Constraint-driven aero-structural twist optimization of 3D-Printed PETG low-Reynolds-number multirotor propellers

Flexible fused-deposition-modelled propellers can lose endurance when deformation changes the designed incidence, while thin sections that appear aerodynamically superior may be structurally inadmissible. This study develops a constraint-driven aero-structural workflow for a 9.4 in two-bladed glycol-modified polyethylene terephthalate (PETG) multirotor propeller at a per-rotor hover thrust of 4.5 N. Six chord-twist and airfoil candidates were evaluated over 2-5 N using blade-element momentum theory (BEMT) and orthotropic finite-element analysis (FEA). Candidates were screened against a 40 MPa stress allowable and a 0.03R tip-deflection limit. The most efficient feasible blade was then refined by constrained stationwise twist redesign using local Reynolds number, inflow angle, and Cl/Cd information while retaining chord, airfoil schedule, diameter, root geometry, and section thickness. The final design was independently checked using steady RANS computational fluid dynamics (CFD) and pressure-mapped FEA. The aerodynamic-only winner failed the 0.03R deflection constraint, whereas the APC/E216 configuration satisfied both stress and stiffness requirements and was selected as the feasible baseline. Across 2-5 N, the local twist redesign reduced the required rotational speed by approximately 11% and increased the hover figure of merit by up to 4.6%. At the 4.5 N design point, outward load migration increased the torque arm while the lower rotational speed reduced combined stress by 24.2%. The associated reduction in centrifugal stiffening increased tip displacement by 45.5%, but the displacement remained within the prescribed limit. RANS-CFD and pressure-mapped FEA recovered the target thrust and confirmed structural feasibility. The results show that aerodynamic improvement cannot be separated from printed-blade stiffness. Twist-induced radial load redistribution can simultaneously improve hover efficiency, reduce centrifugal stress, and decrease centrifugal stiffening. The proposed tiered BEMT/FEA-to-CFD/FEA workflow therefore provides a physically traceable route for balancing aerodynamic performance and structural admissibility in printable low-Reynolds-number multirotor propellers.

Low-Reynolds-number propeller aerodynamics

Propellers are the principal energy-conversion elements of a multirotor aircraft. In hover, each rotor must continuously impart downward momentum to the surrounding air, and relatively small losses in profile drag, induced velocity, or off-design incidence accumulate over the whole mission. This sensitivity is especially pronounced for light unmanned aerial vehicles (UAVs), because their propellers operate at Reynolds numbers for which viscous effects, laminar separation, airfoil thickness, surface quality, and local angle of attack are all consequential (Brandt and Selig, 2011; Giguere and Selig, 1998). At vehicle level, an efficient propeller can extend endurance without enlarging the battery; at component level, however, an aggressively thin or highly loaded blade can deform enough to alter the aerodynamic geometry that produced the apparent gain.

Classical optimum-propeller design distributes circulation and loading to reduce induced and profile losses (Adkins and Liebeck, 1994). For small rotors, blade-element momentum theory (BEMT) remains attractive because it resolves spanwise airfoil behaviour at a small fraction of the cost of three-dimensional computational fluid dynamics (CFD) (Li et al., 2015). Its assumptions are most credible when checked against static test data. The low-Reynolds-number database of Brandt and Selig (Brandt and Selig, 2011) and the multirotor propulsion measurements of Deters et al. (2017) are therefore useful references for preliminary models.

Three-dimensional CFD provides a complementary view of pressure loading, wake contraction, tip flow, and the induced jet. Kutty and Rajendran (Kutty and Rajendran, 2017) combined CFD and experiment for an APC slow-flyer propeller, while Garofano-Soldado et al. (2022) used numerical–experimental comparisons under low-Reynolds-number ground-effect conditions. More recent assessments have examined modelling choices and grid sensitivity (Arafat et al., 2024), and numerical shape studies have reproduced pressure-side overpressure, suction-side depression, and the accelerated downstream wake (Choayb, 2024). These studies support CFD interrogation of a selected design but caution against using one unconverged solution as an optimization engine.

