Center of Lift Formula

[Norman]

Hi Guys. Does anyone know a formula for finding the center of lift of a wing swept back ten degrees?

[Jon Matcho]

There's not going to be that simple of a formula that takes just the sweep of the wing as an input. There are several other variables at play.

 

Try 'googling' the words: airfoil cad to see what comes back. There are several modeling tools that will help you select and analyze wings.

 

You might also try X-Plane, which has some credibility among those who are modeling and experimenting with new designs.

[Aerodynamix]

Hi there. This is my first post on The Canard Zone and my handle "Aerodynamix" is the same I use to post on other forums.

 

Before I answer your question, I feel the need to point out that I have no formal training in aerodynamics and every thing I know I have learned myself over the past decade. Second, aside from some very basic experience with working wood, ceconite, aluminum, and composites, I have never actually built a manned aircraft before. Thirdly, I am not a fully trained pilot. I have started training but due to my current financial situation and a certain medical issue, I don't feel it necessary to continue at this point in time.

 

Also, as Jon mentioned there are several CFD (Computational Fluid Dynamics) programs available and I have used several of them including X-Plane but I feel that there is still room for error and their version of your aircraft should not be taken as gold.

 

Ok, on to your question.

 

The aerodynamic center of a wing or any control surface varies slightly depending on the airfoil you use, however, the rule of thumb is to use an imaginary line spanning from the root to tip at 25% of the wing's chord, measured from the leading edge toward the trailing edge. A wing with a constant chord (Hershey bar) planform (wing shape as viewed from above) with no sweep, it is easy to figure out the Aerodynamic Center (AKA: Center of Pressure). On a swept wing, either fore or aft, the AC can be calculated as:

 

(RootChord + TipChord) / 2 = MAC (Mean Aerodynamic Center)

 

Note that this formula only works when the leading edge and trailing edge is completely straight and not curved like the wing on a Spitfire or Concorde.

 

So at whatever span the MAC happens to be on, just draw an imaginary line parallel to the fuselage center line and where that line intersects the 25% chord line (from root to tip), that's where your Center of Pressure is and that's where your airplane will balance and where all moment arms (horizontal tail or canard or both!) will be measured from.

 

I hope this helped and I'm always open to constructive critisizm when it comes to fine-tuning my knowledge of everything aviation related so everyone, feel free to correct me if necessary.

[H.Zwakenberg]

Also, as Jon mentioned there are several CFD (Computational Fluid Dynamics) programs available and I have used several of them including X-Plane but I feel that there is still room for error and their version of your aircraft should not be taken as gold.

 

 

Aerodynamix:

 

please note that X-Plane is not a CFD.

 

Computational Fluid Dynamics software is used to determine the flow of many, many "air-cells" if you will, that wrap an object (in our case an aircraft) on the outside. Also, this gridding of the space from the object is continued to the outside, very often multiple spans away from the object. For each of these grid cells, CFD software calculates the local air pressure, the air stream 3D direction and the correspondig air velocity. What makes CFD so great, is that the interaction between all those cells is also considered.

 

X-Plane on the other hand only coursly grids the wing(s), control surfaces and propeller blades. It does not grid the outside environment. With this course grid, it does force and moments estimates for each of those points. Calculation the resultant forces, moments and speed is done by an integration of all cells. Austin Meyer, the author of X-Plane, utilizes what is called 'blade element theory' to do these calculations.

 

Blade element theory is much easier to calculate than a full CFD. Current computers can't handle complex CFD jobs that would allow realtime behavior calculations that would be needed for simulations. Blade element theory can do that, but the results are less precise.

 

It's a matter of horses for courses...

 

bye

Hans

[BirdmanZak]

I know this is digging up an old post, but OCD compels me

 

 

The method shown is how to find the aerodynamic centre, not centre of pressure. They're different.

 

page 61; Aerodynamics Aeronautics and Flight Mechanics;McCormick B. W. 1995

 

"Do not confuse the aerodynamic centre with the centre of pressure. Again, the aerodynamic centre is the location about which the moment is constant, and the centre of pressure is the point at which the resultant lift acts."

 

At the centre of pressure (or centre of lift, whichever you'd prefer to call it) there will be zero moment due to aerodynamic forces, as the resultant vector is acting through that point (so zero moment arm -> zero moment).

 

The centre of pressure moves as the angle of attack changes (usually forwards with increasing AoA). Because AoA frequently changes, centre of pressure is not a very useful quantity.

 

There is a point on the wing called the aerodynamic centre which, if lift is measured there, has a constant moment. It is (usually) located at (around) 25% chord. As AoA increases and lift increases, the centre of pressure moves forwards (toward the aerodynamic centre) which reduces the moment arm - resulting in a constant moment around that point.

 

Because the aerodynamic centre is fixed, it is much more useful. It only needs to be found once for an airfoil or wing. The wing may be treated as though lift acts through that point with a constant moment also acting.

 

I hope that's clear.