Loads and coefficientsΒΆ

PyTornado computes different global force and moment coefficients. The definitions are described below. Notice that there are three different reference values:

  • \(S\) : Reference area
  • \(c\) : Reference chord
  • \(b\) : Reference span

There are two sets of force coefficients, the fist being described in the body-fixed system and the second being described in the aerodynamic system (see also Coordinate systems). The global force coefficients \(C_X\), \(C_Y\), \(C_Z\) in the body-fixed system are defined as

\[\begin{split}C_X = \frac{F_x}{q \cdot S} \\ C_Y = \frac{F_y}{q \cdot S} \\ C_Z = \frac{F_z}{q \cdot S}\end{split}\]

where \(F_x\), \(F_y\) and \(F_z\) are global forces in \(X\), \(Y\) and \(Z\) directions, respectively, \(q\) is the dynamic pressure. Global lift, drag and side force coefficients (\(C_L\), \(C_D\), \(C_C\)) describe forces in the aerodynamic coordinate system and are defined as

\[\begin{split}C_L = \frac{F_L}{q \cdot S} \\ C_D = \frac{F_D}{q \cdot S} \\ C_C = \frac{F_C}{q \cdot S}\end{split}\]

where \(F_L\), \(F_D\) and \(F_C\) are global lift, drag and side force (in Newtons) in the aerodynamic system. Moment coefficients are defined with respect to the body-fixed system as

\[\begin{split}C_l = \frac{M_x}{q \cdot S \cdot b} \\ C_m = \frac{M_y}{q \cdot S \cdot c} \\ C_n = \frac{M_z}{q \cdot S \cdot b}\end{split}\]

where \(M_x\), \(M_y\) and \(M_z\) are global moments about the in \(X\), \(Y\) and \(Z\) directions, respectively.

TODO explain gcenter and rcenter