Geometry studies identify chord, twist, airfoil, blade number, and operating speed as coupled variables. Static experiments show that pitch and geometry alter thrust, power, and acoustic response together (Jordan et al., 2020). Blade-number changes can increase thrust but modify efficiency and wake interaction (Lakhdhar et al., 2025). At section level, thickness and camber change lift, drag, separation, and pressure recovery (Ma et al., 2015; Roy et al., 2021). At blade level, twist is particularly influential because tangential speed grows with radius; a single incidence cannot keep every station near an efficient angle of attack. Sun et al. (2023) demonstrated coupled performance and noise effects, while Zhu et al. (2021) related multirotor geometry to measured performance. Propeller loading also has aircraft-level consequences: Rostami et al. (2022) showed that asymmetric blade loading can affect stability and vertical-tail sizing. Although the present hover case is symmetric and isolated, its radial loads must eventually be carried into off-axis and vehicle-interaction analyses.

FDM printed-blade structural limitations

Additive manufacturing makes the aerodynamic–structural conflict more important rather than removing it. Fused-deposition modelling (FDM) can produce replacement propellers without moulds, supports rapid geometry iteration, and enables distributed manufacture (Goh et al., 2017; Baltić et al., 2024). Yet a printed polymer is anisotropic, its elastic response depends on layer orientation and process parameters, and the as-built surface may not reproduce the smooth computational geometry (Özen et al., 2021; Ramos et al., 2025). Manufacturing route can also change propeller performance and acoustic emission (García-Tíscar et al., 2026). A printable propeller should therefore be selected through aerodynamic and structural constraints together, not by thrust or efficiency alone.

Blade flexibility is also an endurance issue. Bending and torsion change local twist, angle of attack, and radial loading, so the motor may have to supply additional speed or power to recover the required thrust. Repeated deformation, thermal softening, and print-to-print modulus variation further reduce the margin between the nominal aerodynamic design and its as-built operating shape. Structural admissibility is therefore an energy-retention requirement as well as a strength requirement (Möhren et al., 2023; García-Tíscar et al., 2026).

Structural studies offer two observations that matter here. First, root stress in a high-speed small propeller can be dominated by centrifugal rather than aerodynamic loading (Fukui and Nishida, 2019). Second, centrifugal loading can stiffen a rotating blade and suppress transverse deflection (Algolfat et al., 2022). Elasticity can then feed back into propeller performance (Möhren et al., 2023). Thus, reducing rotational speed may lower inertial stress while simultaneously removing beneficial geometric stiffness. Recent multi-domain investigations combine aerodynamics and structural integrity (Sourirajan et al., 2025; Rajendran et al., 2025), but the numerical size of this inverse stress–deflection response is often hidden behind a composite objective.

Many optimization studies evaluate ideal smooth geometry and homogeneous material behaviour, with structural qualification performed only after an aerodynamic optimum is identified. That sequence is unsafe for an FDM blade: print-induced anisotropy, finite section thickness, root load transfer, deformation-driven incidence change, surface fidelity, and process feasibility can overturn the aerodynamic ranking. Malim et al. (2024) demonstrated the importance of calibrating and experimentally validating the material-to-blade model for a large 3D-printed propeller. Their result motivates the present separation between numerical screening and the prototype qualification still required for PETG.

Gaps in existing aero-structural optimization

Optimization has moved from analytic distributions toward evolutionary and surrogate-assisted searches. Constrained particle-swarm optimization has combined aerodynamic and structural objectives (Hoyos et al., 2022); differential evolution has been embedded in propeller-design algorithms (Sedelnikov et al., 2024); and NSGA-II studies have addressed multi-objective aerodynamic design (Gao et al., 2026). Validated optimization-oriented programs have also been reported (Schmähl and Hornung, 2026), and high-thrust studies increasingly include noise (Hu et al., 2025). These methods broaden the search space, but they do not by themselves explain why an efficiency change transfers load or alters deformation.

