Talk:Lift coefficient

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[edit] Scientific Usefulness

This article is not really helpful in defining a function for computing the lift coefficient other than to provide an equation to support measuring it through experiment, i.e., solving for the coefficient of lift using the equation for lift. It is like defining π = A/r². This formulation would be helpful in experiments to compute π if methods of measuring the area of a circle were available (such as increasing the number of sides of a circumscribed polygon) but it does not provide an independent method to compute π such as the infinite series,

π = 4(1 - 1/3 + 1/5 - 1/7 ...) [Mathematics for Everyone, Laurie Buxton, 1984]

This is what I was looking for when I went to this article, an independent method. Further, working with lift necessarily includes working with angle of attack whereas this article specifically avoids angle of attack. It does, however, provide a nice graphic of a generic coefficient of lift with respect to the angle of attack of some undisclosed object.

I believe that this article could be improved upon significantly by providing typical lift coefficient computational methods for a series of nominal objects (flat plane, Clark-Y airfoil, a symmetric hypersonic wing, and my primary concern, a warhead reentry vehicle of the cylinder-cone-nose radius form) and include the affects of angle of attack. I'm working on the physics of lifting reentry vehicles and a simplified mathematical representation of this but I am not yet prepared to produce an entry about it - after all, at this time I came here to find those relationships, not explain them. If I do find those explanations, I will certainly recommend the improvement modifications I have outlined above.

(Please forgive my lack of knowledge of the Wiki markup language - I am just learning it).

--JEB 20:49, 27 May 2006 (UTC)

Exactly so. It is a framework used to find lift coefficient by experiment or to calculate lift when the coefficient is known. Unfortunately, unlike with finding π, there is no equation or even large collection of equations that can calculate lift independently. There are other simplifications of course for some conditions. In reality, lift is found by wind tunnel experiments or heavy computer work on small elements. Reality being what it is, the lift equation here has been a mainstay in aerodynamics for a very long time; no doubt about its usefulness. Keep in mind that this article is about this coefficient and corresponding equation, and not about lift in general. By the way, that graph for some unspecified object has a vertical scale that is unlikely. Meggar 23:23, 27 May 2006 (UTC)

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Thank You, Meggar, for your insightful remarks. However, I tend to disagree about there not being some generic simplified equations with respect to the generation of lift coefficients. According to Van Nostrand's Encyclopedia Sixth Edition (Van Nostrand Reinhold Company Inc., 1983, Supersonic Aerodynamics, page 2731) "The lift coefficient for supersonic airfoils of infinite span at moderate angle of attack and Mach number is,

where α is the angle of attack in radians, and M is Mach Number." Using this equation, I have computed the supersonic C_L for 6 angles of attack from 5 to 30 degrees and from Mach 1.2 to Mach 10 As presented in the following figure (This presumes, of course, no stall, which may or may not be the case at supersonic speeds. Note that I am concerned with atmospheric reentry and stall has not been an issue - the U.S. Space Shuttle, for instance, reenters the atmosphere with a positive angle of attack of 40 degrees and uses their control surfaces and the lift and drag forces as they are generated to produce their heat dissipating roll program.):

As can be seen, at Mach 1.2 (the first point in each curve), the C_L values reach a maximum value of nearly 3.5. This prompts me to ask you why you feel that the "graph for some unspecified object has a vertical scale that is unlikely"? I'd like to know if you feel that it was too large or too small and under what conditions it would be unlikely.

To pursue this further with respect to supersonic drag (as I need both) and staying with Van Nostrand, on the same page the article says, "The drag coefficient of airfoils in supersonic flight is composed of several equally important parts. These are pressure drag, friction drag and drag due to lift."

Pressure Drag: Van Nostrand goes on to explain that pressure drag, also known as wave drag, "is similar to subsonic form drag" and is approximated by,

which, since I don't like short cuts and unnecessary rounding, I prefer to write as,

where (t/c) is the thickness ratio or thickness to chord. I have a good friend who is also looking at these issues who says that a different representation of this same supersonic wave drag is presented in a book by Eshbach (I do not know the name or publisher) and does not included the squared factor, using (t/c) as a linear scalar. This is a difference issue that I need to resolve.

