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Is the property of having a neutral point (aerodynamic centre) specific to an airfoil shape or will every arbitrary shape will have one?

Asking in mostly context of fuselages.

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  • $\begingroup$ In general I'd say no. Just think about a non-rotating ball for example: it definitely has no lift nor pitching moment, only drag; so it doesn't have any aerodynamic center. I suppose that the same reasoning apply as well to any body with some symmetry. $\endgroup$
    – sophit
    May 4, 2023 at 18:48
  • $\begingroup$ @sophit curious in the case where a sphere is dropped straight down. There was one video where (an offcentered) ball was dropped from a great height, and it started going Magnus effect. $\endgroup$ May 6, 2023 at 15:02

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That is an interesting question. I'll say right away -- I don't know, but I think we can think our way through this.

The fact that an airfoil has an aerodynamic center (a point around which the moment does not vary) -- and that the location of the ac is c/4 -- and our ability to calculate that moment all come from thin airfoil theory.

We can of course use more complex theories to see these things, but the most simple theory that analytically shows these things is thin airfoil theory. TAF is based on inviscid, incompressible, 2D flow.

So, it is natural to look at an inviscid, incompressible, 2D flow theory on a non-airfoil body to answer your question.

One fact about this flow model is that the flow will always be attached.

The big difference between a non-airfoil body and an airfoil is that we won't have a sharp trailing edge on the body. I.e. we will not apply a Kutta condition.

This means that the non-airfoil body will not support any lift (it will still have moments, but no forces). I know it sounds crazy, but it is true -- in this flow model, a body will not have any lift or drag.

Without enforcing the Kutta condition at the sharp trailing edge, the rear stagnation point will move until it 'finds' the no-load point. If you force separation anywhere else, you will get forces -- but it naturally will find the no-force solution.

So, this means our body has a moment about it, but no forces.

If the body is symmetrical, then at zero alpha, it will have zero moment. However, at some non-zero alpha, it will have non-zero moment. So -- the moment changes with angle of attack.

Since there is no force (to contribute to the moment depending on the moment arm), we know that this is a pure couple -- and it will be the same no matter the reference point for moments.

So, we'll have a non-zero moment that varies with alpha, no matter the location of the moment reference point.

So, no -- non-lifting bodies do not have an aerodynamic center the way airfoils do.

I know everything I've said in this post about non-lifting bodies in potential flow also applies to 3D flow.

I'm comfortable with the incompressible restriction -- the answer could well be different in compressible or supersonic flow, but this discussion should hold true for a lot of subsonic flows.

The big question is the inviscid assumption. Real flows have viscosity. In those flows, the adverse pressure gradient on the aft side of the blunt body determines where the flow separates. This locates the aft stagnation point and can allow the body to have lift. You must be very gentle to allow the flow to find the no-force solution with a real boundary layer.

This blunt-body separation problem is a very challenging problem of aerodynamics. It is hard to study in a wind tunnel because we usually place bodies on a sting mount -- but the sting itself changes the flow in this region.

Blunt bodies like fuselages end up having separation points that move with angle of attack -- and are hard to predict.

So, if you had a fuselage with a feature on the aft side (sharp TE, strakes, flat blunt end, etc) that forced the flow to separate at a consistent location -- then I think it might have an aerodynamic center.

However, if the aft separation point is allowed to move around (reaching the no-load solution, or just wandering a bit depending on alpha), then I do not think you will it behave like it has an aerodynamic center.

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  • $\begingroup$ Although I am not challenging the utility of neutral point calculation for a given configuration. But a neutral point, as we know wrt airfoils should not exist for an aircraft with a fuselage? Say an aircraft with low aspect ratio wings where fuselage moments have significant contribution $\endgroup$
    – Mridul
    May 5, 2023 at 8:33
  • $\begingroup$ I suspect that the fuselage contribution is seldom significant when compared with that of the horizontal tail -- a lifting surface on a moment arm produces a much larger moment than the cm0 of the wing or tail. I suspect the effect you're thinking of exists, but isn't very important. $\endgroup$ May 5, 2023 at 16:02
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Yes, any shape will have a neutral point, the trick is to find it and use it for pitch stability design.

The neutral point is where angle of attack does not affect pitching moment.

Does a sphere have a neutral point? Sure. Right in the middle.

But as always, aviation would be easy if there was no air.

Lifting efficiency and distribution of certain shapes can affect center of pressure, depending on angle of attack, which can affect (pitching and yawing) stability characteristics of an airfoil and/or fuselage.

One of the primary jobs of the tail is to counter-act the forward movement of center of pressure with a cambered airfoil as AoA increases$^1$.

Designers, furthermore, can place the center of gravity further forward of the AC and add some downforce to the tail, increasing longitudinal stability$^2$ and introducing static stability$^3$.

In the end AC is a nuetral pitch stability concept, but behavior of all aerodynamic shapes must be evaluated.

$^1$ symmetrical airfoils do not have this issue

$^2$ ranging from trainers to highly unstable computer controlled aircraft

$^3$ yes, a lifting tail can be staticly stable, but if weight is moved forward, whatever the original (tail) lifting condition, tail lift must be reduced.

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