Low-density rotor studies further demonstrate the value of hierarchical fidelity. Zhao et al. (2019) coupled modified BEMT and CFD for airfoil selection, Tang et al. (2023) combined a neural network, a genetic algorithm, and CFD to optimize chord and twist, and Wang et al. (2024) extended the search to a six-parameter blade and verified it experimentally. Although Martian and terrestrial operating densities differ, these works support low-cost screening followed by high-fidelity flow analysis and final verification.

Against that background, four distinct gaps remain for a printable light-UAV propeller. First, aerodynamic studies commonly rank ideal blades without proving that the winner satisfies a printed-polymer stiffness limit. Second, aero-structural optimizations often report only aggregate objectives, leaving the spanwise transfer of normal and tangential load unexplained. Third, studies that credit lower speed with reduced centrifugal stress rarely quantify the simultaneous loss of centrifugal stiffening and deflection margin. Fourth, final structural predictions based on reduced-order loads are seldom checked against a mapped three-dimensional CFD pressure field on the same printed-blade geometry.

This paper advances the existing work in five ways: It performs a controlled six-configuration comparison at common diameter, thrust, and material assumptions, separating planform/twist effects from main-airfoil thickness effects.

It applies stress, stiffness, and manufacturability gates before accepting the aerodynamic ranking, thereby preventing an efficient but excessively flexible E63 blade from becoming the design baseline.

It formalizes a constrained stationwise twist objective and traces its outcome through local C l / C d, Reynolds number, inflow angle, and radial normal/tangential load migration over 2–5N.

It quantifies both sides of the rotational trade-off: centrifugal-stress relief and the accompanying loss of centrifugal stiffening and displacement margin.

It uses a tiered verification route—BEMT/FEA for screening and RANS-CFD pressure mapping for the final blade—and reports the discrepancy between the two structural load paths.

The remainder of the paper is organized as follows. Section 2 presents the aerodynamic, structural, optimization, and CFD/FEA procedures. Section 3 reports validation, constraint-aware selection, twist optimization, radial load redistribution, and multiphysics cross-verification. Section 4 places the findings in the context of prior work and states the limitations, and Section 5 summarizes the main outcomes.

Algorithm 1 states the hierarchy and its decision gates directly in editable LaTeX pseudocode. The nested for loops evaluate every candidate and thrust level, while explicit if–else statements enforce structural feasibility, stationwise twist constraints, and final CFD/FEA acceptance. Low-cost aerodynamic ranking is intentionally provisional: every candidate must satisfy both structural inequalities before local twist improvement and higher-fidelity verification.

Algorithm 1 Constraint-driven aero-structural design of the printed propeller. 1 Input: candidate set C, thrust set T = { 2,3,4,4.5, 5 } N, σ allow = 40 MPa, δ allow = 0.03 R

2 Output: structurally feasible, locally improved blade b ⋆

3 F ← ∅ //feasible-candidate set

4 for each candidate b ∈ C do

5 feasible ← true

6 for each target thrust T j ∈ T do

7 (Ω, Q, P, F o M, L aero) ← B E M T (b, T j)

8 (σ max, δ tip) ← F E A (b, Ω, L aero)

