Lecture 8 Notes Aircraft Lateral Dynamics

Lecture 8 Notes Aircraft Lateral Dynamics - Lecture 8 Notes...

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Unformatted text preview: Lecture 8 Notes: Aircraft Lateral Dynamics Aircraft Lateral Dynamics • Using a procedure similar to the longitudinal case, we can develop the equations of motion for the lateral dynamics ⎢ v x = Ax + Bu , x = r , u = δ a φ and ψ = r secθ ⎡ ⎢ m ⎢ ( L v + I N ) A = xx ⎢ (I zx L v + N v ) zz where Y m ( L p + I zx N p ) xx (I zx L p + N p ) zz 1 m − U ( L r + I zx N r ) xx (I zx L r + r ) zz tanθ ⎤ gcosθ ⎥ ⎥ ⎥ ⎦ I xx = (I xx I zz − I zx )/ I zz I zz = (I xx I zz − I zx )/ I xx I zx = I zx / (I xx I zz − I zx ) and ⎡ ⎢ (m) − 1 B= ⎣ 0 (I xx ) − 1 I zx ⎤ ⎥ ⎡ Y δ a zx (I) − 1 ⎦ a 0 δ a Y δ ⎤ L δ r ⎦ N δ r Lateral Stability Derivatives • A key to understanding the lateral dynamics is roll-yaw coupling . • L p rolling moment due to roll rate: – Roll rate p causes right to move wing down, left wing to move up → Vertical velocity distribution over the wing W = py – Leads to a spanwise change in the AOA: α r (y) = py/ U 0 – Creates lift distribution (chordwise strips) δ L w (y) = 2 ρU C l α α r (y) c y dy – Net result is...
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