# Optimization of a Human-Powered Aircraft Using Fluid–Structure Interaction Simulations

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Daedalus Models

#### 2.1. CAD Model

#### 2.2. AVL Model

#### 2.3. Two-Dimensional Computational Fluid Dynamics (CFD) Model

#### 2.4. Three-Dimensional CFD Model

## 3. The Daedalus Results

#### 3.1. Results of Two-Dimensional CFD

#### 3.2. Results of AVL

#### 3.3. Results of Three-Dimensional CFD

## 4. Optimization: Method and Cases

#### 4.1. Wing Geometry

#### 4.2. AVL

#### 4.3. Structural Optimizer

#### 4.4. Decision Blocks

#### 4.5. Cases

## 5. Fluid–Structure Interaction (FSI) Simulation

## 6. Sensitivity Study

#### 6.1. Study 1: Dihedral Angle

#### 6.2. Study 2: Wing Span

#### 6.3. Studies 3 and 4: Tip Chord Length and Taper Ratio

#### 6.4. Study 5: Twist Angle

## 7. Optimization: Results

#### Complete Optimized Design

## 8. Final Test

## 9. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- McIntyre, J. Man’s Greatest Flight. AeroModeller. 1988. Available online: http://library.propdesigner.co.uk/daedalus.pdf (accessed on 1 May 2016).
- AVL (Athena Vortex Lattice). Available online: http://web.mit.edu/drela/Public/web/avl/ (accessed on 1 May 2016).
- Regulations and Conditions for the Kremer International Marathon Competition. Available online: http://aerosociety.com/About-Us/specgroups/Human-Powered/Kremer (accessed on 1 May 2016).
- Fazzolari, A.; Gauger, N.R.; Brezillon, J. Efficient aerodynamic shape optimization in MDO context. J. Comput. Appl. Math.
**2007**, 203, 548–560. [Google Scholar] [CrossRef] - Kenway, G.K.W.; Kennedy, G.J.; Martins, J.R.R.A. Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations. AIAA J.
**2014**, 52, 935–951. [Google Scholar] [CrossRef] - Tang, D.; Dowell, E.H. Experimental Aeroelastic Models Design and Wind Tunnel Testing for Correlation with New Theory. Aerospace
**2016**, 3, 12. [Google Scholar] [CrossRef] - Guo, S.; De Los Monteros, J.E.; Liu, Y. Gust Alleviation of a Large Aircraft with a Passive Twist Wingtip. Aerospace
**2015**, 2, 135–154. [Google Scholar] [CrossRef] - ASWING: Configuration Development System for Flexible Aircraft. Available online: http://web.mit.edu/drela/Public/web/aswing/ (accessed on 1 May 2016).
- Drela, M. Low-Reynolds-Number Airfoil Design for the MIT Daedalus Prototype: A Case Study. J. Aircr.
**1988**, 25, 724–732. [Google Scholar] [CrossRef] - Cruz, J.R.; Drela, M. Structural Design Conditions for Human Powered Aircraft. In Proceedings of the 21st OSTIV Conference, Wiener Neustadt, Austria, 1989.
- Katz, J.; Plotkin, A. Low-Speed Aerodynamics, 2nd ed.; Cambridge University Press: New York, NY, USA, 2001. [Google Scholar]
- XFOIL: Subsonic Airfoil Development System. Available online: http://web.mit.edu/drela/Public/web/xfoil/ (accessed on 1 May 2016).
- Hansen, T. Modeling the Performance of the Standard Cirrus Glider using Navier-Stokes CFD. Tech. Soar.
**2014**, 38, 5–14. [Google Scholar] - Morgado, J.; Vizinho, R.; Silvestre, M.A.R.; Páscoa, J.C. XFOIL vs. CFD performance predictions for high lift low Reynolds number airfoils. Aerosp. Sci. Technol.
**2016**, 52, 207–214. [Google Scholar] [CrossRef] - Drela, M. Aerodynamics of Human-Powered Flight. Annu. Rev. Fluid Mech.
**1990**, 22, 93–110. [Google Scholar] [CrossRef]

**Figure 6.**Laminar separation bubble [13].

**Figure 9.**Two-dimensional results of the airfoil FX63-137: (

**a**) lift coefficient versus angle of attack; (

**b**) drag coefficient versus angle of attack; (

**c**) drag polar; (

**d**) lift-to-drag ratio versus angle of attack.

**Figure 10.**Two-dimensional results of the airfoil FX63-137: (

**a**) pressure coefficient distribution at zero degrees angle of attack; (

**b**) comparison of turbulent kinetic energy (upper airfoil: computational fluid dynamics (CFD) without transition; lower airfoil: CFD with transition).