9 if σ max > σ allow or δ tip > δ allow then

10 feasible ← false; break

11 end if

12 end for

13 if feasible then F ← F ∪ { b } else reject b end if

14 end for

15 b 0 ← highest-FoM candidate in F; b ⋆ ← b 0

16 for each radial station r i / R do

17 compute W i, R e i, ϕ i, α i, and (C l / C d) i

18 Δ β i ← stationwise incidence correction

19 if | Δ β i | ≤ 5 ° and stall margin ≥ 2 ° then

20 update β i subject to smoothness, monotonicity, and manufacturability

21 else clip or reject Δ β i end if

22 end for

23 rerun BEMT and screening FEA for b ⋆ over T

24 if stress and deflection constraints pass at every T j then

25 run RANS CFD and map the pressure field to the final ANSYS FEA model

26 if CFD thrust agreement and final structural constraints are satisfied then

27 accept b ⋆

28 else return to the stationwise twist update end if

29 else return to the stationwise twist update end if

30 return b ⋆

Design case and performance measures

The reference vehicle is a DJI F450-class quadrotor with a maximum take-off mass of 1.8kg, four rotors, and a nominal propeller diameter of 9.4in (D = 238.76 m m, R = 119.38 m m). The rounded value g size = 10 m.s − 2 is used only to define a conservative, easily reproducible design target; it is not presented as the standard gravitational acceleration. Where gravity is required in the numerical model, g 0 = 9.81 m.s − 2 is used. The design thrust per rotor is

Hover sizing relation (Equation 1). This is a conservative hover sizing point tied to maximum mass. The analysis covers 2–5N so that the design is not optimized at an isolated operating point.

For a blade element of width d r, relative speed W, chord c, and local lift and drag coefficients C l and C d, elemental loads (Equation 2); thrust/torque relations (Equation 3).

Here, ρ is air density; B = 2 is blade count; r is radial position; W is relative section speed; c is chord; C l and C d are sectional lift and drag coefficients; ϕ is inflow angle; and d L, d D, d T, and d Q are elemental lift, drag, thrust, and torque. Momentum and blade-element relations are iterated with tip/root corrections in QBlade. The local angle of attack is given by the angle relation (Equation 4). where β is geometric twist. The “rotor efficiency” exported from QBlade is used here as the hover figure of merit (FoM), not as a dimensional thrust-to-power ratio FoM relation (Equation 5). where A = π R 2, P i = T T / (2 ρ A) is the ideal actuator-disk hover power, and P = Q Ω is rotor shaft power. The dimensionless coefficients use C T = T / [ ρ A (Ω R) 2 ] and C P = P / [ ρ A (Ω R) 3 ], so the coefficient and dimensional forms are exactly equivalent. The values reported as percentages throughout the paper are 100 F o M. Required power follows P = Q Ω, so a torque rise can offset part of a speed reduction even when the aerodynamic efficiency indicator improves.

Candidate blade architecture

Three chord–twist families were reconstructed from representative DJI 9450-, T-Motor 1344-, and APC 9047SF-type blades and scaled to the common diameter. Scaling preserves the nondimensional radial coordinate, chord ratio, and geometric twist: r t / R t = r s / R s, c t / R t = c s / R s, and β t (r t / R t) = β s (r s / R s), where subscripts s and t denote source and target blades. Thus r t = (R t / R s) r s and c t = (R t / R s) c s, while airfoil thickness and camber remain percentages of the local chord. No independent chord or pitch correction is introduced during scaling. Figure 1 shows the resulting distributions. The DJI family concentrates its largest chord near 0.3 R, the T-Motor family near 0.4 R, and the APC family maintains a chord of approximately 25.4–27.5 mm across 0.4 R – 0.8 R. The APC twist is also highest through most of the lifting span, falling from 26.01 ° at 0.2 R to 8.09 ° at the tip. The importance of spanwise geometry is consistent with the twist sensitivity reported by Sun et al. (2023). Zhu et al. (2021) likewise showed that multirotor propeller geometry strongly conditions measured performance. The present comparison uses these geometric differences as controlled inputs to a common aero-structural screening framework rather than evaluating them in isolation.

All six candidates use the E856 section over 0– 0.2 R to provide an 18.15 % -thick structural root. Configurations 1–3 use the 4.25 % -thick E63 over 0.2 R – R, and configurations 4–6 use the 10.42 % -thick E216. The E63 and E216 have comparable maximum camber (5.38% and 5.17%), which makes the comparison primarily sensitive to thickness and its drag/stiffness consequences. The pointwise validation data are summarized in Table 1. Table 2, Panel A, condenses the geometry mapping together with the design-point feasibility metrics used later for selection.

