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Spinning Quadrotor: Hover Thrust Augmentation with Passive Lifting Surfaces

Aniketh Parkala, Harikumar Kandath

arXiv:2608.23163v1cs.RO

TL;DR

Conventional quadrotors suppress yaw during hover, although yaw regulation is not required for force balance or altitude control. This paper instead develops and validates a spinning-quadrotor architecture with passive lifting surfaces, reporting reduced motor thrust demand and idealized power savings.

  • Problem

    Conventional multirotors actively suppress yaw during hover, motivating investigation of intentional sustained rotation as an alternative hover operating point.

  • Method

    The paper combines a spinning-quadrotor architecture with low-Reynolds-number airfoil selection and multi-fidelity validation through simulation and hardware experiments.

  • Results

    22% lift increase was reported in hardware experiments, while simulation predicted a 57.1% electrical-power reduction under idealized assumptions.

  • Takeaways & Limitations

    Intentional spinning can transfer part of hover lift generation from propellers to rotating aerodynamic surfaces, reducing propeller thrust demand.

Abstract

from arXiv · show

Conventional multirotor aerial vehicles actively suppress yaw rotation during hover, expending power to maintain a fixed heading despite the fact that yaw regulation is not required for force balance or altitude control. This paper challenges that paradigm by proposing a spinning quadrotor architecture that intentionally operates at a sustained yaw rate, converting power traditionally spent on yaw regulation into useful aerodynamic effects. A dynamic model of the spinning quadrotor is developed, analysis for low Re range is conducted to choose an airfoil for lifting surfaces. Preliminary hardware tests show a 22% reduction in thrust required. These findings suggest that intentional yaw rotation, rather than being suppressed, can be exploited as a design mechanism for efficient and robust multirotor flight.

I. INTRODUCTION

The paper proposes sustained intentional yaw rotation for quadrotor hover, using tangential airflow to generate lift from passive radial surfaces and reduce propeller thrust demand.

  • The approach is positioned within prior spinning-quadrotor fault-tolerant control, rotation-driven monocopter, and hybrid rotary-platform research.
  • The paper motivates spinning hover by replacing continuous yaw suppression, exploiting spin-averaging of disturbances, and augmenting lift during hover.
  • The proposed architecture replaces yaw suppression with intentional steady rotation and passive aerodynamic lift augmentation.All rotors are canted in a common direction so the vehicle converges to a steady spin while regulating altitude and reduced attitude.
  • The work selects a low-Reynolds-number airfoil and validates the concept through BEMT, CFD, and hardware experiments.The reported contribution includes a promising 22% lift increase compared with conventional quadrotors.
  • Tangential airflow from steady yaw allows radially mounted lifting surfaces to generate lift in zero-freestream conditions.The lift relationship depends on air density, yaw rate, radial position, wing area, and lift coefficient.

A. Constraints

The spinning-hover regime is bounded by control bandwidth, structural radius, vibration, and low-Reynolds-number aerodynamic constraints, while remaining experimentally realizable.

  • Yaw-rate authority and control bandwidth: Higher yaw rates are limited by motor bandwidth, rate-loop saturation, gyroscopic coupling, mixer authority, and estimator bandwidth.These effects degrade reduced-attitude performance primarily through control and bandwidth limitations.
  • Yaw-rate authority and control bandwidth: The present PX4 implementation defines a practical upper bound of ω ≤10 rad/s and constrains vehicle mass to m < 1 kg for safe experiments.The standard cascaded controller is used without structural modification, with an offset yaw reference for fixed-world-frame roll and pitch commands.
  • Aerodynamic velocity and Reynolds regime: The radial arm length is limited to l ≤0.65 m because greater lengths increase structural flexibility and vibration modes during spin.
  • Aerodynamic velocity and Reynolds regime: Chord lengths of approximately 0.20–0.30 m produce a low-Reynolds-number regime within the velocity bound.Airfoil selection is therefore constrained to profiles optimized for low-Re operation, including glider-inspired airfoils.
  • Aerodynamic velocity and Reynolds regime: Together, these constraints define a bounded but experimentally realizable regime for evaluating aerodynamic lift augmentation.

B. Rotor Forces

The rotor-force model defines thrust from rotor speed and maps canted thrust vectors into net forces and body moments, including roll, pitch, and yaw effects.

