{"id":"211c66df-039f-4253-9a61-a49915f1bbb4","arxiv_id":"2607.20514","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A tensegrity-fin batoid model with body–fluid interaction shows that in-phase tension actuation yields traveling fin waves and predicts that matching fin resonance to flapping frequency gives speed proportional to frequency.","lead":"This paper builds a computer model of a ray-like swimmer whose flexible fins are made of tensegrity-style struts and cables, and uses it to simulate swimming, turning, rolling, and somersaulting. It finds that in-phase cable actuation can produce traveling waves on the fins, and that matching fin stiffness to flapping frequency makes swimming speed scale linearly with frequency.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Resonance-tuning claim uses dry-fin natural frequencies while the fluid model omits added mass; the 'tuned' condition may not be true fluid-structure resonance, so the linear speed–frequency trend is not robust.","rationale":"The reader's weakest assumption is exactly the analytical fluid force model, and I agree that it is the most load-bearing element. The paper's central conclusion about manta-ray fin stiffening relies on the specificity of the resonance condition: within the simulations, the speed–frequency relationship is linear only when the actuation frequency equals the fin's in-vacuo natural frequency. Since the fluid model omits added mass, the condition that produced the linear trend is not the true fluid-coupled resonance. This is not just a quantitative refinement; it concerns the identity of the tuning variable. If a realistic added mass is included, the wet natural frequency would be lower, so the 'ratio = 1' points in Fig. 3b would no longer represent resonance, and the linear trend across the three stiffness cases could break. Because the biological inference—stiffer fins for faster swimming—is built on that three-point line, the fluid model's omission of added mass is the weakest link in the causal chain. At the same time, the paper is careful to label its results as preliminary qualitative trends, and the tensegrity structural formulation is substantial and derived from first principles. The appropriate judgment remains CONDITIONAL: the framework is worth pursuing, but the central biological claim should be re-tested with a fluid model that includes added-mass effects, and ideally with more than three stiffness values. This does not constitute rejection, as the authors openly call for CFD-based evaluation.","tokens_in":20386,"tokens_out":7292,"duration_ms":71164,"concrete_test":"Add an added-mass term to Eq. (A-22) at each virtual wing node—for example, using the inviscid added-mass force −Cm ρ V a_n where V is the local element volume and a_n the normal acceleration, or a 3D added-mass matrix for each tensegrity unit—and repeat the Sec. 3.2 sweeps for the three stiffness values (natural frequencies 0.46, 0.92, 1.83 Hz) with swimming kinematics unchanged. Determine the frequency ratio (relative to the original in-vacuo natural frequency) at which stride length and fin amplitude peak, and re-plot the speed–frequency curve for the tuned cases. If the peak moves away from ratio 1 or the three-point speed–frequency line ceases to be linear, the central resonance-exploitation and manta-ray-stiffening claims are unsupported. A more definitive check would be to replace the analytical model with a boundary-element or CFD solver for one representative swimming case (e.g.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The main qualitative claim with biological significance is that manta rays stiffen their fins to exploit resonance and thereby produce a linear swim-speed versus flapping-frequency relationship (Sec. 3.2, Fig. 3b, Conclusion). This claim depends on the assumption that the fin's natural frequency computed with 'no fluid force applied' (Sec. 3.2) is the correct reference for resonance when the fin is in water. However, the analytical fluid model Eq. (A-22) contains only quasi-steady drag terms, proportional to velocity squared, and explicitly 'the inertial component of fluid force is ignored' (Appendix A4). A neutrally buoyant fin (same density as water, Sec. 2.1/A5) has an added mass of the same order as its own mass; in a real fluid, the wet natural frequency is substantially lower than the dry value. The simulations therefore tune the actuation frequency to the dry natural frequency, not to the coupled fluid-structure resonance. The 'resonance exploitation' observed in Fig. 3a—peak fin amplitude and stride length at frequency ratio 1—may be a consequence of this mismatch rather than a true physical resonance. Because the linear speed–frequency line in Fig. 3b is constructed from the flapping-frequency-ratio-1 points of only three stiffness cases, it could change qualitatively if the reference frequency were the wet natural frequency. Additionally, the omission of added mass alters the local phase between fin velocity and fluid force, so the traveling-wave patterns in Sec. 3.1 and the maneuver kinematics in Sec. 3.4 may also be sensitive to this assumption. The authors do flag the fluid model as simplified and call for CFD, so this is a robustness concern rather than an internal inconsistency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a body–fluid interaction model of a batoid ray propelled by tensegrity pectoral fins. The body trunk is treated as a rigid body with six degrees of freedom, and each pectoral fin is modeled by seven planar tensegrity