Two-dimensional E856, E63, and E216 polars were generated with the XFOIL module available in QBlade. Natural transition was retained, with the standard free-transition amplification factor N crit = 9, no forced upper- or lower-surface trip, and incompressible settings appropriate to the subsonic tip speeds. Converged polars were obtained from − 5 ° to 14 ° at discrete Reynolds numbers spanning 1 0 3 – 1 0 5. QBlade interpolated the coefficients between adjacent polar levels in logarithmic Reynolds-number space. A Viterna-type extrapolation supplied the post-stall coefficients required by the BEMT solver through 360 °; the optimized operating points themselves remain within the converged pre-stall angular interval.

The section Reynolds number was recomputed at every station from Reynolds relation (Equation 6).

Across the 2–5N cases, the complete modeled span gives approximately 4.0 × 1 0 3 ≤ R e ≤ 9.4 × 1 0 4; over the principal lifting span 0.2 R ≤ r ≤ R, the range is approximately 1.0 × 1 0 4 – 9.4 × 1 0 4. Therefore, no Reynolds-number extrapolation beyond the 1 0 3 – 1 0 5 database is used for the reported rotor loads. The 360-degree treatment is an angle-of-attack extrapolation only. The same polar-generation and interpolation settings are applied to all candidates, while sensitivity at the lowest Reynolds numbers remains visible in the validation error.

BEMT validation and screening procedure

Configuration 1 was selected for external validation because its geometry corresponds most closely to the published static-propeller data. Simulated thrust at 2000–7000 rpm was compared with the measurements of Deters et al. (2017). Agreement was quantified using root-mean-square error, via the RMSE relation (Equation 7). mean absolute percentage error (MAPE), and R 2. The model was then run for all six candidates over 2–5N. At 4.5N, radial normal load, tangential load, and C l / C d were exported for structural analysis and mechanistic assessment. For screening FEA, the BEMT normal and tangential line loads are assigned to their corresponding radial blade strips and linearly interpolated between the ten stations. The mapped distribution preserves each station interval’s integrated force and moment. Centrifugal loading is generated separately from the candidate-specific angular speed and material density; the hub attachment is fixed. Aerodynamic and centrifugal contributions are solved both separately and together so that the stress mechanism remains identifiable.

Orthotropic PETG model and feasibility constraints

PETG was selected as a practical FDM material with better toughness and impact tolerance than common brittle printing choices, while remaining accessible for local manufacture (Baltić et al., 2024). The properties are literature-based representative inputs, not measurements from coupons printed for this study. The structural idealization places the blade planform in the printer x y plane, assigns the span/chord directions the in-plane modulus, and assigns z through the blade thickness. The adopted full-density properties are ρ m = 1270 kg.m − 3, E x y = 1900 M P a, E z = 1500 M P a, ν x y = 0.38, ν y z = ν z x = 0.33, G x y = 400 M P a, and G y z = G x z = 150 M P a. These values lie within the spread reported for printed PETG, whose response is process dependent (Özen et al., 2021) and (Ramos et al., 2025). The FEA treats the blade as a homogenized 100%-density solid; individual rasters, voids, perimeter shells, and bead interfaces are not resolved. Consequently, layer height and shell count are not numerical inputs, and the results must not be interpreted as certification of an arbitrary slicer recipe. Exact raster angle, layer height, perimeter count, infill route, filament lot, and nozzle temperature will be fixed and characterized during prototype testing.

Each blade was fixed at the hub, subjected to the BEMT-derived radial aerodynamic load and its candidate-specific angular speed, and discretized with curvature-based tetrahedra refined at the root and edges. The resistance requirement is the stress limit (Equation 8).

