PFR - Aerospace Engineering Sciences Senior Design Projects ...

Project Final Report – CUDBF April 30 th , 2009
ASEN 4028: Aerospace Senior Projects
In order to guarantee that the designed control surfaces could produce the deflections necessary
to trim the aircraft, analysis was done in AVL. Three cases were setup to determine if the
necessary deflections were feasible. Under the worst case scenario (2 rockets on one wing during
takeoff), the maximum deflection necessary from the rudder was 10 degrees, 15 degrees from the
aileron and 15 degrees from the elevator. The maximum possible deflection is approximately 25
degrees. Flow separation occurs over the wing around 25 degrees of deflection. It is clear that
there is enough margin for deflection for all the control surfaces before flow separation occurs.
8.1.5 Stability Analysis
Stability analysis was done in AVL and in MATLAB, the code can be found in Appendix G.
Non-dimensional stability derivatives were obtained from AVL for three different scenarios that
mirror flight missions. The first scenario simulated a case where the centerline fuel tank is flown
on the airplane for cruise conditions, the second scenario was four rockets on the airplane in
cruise, and the third was the worst case scenario of two rockets on one wing tip. To get a clear
understanding of the aircraft’s stability it is important to analyze stability in the longitudinal and
lateral domains. The longitudinal domain refers to the stability of the aircraft about the axis of
pitch. Lateral stability refers to the stability of the aircraft about the yaw and roll axis.
Stability modes in the longitudinal domain are the phugoid and short period and stability modes
in the lateral domain are roll subsidence, dutch roll and spiral divergence. Stability derivatives
represent an incremental change in a force or moment acting on the aircraft to a corresponding
change in any of the following variables: velocity, angle of attack, side slip angle, bank angle,
pitch angle, pitch rate, roll rate and yaw rate. Because aircraft dynamics is fairly complex, it is
necessary that the equations of motions are linearized to assess stability.
The non dimensional stability derivatives outputted from AVL were dimensionalized in
MATLAB to analyze dimensional stability for different modes in the longitudinal and lateral
directions. Matrix methods were used to solve the set of differential equations to obtain the
stability of the aircraft. The aircraft is modeled as a dynamic system where the system receives
input in the form of control surface deflections implemented by the pilot. Equation 15 shows the
longitudinal equations of motion. The plant that describes this system is represented by Equation
16.
0 − cos
= + − sin
0
0 0 1 0
0 0 0
0 −
=
0 0
0 − 1 0
0 0 0 1
Equation 15: Equations of Motion in Matrix Form for Longitudinal Stability
=
Equation 16: Representation of the Dynamic System for Longitudinal Stability
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