radials composed of rigid struts and elastic cables, actuated by changing cable rest lengths. The equations of motion are derived via the Euler–Lagrange formalism using generalized coordinates for body position, orientation, and strut angles; the generalized forces from cables and from an analytical quasi-steady drag fluid model are incorporated through virtual work. The model is exercised in simulations that claim: (i) chord-wise and span-wise traveling waves emerge on the fin despite in-phase actuation; (ii) swim speed increases linearly with flapping frequency only when fin stiffness is tuned so that the fin's (dry) first-mode natural frequency matches the flapping frequency, suggesting that manta rays stiffen their fins to swim faster; (iii) body inertial motion, especially roll during out-of-phase flapping, can make the fin kinematic wave travel faster than the actuation wave; and (iv) maneuvers such as somersaults, rolling, and turning can be generated by asymmetric fin deformation.","tokens_in":20818,"tokens_out":5614,"duration_ms":56213,"significance":"If the qualitative trends are robust, the model provides a useful framework for studying batoid locomotion in the context of neural control and for designing tensegrity-based underwater vehicles. The paper has noteworthy strengths: a detailed multibody derivation, a clear virtual-work treatment of cable and fluid forces, and a demonstration that traveling waves and speed trends emerge from coupled dynamics rather than being prescribed by the actuation. However, the central biological conclusion about resonance exploitation rests on a fluid model that explicitly omits added-mass effects, and the headline linear relationship is based on three-point fits without uncertainty quantification. Because the main claims are load-bearing and currently depend on assumptions that are not tested, the manuscript requires substantial revision before the conclusions can be accepted.","major_comments":[{"comment":"The resonance-exploitation claim is based on comparing flapping frequency with the fin's natural frequency computed from a single-fin model with 'no fluid force applied' (Sec. 3.2). However, the fluid model Eq. (A-22) contains only quasi-steady drag terms and states 'the inertial component of fluid force is ignored' (Appendix A4). Because the fin is neutrally buoyant (Sec. 2.1, A5), the added-mass inertia in water is of the same order as the fin's own inertia, so the wet natural frequency will be substantially lower than the dry value used in Fig. 3. The tuning condition in Fig. 3 is therefore not a genuine fluid–structure resonance, and the linear speed–frequency relationship in Fig. 3b may be an artifact of comparing against the wrong reference frequency. Please estimate the added-mass effect on natural frequency (e.g., by including a linear added-mass term in the fin model) and re-exa","section":"Sec. 3.2 and Appendix A4"},{"comment":"The claim that swim speed increases linearly with flapping frequency when resonance is exploited is based on exactly three data points per line (natural frequencies 0.46, 0.92, and 1.83 Hz), each from a single simulation with no error estimates. A straight line through three points is weak evidence for linearity and does not justify the strong statement that 'swim speed increases linearly with flapping frequency' or the conclusion that manta rays stiffen their fins. Additional intermediate frequencies and a residual analysis, or at least a statement about expected simulation variability, are needed.","section":"Sec. 3.2, Fig. 3b"},{"comment":"The traveling-wave observations—especially the claim in Sec. 3.3 that body roll makes the fin kinematic wave travel faster than the actuation wave—depend on the phase relationship between local fin velocity and fluid force. The quasi-steady drag law (A-22), with no added-mass or unsteady terms, cannot be assumed to reproduce the phase behavior of a real fluid. The authors do acknowledge in the Conclusion that the trends should be evaluated with CFD, but the main text states the qualitative results without this caveat. A sensitivity study varying the fluid model (e.g., adding an added-mass term or a linear unsteady correction) would help establish whether the phase and wave-speed conclusions are robust.","section":"Secs. 3.1, 3.3 and Eq. (A-22)"},{"comment":"The claim that stride length, fin flapping amplitude, and the energy-loss ratio are 'nearly independent' of fin stiffness when resonance is exploited is based on only three stiffness values and one selected damping ratio (0.05). The cable stiffnesses, actuation amplitude proportionality constants, and intersegmental phase lags are hand-tuned or taken from prior work, and no sensitivity analysis is provided. Please report the actual numerical values used in Fig. 3a and provide sweeps over intermediate stiffnesses and damping ratios to justify the invariance claim.","section":"Sec. 3.2"}],"minor_comments":[{"comment":"The figure caption lists only blue, red, yellow, and purple lines, but the text in Sec. 3.2 refers to 'green lines' for propulsion efficiency. Add the missing color to the caption or correct the text.","section":"Fig. 3 caption"},{"comment":"Refs. [27] and [32] appear to be the same paper ('Tensegrity system dynamics in fluids', Nonlinear Dynamics 113, 12971–12984, 2025). Merge the duplicate citation.","section":"References"},{"comment":"Appendix A5 states that the stiffness at the thickest place is set to 54 N/m 'so that the first mode natural frequency of the wing is