Nondimensionalization

Nondimensionalization reduces the dependence of all aerodynamic forces and moments on density and airspeed to a simple factor. Without nondimensionalization, almost every term in the polynomial equations would include V and $\rho$ as variables.

The nondimensional forces and moments are defined by Equations 44-49.

      

$$\equiv X\,/\,(\textstyle{\frac{1}2}\rho V^2S)$$ C_X (44)

$$\equiv Y\,/\,(\textstyle{\frac{1}2}\rho V^2S)$$ C_Y (45)

$$\equiv Z\,/\,(\textstyle{\frac{1}2}\rho V^2S)$$ C_Z (46)

$$\equiv L\,/\,(\textstyle{\frac{1}2}\rho V^2Sb)$$ C_L (47)

$$\equiv M\,/\,(\textstyle{\frac{1}2}\rho V^2Sc)$$ C_M (48)

$$\equiv N\,/\,(\textstyle{\frac{1}2}\rho V^2Sb)$$ C_N (49)

The angle of attack and angle of sideslip, defined by Equations 5 and 6, are the nondimensional replacements for the dimensional wind-relative velocity components ( u_a,v_a,w_a).

Equations 50-52 define nondimensional angular speeds.

   

$$\overline p \equiv$$ pb/V (50)

$$\overline q \equiv$$ qc/V (51)

$$\overline r \equiv$$ rb/V (52)

Unfortunately, there is not a standard definition of nondimensional angular speeds. Some references define the nondimensional speeds with a 2 in the denominator.

One other nondimensional parameter is defined analogously to the nondimensional angular speeds. $\dot\alpha$, the time derivative of $\alpha$, is used to account for the effect of downwash lag. Its nondimensional form is:

$$\overline{\dot\alpha}\,\equiv\,\dot\alpha c/V$$ (53)

The control deflections, which are angles, are already nondimensional.