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REVIEW 3 major objections 4 minor 20 references

Geometric Scaling of Battery Cells and Its Effect on Key Performance Indicators

T0 review · 3 major / 4 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read A lightweight cylindrical-cell scaling model shows cell diameter dominates capacity, resistance, and energy density, with height and electrode loading as secondary trade-offs.

desk verdict Solid engineering packaging of known jelly-roll geometry and resistance relations into a four-input scaling model; diameter dominance is useful within the stated chemistry and manufacturing assumptions, but validation is not fully independent. read the letter →

arxiv 2607.11566 v1 pith:P5B7ZZKI submitted 2026-07-13 eess.SY cs.SY

Tim de Krijger , Jorn van Kampen , Mouhriz Boulghalgh , Theo Hofman This is my paper · ORCID
classification eess.SYcs.SY
keywords batterymodellingscalingdesign-spaceexplorationsensitivityanalysiscylindricallithium-ioncellsDCinternalresistanceenergydensity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Battery packs for vehicles and storage depend on cell geometry and electrode choices, but full electrochemical models are too heavy for early design sweeps. This paper builds a fast geometric scaling model that takes four inputs—cell height, cell diameter, cathode active loading, and cathode porosity—and returns capacity, DC internal resistance, mass, volume, and winding length for cylindrical lithium-ion cells. The model is checked against three commercial cells and stays within a few percent on capacity and resistance. A global sensitivity study then ranks the design variables: diameter is the strongest lever for most performance metrics and generally improves them when increased, while height trades capacity against resistance, and loading and porosity mainly fine-tune the energy-density balance. The result is a practical map of which knobs matter most before a cell enters pack-level or vehicle-level optimization.

What carries the argument

The cylindrical scaling model: jelly-roll arc-length geometry plus capacity from coated area and active loading, and DC resistance split into ionic, electronic, geometric current-collector, and tab contributions, with anode porosity linearly tied to cathode porosity and tab count floor-scaled with diameter.

What would settle it

Apply the same model, without retuning the fixed constants or the porosity/tab rules, to additional cylindrical cells whose geometry, loading, porosity, tab layout, and measured capacity, DCIR, and winding length are independently known; systematic deviations larger than a few percent or a reordered sensitivity ranking would refute the claim.

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Extended reading notes

Core claim

A computationally lightweight scaling model that maps cylindrical cell height, diameter, cathode active loading, and cathode porosity to capacity, DC internal resistance, mass, volume, and winding length is accurate enough on three benchmark cells to support design-space exploration, and that exploration shows cell diameter is the dominant design variable for capacity, resistance, gravimetric energy density, and volumetric energy density, with height, loading, and porosity creating secondary trade-offs.

Load-bearing premise

Anode porosity is forced to follow a fixed linear map of cathode porosity, tab count is forced to scale with diameter from one manufacturing benchmark, and many structural and transport constants are held fixed; if those couplings or constants are wrong for other cells, the claimed diameter dominance and trade-offs need not hold.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper develops a computationally lightweight geometric scaling model for cylindrical Li-ion cells that maps four design variables (cell height H_cell, diameter D_cell, cathode active loading σ_act,cat, cathode porosity ε_cat) to capacity Q_rev, DC internal resistance R_cell, mass, volume and winding length. Capacity is obtained from coated electrode area and active-material mass (Eqs. 4–22); resistance is the sum of ionic, electronic, geometric-collector and tab contributions (Eqs. 27–38) under Bruggeman and plate approximations. Anode porosity is linearly slaved to cathode porosity (Eq. 2) and tab count is floor-scaled with diameter from a manufacturing benchmark (Eq. 35). The model is validated on three commercial cells (capacity/resistance deviations 0.09–2.1 %, winding-length deviations 0.6–6 %) and then used for Monte-Carlo design-space exploration (N = 8192) plus first- and total-order Sobol indices and Spearman correlations, concluding that diameter is the dominant driver of capacity, resistance and both energy densities while height, loading and porosity produce secondary trade-offs.