Friction Drag: Van Nostrand doesn't say much about supersonic friction drag other than to equate it with subsonic friction drag - so this is a question I have no answers for at this time and the theory looks a little messy - hopefully it is not a major issue at supersonic speeds through thin atmosphere - but it may be ... so I need to resolve this as well.

Lift Induced Drag: Van Nostrand points out the following, "Drag due to lift is the component of the resultant pressure force which acts in the drag direction. It too has an exact counterpart in subsonic flow. Drag due to lift is,

The term induced drag used for subsonic flow is not applied to supersonic drags. Induced drag [in] the subsonic case is due to tip losses. Tip losses occur in supersonic flow, but not in the same proportions as in subsonic flow."

Well, the above lift induced drag discussion has me a little baffled and I'm not sure what to do with it. It implies that it is not significant for supersonic flight - so, if this is true, I should probably not be attempting to model it.

BOTTOM LINE: The bottom line here is that I do not feel that I have captured the essence of modeling lifting reentries with the above information. These are my issues:

1. I believe that the lift coefficient modeling is sufficient for my needs. I can assume symmetry of the object and zero lift when the angle of attack is zero. But is the α term really radians, the sine of the angle of attack, or degrees?
2. The pressure drag equation looks reasonable but is the (t/c) term squared or not?
3. When you go to the actual lift and drag equations which are essentially identical with only the choice of the coefficient, lift or drag, there's a question regarding the definition of the aerodynamic reference area. In drag discussions, it is pretty apparent that the drag reference area is the projection of the object on a plane perpendicular to the medium [air] relative velocity or direction of flight through the medium. With respect to lift, the rule appears to be the area of the wing - this is why I believe that the α variable really should be sin(α) because sin(α) times the wing area represents the projection of the object on that same plane normal to the direction of flight. When the angle of attack is small, this projected area is small and hence the lift is small. When the angle is large, the projection and the lift are large. This also suggests to me that the lift induced drag should be a major player in the supersonic physics as well.

Enough said ... I have written this because I am a little frustrated in resolving a simplified lift/drag model which will give me first order answers and possibly second order. I believe that it can be done - tell me one way or the other. --JEB 03:52, 28 May 2006 (UTC)

I'm not a physicist, etc, but here's my take which I've mentioned on other related pages. Anytime you come across a 'coefficient of...' in a physical equation, basically what you are looking at is a cop-out. What it means is that the observed phenomenon is apparently linear, but too complicated to describe in "real" terms. All the odd unknowns are simply bundled into a number which is arrived at to make the equation fit the observations. That doesn't mean it's useless, because it's relatively straightforward to either test your aerofoil in a wind tunnel and measure the coefficient (i.e. fudge it so the numbers come out to fit the equation) or else consult published tables of data for already tested sections. Then you can go on to design a practical aeroplane or whatever. Doing the reverse - deriving the coefficient from first principles - is possibly of academic interest but probably not of interest to the practical engineer. It's interesting that the equations you state above are for foils operating in certain very narrowly (and somewhat exotic) conditions. I'd suggest that a more general solution is too complex to be found, the Navier-Stokes equations being the intractable beasts that they are. Graham 15:58, 30 May 2006 (UTC)

If GRAHAMUK doesn't mind I would like to replace the graph with one for a specific profile and conditions. It would help in adding some numerical info. About that aerodynamic reference area: For wings the plan area is used for both lift and drag coefficients. Lift/drag ratio can then be found simply be dividing on by the other. Also we wouldn't want the reference area going to zero for a thin section at zero angle of attack. I wonder Jebsys, if you have discovered the link to the report server over in the NACA article. There should be some helpfull information there, for example - [1] Meggar 04:27, 1 June 2006 (UTC)

Would it be appropiate to include specific soulutions to known geometric bodies on this page? i.e. the Cl value for a sphere is well known and can be derived, also there are general solutions for cylenders, of inifinite length, etc.--203.45.15.164 15:41, 1 June 2006 (UTC)

[edit] Proposed move

This page should be moved to Lift coefficient to be consistent with Pressure coefficient, and Drag coefficient, among others. -- Kaszeta 15:55, 2 August 2005 (UTC)

Yes. Meggar 16:32, 2005 August 2 (UTC)

• Moved. Uncontroversial, no admin assistance was required. Dragons flight 19:53, August 5, 2005 (UTC)