The 2015 demonstration of the 'Naviator' - the first fully functional multirotor vehicle able to fly in air, navigate submerged, and cross the air-water interface seamlessly - established feasibility with a notional argument: a dual-medium vehicle exists only where the flight envelope (propeller lift and thrust sufficient for a given weight) intersects the swimming envelope (thrust for underwater cruising at near-neutral buoyancy), and it explicitly left the comprehensive quantitative study behind that argument for future work. This problem asks for the program that study requires: a quantitative design basis determining whether and where the flight and swimming envelopes of hybrid aerial-aquatic multirotor vehicles intersect, across vehicle geometries and mission profiles, together with the load-bearing inputs such a theory requires - propulsion characterization (thrust, efficiency, cavitation onset across speed, load, depth, and scale) and three-dimensional rotor-interface transition dynamics - and the specification of its experimental validation on untethered vehicles with independent per-rotor control. A decade of follow-up work has produced propulsion-design methodology, untethered prototypes with repeated transitions, and first studies of rotor-interface physics, yet reviews through 2026 still identify the quantitative design theory, propulsion-regime characterization, and transition dynamics as open, and later measurements partly contradict the source's optimism about aerial propellers operating underwater.

Background

Hybrid aerial-aquatic vehicles (also called hybrid aerial underwater vehicles, HAUVs, or unmanned aerial-aquatic vehicles) are robotic platforms intended to fly in air, navigate submerged in water, and cross the air-water interface repeatedly, with applications in search and rescue, inspection of marine and waterside infrastructure, and survey missions. The concept received early impetus from the DARPA 'Submersible Aircraft' Broad Agency Announcement (2008), and most early prototypes were bio-inspired, imitating flying fish or diving birds with fixed or flapping wings.

A multirotor (a rotary-wing aircraft lifted and propelled by several fixed-pitch propellers, as in a quadcopter; 'VTOL' denotes vertical takeoff and landing) is attractive for this mission because it hovers and maneuvers simply, but it faces a severe media asymmetry: water is roughly one thousand times denser than air, so the same propeller rotating at a given speed in water produces far more thrust - and demands far more torque from its motor - than in air. Cavitation, the formation of vapor cavities in a liquid when local pressure falls below the vapor pressure, is a standard concern for marine propellers because it degrades thrust and erodes blades; avoiding it bounds tip speed and blade loading. Underwater, however, a vehicle that is nearly neutrally buoyant (whose average density is close to that of water, so it neither sinks nor rises appreciably) needs its propellers only for thrust and maneuvering, not to support weight - the observation that makes a dual-medium multirotor conceivable at all.

Within this context, Maia, Soni, and Diez (2015) presented the first fully functional multirotor platform operating in both air and water with seamless crossing of the interface, built on three advances: a transition method in which rotors near the air-water interface slow or stop while the remaining rotors compensate; a dual (top and bottom) propeller system for propulsion in both media; and a design balancing lift, thrust, weight, and near-neutral buoyancy in a roughly 2 kg, eight-propeller prototype. Their feasibility logic is an envelope-intersection argument: flight is possible in a set of conditions in which the propellers can generate the lift and thrust needed for a vehicle of given weight; swimming is possible in a set of conditions in which the propellers provide the thrust needed for underwater cruising at near-neutral buoyancy; a single dual-medium vehicle exists only where these two sets overlap. The paper demonstrated one point in that intersection, under deliberately narrow conditions (per-propeller thrust of 0.5-10 N, underwater propeller speeds below about 250 RPM, cruising at 0.3-1 m/s, no cavitation observed), using a control-oriented dynamic model. Its explicit deferral was (i) a comprehensive quantitative study of the two envelopes and their intersection, stated to be 'beyond the present work'; its reported tests and model additionally documented limitations that leave open (ii) untethered experimental validation with fully independent per-rotor control (the reported pool tests used a telemetry tether and did not implement independent rotor control, which the authors blamed for small discrepancies from simulation); (iii) propeller performance, cavitation onset, and efficiency beyond the tested conditions; and (iv) generalization of the model beyond its simplifications - rotor flapping neglected, residual forces lumped into a placeholder Δ\Delta, and a two-dimensional (planar) reduction for the transition study.

A decade of subsequent work has advanced parts of this agenda: the same group coupled blade-element-momentum propeller analysis (a standard method that models each blade as a sequence of lifting segments and the rotor wake as a momentum balance) with measured motor maps to size propulsion components; untethered prototypes with independent rotor or thruster control and repeated transitions now exist (for example the Loon Copter and the Nezha series); and the first physics studies of rotor-interface interaction have appeared, characterizing free-surface vortices (vortical surface depressions formed above rotating objects, long studied in unbaffled stirred tanks) and the so-called near-water effect - the change in a rotor's thrust, torque, and consumed power when it operates close beneath or above a water surface, analogous to ground effect but modified by waves, spray, and free-surface deformation. How these pieces add up to the deferred quantitative design basis is the subject of this problem.

