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REVIEW 5 major objections 5 minor 67 references

Multi-Objective Aerodynamic Optimization of Ride Height and Rake Angle in a Sedan Car Using CFD and Machine Learning

T0 review · 5 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Simultaneously tuning ride height and rake angle narrows a sedan's aerodynamic optimum to a compact, nearly speed-independent design window, with balanced settings cutting drag about 8% while adding downforce.

desk verdict A workmanlike CFD+ML optimization case study whose headline Re-independence claim is not established: objective variations are below the surrogate's error, and validation geometry differs from the simulation geometry. read the letter →

arxiv 2509.02917 v1 pith:VICFIMSJ submitted 2025-09-03 physics.flu-dyn

Mahdi Kheirkhah , Ehsan Roohi , Mahmoud Pasandidehfard This is my paper · ORCID
classification physics.flu-dyn PACS 47.85.Gj
keywords rideheightrakeanglesedanaerodynamicsdragcoefficientliftGradientBoostingDifferentialEvolutionReynoldsnumberindependence
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

The paper tries to establish that a passenger sedan's aerodynamic posture—ride height and rake angle—can be optimized simultaneously, and that the resulting optimum is confined to a narrow geometric window that barely moves as Reynolds number (vehicle speed) changes from 4.87e6 to 19.48e6. If true, a single suspension setting or a slow-acting adjustable suspension could deliver near-optimal drag and downforce over ordinary road and highway speeds. Using CFD-generated data, the paper trains a Gradient Boosting surrogate to predict drag and lift coefficients from ride height, rake angle, and Reynolds number, then runs Differential Evolution under balanced, drag-focused, and downforce-focused objectives. The balanced optimum cuts drag about 8% while adding downforce; the drag-focused optimum cuts fuel demand about 9%; the downforce-focused optimum more than quadruples negative lift at a roughly 7% drag penalty.

What carries the argument

The central machinery is a Gradient Boosting surrogate model mapping (ride height, rake angle, Reynolds number) to drag and lift coefficients, trained on a CFD dataset spanning five ride heights, six rake angles, and four Reynolds numbers, and then optimized by Differential Evolution on a weighted-sum objective α·Cd + β·Cl. The surrogate makes continuous optimization feasible from sparse CFD samples and yields the narrow optimum region; the weighting choices mark positions on the drag–downforce trade-off rather than the full Pareto front.

What would settle it

Run a high-fidelity scale-resolving simulation or wind-tunnel test on the exact optimized geometry (ride height 1.355 m, rake 2.97 degrees at Re=9.75e6). If drag coefficient deviates from roughly 0.287–0.293 or lift coefficient from roughly −0.062 to −0.083 by more than the reported ML-versus-CFD error, the surrogate or the DrivAer-to-sedan transfer is wrong. A second check: re-optimize on a dense grid near 1.34–1.36 m ride height and 2.8–3.0 degrees rake; if the predicted plateau disappears or the optimum moves more than about 1 cm in ride height or 0.1 degree in rake with Reynolds number, th

Watch

Extended reading notes

Core claim

The central claim is that for the sedan geometry studied, the optimal ride height and rake angle depend only weakly on Reynolds number over a four-fold range: the balanced optimum sits at about 1.355 m ride height and 2.97 degrees rake at the lowest and middle Reynolds numbers, shifting to about 1.34 m and 2.88–2.97 degrees at higher values, with objective values confined between 0.176 and 0.178. The same pattern holds for the drag-minimizing and downforce-maximizing conditions, each occupying a compact design window. The paper therefore concludes that robust aerodynamic performance—both lower drag and increased downforce—can be achieved by a small set of geometric adjustments without retuni

Load-bearing premise

The whole optimization stands on the assumption that a mesh and turbulence setup validated on one car body (the DrivAer Notchback) predicts drag and lift just as accurately on the different sedan body used for all reported results, and that a surrogate trained on a coarse handful of CFD runs is smooth enough to locate the true continuous optimum.

