1. AAE 556 Aeroelasticity Lecture 12
Flexural axis
Control effectiveness
Purdue Aeroelasticity

2. 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

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

4. 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

5. Step #1 Compute angular displacements
Purdue Aeroelasticity

6. 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

7. 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

8. 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

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

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

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

12. Lift expression algebra
Purdue Aeroelasticity

13. Aileron effectiveness measured as aileron lift effectiveness
Purdue Aeroelasticity

14. The reversal dynamic pressure solution
Purdue Aeroelasticity

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

16. 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

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