paladin

Could someone post a general explanation as to the nature and description of the aerodynamic center of an airfoil and its relationship to the center of pressure, and the center of gravity?

Cubdriver

You specify airfoil which suggests 2 dimensions, but there is no gravity for a two-dimensional object. Gravity requires mass to act. Airfoils do not have mass.

The concept called "airfoil" is a way of conceptually, and for the engineers mathematically, analyzing the combined problem of lift, moment, and drag for lifting surfaces. We like to start in 2D to make life easier. Obviously a 2D lifting surface can't lift anything until we extend it into the third plane, but the flow analysis is valid to an extent. In other words, if you can understand how flow goes around a 2D "slice" of a wing, then you have a valid starting point for explaining and modeling the flow around an entire 3D wing. And then can gravity come into play.

Using circulation, Kutta condition, and some handy mathematics like vector components, we can add up the lift obtained from a wing into a single vector that more or less points upwards. Actually it points slightly backwards because when we locate the drag vector the two must be added to find useful lift. The point at which this resultant vector extends from the chord line of the airfoil is the aerodynamic center of lift. Pressure center is the same thing, a resultant vector summation of the various pressure values found around the airfoil.

When we extend the airfoil into the full 3D wing we can find a center of gravity or CG. It slides around fore/aft, left/right depending on the mass distribution of the wing or airplane. If your fat passengers go to the back it slides aft, etc. A single summary vector pointing toward the center of the earth can be determined, the center of gravity. We represent the location with a vector.

Cubdriver

Airfoils and Airflow [Ch. 3 of See How It Flies]

paladin

Thanks for the response Cub. Conceptually I am pretty squared away on the term airfoil and I don’t mean to suggest anything by specifying “airfoil” in my post. I came across the term “aerodynamic center” the other day and I don’t recollect ever seeing the term before. So I thought I would throw it out and take advantage of erudite individuals who post on this forum and maybe learn something new.

From what I have since learned Aerodynamic Center (AC) is an aerodynamic reference point on the chord where all changes in lift take place and the coefficients of moment are constant. It is unlike the center of pressure which is a function of camber and section lift coefficientis and therfore dynamic in nature. The AC’s location is not affected by camber, thickness and AOA. By using the “aerodynamic center” as the location where the aerodynamic force is applied it supposedly eliminates the problem of movement of the center of pressure in aerodynamic analysis. It’s most direct application seems to be longitudinal stability since the explanations I have encountered speak in terms of center of pressure and center of gravity.

I am curious to know if this is just some theory or is there empirical evidence or mathematical proof for the fact that there exists such a point on all airfoils?

Cubdriver

I concur with your explanation. I wrote mine a bit late in the day and should have made the difference more clear. Center of pressure moves, AC doesn't. The part you added about center of moment is also right. And you get the general idea, these are points used in aerodynamic design.

Please try and clarify your use of 2D and 3D terms: 2D/3D distinction is very important in aerodynamics. Airfoils = 2D, Section lift coefficients = 3D. Keep separate, or at least make clear when you are moving from 2D to 3D discussion. This confusion may be why you are mixing in center of gravity with 2D. 2D = no gravity. Center of gravity is irrelevant in 2D aerodynamic discussions.

For a metric ton of real test data on airfoils you want a copy of Abbott and Doenhoff Theory of Wing Sections.

CG impacts lateral directional stability of course. The general topic heading is "stability and control". You might want a decent engineering text; I have Flight Stability and Automatic Control" by Robert Nelson. Pricey, really meant for engineers.

paladin

Thanks Cub I'll be sure and do that next time But I got to tell you I am not an enginneer and at this stage in my life I don't think I care to become one. It's just that I stumbled across the term and it peaked my interest.

Cubdriver

Well you really have my sympathy if that is the case, because genuine study of aerodynamics is long, slow work. Casual study really does not open the door to genuine insight in aerodynamics. You end up falling back on stipulations without satisfying explanations. I graduated an aerospace engineering curriculum and was challenged to learn the subject. It is very hard to teach aerodynamics because it takes so much math, knowledge of the history of the discipline, plus a ton of lab research experience, and if at all possible test flight experience. Almost no teacher has all this and the subject tends to be weakly taught in even the prestigious schools. The best instructor I had was an adjunct professor from an aerodynamics lab. He had to know the subject to do daily research.