# Wake-Tailplane Interaction of a Slingsby Firefly Aircraft

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## Abstract

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## 1. Introduction

## 2. Slingsby Tailplane Tests

#### 2.1. Tailplane Ground Measurements

#### 2.2. Tailplane Airborne Measurements

#### 2.3. Data Processing Error Analysis

_{o}= r = 3140 mm. Further, with respect to the x–z and y–z distance planes, the sub-angles θ

_{xz}and θ

_{yz}are defined by θ

_{xz}= tan

^{−1}(x/z) and θ

_{yz}= tan

^{−1}(y/z), given $\theta ={\mathrm{tan}}^{-1}\left(y/\sqrt{{x}^{2}+{y}^{2}}\right)$.

_{o}, can be estimated from the x–z and y–z radial components r

_{xz}, r

_{yz}such that:

_{o}, the error δr in measurement of the tailplane displacement is simply found from:

_{o}= 3140 mm, the rms displacement error in tailplane measurement is estimated to be δr = ±0.09 mm, equivalent to 2 mrad. It should be noted that for a fisheye lens, this error may vary across the FOV due to manufacturing limitations, particularly near the edge of the FOV. In this case, as the tailplane tip is away from the edge of the field, this error variation should be minimal.

_{sample}, based on the Nyquist criterion, using a fast Fourier transform (FFT), the resolution in frequency will be 2/f

_{sample}, equivalent to 1 pixel in the FFT frequency plane. Hence, with a camera frame rate of 50 Hz, the spectra resolution is estimated to be ±0.04 Hz.

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Tailplane view in-flight from GoPro camera system. Sub-window images indicate tailplane tip sub-window (201 pixels × 221 pixels), reference canopy rail (251 pixels × 101 pixels) and pitch attitude sub-window (910 pixels × 640 pixels).

**Figure 5.**Data processing approach to tailplane, canopy rail reference and pitch attitude estimation.

**Figure 9.**Time series displacement data from GoPro tailplane image sequence, taken from an initial wings level condition. Stall is estimated to be at 22 s.

Parameter | Value | Error | Notes |
---|---|---|---|

Pressure altitude (feet) | 6500 | ±30 | Standard pressure setting used |

Outside air temperature (°C) | 5 | ±0.5 | Based on aircraft temperature gauge |

Aircraft empty weight (kg) | 902 | ±20 | Based on weight schedule |

Pilot and fuel weight (kg) | 138 | ±10 | Based on fuel gauge error with 80 L of fuel at 0.72 kg/m^{3} and 80 kg pilot |

Aircraft stall speed (knots) | 58 | ±3 | Indicated airspeed reduced at 1 knot/s into the stall and buffet until full back stick |

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**MDPI and ACS Style**

Lawson, N.J.; Davies, S.G.; Khanal, B.; Hoff, R.I.
Wake-Tailplane Interaction of a Slingsby Firefly Aircraft. *Aerospace* **2022**, *9*, 787.
https://doi.org/10.3390/aerospace9120787

**AMA Style**

Lawson NJ, Davies SG, Khanal B, Hoff RI.
Wake-Tailplane Interaction of a Slingsby Firefly Aircraft. *Aerospace*. 2022; 9(12):787.
https://doi.org/10.3390/aerospace9120787

**Chicago/Turabian Style**

Lawson, Nicholas J., Simon G. Davies, Bidur Khanal, and Rein I. Hoff.
2022. "Wake-Tailplane Interaction of a Slingsby Firefly Aircraft" *Aerospace* 9, no. 12: 787.
https://doi.org/10.3390/aerospace9120787