  • Each rotor produces thrust according to the thrust coefficient and the square of its angular speed.The model denotes rotor thrust by f_i, thrust coefficient by k_f, and rotor speed by ω_i.
  • The resulting force vector incorporates each rotor’s tangential direction and motor cant angle.
  • The model provides equations for net vertical force and roll, pitch, and yaw control moments.
  • The moment notation distinguishes body-fixed roll, pitch, and yaw moments and includes the propeller torque coefficient.

D. Dynamics of motion

The paper models spinning-quadrotor motion and designs airframe configurations to sustain nonzero yaw through motor canting, extended lever arms, and passive lifting surfaces.

  • The vehicle dynamics are expressed using body-frame velocity, angular rates, inertia, rotation, gravity, and net moment variables.
  • All motors are canted in the same direction to add propeller torque and maintain nonzero yaw against wing drag.Motor mounts are fixed by 3D printing and attached to square carbon arms.
  • Configuration I: Lever-Arm-Optimized Asymmetric Layout: Configuration I places two motors 0.5 m from the center of mass and tilts them outward by 10° to increase rotational authority.The larger lever arm is intended to amplify torque for a given thrust level.
  • Configuration I: Lever-Arm-Optimized Asymmetric Layout: Configuration I uses two additional motors at 0.3 m radial distance and wings spanning 0.4–0.65 m to reduce lifting-surface interference.
  • Configuration II: Symmetric Fully Tilted Distributed Wing Layout: Configuration II uniformly tilts four motors by 10° at 0.3 m radial distance and places one wing along each arm.This layout isolates uniform thrust vectoring and distributed lift generation while removing lever-arm-induced bias.

IV. AIRFOIL SELECTION

The lifting surfaces are selected for a low-Reynolds-number operating regime using candidate-airfoil polars and aerodynamic-efficiency screening, followed by custom geometry interpolation.

  • Limited yaw rates and wing radius produce low-Reynolds-number flow, so candidate airfoils are drawn from glider and low-Reynolds-number families.The expected operating conditions are approximately ω = 8–12 rad/s, r ≤ 0.65 m, and c ≈ 0.25–0.30 m.
  • Eight candidate airfoils are evaluated across Reynolds numbers and angles of attack, using Cl/Cd as the primary screening metric.The candidates are AG-14, RG-14, RG-15, S1223, SD7032, SD7037, SD7062, and NACA 4412.
  • Franky interpolates S1223 and SD7037 with a 26% blend to combine high lift with high low-Reynolds-number efficiency.Franky-2 uses a 60% blend but is not selected because its optimal behavior spans a narrower angle-of-attack range.

C. Reynolds number-Specific Operating-Point Optimization

The wing is optimized at Reynolds-specific operating points by jointly evaluating airfoils and angles of attack, then shaping the planform for the radial airspeed variation during spinning hover.

  • The lifting surfaces operate over Re = 0.040–0.090 ×10^6 during steady spinning hover.The hub has no aerodynamic surfaces, so blade sections remain within this Reynolds-number range.
  • For each Reynolds number, candidate airfoils and angles of attack are evaluated together and normalized within that Reynolds group.
  • The composite score J balances Cl/Cd efficiency, Cl lift generation, and Cp,min-based penalties for aggressive pressure gradients.Cp,min is used as a heuristic proxy for pressure-gradient severity and stall robustness, not as a formal stability criterion.
  • The wing planform matches V(r) = ωr by tapering chord inward and omitting inner sections with minimal incoming airspeed.A transition region at r = 0.40–0.45 m supports smooth aerodynamic handover and reduces root effects without contributing significantly to thrust.

A. MuJoCo Simulation

The MuJoCo simulation models spinning hover with coupled vehicle and wing aerodynamics, showing that rotating wings provide most hover lift while motors sustain spin and the remaining thrust. Under idealized assumptions, this produces a substantial predicted power reduction relative to a motor-only baseline.

