# Leading-Edge Vortex Lift (LEVL) Sample Probe for Venusian Atmosphere

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory—Lift Equation

_{L}is the coefficient of lift, ρ is the fluid density, v

_{fwd}is the airspeed, and A is the planform area of the wing.

#### Intrinsic and Extrinsic Components

_{int}and C

_{ext}; that is, those attributable to the craft in question (mass, area, lift coefficient) and planetary or atmospheric characteristics (acceleration due to gravity, atmospheric density), respectively. There are therefore two equations of proportionality:

## 3. Materials and Methods

#### 3.1. Pre-Existing Data

_{int}to increase (pushing points to the right); removing nut material reduces the mass, causing C

_{int}to decrease (pushing points to the left). If the coefficient of lift, C

_{L}, is unaffected by these modifications (especially the modifications of the wing), it would be expected that these points should lie on a straight line. Visual inspection of the data confirmed by linear regression shows that, indeed, the data for N0–N3 and W0–W3 does lie on a line. Observing that data points W4 and W5 (Figure 1), the most heavily modified wing samples, do begin to deviate from this straight line should give pause for caution if the ultimate probe design deviates heavily from the conventional sycamore seed characteristics.

#### 3.2. Venusian Gravity and Atmospheric Density

^{2}.

#### 3.3. Sycamore Seed Drop Test

#### 3.4. Test Article 1

_{int}= 0.95 kg

^{0.5}/m) and ≈70× heavier. TA1 has a mass of 10.78 g, wingspan (measured from the centre of the seed) of 200 mm and maximum chord of 75 mm; the wing profile and photographs are shown (Figure 5 and Figure 6).

#### 3.5. Test Article 2

^{3}mm

^{2}, thus the intrinsic component, C

_{int}, is 0.87 kg

^{0.5}/m.

#### 3.6. Extrapolation to Venusian Atmosphere

_{ext}, at each altitude, h (this analysis ignores the variation in gravity with height since this is less than 3%). It is then possible to calculate a velocity scale factor Cv by taking the ratio of >C′

_{ext}to C

_{ext}(the latter calculated for the conditions on Earth at sea-level, i.e., the known conditions).

_{v}, and the time to fall from one height to another is a simple summation.

_{L}is constant.

## 4. Results

#### 4.1. Results of the Sycamore Seed Drop Test

#### 4.2. Results of the Test Article 1

#### 4.3. Results of the Test Article 2

#### 4.3.1. Phase 1: Release and Initial Fall (0 < t < 1.3 s)

#### 4.3.2. Phase 2: Release and Initial Fall (1.3 < t < 2.4 s)

#### 4.3.3. Phase 3: Stable Forward Rotation (2.4 < t < 5.6 s)

#### 4.3.4. Phase 4: Unstable Forward Rotation (5.6 < t < 15.7 s)

#### 4.4. Aggregate Data

#### 4.5. Extrapolation to Venusian Atmosphere

## 5. Discussion

## 6. Conclusions

^{2}or a wingspan of 1.6 m and chord of 700 mm. In length terms, TA2 is a third of the way there! An oblate spheroidal shell with major-axis 200 mm and minor-axis 80 mm will accommodate the payload and allow space for “plumbing”.

