AAE 556 Aeroelasticity Lecture 6-Control effectiveness Purdue Aeroelasticity

Purdue Aeroelasticity Today’s goals Review what we have done with the 2 DOF model and draw some conclusions Begin the study of control effectiveness Purdue Aeroelasticity

Purdue Aeroelasticity Reading review Sections 2.1-2.18 Some of these sections are painfully worked example problems – work through them to understand principles discussed in class Skip 2.19 for now (next week) Read 2.20, 2.20.1 and 2.20.2 Purdue Aeroelasticity

Summary-Develop 2 DOF segmented aeroelastic finite wing model Torsional springs fuselage wing tip wing root Torsional degrees of freedom Purdue Aeroelasticity

Purdue Aeroelasticity Lift re-distribution due to aeroelasticity Wing sections support ½ the total W Observation - Outer wing panel carries more of the total load than the inner panel as q increases Purdue Aeroelasticity

The aeroelastic stiffness matrix determinant is a function of q The determinant is where When dynamic pressure increases, the determinant D tends to zero – divergence occurs Purdue Aeroelasticity

Twist deformation vs. dynamic pressure parameter Unstable q region panel twist, qi/ao divergence Outboard panel (2) determinant D is zero Purdue Aeroelasticity

How do we determine divergence for an MDOF system? The general form of the aeroelastic static equilibrium equations is n degrees of freedom Perturb the system by an amount Euler question – “Is there an equilibrium solution to the following relationship?” Purdue Aeroelasticity

Purdue Aeroelasticity Static stability The static stability test reduces to the existence of a homogeneous matrix equation that must hold if the system is neutrally stable ? Purdue Aeroelasticity

Purdue Aeroelasticity Linear algebra says... only if … or This nth order determinant is called the stability determinant or the characteristic equation Purdue Aeroelasticity

Our next goal control effectiveness Demonstrate the aeroelastic effect of deflecting aileron surfaces to increase lift or rolling moment Examine the ability of an aileron or elevator to produce a change in lift, pitching moment or rolling moment Reading – Sections 2.20-2.20.2 Purdue Aeroelasticity

Purdue Aeroelasticity Setting the stage Many of the uncertified minimum ultralights, and perhaps some of the certificated aircraft, have low torsional wing rigidity. This will not only make the ailerons increasingly ineffective with speed (and prone to flutter), but will also place very low limits on g loads. http://www.auf.asn.au/groundschool/flutter.html#flutter Purdue Aeroelasticity

Purdue Aeroelasticity The ability of an aileron or elevator to produce a change in lift, pitching moment or rolling moment is changed by aeroelastic interaction aileron deflection Purdue Aeroelasticity

Herman Glauert’s estimators for CLd and CMACd The flap-to-chord ratio is Purdue Aeroelasticity

1 DOF idealized model – no camber Sum moments about the shear center Linear problem (what does that mean?) e Remember Purdue Aeroelasticity

Solve for the twist angle due only to aileron deflection d Lift Purdue Aeroelasticity

The aeroelastic lift due to deflection Compare answer to the lift computed ignoring aeroelastic interaction Purdue Aeroelasticity

One definition for the reversal condition Is this possible? We usually use an aileron to produce a rolling moment, not just lift. What is the dynamic pressure to make the lift or rolling moment zero even if we move the aileron? Purdue Aeroelasticity

How do I make the numerator term in the lift expression equal to zero? L=0, reversal L=infinity, divergence Purdue Aeroelasticity

Solve for the q at the reversal condition numerator=0 or Why the minus sign? Purdue Aeroelasticity

Purdue Aeroelasticity Summary Control surfaces generate less lift because the control deflection creates a nose-down pitching moment as it generates lift. At a special dynamic pressure (a combination of airspeed and altitude) the deflection of an aileron creates more downward lift due to nose-down deflection than upward lift Purdue Aeroelasticity