**Figure 12.**Transition from laminar to turbulent flow on the Daedalus visualized by the constrained streamlines and the turbulent kinetic energy.

**Figure 17.**Fluid–Structure Interaction (FSI) procedure: (

**a**) Initial geometry for AVL; (

**b**) deflection of the wing based on the initial forces from AVL; (

**c**) deflected geometry for AVL with linear variation of the deflection along the span; (

**d**) deflection of the wing based on the updated forces from AVL.

**Figure 19.**Sensitivity study: wing span. (

**a**) Drag; (

**b**) angle of attack; (

**c**) mass of the spar; (

**d**) maximal stress.

**Figure 21.**Sensitivity study: twist angle. (

**a**) Drag; (

**b**) angle of attack; (

**c**) mass of the spar; (

**d**) maximal stress.

**Figure 22.**Comparison of wing and fuselage (upper: Daedalus; lower: optimized dual-Human-Powered Aircraft (HPA)).

Name | Mass (kg) | ${\mathbf{x}}_{\mathit{CG}}$ (m) | ${\mathbf{y}}_{\mathit{CG}}$ (m) | ${\mathbf{z}}_{\mathit{CG}}$ (m) |
---|---|---|---|---|

Wing | 17.10 | 0 | 0 | 0.94 |

Fuselage | 1.91 | 0.76 | 0 | −0.85 |

Elevator | 0.52 | 5.33 | 0 | 0.31 |

Rudder | 0.52 | 6.10 | 0 | 0.26 |

Tail boom | 1.49 | 1.55 | 0 | 0 |

Propeller | 1.36 | −1.98 | 0 | 0 |

Gearbox | 0.91 | −0.91 | 0 | 0 |

Crank set | 1.36 | −0.91 | 0 | −1.52 |

Water | 5.44 | −0.06 | 0 | −1.68 |

Pilot | 74.84 | 0 | 0 | −1.22 |

Daedalus | 105.44 | 0.04 | 0 | −0.83 |

Property | MIT [15] | AVL Model | CFD Model |
---|---|---|---|

Flight Velocity (m/s) | 6.7 | 6.7 | 6.7 |

Gliding Drag (N) | 27 | 22.2 | 26.2 |

Induced (N) | 10.5 (35%) | 11.2 | − |

Profile (N) | 12.0 (40%) | 9.7 | − |

Parasite (N) | 4.5 (15%) | 1.3 | 2.5 |

Lift (N) | 1034.4 | 1034.4 | 1034.8 |

Propulsive Efficiency | 0.90 | 0.90 | 0.90 |

Pilot Power (W) | 201 | 165 | 195 |

AoA Aircraft (${}^{\circ}$) | − | 2.76 | 2.76 |

AoA Elevator (${}^{\circ}$) | − | −4.6 | −4.6 |

Calculation time | − | 9.94 s | 1 day |

Property | Lower Boundary | Upper Boundary | Step Size |
---|---|---|---|

$x/c$ | 0.33 | − | − |

$\Gamma \phantom{\rule{4pt}{0ex}}\left({}^{\circ}\right)$ | 6 | − | − |

b (m) | 15 | 40 | 0.25 |

${c}_{\mathrm{tip}}$ (m) | 0.35 | 0.5 | 0.01 |

λ | 0.25 | 1 | 0.01 |

$\theta \phantom{\rule{4pt}{0ex}}{(}^{\circ})$ | 0 | − | − |

Property | Single-Pilot | Dual-Pilot |
---|---|---|

${m}_{\mathrm{pilot}\left(\mathrm{s}\right)}$ (kg) | 56.4 | 56.4 + 50.2 |

${\rho}_{\mathrm{spar}}$ (kg/m${}^{3}$) | 1600 | 1600 |

${E}_{\mathrm{spar}}$ (GPa) | 200 | 200 |

$T{S}_{\mathrm{spar}}$ (MPa) | 1600 | 1600 |

$S{F}_{\mathrm{spar}}$ | 4 | 4 |

$MB{L}_{\mathrm{LW}}$ (MPa) | 1570 | 1570 |

$S{F}_{\mathrm{LW}}$ | 4 | 4 |

${d}_{\mathrm{LW}}$ (mm) | 18 | 25 |

Geometrical | Structural | ||
---|---|---|---|

b | 20 m | ${m}_{\mathrm{pilot}}$ | 56.4 kg |

${c}_{\mathrm{tip}}$ | 0.5 m | ${m}_{\mathrm{aircraft}}$ | 30.6 kg |

λ | 0.5 | ${\rho}_{\mathrm{spar}}$ | 1600 kg/m${}^{3}$ |

θ | 0 ${}^{\circ}$ | ${E}_{\mathrm{spar}}$ | 200 GPa |

Iteration | L (N) | ${\mathit{u}}_{\mathit{tip}}$ (m) | $\mathbf{\Gamma}\phantom{\rule{4pt}{0ex}}{(}^{\mathbf{\circ}})$ | ${\mathit{\sigma}}_{\mathit{max}}$ (MPa) | ${\mathit{\tau}}_{\mathit{max}}$ (MPa) |
---|---|---|---|---|---|

