Frames and axes

Updated December 2, 2023



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Context

Several system of axes are commonly used in aerodynamic calculations, and the choice of the frame may change depending on the method used or the type of results being calculated.

In addition, common conventions used to define the positive signs of pitch, roll and yaw may or may not be consistent with the definition of the frames and axes.

Typically, the geometry of the airplane is defined in a set of body axes called geometry axes in the case of flow5.
The lift, drag and side force coefficients are conventionally defined in wind axes, or pseudo wind axes ignoring sideslip.
Stability calculations are made in another set of body axes called stability axes.
Forces and moments can be output in any of these frames.

AVL offers options to output results in either body or stability axes, with an option in each case to have the axes defined in the geometric or standard conventions, which makes for a total of four possible frames.

flow5 up to v7.23 has not been explicit about which system of axes it has used, and the sign conventions between linear T123578 polars and non-linear T6 polars has not been consistent.

Starting in v7.24, the frames and signs used in flow5 have been homogenized internally and aligned with the convention in AVL defined by the options:
A xis orient. : Geometric axis orientation, X aft, Z up
R ate,mom axes: Rates,moments about Stability Axes, X along Vinf

The purpose of this page is to clarify which frames flow5 uses in each case from v7.24 onwards.

Axes and frames of reference

Body axes

This term may refer to any system of axes which is fixed to the airplane and moves and rotates with it.

Geometry axes

In the case of flow5, this is the set of body axes in which the geometry is defined. It is also the set of axis in which the calculations are performed internally, even though the results may be output in a different set of axes.

Wind axes

This is the frame of reference aligned with the wind.

  • The x-axis and z-axis are rotated by the angle of attack from the geometry axes.
  • The x-axis is aligned with the wind direction and points backwards.
  • The z-axis is in the vertical plane and points upwards.
  • The y-axis is rotated around the wind's z-axis by the sideslip angle.

This system of axis is not used in flow5.

Instead for consistency with AVL flow5 calculates coefficients lift, drag and side force coefficients in "pseudo wind axes" in which the sideslip is ignored. From AVL's documentation: "It must be pointed out that if sideslip (beta) is nonzero, then CD and CY are not the true "drag" and "side-force" aligned with the relative wind direction. Likewise for moments Cl and Cm."

Practically, these pseudo wind axes are the same as the stability axes defined below, with opposite directions of the x and z axes.

Stability axes

The stability axes are those defined in Etkin & Reid's "Dynamics of Flight" which is the theory implemented for the stability calculations in both xflr5 and flow5. A summary of the theory and a description of the frames are given in lecture notes 16 to 18 of this MIT course.

  • The x-axis is aligned with the wind direction and points forward.
  • The y-axis is the same as in the geometry frame
  • The z-axis is perpendicular to both and points downwards.
The sideslip is ignored.

Choice of reference frame

Up to flow5 v7.23, lift, drag and side force have been output in wind axes, and moments have been output in geometric axes.
From v7.24 onwards, moments are output in pseudo-wind axes for consistency with AVL.
This does not change the pitching moment M since the y-axis is the same in both cases, but does modify slightly the lateral moments L and N around the longitudinal and vertical axes. The difference is well within the precision of panel methods anyway.