Editorial extensions

If this is right

  • A fixed suspension setting near 1.35 m ride height and 2.9 degrees rake yields a near-balanced drag/downforce compromise across speeds from roughly 55 to 220 km/h.
  • Minimum-drag tuning reduces fuel consumption by about 9.1% over a 100 km drive, while maximum-downforce tuning increases downforce by more than 500% at a 14.3% increase in required engine force.
  • An active suspension system can use a slow, speed-independent target rather than a continuous speed-to-geometry map, simplifying control logic.
  • Because the surrogate predicts drag coefficient within about 3% of CFD at the optimized points, inexpensive design-space exploration is feasible before final CFD or wind-tunnel validation.
  • The trade-off structure makes it possible to choose weighting coefficients in advance to land on a desired drag-versus-downforce compromise without computing the full Pareto front.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A fixed mechanical lowering with a slight positive rake could capture most of the balanced benefit without any active suspension, since the optimal ride height and rake stay within roughly 1.34–1.36 m and 2.9–4.8 degrees across the tested speed range.
  • Because the surrogate is trained on a coarse grid of only a few dozen CFD runs, the 'narrow optimum' could partly reflect interpolation smoothness; testing denser combinations near 1.34–1.36 m and 2.8–3.0 degrees would reveal whether the plateau is physical.
  • The balanced result uses weights α=0.7, β=0.3; shifting these weights would slide the optimum along the same narrow geometric band, so quantifying that band for other weights is a direct extension of the paper's method.
  • The Reynolds-number robustness may extend to other notchback sedans if underbody flow remains attached and the minimum-ground-clearance constraint is not active, but that extension is speculative.
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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

5 major / 5 minor

Summary. The paper combines steady RANS CFD (SST k-omega) on a SolidWorks Audi A4 sedan with ML surrogates (Random Forest, Gradient Boosting, LightGBM) and Differential Evolution to optimize ride height and rake angle under three scalarized objectives. It reports a baseline Cd=0.313/Cl=+0.0288, a balanced optimum Cd=0.287/Cl=-0.0826, a minimum-drag optimum Cd=0.285, and a maximum-downforce optimum Cl=-0.1084. The central claim is that the optimum geometry is almost independent of Reynolds number over 4.87e6-19.48e6, which the authors present as enabling a single ride-height/rake setting to remain near-optimal across a wide speed range. A mesh-independence study and a 3.25% Cd validation against DrivAer Notchback wind-tunnel data are reported, and three optimized configurations are re-evaluated with CFD in Table 4.

Significance. If the results hold, the paper provides a practical workflow: coarse CFD plus ML surrogate plus evolutionary optimization can identify a narrow ride-height/rake region with robust performance, simplifying active-suspension set-point selection. Strengths include explicit multi-Reynolds-number design, external CFD re-validation of three ML-identified optima (Table 4), and a clear quantification of the drag/downforce trade-off. However, the two headline claims are not yet fully supported: the absolute optimized coefficients rest on a validation performed on a different geometry (DrivAer, not the Audi A4), and the Reynolds-number independence is inferred from a surrogate whose error is the same order as the observed objective variation. The paper's practical conclusions are therefore plausible but require additional CFD checks or a more cautious framing.

major comments (5)
  1. [§3.5, §3.1, §4.11] The mesh-independence and validation (3.25% Cd deviation from DrivAer wind-tunnel data) are performed on the DrivAer Notchback, while all production simulations and optimization results use the SolidWorks Audi A4 model. Section 3.5 does not validate the Audi geometry itself. Since the absolute coefficients and percentage improvements in the abstract and Tables 3-4 are computed on the Audi geometry, the transfer of the DrivAer validation error is an unproven assumption. Please either validate the actual Audi model or explicitly restate the results as based on an unvalidated Audi geometry with only the DrivAer-related mesh/turbulence setup checked.
  2. [§4.7, Table 1, Table 4] The Reynolds-number independence of the optimum is a surrogate-only conclusion. The balanced objective varies by only 0.1761-0.1776 (~0.0015), while the test RMSE of the objective implied by Table 1 (0.7*Cd + 0.3*Cl) is about 0.003. The optimal ride height and rake angle also shift less than the 5 cm / 1 degree sampling. The CFD re-validation in Table 4 is performed only at Re=9.75e6, so it cannot test whether the optimum shifts at other Re. To support the central claim, add CFD checks at at least one lower and one higher Re, or report uncertainty bounds and soften the Re-independence conclusion accordingly.
  3. [§4.11, Table 4, Abstract] Table 4 contains an inconsistency for the Balanced case: predicted Cl=-0.0826 and simulated Cl=-0.062 imply a relative error of about 33% (0.0206/0.062), not the reported 9.10%. The text's statement that 'the relative error in the lift coefficient is around 9-10%' is therefore not supported. Since the abstract's headline Cd=0.287 and Cl=-0.0826 are ML predictions rather than CFD values, the abstract overstates what was 'achieved'; the CFD re-simulation gives Cd=0.293 and Cl=-0.062. Correct the table and rephrase the abstract/claims to distinguish predicted from simulated coefficients.
  4. [§4.3, §4.6-§4.9] The paper defines a minimum ground clearance of 100 mm and states that at ride height 1.336 m only rake=1 degree is valid. The optimization appears to optimize the surrogate over the full input rectangle without re-imposing the clearance constraint. Some reported optima (e.g., h=1.355 m, rake=2.968 degrees at Re=9.75e6) lie in regions that were not simulated at the nearest lower ride height, so feasibility is not established. Please specify how the 100-mm constraint is enforced in the Differential Evolution loop or verify that the optimized geometries satisfy the constraint.
  5. [§4.12, Eq. (11)] Equation (11) uses A_top to convert Cl to lift force. The standard reference area for lift coefficient in vehicle aerodynamics is the frontal area, and A_top is neither defined nor used elsewhere. This affects the rolling-resistance correction and hence the fuel-consumption numbers in Section 4.12, including the 9.1% fuel-saving claim. The area should be corrected and the calculations repeated.
minor comments (5)
  1. [§1, §4.4] The introduction says 'XGBoost Regressor', but the models implemented and compared are Random Forest, Gradient Boosting (Scikit-learn), and LightGBM. Please harmonize the nomenclature.
  2. [Abstract, §3.5] The abstract says the model was 'validated against DrivAer Notchback wind-tunnel data', but the production geometry is an Audi A4. Reword to avoid implying that the Audi geometry itself was validated.
  3. [§4.4.2, Figure 10] The subpanels in Figure 10 are not labeled with the model names in the caption. Please identify each panel explicitly.
  4. [Data Availability] Data and code are only available 'upon request'. For reproducibility, please provide the trained model parameters for Gradient Boosting (Table 2 gives only the RF_Tuned hyperparameters) and, if possible, the processed dataset.
  5. [References] Several references are incomplete or non-archival (e.g., [11], [12], [13]). Please standardize citation format and provide DOIs where available.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: surrogate optimization is externally checked by CFD; the Re-independence claim is under-validated but not circular.