  • Simulation framework: The coupled framework combines a rigid-body multirotor model with tilted motors and blade-element momentum theory for rotating lifting surfaces.Wing aerodynamics use Reynolds-number-dependent airfoil polars, while a PID altitude controller regulates total motor thrust.
  • Torque balance: Steady-state motor yaw torque and wing drag torque are 1.033 N·m and 1.043 N·m, respectively, agreeing within 1% and establishing constant spin.The motor yaw torque is dominated by thrust-induced torque from motors tilted 44° in simulation.
  • Lift distribution: 5.27 N (67.2%) of the 7.85 N vehicle weight is supplied by rotating wings, while motors provide 2.58 N (32.8%).This approximately 2:1 wing-to-motor lift ratio reduces propeller thrust requirements; the effective wing lift-to-drag ratio is approximately 2.5.
  • Hover behavior: The simulation converges to steady spinning hover, with altitude reaching 1.473 m and yaw rate stabilizing at 9.27 rad/s (88.5 RPM).The target altitude is 1.5 m, with a reported steady-state error of 0.008 m.
  • Power analysis: 57.1% reduction in electrical power is predicted relative to a 122.0 W motor-only baseline, with spinning hover estimated at 52.3 W.The estimate is an upper-bound prediction under quasi-steady aerodynamics and constant motor efficiency assumptions.

B. CFD Cross-Validation

CFD cross-validation evaluates the complete rotating four-wing assembly at low Reynolds number while excluding propeller-induced flow to isolate aerodynamic lift. The analysis provides a more accurate system-level bound than the lower-fidelity approximation, while omitting detailed three-dimensional interaction effects.

  • CFD setup: ANSYS Fluent CFD uses a multiple reference frame formulation at ω = 10 rad/s with a low-Reynolds-number k–ω SST model in the Re ∼ 10^5 regime.The complete four-wing assembly is simulated in rotation without propeller-induced flow to isolate wing-generated lift.
  • Configurations: The tested airframe configurations include an orthogonal wing–motor layout with asymmetric motor tilt and a fully tilted motor layout with distributed wings.Representative flight tests are shown for all configurations in the supplementary video.
  • Cross-validation: The CFD analysis integrates lift from the complete four-wing assembly to provide a more accurate bound than MuJoCo.The system-level approximation does not capture three-dimensional aerodynamic blade–blade interactions or detailed flow effects.

C. Hardware Hover Performance

Hardware tests compared spinning and stationary quadrotor configurations at identical mass, showing that rotating wings supplied substantial hover lift while reducing motor demand. The four-wing configuration also exhibited lower per-wing lift than the two-wing configuration, attributed to aerodynamic interaction and wake interference.

  • Experimental setup: Tests used four hardware cases spanning spinning and non-spinning asymmetric two-wing and symmetric four-wing configurations at identical vehicle mass.Hover intervals excluded transient ascent and descent phases and selected steady-state motor-command regions.
  • Thrust and lift contribution: Four-wing spinning hover required an 18% lower motor command than the stationary four-wing baseline.The motors produced 758 g total thrust and 746 g vertical force after accounting for the 10° tilt.
  • Thrust and lift contribution: 22.3% of vehicle weight, or 214 g, was supplied by rotating wings in the four-wing configuration.The reported wing contribution was nearly equivalent to an additional motor.
  • Thrust and lift contribution: Two-wing spinning hover required a 15% lower motor command than its stationary baseline, with rotating wings supplying 147 g of lift.The wing lift corresponded to 22.3% of vehicle weight.
  • Aerodynamic interaction: Per-wing lift was 73.4 g with two wings versus 53.5 g with four wings, despite similar total lift fractions.The reduced four-wing value was attributed to wake overlap and induced-velocity effects lowering downstream effective angle of attack.

VI. CONCLUSION AND FUTURE WORK

The paper concludes that intentional spinning hover can transfer part of lift generation from propellers to rotating wings, with simulations and hardware experiments supporting feasibility. It identifies fault-tolerant control under partial motor failure as a primary direction for future work.

  • Conclusion: Intentional spinning hover reduced propeller thrust demand by transferring lift generation to rotating aerodynamic surfaces.Simulations established an upper bound, while hardware experiments confirmed practical feasibility.
  • Conclusion: In spinning configurations, the wings generated lift comparable to one motor's stationary-hover contribution.This highlights the meaningful aerodynamic contribution of the passive lifting surfaces.
  • Future work: Future work will focus on fault-tolerant control that sustains stability and lift under partial motor failure.The proposed strategies are intended to leverage rotational dynamics and passive aerodynamic stabilization under actuator degradation.
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