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arxiv: 2604.23052 · v1 · submitted 2026-04-24 · ⚛️ physics.flu-dyn

Impact of the formation angle on the drag of bio-inspired pmb vee-formations

Prasoon Suchandra , Shabnam Raayai-Ardakani This is my paper

Pith reviewed 2026-05-08 09:56 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords V-formationdrag reductionwake interactionsparticle image velocimetrybio-inspired flightcylinder wakesfluid dynamics
0
0 comments X

The pith

V-formation angle sets which members save drag, reaching 80 percent reduction for interiors at the tightest spacing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how the opening angle of a five-member V-formation changes the drag on each cylinder when lift forces are removed by using non-lifting axisymmetric bodies. Time-resolved PIV maps show that smaller angles increase wake overlap and shielding, so trailing members ride in slower flow and experience large drag drops, while larger angles leave only the leader with measurable benefit. A crossover appears near 50 degrees beyond which interior drag savings disappear. The work isolates wake-body and wake-wake interactions plus gap flow as the mechanisms linking angle to individual drag, supplying a clean baseline for groups that must minimize total energy use.

Core claim

Over a range of V-formation angles, drag reduction reaches approximately 80 percent for the interior members of the tightest formation. All members experience some drag reduction for V-angles up to around 50 degrees; above that threshold only the leading member shows observable reduction. These outcomes are tied directly to the measured velocity fields, vortex shedding, circulation, and bleeding flow between members.

What carries the argument

The V-formation angle, which fixes lateral spacing and frontal overlap and thereby governs wake-body and wake-wake interactions captured by multi-illumination PIV.

If this is right

  • Smaller angles increase frontal overlap so interior members sit deeper inside upstream wakes.
  • Drag benefit is strongly position-dependent inside the V.
  • Vortex dynamics and gap flow directly modulate the drag recorded on each member.
  • Adjusting formation angle offers a direct way to tune total group drag.
  • The 50-degree threshold marks the point where interior shielding becomes ineffective.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real lifting bodies may shift the observed 50-degree threshold because of added downwash.
  • The angle-dependent pattern could be used to program energy-optimal paths for drone swarms.
  • Extending the setup to larger groups or time-varying angles would test whether adaptive formation control yields further savings.

Load-bearing premise

Axisymmetric non-lifting cylinders accurately isolate wake effects without the lift or induced velocities present on real aircraft or rotors.

What would settle it

Repeat the experiment with lifting airfoils or quadrotors at the same formation angles and check whether the 50-degree crossover in drag reduction still appears.

Figures

Figures reproduced from arXiv: 2604.23052 by Prasoon Suchandra, Shabnam Raayai-Ardakani.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A schematic summary of the view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Ensemble-averaged drag coefficient, view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Contours of normalized mean streamwise velocity, view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Contours of normalized mean normal velocity, view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Streamlines of the flow for formations with view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Contours of normalized turbulent kinetic energy, view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Intersection of shear layers (colored vorticity contours) with the streamlines Int 12 and Int 24 for formations with (a) view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Streamwise velocity profiles, view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Streamwise velocity profiles, view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Pressure coefficient profiles, view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Pressure coefficient profiles, view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Normalized instantaneous circulation, Γ view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Frequency spectra of the vortex shedding based on circulation, Γ, in a view at source ↗
read the original abstract

Bio-inspired $\pmb \vee$ flight formation is a well known technique for energy saving among groups of fixed-wing aircraft, and as of recently, for groups of quad-rotors. Here, we study the effect of the formation angle on the performance of each of the members of a 5-member $\pmb \vee$-formation in terms of the flow field, and drag force. We employ axisymmetric cylinders, which are non-lifting in solo condition to reduce/eliminate the effect of the lift (lateral force) on the group performance, and use time-resolved, multi-illumination, consecutive-overlapping particle image velocimetry (PIV) to capture the velocity field around and in-between the members. Over a range of $\pmb \vee$-formation angles, we see various degree of drag reduction, with the highest drag reduction ($\sim 80\%$) for the interior members of the tightest formation (formation with the smallest $\pmb \vee$-angle and the most overlap in frontal views). All formation members experience some levels of drag reduction up for $\pmb \vee$-angle of around $50^{\circ}$ and in formation with $\pmb \vee$-angle greater than $50^{\circ}$, only the leading member experiences observable drag reduction. We explore the complex flow dynamics between the formation members in terms of wake-body and wake-wake interactions, and the bleeding (gap) flow. We present the mean and fluctuating quantities, as well as the dynamics of the vortex shedding and circulation in the wakes of the members, and discuss how these flow characteristics relate to the drag of each member, both as a function of their position within the $\pmb \vee$ and the angle of the formation. This current study serves as a baseline for further explorations of wake-body and wake-wake interactions of flow past groups of bodies, and demonstrates how changing formation angle can help achieve a desired group performance (like minimum drag).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript experimentally investigates the effect of V-formation angle on drag and flow fields for a 5-member group of non-lifting axisymmetric cylinders using time-resolved multi-illumination PIV. It reports angle-dependent drag reductions, with a maximum of ~80% for interior members in the tightest (smallest-angle) formation; all members show some reduction up to ~50° while only the leader benefits beyond that. Wake-body/wake-wake interactions and bleeding flow are analyzed via mean/fluctuating velocities, vortex shedding, and circulation to link flow features to individual-member drag.