Significance. If the reported accuracy and sensitivity rankings hold, the model supplies a fast, transparent cell-level surrogate that can be embedded in pack- and vehicle-level optimizers—an acknowledged gap relative to full electrochemical or multi-physics models. Strengths include fully explicit algebraic mappings, a reproducible Sobol design with large sample size, quantitative three-cell validation numbers, and clear identification of geometric versus electrode-level trade-offs. These features make the work useful for early-stage design-space exploration even if later refinements (temperature, ageing, multi-chemistry) are required.

major comments (3)
  1. [III-A, Table II] Section III-A states that multiple design-variable combinations can yield essentially the same capacity but different resistances; the authors then ‘select the value that matches most closely in both capacity and resistance’ before checking winding length. This selection step renders the reported 0.1–2.1 % capacity/resistance errors non-independent of the very geometric–resistance mapping later used to rank D_cell as dominant (Figs. 3–4). An out-of-sample protocol that freezes all free parameters (Table III) and predicts capacity, resistance and winding length without post-hoc selection is needed to support the design-space conclusions.
  2. [II-B, Eq. (41); Fig. 4] Gravimetric energy density (Eq. 41) is a central performance indicator, yet the manuscript never supplies the mass model W_cell. Only capacity and resistance receive full derivations; mass is mentioned in the abstract and §II-A but left undefined. Without an explicit, reproducible mass expression the Sobol indices and ‘high-gravimetric’ box-plots in Fig. 4 cannot be verified or reproduced.
  3. [II-A, Eqs. (2) and (35)] Two structural assumptions that directly affect resistance (and therefore the diameter ranking) are imposed without sensitivity testing: (i) anode porosity is forced to a linear map of cathode porosity (Eq. 2) and (ii) tab count is forced to floor-scale with diameter from a single manufacturing family (Eq. 35). Because Cells 1–2 used for validation belong to that same family, the low resistance errors partly reflect the calibration of Eq. 35 rather than an independent test of the geometric scaling. A brief parametric study releasing these two constraints (or reporting total-order indices with respect to the free parameters of Eqs. 2 and 35) is required before the dominance of D_cell can be claimed more generally.
minor comments (4)
  1. [Figs. 3–4] Figure captions and axis labels contain OCR artefacts (‘<act;cat’, ‘"cat’, ‘;i’) that render the Sobol and box-plot panels difficult to read; clean vector graphics are needed.
  2. [Appendix A, Table III] Table III lists many parameters as ‘assumed’ or ‘estimated’ without uncertainty ranges; a short column of literature sources or typical ranges would improve transparency.
  3. [II-B, Eq. (42)] The volumetric indicator (Eq. 42) uses the external can volume; it would be helpful to state whether this is the intended packaging volume or whether head-space and wall-thickness corrections are applied consistently with the capacity calculation.
  4. [Title page] The arXiv identifier and ‘accepted for 2026 IEEE VPPC’ dates appear future-dated; confirm final bibliographic metadata.

Circularity Check

2 steps flagged · score 3.0 of 10

Mild validation circularity: free electrode parameters are chosen to match capacity and resistance before winding-length is checked; the model equations themselves are not tautological.

  1. fitted input called prediction [Section III-A (Model Validation), paragraph on capacity/resistance/winding comparison; Table II]
    "When comparing the model's predicted capacity, winding length, and resistance, there is a relationship among the accuracies, since the model predicts some combinations of the design variables that provide approximately the same capacity but different resistance values. The value that matches most closely in both capacity and resistance is selected and then validated for winding length."

    For fixed can size, free electrode design variables (active loading, porosity, and related manufacturing choices) are selected so that capacity and resistance already match the benchmark; the reported capacity and resistance deviations (Table II: 0.09–2.1%) are therefore not independent predictions of those quantities. Only winding length is checked after that selection. The low capacity/resistance errors used to claim the model is 'accurate enough' for design-space conclusions are partly forced by the choice of inputs rather than by an out-of-sample test of the geometric–resistance map.

  2. fitted input called prediction [Section II-A.2 Resistance Relation, Eq. 35; Section III-A on tabs for Cells 1–2]
    "Ntab,i =⌊D cell · Ntab,benchmark / Dcell,benchmark⌋ ... For the specific cells, there are two from the same manufacturer. ... The first two cells (Cell 1 and 2) have five tabs on the current collectors, two for the cathode and three for the anode ... Since the overall goal is to optimize the battery design, the manufacturing methods for cells 1 and 2 are adapted to the model."