full rationale

The central chain (CFD samples -> Gradient Boosting surrogate -> Differential Evolution -> optimum geometry -> independent CFD re-simulation) is not circular: Table 4 re-runs CFD at the three optimized geometries and reports Cd errors of 0.9-2.5% and Cl errors ~9-10%, providing an external check on the surrogate's predictions. The optimization is not a fit renamed as a prediction because the objective is a weighted sum of surrogate outputs and the final geometries are re-evaluated in the solver. The headline Re-independence result, however, is read directly from the fitted surrogate (Sec. 4.7: "A key finding is that the optimized conditions remained within narrow geometric intervals, showing only very weak dependence on Reynolds number across the considered range") and the CFD validation is performed only at Re=9.75e6 (Sec. 4.11: "all CFD analyses were carried out at a Reynolds number of 9.75 x 10^6. Since the influence of Reynolds number on the location of the optimized conditions was found to be negligible..."). This is a validity/robustness limitation - the claimed Re-insensitivity is not independently confirmed at other Reynolds numbers and differences are of order the surrogate RMSE - but it is not circularity in the strict sense: Re is an input feature, not a parameter fitted to the output claim. The paper's self-citations ([27], [34]) support generic background statements and are not load-bearing. The acknowledged limitations (no crosswind, simplified geometry, steady state) are correctly stated in the conclusion and do not hide a definitional circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard CFD closures, validation transfer, ML generalization, and fuel-model constants. No new physical entities are introduced. The free parameters are the scenario weights and the clearance constraint, which shape the optimization directly.

free parameters (3)
  • Scenario weighting factors alpha and beta in scalarized objective = Balanced 0.7/0.3; drag-focused 0.999/0.001; downforce-focused 0.001/0.999
    Eq. (9) defines Objective = alpha*Cd + beta*Cl. The weights are chosen by hand to define the three optimization scenarios and directly determine the reported optimal points.
  • Minimum ground clearance constraint = 100 mm
    Used in sections 4.1 and 4.3 to exclude invalid rake/ride-height combinations, which removes cells at the lowest ride height and shapes the design space.
  • ML random state and RF_Tuned hyperparameters = random_state=42; RF n_estimators 141/147, max_depth 23/25
    Fixed split and tuning choices affect the reported R2 values; Gradient Boosting hyperparameters are not reported, which limits reproducibility.
assumptions (5)
  • domain assumption SST k-omega RANS closure adequately predicts drag and lift for this automotive geometry
    Used throughout (sections 2.3, 3.5); no scale-resolving simulation is performed. The accuracy of the turbulence closure is taken as given.
  • domain assumption Steady incompressible RANS is valid for these flow conditions (Mach below 0.3)
    Stated in section 3.4; neglects transient vortex shedding and compressibility effects.
  • domain assumption DrivAer Notchback experimental data is an acceptable proxy for validating the Audi A4 model
    The validation in section 3.5 is performed on the DrivAer geometry, not the modeled Audi A4; transfer to the actual geometry is assumed, not demonstrated.
  • domain assumption ML surrogate trained on the coarse CFD dataset generalizes over the continuous design space
    The optimization over continuous ride height and rake (sections 4.6-4.9) and 'continuous Reynolds number' (section 4.7) extrapolates the surrogate beyond the sampled grid points; no uncertainty quantification is given.
  • domain assumption Vehicle and fuel model constants (m=1600 kg, Cr=0.01, engine efficiency 0.3, gasoline 33 MJ/L)
    Used in section 4.12 to convert aerodynamic coefficients into fuel-consumption claims; these are external assumptions not derived in the paper.

