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Old 27th May 2004, 19:47
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Keith.Williams.
 
Join Date: Aug 2001
Location: Dorset
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Hello again Hawk,

I'm afraid I cannot give any internet references. Sadly I am not a great user of the internet search facility.

The pressure envelope diagrams are in almost every book on aerodynamics and may well be the CP diagrams you mention. They are simply profiles of aerofoils with an eliptical line above and below to indicate the degreee of pressure change at each point along the curve.

For a cambered aerofoil at zero-lift angle of attack (usualy quoted to be about -4 degrees) the stagnation point is above the leading edge. This causes rapid acceleration around the underside of the leading edge, so the greatest pressure drop below the aerofoil is just behind the leading edge. The pressure drop then gradually reduces to zero at the trailing edge.

This entire lower envelope represents reduced pressure so the resulting force is downwards. If we guestimated the lower surface CP is it would be fairly close to, but under the leading edge. So we have a force tending to pull the leading edge downwards.

At this same zero-lift angle the lowest pressure above the wing would be at about 30% chord. So the upward force acting on the upper surface would be behind the downward force acting on the lower surface. These two forces would therefore produce a nose-down pitching moment. So at zero-lift angle of attack a cambered aerofoil produces a negative pitching moment.

As angle of attack increases the stagnation point moves down and aft, so there is less acceleration under the leading edge and more acceleration above it. This causes the lower CP to move aft and the upper CP to move forward. At some angle of attack the two CPs are directly one above the other, so there is zero pitching moment.

At still greater angles of attack the upper CP moves further forward while that below moves further aft. This creates an increasing nose up pitching moment.

At very high angles of attack the stagnation bubble (which is an increased pressure) enevelopes the entire lower surface, with its CP close to the 50% chord point. We now have both the upper and lower surfaces producing positive lift, so the overall CP starts to move aft again.

The problem with using the CP as our reference is that it moves about as angle of attack changes. It is far easier to do the maths if we can find a fixed point to use as our datum, particularly if the pitching moment about this point is constant. This point is the Aerodynamic Centre or AC.

To understand this we need to carry out a little mental (or physical experiment) Imagine that we have made a small aerofoil section out of thin card and pinned it to a board using a drawing pin through the trailing edge. Any lift force acting upward will cause the aerofoil to pitch nose up. The magnitude of the nose up pitching moment is equal to the lift force multiplied by the distance between the CP and the drawing pin at the trailing edge.

Now if we imagine what happens as angle of attack increases, the lift force increases and the CP moves forward. This cause the nose up pitching moment to increase. So if we measure pitching moments about the trailing edge they are nose up and increase as angle of attack increases.

Now if we pull out the drawing pin and push it through the leading edge we will find the opposite effects. The pitching moment is nose down and increases as angle of attack increases.
So piching moment about the leading edge is always nose down and increases as angle of attack increases.

We must now pull out the pin and try again, first with the pin one inch in front of the trailing edge then with it one inch behind the leading edge. We will find that the pitching moment are as described in our first tests but that the rate of change with angle of attack are less. If we keep repeating the process gradually brining the two pin holes closer together we will eventually find a point at which the rates of change of nose up and nose down moments exactly balance, giving a constant nose-down moment. This point is the AC of the aerofoil.

Any numbers used in this description are of course generalisations but hopefully it all makes sense. I wouldn't be too concened if some of this subject appears to be a bit mind boggling. I have been reading it on and off for years and still don't understand it.
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