    Tab count, which enters geometric and tab resistance (Eqs. 33–37) and therefore total R_cell, is forced by a floor-scaling rule calibrated to a benchmark cell of the same manufacturing family used as validation Cells 1–2, and manufacturing methods for those cells are explicitly adapted to the model. Resistance agreement for those cells is therefore partly enforced by the tab rule fitted to the same family rather than predicted from geometry alone.

full rationale

The scaling model is a forward engineering map: capacity is computed from coated area, active loading and fixed chemistry parameters (Eqs. 4–22), and DCIR is the sum of ionic, electronic, geometric and tab terms (Eqs. 27–38). Those relations are not defined in terms of the outputs they produce, and the Sobol/Spearman design-space results are simply evaluations of that map over the stated bounds. There is no self-citation uniqueness chain, no renamed known theorem, and no load-bearing self-citation of the present authors. The only circularity is in how validation is performed and presented. For fixed can size the model admits multiple (σ_act,cat, ε_cat) combinations that give nearly the same capacity but different resistance; the authors select the combination that already matches both capacity and resistance, then report the resulting ~0.1–2.1% deviations and only afterwards check winding length. Tab count is likewise floor-scaled from a benchmark manufacturing family that includes Cells 1–2 (Eq. 35), and several structural/transport constants in Table III are assumed or estimated and held fixed. That procedure makes the capacity/resistance agreement partly by construction rather than an independent out-of-sample test of the geometric–resistance mapping later used to rank diameter. The winding-length check and the external chemistry parameters retain some independent content, so the circularity is partial and does not collapse the model derivation itself. Score 3 reflects one clear fitted-input validation step without a self-definitional core.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central claim rests on standard battery geometry and porous-electrode transport plus several paper-specific couplings and many fixed numerical constants. No new physical entities are introduced; free parameters and domain assumptions do most of the work that lets four design variables map to KPIs and sensitivity rankings.

free parameters (7)
  • Bruggeman exponent β = 1.5
    Fixed at 1.5 for ionic and electronic effective conductivities (Eqs. 28, 31); controls how porosity maps to resistance.
  • Geometric factor for radial collector resistance = 3
    Plate approximation uses factor 3 in Eq. 33 instead of a pure L/A model; chosen to match literature deviation.
  • Mandrel diameter scaling slope = 1/20000
    D_mandrel linear in D_cell with reported factor 20000 (Eq. 25); sets hollow-core length and thus winding length.
  • N/P capacity ratio NPR = 1.10
    Fixed at 1.10 to set anode loading from cathode areal capacity (Eqs. 20–21); enforces plating-safe designs.
  • Structural offsets and thicknesses (t_cell, t_cap, H_headspace, ΔH_cat, ΔL_cathode, foil thicknesses, tab geometry) = see Table III (mixed assumed/estimated)
    Many Table III entries labeled assumed/estimated; they directly set coated height/length and geometric resistance.
  • Tab-count benchmark (N_tab,benchmark / D_cell,benchmark) = cell-dependent (e.g. 2+3 or 1+2 tabs)
    Eq. 35 floor-scales tab count from a manufacturing benchmark; dominates geometric and tab resistance.
  • Anode/cathode porosity bounds for linear map = from cited feasible ranges [9],[10]
    ε_an is not free; Eq. 2 interpolates between fixed min/max anode porosities given ε_cat.
assumptions (7)
  • ad hoc to paper Anode porosity is a linear function of cathode porosity (Eq. 2) to keep electrode pairs feasible.
    Reduces design dimension; not derived from first principles in the paper.
  • domain assumption Jelly-roll winding length follows the spiral arc-length formula (Eqs. 11–12, 23–24).
    Standard geometric model for cylindrical cells; cited via [6].
  • domain assumption Effective ionic/electronic conductivities follow Bruggeman porosity scaling with β=1.5.
    Common porous-electrode approximation from [8]; used in Eqs. 28 and 31.
  • ad hoc to paper Number of tabs scales linearly (floor) with cell diameter from a manufacturing benchmark (Eq. 35).
    Manufacturing-dependent; chosen as the lowest-resistance method for the scaling model.
  • domain assumption Radial current-collector resistance can be approximated as a plate with geometric factor 3 (Eq. 33).
    Simplification relative to FEM used in [6]; factor absorbs 1-D model error.
  • domain assumption Single fixed NMC-811 / SiOx-graphite chemistry with constant first-cycle efficiencies and material densities.
    All design-space and sensitivity results are for one chemistry parameter set (Table III).
  • standard math Uniform independent sampling of design variables within Table I bounds is adequate for Sobol/Spearman analysis.
    Standard global sensitivity setup with Jansen estimators [17]; N=8192.

