AIAA does not respond to any point in our rebuttal connected to our article. In fact, AIAA does not give any evaluation of the New Theory of Flight at all, and in particular does not claim that it is incorrect. What AIAA does is only to defend the Old Theory according to the following plan:
- After reading your paper and your responses to the reviewers’ comments, I can see several misconceptions you have concerning basic concepts in fluid mechanics. My goal below is not simply to reiterate the comments of the reviewers, but to help you see some of the areas where you need to improve your understanding. I will try to be clear and direct in my comments to avoid any misunderstanding.
- High Reynolds number flow around an airfoil (or a wing in 3-D) is, as reviewer 1 said, a singular perturbation problem, where a small parameter (1/Re) multiplies the term in the momentum equation with the highest order derivative. The potential flow solution you object to is only the leading order inviscid (outer) solution. The complete theory treats the coupled viscous-inviscid interaction by determining the viscous boundary layer (inner) solution, finding the displacement thickness of the boundary layer, adding that to the starting geometry to find the effective shape of the airfoil (thus accounting for the viscous displacement of the streamlines in the outer inviscid part of the flow field), recomputing the potential flow solution, and then iterating this process until a converged solution is found. This results in a pressure distribution that does not have a high value of pressure at the trailing edge, in agreement with experimental measurements. This iteration process is what is done by the airfoil analysis program XFOIL, which reviewer 2 mentioned. XFOIL is widely used in teaching aerodynamics, and I use it in my classes.
- Unfortunately, the complete theory is not always taught, with the result that many students have misunderstandings concerning flow over airfoils and wings. In my department we do not require our students to take a course in perturbation methods; as reviewer 1 said, aerospace engineers today use computational fluid dynamics; and, as a result, they lose sight of some of the theoretical underpinnings of what we study.
- Many of the concepts associated with viscous boundary layers, viscous-inviscid interactions, circulation, vorticity and the generation of lift, are not intuitively obvious.
- One of my main jobs as an educator in the area of fluid mechanics is to build up my students’ intuition by increasing their understanding of basic concepts.
- The generation of vorticity on solid surfaces is one of the more difficult subjects included in my graduate introductory fluid mechanics course. The fact that some of the concepts are difficult to understand does not make them wrong.
- Lastly, both reviewer 1 and I had suggested that you contact colleagues at KTH who could help explain some of these concepts to you. In response to one of your previous comments, I want to say that doing so is not a requirement for submitting papers to AIAA. That suggestion was made because there are basic concepts in fluid mechanics that you do not understand, and it is easier to explain those concepts face to face over a period of time, rather than through the limited medium of email. I know some of your colleagues in the Mechanics Department at KTH, and I have a lot of respect for their knowledge of fundamental fluid mechanics and applied mathematics. I strongly suggest you talk with them, or take some of the courses they offer.
Summary: AIAA does not claim that the New Theory is incorrect, that our 3d Navier-Stokes/slip computations do not describe the real physics of the flow around a wing, or that our analysis of the computations is incorrect. AIAA only defends the Old Theory, while admitting that it is so difficult that it cannot be taught to new generations of engineers responsible for constructing the new airplanes to carry new generations of people safely and efficiently.