Flying wing preliminary design and XFoil pitch stability analysis


New member

I am relatively new to flying wing design and I am trying to understand the design process. In order to choose an airfoil, I created a small MATLAB script working with XFoil to select one between some of the NACA5 (reflex) foils. According to my requirements (very large thickness, specific Cl range, optimum Cl/Cd, positive Cm) I ended up choosing the NACA54129. I know that XFoil is a 2D analysis program and that results can be radically different when switching to 3D but I first want to understand the 2D design process. Now that I have an airfoil that can generate enough lift, I need to guarantee longitudinal stability.

From what I learned, if Cm is positive and CG is ahead of the AC then the distance between the CG and the AC must accomplish the following: equilibrium between the pitching moment at AC and the lift moment arm (xAC-xCG)*L during cruise (trim), and the desired static stability margin is satisfied (the smaller the distance, the less stable it is and vice-versa). My 2 variables being the cruise AoA and the CG coordinate (that can be adjusted with the electronics placement), I have enough freedom to solve for a specific static margin, and moment balance at trim. If Cm is constant, as it is the case at the AC, it seems like a pretty straightforward calculation.

However the XFoil generated Cm is taken at 0.25 chord, which is not always the AC, and in my case Cm is in fact not constant. I tried finding the AC by finding the "most" constant Cm by computing in MATLAB Cm=Cm_0.25+x*Cl for different values of x, but this ended up not being very conclusive. From the results that XFoil gives me, how would I go about placing the CG in order to satisfy static stability? Should I work with the Cm results at 0.25 chord or should I find the AC and work with Cmac? Should I design the flying wing with a radically different approach (maybe not using XFoil)? Also, my analysis uses Re=300,000 and 17m/s, Ncrit=9.

Linked is the NACA54129 airfoil, and XFoil polar plots

Matt LC


  • NACA54129.PNG
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  • NACA54129_Polar.PNG
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Why is your Cm not constant? Are you burning fuel?
You can get a good idea of Cg simply from the geometry of the wing. This is a decent cg calculator: If your wing is more complex in planform, click on the "Extended Version," link at the bottom of the page.

You can increase the distance between the Cm and center of pressure by increasing wing sweep. Modifying the wing taper plays into this as well. Why do you need such a thick airfoil?