1. The Optimization of the Flapping Wings for a Micro Air Vehicle (MAV)
29 November, 2018
Hugo Peters

2. Micro Air Vehicles Applications Appearance Espionage Observation
Entertainment
University of Notre Dame
DelFly Micro
29 November, 2018

3. Micro Air Vehicles (cont.)
Atalanta project
- Flapping wings
- Biologically inspired
Resonating ring structure
Flapping wings
- Hovering
- Scaling down
- Robustness
Flapping wings:
Hovering: fixed wings need a speed to stay aloft. Insects are able to hover
Scaling down: there are very small insects using flapping wings. Energy scales favorable with scaling down by using flapping wings.
Robustness: It is not a problem if this mav hits the wall a few times other MAVs would be broken
29 November, 2018

4. Main question Wing performance Main question: Expectations
For which wing planform and for what wing kinematics
is the overall performance of a flapping wing optimal?
29 November, 2018

5. Contents Introduction Model building Wing performance
Wing optimization
Recommendations
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

6. Kinematics Hovering flying state Horizontal stroke plane
Symmetric flapping behaviour
Downstroke
Upstroke
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

7. Kinematics (cont.) Main sweeping motion Heaving motion Pitching motion
Downstroke
Main sweeping motion
phi:
Heaving motion
theta:
Pitching motion
eta: m z Á ( t ) = m s i n 2 f Á
Upstroke y x ( t ) = 9
eta_m erin tekenetn
Sinus figuren toevoegen om de phase difference duidelijk te maken
Simulatie movie later ( t ) = m s i n 2 f +
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

8. Aerodynamics Aerodynamics loads Aerodynamic complex phenomena
Requirements aerodynamic model:
- Include complex phenomena
- Limited computational time
Movies automathisch laten starten en loopen zodat ze doorgaan
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

9. Aerodynamic model Semi-empirical quasi-steady model Limitation
Loads on geometric centre
Two-dimensional
Limitation
Based on empirical data
Insect related
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

10. Model variables 2 6 : 3 H z Kinematics Á ( t ) = s i n 2 ¼ f µ ( t ) =
- Sweeping angle:
- Heaving angle:
Pitching angle: Á ( t ) = m s i n 2 f ( t ) = ( t ) = m s i n 2 f + 2 5 m 8 9
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

11. Model variables (cont.)= : 5 1 9 m
Planform
- Chord length r c ( r ) : 1 c ( r ) 2 5
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12. Wing strip performance1 F l i f t
Average lift force
Required power:
Ratio between average lift force and required power
Performance total wing: summation r 5 5 1 F d r a g ; 5 P i = M _ Á P 5 = ( F d r a g ; ) _ Á _ Á
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

13. Flapping wing
29 November, 2018

14. Performance visualization[ ] [ ]
Fifth strip: [ ]
Ratio,
Required power,
Average lift force, F l i f t ; 5 = P P 5 F l i f t ; 5
Meer stripjes laten zien
Een pagina toevoegen met alleen maar resultaten zodat mensen de verschillen tussen de stripjes kunnen zien.
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

15. 29 November, 2018

16. Conclusions performance
Influence first strips is small
Not sensitive w.r.t. variables
Maximum average lift force:
- Pitching amplitude decreases towards the wingtip
- Chord length is maximum
Required power is minimized for high pitching amplitude
Best ratio: pitching amplitude increases towards the wingtip [ ]
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

17. Wing strip optimizationm P :
Optimization problem:
Lagrange formulation:
Minimize P : F l i f t ;
but: F l i f t ; c ( r )
Heel snel doorheen gaan L ( x ; ) = P + F l i f t
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

18. Stationary point f : = First order information = @ L = = @ P ´ ¡ ¹ F =x =
First order information d f x = @ L = = @ P m F l i f t d f x = = @ P c ( r ) F l i f t x
Not sufficient waarschijnlijk weg.
Hierna moet ik presenteren wat de resultaten van de verschillende optimalizaties zijn bij beide formuleringen
Het blijft dat wanneer beide formuleringen gebruikt worden er verschillende planforms gevonden worden terwijl de performances hetzelfde zijn
Dit zorgt ervoor dat er gekeken moet worden naar second order informatie wat er nu eigenlijk aan de hand is = F l i f t ;
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

19. Minimize required power
Optimization:
Minimize P :
but: F l i f t ;
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20. Maximize average lift force
Optimization:
Maximize F l i f t
but: P
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21. Comparison First formulation Second formulation - Minimize power
Maximize lift
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22. 29 November, 2018

23. Constrained minimum f : ´ < Second order information2 f x
<
Second order information
Nature of stationary points
- Local minimum:
Valley: P : d 2 f x = @ 2 L x F l i f t ; d 2 f x
> c ( r ) x
Consequence:
Possible deviation around optima
Laatse plaatje misschien verwijderen
Het is dus helemaal niet gek dat er meerdere optimale punten gevonden worden omdat we te maken hebben met een valley 1 ; 2
> 1 = ; 2
>
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

24. Optimization results
Deze slide kan dus naar voren, voor de second order information
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

25. Control case Given planform Optimization: Comparison: F P · ¢ : 1 W !
(a) – (b):
(b) – (c):
Maximize F l i f t
but: P
Misschien dit veel korter doen als ik in tijdnood kom!
Dat kan zeker voorkomen gezien het huidige programma
Design variables:
Pitching amplitude of each strip : 1 W ! 2 m N : 1 W ! 4 6 m N
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

26. Optimization case (cont.)
Pitching amplitude
Monotonicity
Deze pagina kan misschien helemaal weg als er tijdnood is
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

27. Conclusions wing optimization
High differences in performance
Optimization problem is non-convex
- Different starting points
Performance of different planforms might be identical
Pitching amplitude:
- Low lift requirements: increase towards wing tip
- High lift requirements: decrease towards wing tip
Adjustment of pitching amplitude to control MAV f : x
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

28. Recommendations Experimental setup More advanced modelling technique
- Validate current model
- Test influence minor structural details
- Apply optimization strategy based on experiments
More advanced modelling technique
- Fully unsteady aerodynamic model
- Mechanical FEM model
- Higher computational costs
Model building – Wing performance – Wing optimization – Recommendations
29 November, 2018

29. “Aerodynamically, the bumble bee shouldn't be able
to fly, but the bumble bee doesn't know it
so it goes on flying anyway.”
(Mary Kay Ash)
29 November, 2018