The 40 MPa value is a conservative numerical design allowable selected below commonly reported printed-PETG longitudinal tensile strengths; it includes a screening reserve for process variability but is not a formal certification factor based on the exact as-built material. Safety factors reported below are therefore ratios to this design allowable, not to a measured ultimate strength. To limit aerodynamic shape change, the stiffness requirement follows the 3 % -of-radius rule motivated by elasticity studies (Möhren et al., 2023):

Deflection limit (Equation 9). This is a serviceability constraint: it limits twist/camber distortion and protects the clearance and incidence assumed by the aerodynamic model; it is not a PETG failure strain. The 0.03 R threshold is deliberately stated as an engineering screening rule because no universal printed-propeller deflection standard exists. A candidate is feasible only if both inequalities hold. This intersection of constraints is central: stress alone would retain all six candidates, whereas the displacement criterion removes the three thin-main-span E63 designs.

Stationwise twist redesign

Configuration 6 is used as the initial design because it is the most efficient structurally feasible candidate. Chord, radius, airfoil schedule, material, and hover thrust are held fixed. For each of ten radial stations, BEMT supplies local Reynolds number and inflow angle at T ref. The polar appropriate to that Reynolds number is searched for the angle α opt that maximizes C l / C d, and the updated twist is via the twist update (Equation 10).

The operational objective is FoM objective (Equation 11). subject to | β i − β i, 0 | ≤ 5 °, − 5 ° ≤ α i ≤ 12 ° (a two-degree stall margin below the converged upper polar bound), β i + 1 ≤ β i, σ max ≤ 40 M P a, and δ tip ≤ 0.03 R over the assessed thrust set. Chord, airfoil schedule, diameter, root geometry, and section thickness are fixed. Trial station values follow Equation 10; values between the ten stations use shape-preserving piecewise-linear interpolation, which introduces no overshoot and no additional smoothing parameter. The coupled BEMT solution is then repeated, so the procedure is a constrained local improvement rather than ten independent section maxima. The final geometry is rerun through both structural inequalities. This physically traceable redesign complements evolutionary approaches (Hoyos et al., 2022; Sedelnikov et al., 2024; Gao et al., 2026) by making the radial mechanism visible.

Three-dimensional CFD and pressure-mapped FEA

The optimized two-bladed rotor is analysed in ANSYS Fluent using steady incompressible Reynolds-averaged Navier–Stokes (RANS) equations, a multiple-reference-frame (MRF) rotating subdomain, and the k - ω shear-stress-transport (SST) turbulence model. The outer cylindrical domain has diameter and height 8 D, while the rotating subdomain has diameter 1.1 D and height 0.4 D. Air is modelled with ρ = 1.225 kg.m − 3 and μ = 1.7894 × 1 0 − 5 P a s. The outer cylinder’s upper, lower, and radial faces are open boundaries at 0Pa gauge pressure; the blade and hub are no-slip walls; and the stationary/rotating interface is conservative and fully coupled. The rotating cell zone uses the design-point speed of approximately 4828 rpm, with blade and hub walls stationary relative to that frame. Second-order spatial discretization, SIMPLE pressure–velocity coupling, and least-squares cell gradients are used.

The blade surface size is 0.8 mm; the rotating region and interface use 5 mm; and the outer region uses 40 mm. Twelve inflation layers start at 0.0115 mm with growth ratio 1.19. A flat-plate skin-friction estimate made before meshing gives an expected y + range of approximately 0.6–2.8 over the resolved blade surface at the design condition, so the first cell is intended for integration to the wall with the SST model rather than a wall-function placement. A solver-exported surface y + histogram was not retained in the supplied project archive; the quoted range is therefore a mesh-design estimate and not an a posteriori field statistic. An initial tetrahedral mesh is converted to polyhedra in Fluent. Grid independence is examined at 562,766, 622,505, and 686,913 cells using both thrust and torque; acceptance requires successive changes below 1% in both quantities. The final CFD pressure field is transferred to an ANSYS Mechanical model with 35,415 tetrahedral elements and 58,113 nodes. The same orthotropic properties, root fixture, and angular speed are used, enabling a direct comparison with the BEMT-loaded structural model. The earlier screening FEA and this final ANSYS cross-check are kept distinct: the screening model is used for relative design selection and before/after optimization changes, whereas the final ANSYS model is used only to compare BEMT-derived forces with mapped CFD pressure on the optimized geometry. One-way coupling is appropriate for this verification stage because the mapped result remains below the serviceability limit (δ tip = 2.83 m m = 0.0237 R) and the aim is to compare load-transfer routes without the cost of iterative mesh deformation. This choice does not imply that aerodynamic feedback is negligible; two-way fluid–structure interaction is retained as necessary follow-up. Curvature refinement at the root and attachment transition is retained because peak stress occurs there. Intermediate structural-grid result files were not present in the supplied archive, so a numerical three-grid FEA convergence table is not reported. The final element/node counts and independent load-route comparison are given for transparency, and peak-stress mesh sensitivity remains a required rerun before certification-level use.

