## Tesi etd-05122010-103814 |

Thesis type

Tesi di dottorato di ricerca

Author

RIZZO, EMANUELE

URN

etd-05122010-103814

Title

Optimization methods applied to the preliminary design of innovative, non conventional aircraft configurations

Settore scientifico disciplinare

ING-IND/04

Corso di studi

INGEGNERIA AEROSPAZIALE

Commissione

**tutor**Prof. Frediani, Aldo

Parole chiave

- SQP
- Optimization
- PrandtlPlane
- smoothing technique
- non conventional configurations
- Mads
- direct search
- induced drag
- aerodynamics

Data inizio appello

07/12/2007;

Consultabilità

parziale

Data di rilascio

07/12/2047

Riassunto analitico

The present work takes origin from studies carried out at the Department of<br>Aerospace Engineering of University of Pisa on innovative aircraft configurations.<br>In 1924 the German scientist and father of modern aerodynamics Prof. Ludwing<br>Prandtl demonstrated the existence of a wing system producing the minimum<br>induced drag, and he called it Best Wing System (BWS). This wing system is made<br>of four wings connected together at their tips so that it looks like a box in a frontal<br>view. The condition of minimum induced drag found by Prandtl states that the two<br>horizontal wings must have the same lift distribution whereas the vertical wings, or<br>bulkheads, must carry a butterfly shaped lift distribution. The induced drag of this<br>system is the lowest among all possible wings carrying the same total lift with a<br>given wingspan, and the efficiency increases as the vertical gap to wingspan ratio<br>( h b ) does. The Prandtl’s calculations were based on an approximated method<br>predicting an induced drag of the BWS as the non-dimensional gap h b! " that<br>is 0.16 times the reference monoplane induced drag. This is in contradiction with<br>the fact that when the two equally loaded horizontal wings are at infinite distance,<br>they can be treated as isolated, therefore they have half of the induced drag of the<br>equivalent monoplane.<br>In 1999 Prof. Aldo Frediani at University of Pisa gave a new demonstration based<br>on more accurate calculations. He obtained the same results as Prandtl in the<br>range of low values of h b , but now the asymptote is, according with theory, at 0.5.<br>At the same time, he started the translation into an engineering product of the<br>mathematical intuition of Prandtl and he called this aircraft PrandtlPlane in his<br>honor.<br>The PrandtlPlane is, hence, a new aircraft concept, based on the general aim to<br>reduce induced drag. Besides, this configuration has showed potential benefits in<br>different aircraft categories: from Very Large Aircraft (VLA) to small ULM airplanes.<br>The unconventional nature of this aircraft gives rise to new design challenges<br>mainly due to a lack of experience and of statistical data; the space of solutions is,<br>therefore, unexplored. For this reason a solution satisfying different conflicting<br>requirements such as wings with the same lift, static stability of flight and trim<br>condition in every point of the flight envelope may be hard to find.<br>The problem of finding the PrandtlPlane wing planform can be formulated in terms<br>of optimization, which is to find the geometric parameters defining the wings such<br>that the drag is minimized and the constraints are satisfied. Constraints involve the<br>equilibrium and the static stability during cruise and landing, maximum speed stall,<br>geometrical constraints, and so on. Boundaries on the variables are defined as<br>well: minimum/maximum swept angles, minimum/maximum dihedral angles,<br>minimum/maximum elevator and flaps deflections, and so on.<br>An overview of the main methods and algorithms for the search of minima of<br>unconstrained and constrained optimization problems is presented. Moreover, an<br>algorithm based on a derivative free method (MADS) for the search of minima of<br>unconstrained problems and its extension to constrained problems are presented.<br>An algorithm for the search of global minima is presented and it is tested on<br>benchmarking problems.<br>Finally, these methods are extensively applied to find solutions of a ULM version of<br>the PrandtlPlane aircraft and a flying model coming from the optimizer is<br>manufactured and tested.

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