By John H Blacelock
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Extra resources for Automatic Control of Aircraft and Missiles
Aircraft flexibility and compressibility also affect this term. In the transonic region the static stability of the aircraft can vary considerably. Below the transonic region Cmu can be safely neglected for jets. The changes in Cmu are due to the shift, usually rearward, of the center of pressure as the aircraft enters the transonic region, making Cm negative. Cx is the change in the force in the x direction due to a change in a caused by a change in w. Because the aircraft axes are fixed to the aircraft, a disturbance resulting in a vertical velocity produces lift and drag vectors that are no longer perpendicular to and parallel to the X axis (see Figure 1-7).
The flow is quasisteady (to be explained in Section 1-7). These equations require that the X axis be aligned with the aircraft velocity vector while the aircraft is in equilibrium flight. The stability derivatives are defined in Table I-land are derived in Section 1-7. d t 26 LONGITUDINAL DYNAMICS It should be remembered that in these equations U = Uo, q = tpuo2 , 'u=ujUo, 'a=wjUo, and 'a=wjUo. These equations are nondimensional; thus all angles and their derivatives must be in radian measure. In deriving the longitudinal equations of motion certain nondimensional coefficients, referred to as stability derivatives, were introduced.
Thus Eq. 1-78 becomes = L _ aD = L _ aD ( aFx ) a'a 'a-O a'a aa as a'a -=1 aa (1-79) Multiplying by 1/ Sq to obtain the nondimensional coefficient, Eq. 1-79 becomes D 1 (aFx) aC CXa -aa- -C Sq - L -aa (1-80) Cz is the variation of the Z force with angle of attack. This term is very similar to the case of Cx a , and referring to Figure 1-7, the new force in the Z d 32 LONGITUDINAL DYNAMICS direction can be expressed as Fz = - Lcos'a - Dsin'a (1-81) Differentiating, 8Fz 8 'a - 8L 8D cos'a + Lsin'a - -sin'a - Dcos'a 8'a 8 'a =- - (1-82) Evaluating at 'a = 0, as before, Eq.