# Comparison of Power Requirements: Flapping vs. Fixed Wing Vehicles

## Abstract

**:**

## 1. Introduction

## 2. Performance Relations

## 3. Flapping Wing Vehicles

#### 3.1. Modeling of Lift Characteristics of Flapping Wing Vehicles

**Q**is the vector of conservative variables times the Jacobian transformation,

**J**, and

**F**,

**G**, and

**H**are the conservative fluxes with respect to the ξ, η and ζ, directions.

#### 3.2. Modeling of Drag Characteristics of Flapping Wing Vehicles

- (1)
- Tilting of lift vector due to flapping the wings, resulting in the term ${\mathrm{cos}}^{2}{v}^{*}$.
- (2)
- Changes in the amount of the lift vector in the course of the flapping cycle, resulting in the term ${\Delta}_{av}^{2}$.

#### 3.3. Power Requirements of Flapping Wing Vehicles

## 4. Fixed Wing Vehicles

## 5. Comparison of Power Required by Flapping and Fixed Wing Vehicles

## 6. Conclusions

## Conflicts of Interest

## Nomenclature

$b$ | wing span |

${C}_{D}$ | drag coefficient |

${C}_{L}$ | lift coefficient |

$D$ | drag |

$g$ | acceleration due to gravity |

$k$, ${k}_{flap}$ | lift dependent drag factor |

$L$ | lift |

$m$ | mass |

$P$ | power |

$S$ | reference area |

$t$ | time |

$V$ | speed |

${V}^{*}$ | minimum-drag speed |

$\overline{V}$ | non-dimensional speed, $\overline{V}=V/{V}^{*}$ |

${\rm A}$ | aspect ratio, ${\rm A}={b}^{2}/S$ |

$\nu $ | tilt angle of lift vector |

${\eta}_{prop}$ | propeller efficiency |

$\rho $ | air density |

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**Figure 2.**Wing geometry and generated mesh. (

**a**) Wing planform and wing profile at zero flapping angle; (

**b**) Wing at 45.0° flapping angle.

**Figure 4.**Drag polar showing relation between drag coefficient and lift coefficient acting in vertical direction.

**Figure 6.**Propeller efficiency for a light aircraft (reproduced from [24], Piper Cherokee Arrow PA-28R).

**Figure 7.**Propeller efficiency for an ultralight vehicle (reproduced in part from [25]).

**Figure 8.**Propeller efficiency of a small-scale propeller (reproduced in part from [26], propeller diameter: 0.2286 m).

**Figure 9.**Propeller efficiency of a small-scale propeller (reproduced in part from [26], propeller diameter: 0.2286 m).

© 2016 by the author; 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/).

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**MDPI and ACS Style**

Sachs, G.
Comparison of Power Requirements: Flapping vs. Fixed Wing Vehicles. *Aerospace* **2016**, *3*, 31.
https://doi.org/10.3390/aerospace3040031

**AMA Style**

Sachs G.
Comparison of Power Requirements: Flapping vs. Fixed Wing Vehicles. *Aerospace*. 2016; 3(4):31.
https://doi.org/10.3390/aerospace3040031

**Chicago/Turabian Style**

Sachs, Gottfried.
2016. "Comparison of Power Requirements: Flapping vs. Fixed Wing Vehicles" *Aerospace* 3, no. 4: 31.
https://doi.org/10.3390/aerospace3040031