AAE 556 Aeroelasticity Lecture 12 Flexural axis Control effectiveness Purdue Aeroelasticity

Flexural axis (FA) concept an attempt to explain aeroelastic effects FA Definition - a line (locus of points) along which the streamwise (or chordwise) angle of attack does not change when a discrete load is applied there (and the air is off). L plus yo xo minus upward load Purdue Aeroelasticity

What is the difference between flexural axis and elastic axis? The air is off flexural axis b x upward load y Purdue Aeroelasticity

Purdue Aeroelasticity Locate the flexural axis by choosing an arbirary y position and poking around the wing in the x-direction yo xo Purdue Aeroelasticity

Step #1 Compute angular displacements Purdue Aeroelasticity

Use flexural axis definition to solve for the x,y coordinates The flexural axis location is always forward of the elastic axis if the wing is swept back. Increased sweepback rotates the flexural axis forward and increases the distance between aero load and the flexural axis. The red dot is the position of the resultant lift force. The dashed green line is the flexural axis. The dashed green line is the reference for wing sweep. Purdue Aeroelasticity

Purdue Aeroelasticity Example calculation dependence of flexural axis angle on stiffness ratio – notice that when the bending stiffness is infinite then the flex axis and the elastic axis are identical Flexural axis angle in degrees Wing sweep angle in degrees Purdue Aeroelasticity

Purdue Aeroelasticity How much wing sweep does it take to exactly place the flexural axis on the aero load position at y = b/2 and x = -e? Purdue Aeroelasticity

Switch gears - Control effectiveness rigid wing/springs model aileron Purdue Aeroelasticity

Purdue Aeroelasticity Invert the aeroelastic stiffness matrix Then solve for the two deflections Purdue Aeroelasticity

Swept wing lift due to full-span aileron deflection Purdue Aeroelasticity

Lift expression algebra Purdue Aeroelasticity

Aileron effectiveness measured as aileron lift effectiveness Purdue Aeroelasticity

The reversal dynamic pressure solution Purdue Aeroelasticity

Purdue Aeroelasticity Example - effects of sweep on aileron effectiveness unswept wing divergence at 250 psf. (qo) Reversal at 150 psf. Purdue Aeroelasticity

Summary-swept wing control effectiveness wing sweep changes the divergence dynamic pressure and lift effectiveness sweepback stabilizing - slight sweep only Sweep forward is aeroelastically destabilizing sweepback reduces lift effectiveness and control effectiveness Sweep forward increases lift effectiveness and control effectiveness Purdue Aeroelasticity

Purdue Aeroelasticity Homework for next week f1 f2 W K1 K2 Purdue Aeroelasticity