Problem Statement

Establish a quantitative design basis that determines whether - and for which vehicle geometries, masses, buoyancy sizings, and propulsion components - the flight envelope and the swimming envelope of a hybrid aerial-aquatic multirotor vehicle intersect, and specify how that basis is to be experimentally validated on untethered vehicles with independent per-rotor control. Concretely:

  1. Envelope-intersection theory. Develop a quantitative framework that maps, for a specified vehicle design, (a) the envelope of conditions in which the propulsion system can generate the lift and thrust required for flight at a given weight, and (b) the envelope of conditions in which it provides the thrust required for underwater operation at near-neutral buoyancy within motor torque, current, and cavitation-onset limits, and that characterizes the intersection (or emptiness) of these envelopes across representative vehicle geometries and mission profiles - replacing the notional, single-point feasibility argument of the 2015 demonstration.

  2. Regime-wide propulsion characterization. Model propeller and motor performance - thrust, torque, efficiency, and cavitation onset - across speed, load, depth, and vehicle-scale regimes substantially broader than the 2015 tests (which covered per-propeller thrust of 0.5-10 N, underwater propeller speeds below about 250 RPM, and cruising at 0.3-1 m/s), specifying the measurements that would identify and validate the model, since these characteristics are the load-bearing inputs of the envelope maps.

  3. Interface-transition dynamics. Generalize the vehicle dynamic model beyond the planar, lumped-drag simplification to three-dimensional motion that captures the rotor-air-water interaction during crossing (including free-surface vortex formation and the near-water effect of rotor wakes), so that transition behavior is predicted rather than tuned.

  4. Experimental validation. Specify how the framework is to be experimentally validated on untethered vehicles with fully independent per-rotor control, quantitatively comparing observed flight, swimming, and transition behavior against model predictions and using published measurements where they are available.

Deliverables 2 and 3 supply the physical inputs without which the envelope maps of deliverable 1 are unfounded, and deliverable 4 specifies how the resulting predictions are to be checked against observed behavior.

The resolving artefact is this design basis itself - the envelope maps of deliverable 1, the load-bearing models of deliverables 2 and 3, and the measurement and validation methods they specify - established by analysis and by explicit prediction against published measurements, not by newly conducted primary experiments.

References

  1. Marco M. Maia, Parth Soni, Francisco J. Diez. 'Demonstration of an Aerial and Submersible Vehicle Capable of Flight and Underwater Navigation with Seamless Air-Water Transition.' arXiv:1507.01932 (2015). DOI: 10.48550/arXiv.1507.01932. https://arxiv.org/abs/1507.01932
  2. Arturo Villegas, Victor Mishkevich, Yuriy Gulak, F. J. Diez. 'Analysis of key elements to evaluate the performance of a multirotor unmanned aerial-aquatic vehicle.' Aerospace Science and Technology 70:412-418 (2017). DOI: 10.1016/j.ast.2017.07.046. https://doi.org/10.1016/j.ast.2017.07.046
  3. Hamzeh Alzu'bi, Iyad Mansour, Osamah Rawashdeh. 'Loon Copter: Implementation of a hybrid unmanned aquatic-aerial quadcopter with active buoyancy control.' Journal of Field Robotics 35:764-778 (2018). DOI: 10.1002/rob.21777. https://doi.org/10.1002/rob.21777
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  10. Hongfei Xie, Yufei Jin, Yuanbo Bi, Zheng Zeng. 'Nezha-D: Dynamic Characteristics and Design of a Ducted HAUV.' Journal of Intelligent & Robotic Systems 111(1):20 (2025). DOI: 10.1007/s10846-024-02133-z. https://doi.org/10.1007/s10846-024-02133-z
  11. Logan Patrick Honts, Yuanhang Zhu, Daniel B. Quinn. 'Free surface vortex dynamics during water-to-air amphibious rotor transitions.' Journal of Fluid Mechanics 1022:A18 (2025). DOI: 10.1017/jfm.2025.10778. https://doi.org/10.1017/jfm.2025.10778
  12. Xingzhi Bai, Mingqing Lu, Qi Zhan, Yu Wang, Daixian Zhang, Xiao Wang, Wenhua Wu. 'Review of the Near-Water Effect of Rotors in Cross-Media Vehicles.' Drones 9(3):195 (2025). DOI: 10.3390/drones9030195. https://doi.org/10.3390/drones9030195
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