Fa2004 16.3336-4 Approximate Aircraft Dynamic Models It is often good to develop simpler models of the full set of aircraft namIcs Provides insights on the role of the aerodynamic parameters on the frequency and damping of the two modes Useful for the control design work as well Basic approach is to recognize that the modes have very separate sets of states that participate in the response Short Period -primarily g and w in the same phase The u and q response is very small Phugoid -primarily 0 and u, and 0 lags by about 90 The w and g response is very smal Full equations from before △Xe △Zc q Mu+Zurl Mu+Zurl Ma+(gtmo)r q △MeFall 2004 16.333 6–4 Approximate Aircraft Dynamic Models • It is often good to develop simpler models of the full set of aircraft dynamics. – Provides insights on the role of the aerodynamic parameters on the frequency and damping of the two modes. – Useful for the control design work as well • Basic approach is to recognize that the modes have very separate sets of states that participate in the response. – Short Period – primarily θ and w in the same phase. The u and q response is very small. – Phugoid – primarily θ and u, and θ lags by about 90◦. The w and q response is very small. • Full equations from before: ⎡ ⎤ ⎡ Xu u˙ m ⎣ w˙ Zu w ⎦ = ⎣ [Mu+ZuΓ] m−Z ˙ q˙ θ ˙ Iyy 0 Xw m Zw m−Zw˙ [Mw+ZwΓ] Iyy 0 0 Zq+mU0 m−Zw˙ [Mq+(Zq+mU0)Γ] Iyy 1 −g cos Θ0 ⎤� � � � u ΔXc −mg sin Θ0 m−Z ˙ w ΔZc −mg sin Θ0Γ w ⎦ q + ΔMc Iyy 0 θ 0