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Pith. "Pith review of Geometric Scaling of Battery Cells and Its Effect on Key Performance Indicators." pith.science (2026). https://pith.science/paper/P5B7ZZKI

@misc{pith2026260711566,
  author       = {Pith},
  title        = {Pith review of: Geometric Scaling of Battery Cells and Its Effect on Key Performance Indicators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P5B7ZZKI}},
  note         = {Machine review of arXiv:2607.11566}
}
read the original abstract

This paper presents a computationally lightweight scaling model for cylindrical lithium-ion battery cells, intended for early-stage battery design-space exploration. The model maps selected geometric and electrode-level design variables, including cell height, cell diameter, cathode active loading, and cathode porosity, to cell-level performance indicators such as capacity, DC internal resistance, mass, volume, and winding length. The scaling model is validated against available cylindrical cell data by comparing predicted capacity, internal resistance, and winding length. The validated model is subsequently used in a single-cell design-space exploration and global sensitivity analysis to evaluate capacity, internal resistance, gravimetric energy density, and volumetric energy density. The results identify the dominant design variables, favourable parameter directions, and key trade-offs between cell geometry, electrode loading, resistance, and energy density. The proposed model provides a basis for future integration into higher-level battery system and vehicle optimization frameworks.

Figures

Figures reproduced from arXiv: 2607.11566 by the authors.

Figure 1
Figure 1. Overview of the geometric scaling principles used to map cylindrical [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Visualization of the feasible design space with validation cell 1 and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Global sensitivity and parameter distributions for cell capacity and internal resistance. Subplots (a) and (b) show the first-order Sobol indices [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Global sensitivity and parameter distributions for volumetric and gravimetric energy density. Subplots (a) and (b) show the first-order Sobol indices [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Reference graph

Works this paper leans on

20 extracted references

  1. [1]

    A comprehensive review of lithium ion capacitor: development, modelling, thermal management and applications,

    M. Soltani and S. H. Beheshti, “A comprehensive review of lithium ion capacitor: development, modelling, thermal management and applications,”Journal of Energy Storage, vol. 34, p. 102019, 2 2021

    2021

  2. [2]

    (2016, 5) Tesla Model S Drive train Assembly

    Dhuri, S. (2016, 5) Tesla Model S Drive train Assembly. CAD model accessed from GrabCAD. [Online]. Available: https://grabcad. com/library/tesla-model-s-2

    2016

  3. [3]

    18650 vs. 21700 li-ion cells – a direct comparison of electrochemical, thermal, and geometrical properties,

    T. Waldmann, R. G. Scurtu, K. Richter, and M. Wohlfahrt-Mehrens, “18650 vs. 21700 li-ion cells – a direct comparison of electrochemical, thermal, and geometrical properties,”Journal of Power Sources, vol. 472, p. 228614, 10 2020

    2020

  4. [4]

    Contrasting a byd blade prismatic cell and tesla 4680 cylindrical cell with a teardown analysis of design and performance,

    J. Gorsch, J. Schneiders, M. Frieges, N. Kisseler, D. Klohs, H. Heimes, A. Kampker, M. M. Castro, and E. Siebecke, “Contrasting a byd blade prismatic cell and tesla 4680 cylindrical cell with a teardown analysis of design and performance,”Cell Reports Physical Science, vol. 6, p. 102453, 3 2025

    2025

  5. [5]

    Size effect on the thermal and mechanical performance of cylindrical lithium-ion batteries,

    J. Liu, C. Chen, J. Wen, Z. Chang, P. H. Notten, and Y . Wei, “Size effect on the thermal and mechanical performance of cylindrical lithium-ion batteries,”Applied Energy, vol. 375, p. 124056, 12 2024

    2024

  6. [6]

    Fast-charging performance and optimal thermal management of large- format full-tab cylindrical lithium-ion cells under varying environmental conditions,

    H. Pegel, D. Wycisk, A. Scheible, L. Tendera, A. Latz, and D. U. Sauer, “Fast-charging performance and optimal thermal management of large- format full-tab cylindrical lithium-ion cells under varying environmental conditions,”Journal of Power Sources, vol. 556, p. 232408, 2 2023

    2023

  7. [7]

    Manufacturing of tabless cylindrical lithium-ion cells: Quantifying the influence of cell dimensions and housing material via process-based cost modeling,

    H. Pegel, A. Grimm, C. Frey, V . Seefeldt, S. Baazouzi, and D. U. Sauer, “Manufacturing of tabless cylindrical lithium-ion cells: Quantifying the influence of cell dimensions and housing material via process-based cost modeling,”Journal of Energy Storage, vol. 98, p. 112863, 9 2024

