can thus gain the main features needed for lift when he is upside down.

inverted aerofoil

However the plane will certainly be much less efficient upside down. Planes are designed very carefully (and the shape of the wings in particular) to maximise lift and minimise drag, and the designers will assume most of the time that the plane is going to be flying the right way up. So while our pilot's plane can fly very comfortably the right way up it could well struggle to maintain sufficient speed and lift upside down, even if it is a stunt plane and upside down flying has been accounted for in the design.

There is also a problem with the act of turning upside down. Those of you who know a little fluid dynamics might recall that the lift generated by an aerofoil is due to the circulation of air about it. Suppose then that an aeroplane is flying along the right way up with a nice healthy circulation that gives it lift, and then flips upside down in any manner you choose. If the circulation stayed the same (in particular it stayed in the same sense about the wing) the wings would then have a downforce on them by the same mechanism that gave them an upforce when they were the right way up. Given that the plane does keep flying, the circulation must have changed direction, which means the wings must have shed vortices about twice as strong as the ones they ordinarily shed when taking off. In addition there must have been a point during the turning over at which the circulation (and so the lift) was zero. This seems to me a difficult and dangerous thing to do, probably explaining why you don't see many planes doing it.

I'd be interested to hear what other people think of this problem. Hope this has helped answer your question Ed.
Richard Dwight.

By Ed Tolputt (M274) on Monday, January 17, 2000 - 08:30 pm:

Thanks Richard - That was interesting and informative.

Ed

By Graham Lee (P1021) on Thursday, January 20, 2000 - 10:52 pm:

The way I worked it out was like this.
A standard aerofoil has a flat bottom edge, and a curved upper edge (similar to the upper edge in your diagram). If flying correct way up, the flat edge is parallel with the airflow, and the upper edge forces the air to take a longer path, and lowers the pressure hence causing lift. Now, when turned upside down, if you angle the wing carefully enough, the large leading edge of the wing can act such that the bottom (top of the wing, but it is lower) presents an almost flat profile, and the top (bottom of the wing) still forces the air pressure to reduce.
Another consideration is that by pointing the aircraft slightly upwards (i.e. nose up), the engine is producing a force in the upwards direction that can counteract the weight force as well.

GL.

By Graham Lee (P1021) on Thursday, January 20, 2000 - 10:55 pm:

P.S. there is never zero circulation across the wing I think, it changes direction with the plane. So if you "barrel" to invert the plane, then there will be a point where the "lift" is parallel with the ground, and if you "loop" to achieve the same, and get it so that you stall (not literally, but your forward airspeed is zero), you should be rocketing along in the direction of your head.

By Richard Dwight (Rpd25) on Sunday, January 23, 2000 - 12:06 am:

Sorry Graham but the idea that an aerofoil generates lift by having a flat bottom and curved top and that this makes the air flow at different speeds is a bit of a fallacy. A perfectly symmetrical aerofoil will generate lift if the angle of attack is right.

The aerofoil I drew in my last message shows a symmetric aerofoil given "camber", i.e. bent down. This is a feature of an aerofoil that gives a circulation (and so a lift) even when the angle of attack is zero, as well as exrta lift when the angle of attack is non-zero.

In aeroplane wings, the camber of the aerofoil is generally much less than this, and indeed most of the time is small enough that the lower surface of the wing is still convex. This gives the wing of a flatter bottom, but this is incidental to the lifting mechanism, the flatness of the bottom is not directly related to the lift. The aerofoil I drew is more typical of the sort of thing you'd find in an jet engine or on a propeller where even greater cambers than shown are used.

Incidentally, the camber of the 'foil is going to be one of the reasons that our stunt plane is going to have difficulty flying upside down. The camber as well as increasing the capacity for lift in the "right" direction, decreases the capacity for lift in the opposite direction, so when flying upside down the camber puts the plane at a disadvantage. Because of this I would guess that display/stunt planes generally have less cambered wings than conventional aircraft, (if anyone knows, and can confirm or refute this I would love to hear from them).

As for the circulation, I think you're wrong; I'll try to demonstrate: To simplify things let's say the circulation is planar; then around a wing it can be represented by a vector perpendicular to the plane of circulation (along the axis of the wing). The direction of the vector indicates the sense of the circulation. Let's say that a healthy lifting circulation is a vector that points away from the fuselage on the starboard wing (and so towards the fuselage on the port wing). Now the plane is inverted (method is irrelevant). If there were no change in circulation the circulation vectors now point away from the fuselage on the new port wing and towards on the new starboard wing. Thus the sense of the circulation is opposite to that of a healthy circulation. Conclusion: if the wings are still providing lift, the circulation must have changed sign.

I think this is right. If it is then there must be a point at which the circulation is zero as it changes sign. Is it a different point that you're making?

Richard Dwight.