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Cite this review

Pith. "Pith review of Multi-Objective Aerodynamic Optimization of Ride Height and Rake Angle in a Sedan Car Using CFD and Machine Learning." pith.science (2026). https://pith.science/paper/VICFIMSJ

@misc{pith2026250902917,
  author       = {Pith},
  title        = {Pith review of: Multi-Objective Aerodynamic Optimization of Ride Height and Rake Angle in a Sedan Car Using CFD and Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VICFIMSJ}},
  note         = {Machine review of arXiv:2509.02917}
}
read the original abstract

This study investigates the aerodynamic performance of an Audi A4 sedan using CFD analysis. A 3D model was developed in SolidWorks and validated against DrivAer Notchback wind-tunnel data, showing only a 3.25 percent deviation in drag coefficient (Cd). Ride height varied from 1.336 to 1.536 m and rake angle from 0 to 5 degrees, across four Reynolds numbers. Gradient Boosting emerged as the most accurate predictive model (R square = 0.97 for Cd and 0.96 for lift coefficient, Cl), outperforming Random Forest and LightGBM. Differential Evolution optimization was performed under balanced, drag-focused, and downforce-focused conditions. Reynolds number had minimal impact on optimum location; therefore, detailed results are reported for one Reynolds number, with other Re showing similar trends. The baseline geometry exhibited Cd = 0.313 and Cl = 0.0288. Balanced optimization achieved Cd = 0.287 and Cl = - 0.0826. Minimum drag condition reached Cd = 0.285 with slight positive lift (Cl = 0.0142), while maximum downforce optimization reached Cl = - 0.1084 with a 6.71 percent drag penalty (Cd = 0.334). Near-optimal solutions were found within ride heights of 1.341 to 1.365 m and rakes of 0.158 to 4.610 degrees, indicating robust aerodynamic performance. Machine learning predictions were further validated against CFD with a small error in Cd.

Figures

Figures reproduced from arXiv: 2509.02917 by the authors.

Figure 1
Figure 1. The two-dimensional schematic representations include: (a) the designed body of the Audi A4, modeled in SolidWorks 2020 based on blueprint drawings (dimensions in meters); and (b) the DrivAer Notchback model, constructed in SolidWorks 2020 using the publicly available 3D data provided by the Technical University of Munich [19] [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. The geometry and dimensions of the computational domain, along with the applied boundary conditions [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. (a) The computational meshes generated in the ANSYS Meshing 2019 environment, around the DrivAer Notchback model in the symmetry plane (b) Meshing and inflation details around the body (c) y⁺ distribution on body and wheels [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Variation of the total drag coefficient for the DrivAer Notchback model with respect to (a) mesh resolution and (b) Reynolds number [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Distribution of the static pressure coefficient over the upper surface of the DrivAer Notchback model for different mesh resolutions, compared with experimental wind tunnel data [5] along the centerline [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Three-dimensional schematic of the Audi A4 vehicle at zero rake angle under five different ride heights: a) 1.336 m, b) 1.386 m, c) 1.436 m, d) 1.486 m, and e) 1.536 m; and at the baseline ride height of 1.436 m under various rake angles: f) 1°, g) 2°, h) 3°, i) 4°, an…
Figure 8
Figure 8. Figure 8: A depiction of the rake angle position and the minimum ground clearance beneath the vehicle for a sample case with a 4-degree rake angle and an ride height of 1.436 meters (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 10
Figure 10. Figure 10: Parity plots of actual vs. predicted aerodynamic coefficients for RF (a) Cd, (b) Cl, XGBoost (c) Cd, (d) Cl, and LightGBM (e) Cd, (f) Cl, RF_Tuned (g) Cd, (h) Cl [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: Schematic of the machine learning workflow and model selection process [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]
Figure 18
Figure 18. Figure 18: Pressure-coefficient (Cp) distribution with streamlines on the symmetry plane at optimum ride height h=1.341, optimum rake angle =0.158∘ , and Re=9.75×106 Considering the minor influence of Reynolds number on the optimal parameters, the pressure coefficient and stream…

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.