## 7. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Krishnamoorthy, S.; Martire, L.; Bowman, D.; Komjathy, A.; Cutts, J.A.; Pauken, M.T.; Garcia, R.; Mimoun, D.; Lai, V.H.; Jackson, J.M. Advances towards Balloon-Based Seismology on Venus; Sandia National Lab. (SNL-NM): Albuquerque, NM, USA, 2019. [Google Scholar]
- Babu, K.M.K.; Pant, R.S. A review of Lighter-than-Air systems for exploring the atmosphere of Venus. Prog. Aerosp. Sci.
**2020**, 112, 100587. [Google Scholar] [CrossRef] - Hein, A.M.; Lingam, M.; Eubanks, T.M.; Hibberd, A.; Fries, D.; Blase, W.P. A precursor Balloon mission for Venusian astrobiology. Astrophys. J. Lett.
**2020**, 903, L36. [Google Scholar] [CrossRef] - Hall, J.L.; Pauken, M.; Schutte, A.; Krishnamoorthy, S.; Aiazzi, C.; Izraelevitz, J.; Lachenmeier, T.; Turner, C. Prototype Development of a Variable Altitude Venus Aerobot. In Proceedings of the AIAA Aviation 2021 Forum, Virtual, 2–6 August 2021; p. 2696. [Google Scholar]
- Arredondo, A.; Hodges, A.; Abrahams, J.N.H.; Bedford, C.C.; Boatwright, B.D.; Buz, J.; Cantrall, C.; Clark, J.; Erwin, A.; Krishnamoorthy, S.; et al. VALENTInE: A Concept for a New Frontiers–Class Long-duration In Situ Balloon-based Aerobot Mission to Venus. Planet. Sci. J.
**2022**, 3, 152. [Google Scholar] [CrossRef] - Seager, S.; Petkowski, J.J.; Carr, C.E.; Grinspoon, D.; Ehlmann, B.; Saikia, S.J.; Agrawal, R.; Buchanan, W.; Weber, M.U.; French, R. Venus Life Finder Mission Study. arXiv
**2021**, arXiv:2112.05153. [Google Scholar] - French, R.; Mandy, C.; Hunter, R.; Mosleh, E.; Sinclair, D.; Beck, P.; Seager, S.; Petkowski, J.J.; Carr, C.E.; Grinspoon, D.H.; et al. Rocket Lab Mission to Venus. Aerospace
**2022**, 445, in press. [Google Scholar] [CrossRef] - Grzebyk, T.; Szyszka, P.; Dziuban, J. Identification of a gas composition based on an optical spectrum of plasma generated in MEMS ion spectrometer. In Proceedings of the 2021 IEEE 20th International Conference on Micro and Nanotechnology for Power Generation and Energy Conversion Applications (PowerMEMS), Virtual, 6–8 December 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 148–151. [Google Scholar]
- Grzebyk, T.; Bigos, M.; Górecka-Drzazga, A.; Dziuban, J.A.; Hasan, D.; Lee, C. Mems Ion Sources For Spectroscopic Identification Of Gaseous And Liquid Samples. In Proceedings of the 2019 19th International Conference on Micro and Nanotechnology for Power Generation and Energy Conversion Applications (PowerMEMS), Krakow, Poland, 2–6 December 2019; IEEE: Piscataway, NJ, USA, 2019; pp. 1–3. [Google Scholar]
- Desenfans, P. Aerodynamics of the Maple Seed; Aircraft Design and Systems Group (AERO), Department of Automotive: Hamburg, Germany, 2019. [Google Scholar]
- Lentink, D.; Dickson, W.B.; Van Leeuwen, J.L.; Dickinson, M.H. Leading-edge vortices elevate lift of autorotating plant seeds. Science
**2009**, 324, 1438–1440. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Anderson, J.D. Introduction to Flight; McGraw-Hill Education: New York, NY, USA, 2015; pp. 294–298. [Google Scholar]
- Varshney, K.; Chang, S.; Wang, Z.J. The kinematics of falling maple seeds and the initial transition to a helical motion. Nonlinearity
**2011**, 25, C1. [Google Scholar] [CrossRef] [Green Version] - Lebonnois, S.; Schubert, G. The deep atmosphere of Venus and the possible role of density-driven separation of CO
_{2}and N_{2}. Nat. Geosci.**2017**, 10, 473–477. [Google Scholar] [CrossRef] [Green Version] - Haque, A.M.; Bell, A.; Morgan, C.T.; Crossley, M.; Swar, K.; Shadbolt, L.; Staab, D.; Garbayo, A. Development of an Additive Manufactured Mass, Volume and Cost Optimised Ti-6AL-4V Fuel Tank for Microsatellite Propulsion Systems MiniTANK. In Proceedings of the 36th International Electric Propulsion Conference, University of Vienna, Vienna, Austria, 15–20 September 2019. [Google Scholar]
- Wu, Z.; Narra, S.P.; Rollett, A. Exploring the fabrication limits of thin-wall structures in a laser powder bed fusion process. Int. J. Adv. Manuf. Technol.
**2020**, 110, 191–207. [Google Scholar] [CrossRef]

**Figure 1.**Most heavily modified seeds. Profiles of wing-cut samples 4 and 5 (herein labelled W4 and W5). Reprinted/adapted with permission from Ref. [13]. © IOP Publishing Ltd. and London Mathematical Society 2011. Reproduced with permission. All rights reserved.

**Figure 2.**Sycamore seed results. Terminal velocity, v

_{t}, is plotted as a function of intrinsic component,

**C**. Actual data points are shown as well as linear regression line covering data for samples N0–N3 and W0–W3.

_{int}**Figure 3.**Venusian atmosphere. Atmospheric density (blue solid line) is plotted against the left-hand scale; atmospheric temperature (orange dashed line) is plotted against the right-hand scale. The approximate heights of the bottom (labelled VB, green) and top (labelled VT, red) of the cloud layer are indicated by vertical lines.

**Figure 6.**Photograph of TA1. The probe head has holes which would be used for sample collection in large probe design.

**Figure 9.**Cross-section through printed “seed” showing location of IMU; the seed OD is 146 mm and the IMU dimensions (hatched) are 60 × 24 × 23 mm (deep).

**Figure 14.**Sycamore seed data. Authors’ own data (orange dashed line) plotted alongside Varshney 2012 data (blue solid line). Note that the authors’ data uses average falling speed, including transition, whereas the Varshney 2012 data is for terminal velocity. Varshney 2012 data reprinted/adapted with permission from Ref. [13]. © IOP Publishing Ltd. and London Mathematical Society 2011. Reproduced with permission. All rights reserved.

**Figure 17.**TA2 linear acceleration and rotation rate for 0 < t < 2.5 s. Note in particular the change in sign of rotX and rotZ between t = 1.5 s and t > 1.6 s.

**Figure 22.**Velocity against intrinsic component for Varshney 2012 data, the author’s own sycamore seed data, TA1 and TA2. Varshney 2012 data reprinted/adapted with permission from Ref. [13]. © IOP Publishing Ltd. and London Mathematical Society 2011. Reproduced with permission. All rights reserved.

