2. Equations of Motion for a High Performance Fighter A Simplified Dynamical Model Based on Elementary Physics

3. F18 Hornet - High Performance Fighter - How do we model such a system?

4. Simplified Aircraft Schematic Note: Aircraft is unstable iff i.e. c.g. aft of c.p. produces “pitch-up instability” Instability desirable for increased maneuverability (high-g maneuvers) - High Performance Fighter

5. Aircraft Parameters Fuselage damping coefficient: Lift produces cw moment: - Lift coefficient: - Lift moment arm can be +/- Elevator produces ccw moment: - Elevator coefficient: - Typically - High Performance Fighter

6. Aircraft Pitch Angle Dynamics Moment from control surface (elevator) deflection (CCW) Moment from lift force (CW) Fuselage rotational damping moment (CW) - Apply Newton’s 2 nd Law of Motion Moment of inertia

7. Aircraft Pitch Angle Dynamics Elevator term substitution: Lift term substitution: - Capture effect of elevator and lift

8. Aircraft Pitch Angle Dynamics - Rewrite 2 nd Order Ordinary Differential Equation (ODE) in standard form.

9. Pitch Angle Dynamics - Transform pitch angle t-domain dynamics to s-domain - Assume zero initial conditions - Apply Laplace Transform Differentiation Rule

10. Pitch Angle Dynamics - Express pitch angle dynamics as a transfer function Note: Poles capture aircraft’s natural modes Aircraft is unstable iff

11. How Do Aircraft Dynamics Depend On System Parameters?

12. Dependence on Moment of Inertia

13. Simplified Aircraft Dynamics for - Approximate Pitch Dynamics - Approximate Vertical Dynamics first order rotational damping double integrator and first order rotational damping