0 | 426.72 | 1.1720 | 6.6843 | 324.38 | 3.05 |

1 | 426.70 | 1.1694 | 6.6699 | 323.77 | 3.04 |

2 | 426.70 | 1.1694 | 6.6701 | 323.78 | 3.04 |

3 | 426.70 | 1.1694 | 6.6701 | 323.78 | 3.04 |

4 | 426.70 | 1.1694 | 6.6701 | 323.78 | 3.04 |

5 | 426.70 | 1.1694 | 6.6701 | 323.78 | 3.04 |

**Table 7.**Overview of the sensitivity studies. An asterisk * indicates the desired value during flight.

Property | Study 1 | Study 2 | Study 3 | Study 4 | Study 5 |
---|---|---|---|---|---|

Airfoil | DAE11 | DAE11 | DAE11 | DAE11 | DAE11 |

$x/c$ | 0.33 | 0.33 | 0.33 | 0.33 | 0.33 |

$\Gamma \phantom{\rule{4pt}{0ex}}{(}^{\circ})$ | 0–10 | 6* | 6* | 6* | 6* |

b (m) | 20 | 15–30 | 20 | 20 | 20 |

${c}_{\mathrm{tip}}$ (m) | 0.5 | 0.5 | 0.35–0.75 | 0.5 | 0.5 |

λ | 1 | 1 | 0.5 | 0.25–1 | 1 |

$\theta \phantom{\rule{4pt}{0ex}}{(}^{\circ})$ | 0 | 0 | 0 | 0 | 0–5 |

**Table 8.**Geometrical and structural data of optimal designs (upper table: single-pilot; lower table: dual-pilot). The line in bold indicates the design which requires the lowest power per pilot.

Single-Pilot | b | ${\mathit{c}}_{\mathit{tip}}$ | λ | Γ | ${\mathit{t}}_{\mathit{root}}$ | ${\mathit{t}}_{\mathit{tip}}$ | ${\mathit{m}}_{\mathit{spar}}$ | ${\mathit{\sigma}}_{\mathit{spar}}$ | ${\mathit{\sigma}}_{\mathit{LW}}$ | $\mathit{AoA}$ | D | $\mathit{P}/\mathit{pilot}$ |

Airfoil | (m) | (m) | − | (°) | (mm) | (mm) | (kg) | (MPa) | (MPa) | (°) | (N) | (W) |