**Table 1.**Properties of falling seeds. Table lists mass and area of seeds in various states of modification of nut and wingplus the resulting terminal velocity. Reprinted/adapted with permission from Ref. [13]. © IOP Publishing Ltd. and London Mathematical Society 2011. Reproduced with permission. All rights reserved.

Modification | ID | Mass, m (mg) | Area, A (mm^{2}) | Terminal Velocity, v_{t} (m/s) |
---|---|---|---|---|

W0 | 170.6 | 612.8 | 0.94 | |

Wing | W1 | 166.1 | 503.6 | 1.04 |

Wing | W2 | 158.6 | 344.8 | 1.00 |

Wing | W3 | 154.2 | 287.4 | 1.11 |

Wing | W4 | 149.4 | 202.0 | 2.95 |

Wing | W5 | 146.4 | 191.6 | 4.30 |

N0 | 195.8 | 546.1 | 1.18 | |

Nut | N1 | 162.9 | 528.5 | 0.92 |

Nut | N2 | 127.4 | 504.1 | 0.96 |

Nut | N3 | 92.2 | 486.9 | 0.88 |

**Table 2.**Sycamore seed results. Mass, time to fall 2 m, average speed falling 2 m, surface area and intrinsic component. ID denotes the order in which the seed where dropped.

ID | Mass, m (mg) | Fall Time, t (s) | Average Speed, $\stackrel{-}{\mathrm{v}}$ (m/s) | Area (mm^{2}) | Intrinsic Component, C (kg_{int}^{0.5}/m) |
---|---|---|---|---|---|

25 | 150 | 1.35 | 1.48 | 610.0 | 0.50 |

22 | 159 | 1.65 | 1.21 | 635.8 | 0.50 |

20 | 173 | 1.80 | 1.11 | 656.2 | 0.51 |

18 | 121 | 2.05 | 0.98 | 469.8 | 0.51 |

16 | 58 | 2.40 | 0.83 | 354.6 | 0.40 |

14 | 85 | 1.70 | 1.18 | 231.3 | 0.61 |

13 | 153 | 1.80 | 1.11 | 554.5 | 0.53 |

11 | 111 | 1.45 | 1.38 | 402.9 | 0.52 |

9 | 160 | 1.30 | 1.54 | 626.1 | 0.51 |

7 | 176 | 1.50 | 1.33 | 574.0 | 0.55 |

5 | 179 | 1.40 | 1.43 | 641.6 | 0.53 |

3 | 154 | 1.30 | 1.54 | 538.7 | 0.53 |

1 | 144 | 1.65 | 1.21 | 535.1 | 0.52 |

0 | 52 | 2.25 | 0.89 | 259.5 | 0.45 |

24 | 59 | 1.55 | 1.29 | 183.2 | 0.57 |

23 | 219 | 1.70 | 1.18 | 619.5 | 0.59 |

21 | 66 | 2.45 | 0.82 | 351.4 | 0.43 |

19 | 147 | 1.60 | 1.25 | 600.7 | 0.49 |

17 | 164 | 1.80 | 1.11 | 611.0 | 0.52 |

15 | 175 | 1.60 | 1.25 | 632.0 | 0.53 |

12 | 107 | 2.10 | 0.95 | 443.5 | 0.49 |

10 | 185 | 2.00 | 1.00 | 574.0 | 0.57 |

8 | 185 | 1.70 | 1.18 | 498.4 | 0.61 |

6 | 137 | 1.95 | 1.03 | 508.6 | 0.52 |

4 | 56 | 2.30 | 0.87 | 325.0 | 0.42 |

2 | 78 | 2.20 | 0.91 | 389.3 | 0.45 |

Earth acceleration under gravity, gₑ | 9.81 m/s^{2} |

Density of atmosphere at ESL, ρ_{ESL} | 1.225 kg/m^{3} |

Hence extrinsic component at ESL, C_{ext} | 0.288 kg^{0.5}/m |

Assumed terminal velocity of probe at ESL | 2 m/s |

Venusian acceleration under gravity, gᵥ | 8.87 m/s^{2} |

Height of top of Venusian cloud deck, VT | 70 km |

Height of bottom of Venusian cloud deck, VB | 48 km |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Isaac, C.; Jones, N.
Leading-Edge Vortex Lift (LEVL) Sample Probe for Venusian Atmosphere. *Aerospace* **2022**, *9*, 471.
https://doi.org/10.3390/aerospace9090471

**AMA Style**

Isaac C, Jones N.
Leading-Edge Vortex Lift (LEVL) Sample Probe for Venusian Atmosphere. *Aerospace*. 2022; 9(9):471.
https://doi.org/10.3390/aerospace9090471

**Chicago/Turabian Style**

Isaac, Christopher, and Nick Jones.
2022. "Leading-Edge Vortex Lift (LEVL) Sample Probe for Venusian Atmosphere" *Aerospace* 9, no. 9: 471.
https://doi.org/10.3390/aerospace9090471