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How to define static margin of guided artillery rocket with canard-free rotating tail configuration? In the E. Fleeman book, the aerodynamic center ($X_{ac}$) was used:

$ SM = {X_{ac}-X_{cg} \over d} $

But in other books about rockets, the term center of pressure ($X_{cp}$) was used:

$ SM = {X_{cp}-X_{cg} \over d} $

Which formula is correct for such canard-free rotating tail configuration?

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Since rockets/missiles typically use symmetric airfoils and fuselages the aerodynamic center and the center of pressure are the same, because the zero-lift moment coefficient is zero.

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  • $\begingroup$ But it is strange when i do some cfd simulations in Ansys Fluent at supersonic speed, the aerodynamic center and the center of pressure are not the same. The aerodynamic center is far forward the center of pressure. Note: Xac is calculated by ploting moment coefficient cm vs angle of attack and by finding the point at which moment coefficient is constant. Xcp is calculated by integrating static pressure over whole surface of the rocket. $\endgroup$
    – TVH1986 ct
    Jun 23 at 1:47
  • $\begingroup$ Is your body not symmetric? Can you show a picture, or show us the curves and plots that indicate that aerodynamic center and center of pressure don't match? $\endgroup$
    – Raketenolli
    Jun 23 at 14:34
  • $\begingroup$ The missile is axisymmetric with von karman nose, 4 canards on the nose and 6 tail fins freely rotating. The missile length is about 4.7 m, the Xac=1.98 m at M=3.5, the Xcp=2.4 m at M=3.5 and AoA=0. The Xcp is calculated by intergrating static pressure over missile surface. The Xac is calculated by ploting Cm at various points along missile axial axis and find the point at which Cm=const. $\endgroup$
    – TVH1986 ct
    Jun 25 at 14:54
  • $\begingroup$ I believe most texts are ignoring the contribution of the body and only including the wings -- or possibly even only looking at a single set of finds. Fleeman's definition is correct. Xcp is a useless quantity. Drive it from your mind and never use it again. Question any resource that uses it with suspicion. $\endgroup$
    – Rob McDonald
    Nov 19 at 21:11

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