The 2011 discovery that waterlily beetles (Galerucella nymphaeae) propel themselves by flapping-wing flight confined to the air–water interface left two linked open problems: the complete force budget of this two-dimensional flight — aerodynamic lift and thrust, surface-tension contact forces, viscous drag, buoyancy, and capillary–gravity wave drag — has never been measured directly on a living insect, and the idealization of legs as rigid smooth cylinders leaves the effects of leg compliance, contact-line pinning dynamics, and hairy tarsal microstructure unquantified; and the taxonomic breadth of wing-driven surface locomotion, a direction the source itself gestures toward, and — in the wider origin-of-flight debate to which that gesture connects — whether such surface-associated wing use can supply selection gradients sufficient to drive the evolution of the flight apparatus (the surface-skimming or water-up scenario for the origin of insect flight), which remains contested. A 2016 follow-up supplied the first quantitative biomechanical model, establishing surface-tension dominance at the model level, but direct measurement of the force suite during interfacial flight in any insect, quantification of the microstructural and compliance corrections, and resolution of the origin-of-flight debate all remain open.

Background

Interfacial flight (also called two-dimensional flight or surface skimming) is a locomotor mode in which a winged insect flaps its wings while its legs remain in permanent contact with a water surface, so that propulsion and support involve both aerodynamic and interfacial forces. Beyond the lift, thrust, and drag of ordinary (3D) flight, the insect experiences viscous drag on partly immersed legs, buoyancy, capillary surface-tension forces at the legs' contact lines (the curves where air, water, and the solid leg meet), and capillary–gravity wave drag — the resistance arising from the waves emitted by a body moving near the minimum phase speed of gravity–capillary waves. The relative sizes of these forces are conventionally summarized by the Reynolds number (ratio of inertial to viscous forces), Froude number (ratio of inertial to gravitational forces), and Weber number (ratio of inertial to surface-tension forces). Prakash and Kim documented this mode in adult waterlily beetles (Galerucella, about 5–6 mm body length) using 3000 frames-per-second video, finding speeds near 30 cm/s with two or four leg contact points and the ordering surface tension ≫ inertia > gravity > viscosity (arXiv:1110.3515). Their non-dimensional analysis rested on stated simplifications — a rigid body and legs, legs represented as smooth cylinders despite being clothed in microscopic hairs, and assumed rather than measured drag coefficients — and they noted the connection to a long-standing evolutionary hypothesis: surface-skimming stoneflies as an intermediate stage toward true flight (Marden and Kramer 1994), for which their beetles were the first evidence outside stoneflies; subsequent work documented skimming and rowing with wings and winglets in stoneflies and mayflies (Marden et al. 2000). The direct scientific successor, Mukundarajan, Bardon, Kim and Prakash (2016), built the first quantitative biomechanical model of interfacial flight in any insect: high-speed kinematics of Galerucella nymphaeae plus a Newtonian force balance combining aerodynamics, buoyancy, capillary–gravity wave drag (computed from low-Weber-number dipolar wave theory), and oscillatory surface-tension forces with the contact line pinned at the tarsal claws. That model showed that surface tension dominates the force landscape, that interfacial flight at beetle-typical speeds requires more wing thrust than airborne flight at the same speed, that trajectories can be chaotic, and that surface tension acts as an energy trap opposing take-off from the interface. Related measurement capability exists in neighboring systems — direct sensing of water-strider rowing forces with a bio-appropriating probe (Uesugi et al. 2023), thrust inferred from wave and jet momentum for honeybees propelled by hydrofoiling wetted wings on water (Roh and Gharib 2019, a mode the authors distinguish from skimming), traction measurements of Galerucella's underwater tarsal adhesion (Grohmann et al. 2022), and laboratory measurement of unsteady hydrodynamic resistance of oscillating floating bodies (Ho, Kumar and Harris 2026) — but no study has directly measured the force suite acting on an insect during flapping interfacial flight. On the evolutionary side, the origin of insect flight is debated between trees-down scenarios (directed aerial descent from plants) and water-up scenarios, in which protowings first served aquatic or surface functions such as respiration, steering, or surface propulsion before supporting weight in air; a 2013 exchange in Evolution over the reinterpretation of the earliest winged-insect trace fossil as a surface-skimming neopteran (Marden 2013 versus Benner, Knecht and Engel 2013) left the hypothesis contested, and the 2024 state-of-the-field review by Treidel, Deem, Salcedo, Dickinson and colleagues states that the initial function and selective pressures leading to wings and flight remain an area of active research that future phylogenomic, fossil, developmental, physiological, behavioral, and ecological work must disentangle (Alexander 2018; Treidel et al. 2024). Robotic demonstrations of interfacial flight at insect scale (Gao, Jung and Helbling 2024) make the force landscape an engineering concern as well.