DAE11 | 20.75 | 0.35 | 0.58 | 6 | 0.80 | 0.80 | 3.53 | 249 | 334 | 3.38 | 16.85 | 202 |

DAE21 | 21.00 | 0.35 | 0.58 | 6 | 0.81 | 0.81 | 3.31 | 298 | 367 | 3.11 | 15.58 | 187 |

DAE31 | 20.25 | 0.35 | 0.62 | 6 | 1.09 | 1.09 | 3.83 | 274 | 359 | 3.20 | 15.22 | 183 |

E395 | 22.00 | 0.35 | 0.64 | 6 | 1.00 | 1.00 | 4.18 | 273 | 388 | 2.21 | 14.18 | 170 |

E396 | 22.50 | 0.35 | 0.62 | 6 | 0.81 | 0.81 | 3.77 | 287 | 392 | 1.79 | 14.62 | 175 |

E397 | 22.75 | 0.35 | 0.63 | 6 | 0.80 | 0.80 | 3.89 | 277 | 391 | 1.92 | 14.92 | 179 |

E398 | 23.25 | 0.35 | 0.64 | 6 | 0.80 | 0.80 | 4.13 | 264 | 392 | 1.95 | 15.05 | 181 |

E399 | 23.50 | 0.35 | 0.66 | 6 | 0.80 | 0.80 | 4.30 | 252 | 391 | 2.00 | 15.44 | 185 |

FX63-137 | 23.50 | 0.35 | 0.60 | 6 | 0.80 | 0.80 | 4.18 | 264 | 392 | -0.49 | 14.65 | 176 |

FX76MP120 | 18.75 | 0.35 | 0.70 | 6 | 0.89 | 0.89 | 3.00 | 295 | 342 | 1.35 | 17.10 | 205 |

FX76MP140 | 19.50 | 0.35 | 0.70 | 6 | 0.80 | 0.80 | 3.28 | 250 | 329 | -2.22 | 17.15 | 206 |

L7769 | 20.25 | 0.35 | 0.58 | 6 | 0.98 | 0.98 | 3.52 | 285 | 355 | 7.00 | 16.93 | 203 |

Dual-Pilot | $\mathit{b}$ | ${\mathit{c}}_{\mathit{tip}}$ | λ | Γ | ${\mathit{t}}_{\mathit{root}}$ | ${\mathit{t}}_{\mathit{tip}}$ | ${\mathit{m}}_{\mathit{spar}}$ | ${\mathit{\sigma}}_{\mathit{spar}}$ | ${\mathit{\sigma}}_{\mathit{LW}}$ | $\mathit{AoA}$ | $\mathit{D}$ | $\mathit{P}/\mathit{pilot}$ |

Airfoil | (m) | (m) | − | (°) | (mm) | (mm) | (kg) | (MPa) | (MPa) | (°) | (N) | (W) |

DAE11 | 27.50 | 0.35 | 0.47 | 6 | 1.21 | 1.21 | 8.01 | 284 | 388 | 4.50 | 25.72 | 154 |

DAE21 | 27.75 | 0.35 | 0.46 | 6 | 1.62 | 1.62 | 9.94 | 255 | 392 | 4.27 | 24.15 | 145 |

DAE31 | 27.25 | 0.35 | 0.46 | 6 | 1.89 | 1.89 | 10.52 | 253 | 392 | 3.79 | 23.42 | 141 |

E395 | 28.75 | 0.35 | 0.46 | 6 | 1.65 | 1.65 | 10.94 | 239 | 388 | 2.88 | 22.47 | 135 |

E396 | 28.75 | 0.35 | 0.46 | 6 | 1.36 | 1.36 | 9.68 | 250 | 392 | 2.79 | 23.04 | 138 |

E397 | 28.50 | 0.35 | 0.48 | 6 | 1.32 | 1.32 | 9.38 | 253 | 392 | 3.27 | 23.35 | 140 |

E398 | 29.25 | 0.35 | 0.47 | 6 | 1.20 | 1.20 | 9.32 | 250 | 392 | 2.98 | 23.86 | 143 |

E399 | 28.75 | 0.35 | 0.46 | 6 | 0.90 | 0.90 | 7.33 | 284 | 392 | 2.86 | 24.26 | 146 |

FX63-137 | 29.50 | 0.35 | 0.42 | 6 | 1.03 | 1.03 | 8.38 | 265 | 392 | 0.12 | 23.35 | 140 |

FX76MP120 | 26.25 | 0.35 | 0.55 | 6 | 1.93 | 1.93 | 10.20 | 255 | 392 | 2.17 | 24.99 | 150 |

FX76MP140 | 27.00 | 0.35 | 0.57 | 6 | 1.46 | 1.46 | 9.22 | 258 | 392 | -1.17 | 24.75 | 149 |

L7769 | 27.25 | 0.35 | 0.43 | 6 | 1.64 | 1.64 | 9.45 | 266 | 391 | 7.49 | 26.72 | 160 |

Property | Daedalus | Optimized |
---|---|---|

Total Mass (kg) | 105.4 | 147.0 |

Flight Velocity (m/s) | 6.7 | 12 |

AoA Aircraft (${}^{\circ}$) | 2.76 | 1.30 |

Gliding Drag (N) | 26.2 | 32.3 |

Wing (N) | 23.67 | 22.76 |

Fuselage (N) | 1.05 | 4.24 |

Elevator (N) | 0.44 | 2.36 |

Rudder (N) | 0.53 | 1.60 |

Tail Boom (N) | 0.47 | 1.32 |

Lift (N) | 1034.8 | 1465.5 |

Propulsive Efficiency | 0.90 | 0.90 |

Total Power (W) | 195 | 430 |

Pilot Power (W) | 195 | 215 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vanderhoydonck, B.; Santo, G.; Vierendeels, J.; Degroote, J.
Optimization of a Human-Powered Aircraft Using Fluid–Structure Interaction Simulations. *Aerospace* **2016**, *3*, 26.
https://doi.org/10.3390/aerospace3030026

**AMA Style**

Vanderhoydonck B, Santo G, Vierendeels J, Degroote J.
Optimization of a Human-Powered Aircraft Using Fluid–Structure Interaction Simulations. *Aerospace*. 2016; 3(3):26.
https://doi.org/10.3390/aerospace3030026

**Chicago/Turabian Style**

Vanderhoydonck, Bob, Gilberto Santo, Jan Vierendeels, and Joris Degroote.
2016. "Optimization of a Human-Powered Aircraft Using Fluid–Structure Interaction Simulations" *Aerospace* 3, no. 3: 26.
https://doi.org/10.3390/aerospace3030026