    2024

  8. [8]

    Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell,

    M. Doyle, T. F. Fuller, and J. Newman, “Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell,”Journal of The Electrochemical Society, vol. 140, no. 6, pp. 1526–1533, 6 1993

    1993

Show all 20 references
  1. [9]

    Modeling of lithium-ion battery capacity fade with aging,

    I. V . Thorat, D. E. Stephenson, M. R. Zachariah, J. N. Harb, and D. R. Wheeler, “Modeling of lithium-ion battery capacity fade with aging,” Journal of Power Sources, vol. 188, no. 2, pp. 132–140, 9 2009

    2009

  2. [10]

    Development of experimental techniques for param- eterization of multi-scale lithium-ion battery models,

    C.-H. Chen, F. Planella, K. O’Regan, D. Gastol, W. D. Widanage, and E. Kendrick, “Development of experimental techniques for param- eterization of multi-scale lithium-ion battery models,”Journal of The Electrochemical Society, vol. 167, no. 8, p. 080534, 5 2020

    2020

  3. [11]

    Understanding calendar aging degradation in cylindrical lithium-ion cell: A novel pseudo-4-dimensional electrochemical-thermal model,

    P. Di Prima, D. Dessantis, D. Versaci, J. Amici, S. Bodoardo, and M. Santarelli, “Understanding calendar aging degradation in cylindrical lithium-ion cell: A novel pseudo-4-dimensional electrochemical-thermal model,”Applied Energy, vol. 377, p. 124640, 1 2025

    2025

  4. [12]

    Influence of cell dimensions and housing material on the energy density and fast-charging performance of tabless cylindrical lithium-ion cells,

    H. Pegel, D. Wycisk, and D. U. Sauer, “Influence of cell dimensions and housing material on the energy density and fast-charging performance of tabless cylindrical lithium-ion cells,”Energy Storage Materials, vol. 60, p. 102796, 6 2023

    2023

  5. [13]

    Electrical constriction resistance in current collectors of large-scale lithium-ion batteries,

    P. Taheri, A. Mansouri, B. Schweitzer, M. Yazdanpour, and M. Bahrami, “Electrical constriction resistance in current collectors of large-scale lithium-ion batteries,”Journal of The Electrochemical Society, vol. 160, no. 11, pp. A1736–A1742, 8 2013

    2013

  6. [14]

    Effect of thickness on the maximum potential drop of current collectors,

    J. M. Campillo-Robles, X. Artetxe, and K. del Teso Sanchez, “Effect of thickness on the maximum potential drop of current collectors,”Applied Physics Letters, vol. 111, no. 9, p. 093901, 8 2017

    2017

  7. [15]

    Is the molicel p50b “tabless

    BatteryMooch, “Is the molicel p50b “tabless”? i tore one down to find out...” 7 2024, forum discussion on Endless- Sphere. [Online]. Available: https://endless-sphere.com/sphere/threads/ is-the-molicel-p50b-tabless-i-tore-one-down-to-find-out.124666/

    2024

  8. [16]

    Cutting open the best li-ion cell in fpv: Molicell p45b,

    C. Rosser, “Cutting open the best li-ion cell in fpv: Molicell p45b,” 2023, youTube video. [Online]. Available: https://www.youtube.com/ watch?v=GetzMfpY5mg

    2023

  9. [17]

    Analysis of variance designs for model output,

    M. J. Jansen, “Analysis of variance designs for model output,” Computer Physics Communications, vol. 117, no. 1, pp. 35–43, 1999

    1999

  10. [18]

    Battery data platform,

    About:Energy, “Battery data platform,” accessed: Feb. 2026. [Online]. Available: https://www.aboutenergy.io/

    2026

  11. [19]

    Why n/p ratio matters in lithium-ion cells,

    K. Batus ¸, “Why n/p ratio matters in lithium-ion cells,” AION Engineering INC, 9 2025. [Online]. Available: https: //www.batterydesign.net/why-n-p-ratio-matters-in-lithium-ion-cells/

    2025

  12. [20]

    Cell analysis and modelling system (cams) v2.0,

    The Faraday Institution, “Cell analysis and modelling system (cams) v2.0,” The Faraday Institution, 5 2025. [Online]. Available: https://www.faraday.ac.uk/fi-cell-modelling-workbook/ APPENDIXA MODELPARAMETERS A. Battery Model Parameters Table III ELECTROCHEMICAL CELL MODEL PAR...

    2025

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