Problem Statement

The problem has one overarching objective — establishing the mechanical and evolutionary viability of surface-associated (two-dimensional) wing use as a precursor to powered insect flight — and comprises three linked open questions. (1) Force budget by direct measurement: measure directly and simultaneously, on an insect performing sustained interfacial flight (flapping wings with legs in permanent water contact), the full suite of forces — aerodynamic lift and thrust, surface-tension contact forces at the leg contact lines, viscous drag, buoyancy, and capillary-gravity wave drag — over complete wingbeat cycles and across the natural range of speeds and two- versus four-leg contact modes, closing the balance against independently measured kinematics. (2) Microstructural and mechanical corrections: determine how leg compliance, the pinning and depinning dynamics of the contact line at the tarsal claws, and the hairy microstructure of real legs modify each force component relative to the rigid smooth-cylinder idealization underlying the existing model, and quantify the resulting corrections to the evaluated Reynolds-, Froude-, and Weber-number regimes and to the predicted thrust requirement and take-off threshold. (3) Evolutionary viability: determine the taxonomic and ecological breadth of wing-driven surface locomotion, relate morphology to the propensity for and performance of surface skimming, and establish whether surface-associated wing use can produce selection gradients sufficient to drive the morphological and neuromuscular changes of the flight apparatus — the water-up (surface-skimming) scenario for the origin of insect flight versus terrestrial alternatives.

Each of the three questions is independently resolvable, and an answer to any one of them establishes the corresponding part of the overarching objective without presupposing the others: resolving questions (1) and (2) establishes the mechanical strand without settling the evolutionary one, and progress on question (3) does not presuppose completion of the force measurements. Question (3) lies within the long-running, actively contested debate on the origin of insect flight; it is resolved by bounded comparative or evidential results — the documented taxa exhibiting wing-driven surface locomotion together with the morphology-performance relations inferred for them, or fossil and phylogenomic evidence bearing on the water-up scenario — and not by settling that debate.

References

  1. Manu Prakash and Donald Kim, "Flying in Two Dimensions", arXiv:1110.3515 (2011), https://arxiv.org/abs/1110.3515
  2. James H. Marden and Melissa G. Kramer, "Surface-Skimming Stoneflies: A Possible Intermediate Stage in Insect Flight Evolution", Science 266:427-430 (1994), doi:10.1126/science.266.5184.427, https://doi.org/10.1126/science.266.5184.427
  3. James H. Marden, Brigid C. O'Donnell, Michael A. Thomas and Jesse Y. Bye, "Surface-Skimming Stoneflies and Mayflies: The Taxonomic and Mechanical Diversity of Two-Dimensional Aerodynamic Locomotion", Physiological and Biochemical Zoology 73:751-764 (2000), doi:10.1086/318109, https://doi.org/10.1086/318109
  4. Haripriya Mukundarajan, Thibaut C. Bardon, Dong Hyun Kim and Manu Prakash, "Surface tension dominates insect flight on fluid interfaces", Journal of Experimental Biology 219:752-766 (2016), doi:10.1242/jeb.127829, https://doi.org/10.1242/jeb.127829
  5. Chris Roh and Morteza Gharib, "Honeybees use their wings for water surface locomotion", Proceedings of the National Academy of Sciences 116:24446-24451 (2019), doi:10.1073/pnas.1908857116, https://doi.org/10.1073/pnas.1908857116
  6. Constanze Grohmann, Anna-Lisa Cohrs and Stanislav N. Gorb, "Underwater Attachment of the Water-Lily Leaf Beetle Galerucella nymphaeae (Coleoptera, Chrysomelidae)", Biomimetics 7:26 (2022), doi:10.3390/biomimetics7010026, https://doi.org/10.3390/biomimetics7010026
  7. Hang Gao, Sunghwan Jung and E. Farrell Helbling, "High-speed interfacial flight of an insect-scale robot", 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 6006-6013 (2024), doi:10.1109/ICRA57147.2024.10611592, https://doi.org/10.1109/ICRA57147.2024.10611592
  8. Ian Ho, Ajay Harishankar Kumar and Daniel M. Harris, "Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies", arXiv:2606.12570 (2026), https://arxiv.org/abs/2606.12570
  9. Kaoru Uesugi, Hiroyuki Mayama and Keisuke Morishima, "Analysis of Rowing Force of the Water Strider Middle Leg by Direct Measurement Using a Bio-Appropriating Probe and by Indirect Measurement Using Image Analysis", Cyborg and Bionic Systems 4:0061 (2023), doi:10.34133/cbsystems.0061, https://doi.org/10.34133/cbsystems.0061
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  12. David E. Alexander, "A century and a half of research on the evolution of insect flight", Arthropod Structure & Development 47:322-327 (2018), doi:10.1016/j.asd.2017.11.007, https://doi.org/10.1016/j.asd.2017.11.007
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