around 1 Hz', while Sec. 3.2 reports first-mode natural frequencies of 0.92, 0.46, and 1.83 Hz. Clarify which stiffness values correspond to which natural frequency and how the 54 N/m baseline relates to the three cases.","section":"Appendix A5 and Sec. 3.2"},{"comment":"There are numerous typos and minor language issues (e.g., 'difficult' in the Abstract, 'momentum of inertial' in Appendix A2). A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the modeling framework is potentially valuable, but the central resonance conclusion is not yet supported because the fluid model omits added mass and the linear relationship is based on a three-point fit. I would encourage the editor to request a revised version that either includes an added-mass/wet-resonance analysis or substantially softens the claims, together with additional data points for the speed–frequency relationship."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What to know: this paper builds the first full body–fluid interaction model of a batoid with dynamic tensegrity pectoral fins, free swimming, and it shows real phenomena emerging from the coupling — in-phase actuation producing chord-wise and span-wise traveling waves, body inertia changing fin kinematics. That framework is the contribution. The resonance-exploitation story, which the authors tie to manta rays stiffening their fins, is not robust yet.\n\nWhat the paper does well: the multi-body derivation is extensive and consistent; the tensegrity fin with cable actuation is a credible musculoskeletal analog; and the simulations are set up to test genuine mechanisms rather than enforce them. The traveling-wave emergence is a real result, not an artifact of prescribed kinematics. The body-inertial effects in Section 3.3 are interesting and worth following up. The authors also label their results as qualitative trends and call for CFD, which is honest.\n\nSoft spots: the fluid force model is quasi-steady drag only, with no added mass. The fin is neutrally buoyant, so in water its wet natural frequency would be substantially lower than the dry value used in Section 3.2. That means the 'resonance' peak in Fig. 3a and the linear speed–frequency line in Fig. 3b are tuned against the dry fin, not the coupled fluid-structure system. The linear relationship is also drawn through three points per stiffness case, so it is not a strong empirical claim. The same added-mass omission could shift the phase relationships behind the traveling-wave and maneuver results. The drag coefficients are taken from prior work with no sensitivity checks; cable stiffness and damping are effectively hand-tuned; and there is no convergence or resolution analysis for the discretized fluid loads. None of these are fatal if the paper is read as a model-development contribution, but they are load-bearing for the biological claim.\n\nThe citation pattern is heavy on the authors' own prior work, but the central results — emergent traveling waves, resonance trends, inertia effects — are computed from the model, not built in by construction. So the circularity concern is minor.\n\nWho this is for: researchers in bio-inspired underwater robotics and batoid neuromechanics. It deserves a serious referee: the modeling framework is substantial, original, and likely to be reused even if the specific trends need revision. I would send it to review, with the expectation that the resonance section be rewritten to account for added mass or explicitly reframed as a dry-fin sensitivity study.\n\nRecommendation: accept conditional on addressing the wet-frequency issue and providing some sensitivity analysis; otherwise the structural contributions are worth publishing even as a model paper.","headline":"A genuinely useful tensegrity swimming model whose headline resonance claim rests on a fluid model that ignores added mass — treat the qualitative trends as provisional.","tokens_in":21293,"tokens_out":1332,"would_cite":true,"duration_ms":16695,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A tensegrity-wing model of ray swimming reproduces manta-ray speed trends and points to fin stiffening as the speed control.","keywords":["batoid swimming","tensegrity pectoral fin","body-fluid interaction","free swimming simulation","fin stiffness tuning","resonance exploitation","traveling waves","bio-inspired underwater vehicle"],"falsifier":"A decisive check would be to rerun the same tensegrity-fin simulations with an unsteady or CFD fluid model and see whether (i) traveling waves still emerge from perfectly in-phase actuation and (ii) the linear swim-speed–flapping-frequency relation still appears only when fin natural frequency is tuned to flapping frequency. Alternatively, an experimental robotic ray with adjustable cable stiffness could measure stride length and speed across a stiffness sweep, looking for a peak at the model's predicted resonance frequency.","tokens_in":20293,"feed_emoji":"🐟","tokens_out":7403,"duration_ms":64000,"temperature":0.7,"pith_summary":"The paper develops a simulation of a ray-like swimmer in which the flexible pectoral fins are modeled as tensegrity structures—rigid struts linked by elastic cables—actuated by pulling the cables. With a simplified analytical fluid-force model, the simulation reproduces two signature features of real batoid swimming: traveling waves appear on the fin even when all actuation signals are in phase, and the linear rise of swim speed with flapping frequency observed in manta rays appears only when fin stiffness is tuned so the fin's