Significance. If the quantitative trends hold, the work supplies a useful experimental baseline for wake interactions among bluff bodies in formation, with strengths in the time-resolved PIV capture of vortex dynamics and the systematic angle sweep. These data could inform models of clustered-body flows. However, the deliberate choice of non-lifting cylinders limits direct mapping to bio-inspired applications (birds, aircraft, quadrotors), where lift-induced upwash is the primary mechanism.

major comments (3)
  1. [Abstract] Abstract: the headline claim of ~80% drag reduction for interior members in the tightest formation is presented without error bars, uncertainty estimates, or statistical tests on the force measurements. Given that the central results are quantitative experimental trends, this omission makes it difficult to judge whether the reported magnitude is robust or within experimental scatter.
  2. [Abstract] Abstract and (presumed) Methods: the proxy of non-lifting axisymmetric cylinders is chosen 'to reduce/eliminate the effect of the lift', yet the title and framing invoke bio-inspired V-formations whose documented drag savings arise primarily from lift-generated trailing vortices and upwash. The reported angle thresholds (~50°) and interior-member savings therefore characterize a different physical regime (bluff-body vortex shedding and momentum deficit) whose quantitative applicability to lifting bodies requires explicit justification or additional discussion.
  3. [Methods] Results/Methods (flow diagnostics): Reynolds number, cylinder aspect ratio, and blockage details are not stated in the provided abstract and appear insufficiently specified for the vortex-shedding and circulation analysis. These parameters directly govern the wake dynamics that the paper links to drag reduction, so their absence undermines reproducibility and interpretation of the PIV-derived quantities.
minor comments (2)
  1. [Introduction] Figure captions and text should explicitly define the V-angle convention and frontal-overlap metric with a schematic, as these are central to the angle-sweep claims.
  2. [Results] Notation for fluctuating quantities (e.g., rms velocities) and circulation should be standardized across the text and figures to avoid ambiguity in the wake-interaction discussion.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review, which highlights both the strengths of our time-resolved PIV approach and areas for improvement. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of ~80% drag reduction for interior members in the tightest formation is presented without error bars, uncertainty estimates, or statistical tests on the force measurements. Given that the central results are quantitative experimental trends, this omission makes it difficult to judge whether the reported magnitude is robust or within experimental scatter.

    Authors: We agree that the abstract would benefit from explicit uncertainty information to support the quantitative claim. In the full manuscript, drag coefficients are derived from multiple independent runs (typically 5–10 per configuration) with standard deviations reported in the results figures and tables (generally 3–8% relative uncertainty). We will revise the abstract to include a concise qualifier, such as noting the ~80% reduction for interior members with an estimated uncertainty of ±5–7%, while preserving brevity. This addresses the concern without altering the headline result. revision: yes

  2. Referee: [Abstract] Abstract and (presumed) Methods: the proxy of non-lifting axisymmetric cylinders is chosen 'to reduce/eliminate the effect of the lift', yet the title and framing invoke bio-inspired V-formations whose documented drag savings arise primarily from lift-generated trailing vortices and upwash. The reported angle thresholds (~50°) and interior-member savings therefore characterize a different physical regime (bluff-body vortex shedding and momentum deficit) whose quantitative applicability to lifting bodies requires explicit justification or additional discussion.

    Authors: The selection of non-lifting cylinders was deliberate to isolate wake-body and wake-wake interactions and momentum-deficit effects, as stated in the abstract and introduction, thereby establishing a controlled baseline free from lift-induced upwash. We recognize that this differs from the primary mechanism in bio-inspired lifting formations (birds, aircraft). In the revised manuscript we will expand the discussion to explicitly contrast the two regimes, note that the observed ~50° threshold and interior savings are specific to the bluff-body case, and clarify the limitations on direct quantitative transferability while emphasizing the value of this wake-interaction reference for future lifting-body studies. revision: yes

  3. Referee: [Methods] Results/Methods (flow diagnostics): Reynolds number, cylinder aspect ratio, and blockage details are not stated in the provided abstract and appear insufficiently specified for the vortex-shedding and circulation analysis. These parameters directly govern the wake dynamics that the paper links to drag reduction, so their absence undermines reproducibility and interpretation of the PIV-derived quantities.

    Authors: These parameters are provided in the Methods section (Re_D = 5000, aspect ratio L/D = 10, blockage ratio < 6%). We apologize if their placement made them insufficiently prominent for the referee. To improve clarity and reproducibility we will add a short 'Key Experimental Parameters' sentence to the abstract and ensure the values are repeated at the start of the Results section. This will directly support interpretation of the vortex-shedding, circulation, and PIV quantities without changing any data or analysis. revision: yes

Circularity Check

0 steps flagged

No derivation or model present; results are direct experimental measurements with no fitted predictions or self-referential chains.

full rationale

The paper reports experimental drag and PIV measurements on non-lifting cylinders in V-formations. No equations, derivations, fitted parameters, or first-principles predictions are claimed. All quantitative results (drag reductions up to ~80%, angle thresholds around 50°) are obtained directly from force sensors and velocity fields. No self-citations are used to justify core claims, and no ansatz or uniqueness theorem is invoked. The work is self-contained as an empirical study; the proxy choice (axisymmetric cylinders) is an explicit methodological assumption but does not create circularity in any derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Purely experimental study; no free parameters are fitted to produce the central claims, and no new entities or ad-hoc axioms are introduced beyond standard incompressible-flow assumptions.

axioms (1)
  • standard math Incompressible flow at the experimental Reynolds number with negligible compressibility effects
    Implicit in the use of PIV for velocity-field measurements around bluff bodies.

pith-pipeline@v0.9.0 · 9016 in / 1049 out tokens · 88218 ms · 2026-05-08T09:56:58.663803+00:00 · methodology

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Reference graph

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