natural frequency matches the flapping frequency. The authors read this as evidence that rays actively stiffen their fins to swim faster, and that exploiting resonance makes stride length and energy loss nearly independent of speed. The model is offered as a tractable platform for neural-control studies and for engineering ray-like underwater vehicles.","feed_headline":"Ray fins stiffen to swim faster, tensegrity model suggests","feed_subtitle":"A cable-and-strut simulation reproduces manta-ray speed scaling and points to stiffness as the speed-control knob.","key_machinery":"The central machinery is the tensegrity pectoral fin: a planar network of rigid struts connected by elastic cables, with cable rest lengths driven by actuation inputs. The fin's elastic deformation, governed by Lagrangian equations of motion coupled to a six-degree-of-freedom rigid trunk, converts cable tension changes into fin shape; it is the mechanism by which in-phase actuation becomes traveling waves and by which matching the fin's natural frequency to the flapping frequency produces resonance-enhanced stride length and reduced damping losses.","core_discovery":"The paper's central claim is that a body–fluid interaction model with a rigid trunk and two tensegrity pectoral fins—each fin actuated by changing the rest lengths of its elastic cables—captures the essential swimming physics of batoids without prescribing fin motions. Driven by sinusoidal cable-tension signals with all units in phase, the fin surface still develops chord-wise and span-wise traveling waves because elasticity and fluid forces shape the deformation. In straight-line swimming, swim speed increases linearly with flapping frequency only when fin stiffness is chosen so that the first-mode natural frequency of the fin matches the flapping frequency; with stiffness held fixed, the l","pith_inferences":["The resonance-tuning result suggests a control strategy for ray-like robots: adjust cable stiffness on the fly to match flapping frequency, which would make stride length robust to speed changes—an implicit design guideline in the paper.","Because the model treats the fin as a network of struts and cables, it could be extended to map muscle-activation patterns to neural commands, a step the authors mention but do not develop.","The out-of-phase result implies that asymmetric body motion can accelerate the kinematic wave; an untested corollary is that turning maneuvers could be executed not just by cutting one fin's drive but also by introducing phase offsets that induce roll."],"forward_implications":["If the resonance picture is right, a robotic ray can maximize stride length and minimize damping-energy loss by tuning fin stiffness to flapping frequency, making stride length nearly independent of speed.","The linear swim-speed–frequency relation in manta rays can be explained as a consequence of stiffness tuning, implying fin stiffness is an active control variable rather than a fixed property.","The model can generate free-swimming fin kinematics and actuation signals without in vivo measurements, making it useful for studying neural control of batoid swimming.","Body inertial motion—especially roll during out-of-phase flapping—can speed up or slow down the fin kinematic wave relative to the actuation wave, so gait selection directly affects wave speed.","Flapping a fin about a deformed configuration produces net pitch and roll torques, giving a principled way to generate somersault, rolling, and turning maneuvers in underwater vehicles."],"fun_headline_variants":["Tensegrity fins: stiffness match to flapping boosts ray speed","Cable-tension fins self-shape into waves in batoid model","Ray swim model: fin stiffness is the speed control knob","Stiffness resonance drives ray speed in tensegrity simulation","Batoid fin model: resonance tuning increases swim speed"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Every simulation result rests on the assumption that the analytical fluid-force model—constant tangential and normal drag coefficients (ct = 0.097, cn = 1.18) with no added-mass or unsteady forces—faithfully represents the fluid forces on the body and fin surfaces.","fun_headline_variants_meta":{"raw":{"variants":["Tensegrity fins: stiffness match to flapping boosts ray speed","Cable-tension fins self-shape into waves in batoid model","Ray swim model: fin stiffness is the speed control knob","Stiffness resonance drives ray speed in tensegrity simulation","Batoid fin model: resonance tuning increases swim speed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000197,"raw_usage":{"total_tokens":1168,"prompt_tokens":677,"completion_tokens":491,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":421,"completion_tokens_details":{"reasoning_tokens":404}},"tokens_in":421,"tokens_out":491,"duration_ms":6290,"temperature":1.0,"reasoning_tokens":404,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T08:19:33.369787+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to rerun the same tensegrity-fin simulations with an unsteady or CFD fluid model and see whether (i) traveling waves still emerge from perfectly in-phase actuation and (ii) the linear swim-speed–flapping-frequency relation still appears only when fin natural frequency is tuned to flapping frequency. Alternatively, an experimental robotic ray with adjustable cable stiffness could measure stride length and speed across a stiffness sweep, looking for a peak at the model's predicted resonance frequency.","supporting_citations":[],"review_version":1}