BEMT validation against static measurements

Figure 2 compares the calculated and measured thrust. Both series show the expected near-quadratic increase with speed. The BEMT curve is conservative at every point: the difference falls from − 29.62 % at 2000 rpm to only − 1.47 % at 7000 rpm. Across all six points, RMSE is 0.1761N, MAPE is 11.25%, and R 2 = 0.9924. The high R 2 establishes trend capture only; it does not negate the non-negligible MAPE or the large low-speed bias. Accordingly, the model is treated as a relative screening tool whose absolute agreement is most credible near the design-relevant high-rpm range. Brandt and Selig (Brandt and Selig, 2011) established the sensitivity of small-propeller data in this Reynolds-number range. Deters et al. (2017) further demonstrated the strong speed dependence of multirotor static performance. Against that background, the close agreement in the design-relevant high-rpm range provides a defensible basis for using BEMT as the first screening level in the present workflow.

The pointwise table makes the scope of validation explicit. The high R 2 indicates trend capture, not uniformly small error: MAPE is 11.25%, and the 2000-rpm bias is substantial. BEMT is therefore used primarily for relative screening, especially near the design-relevant high-rpm range; it is not claimed as a uniformly accurate absolute predictor at the lowest thrust.

The direction and speed dependence of the discrepancy are physically plausible. At low rpm, section Reynolds number is smallest and the BEMT result is sensitive to laminar separation and polar extrapolation. Three-dimensional root and tip flow, blade surface condition, and exact experimental geometry also differ from the idealized model. At 6000–7000 rpm, which brackets the thrust range relevant to the original candidates, absolute discrepancies shrink to 0.175 and 0.094N. This validation quality is comparable in purpose to prior numerical–experimental small-propeller studies (Kutty and Rajendran, 2017) and (Garofano-Soldado et al., 2022): it supports BEMT as a ranking tool, but not as a substitute for final flow-field verification.

Aerodynamic screening

The three performance metrics in Figure 3 reveal a consistent geometry hierarchy. At 4N, APC-derived configurations 3 and 6 require 5100 and 5200 rpm, below the DJI-derived designs (5680 and 5800 rpm) and far below T-Motor-derived designs (6400 and 6450 rpm). The APC advantage arises from its larger outer-span chord and higher twist, which generate more useful normal force where tangential velocity is high. This result complements the section-level thickness trends reported by Ma et al. (2015). Roy et al. (2021) also showed that low-Reynolds-number airfoil geometry changes lift and drag through separation and pressure-recovery effects. Here, those airfoil effects are carried into a complete rotor-level comparison under the same thrust requirement.

Airfoil thickness produces a second, separable trend. For a fixed chord–twist family, the thin E63 configurations rotate more slowly and are more efficient than the E216 counterparts. At 4N, replacing E63 with E216 reduces efficiency from 66.00% to 61.36% for DJI, 63.94% to 58.51% for T-Motor, and 68.14% to 63.28% for APC. The corresponding penalties are 4.64, 5.43, and 4.86 percentage points. This is consistent with low-Reynolds-number airfoil studies showing that increasing thickness changes the pressure recovery and viscous drag (Ma et al., 2015) and (Roy et al., 2021). It is also why an aerodynamic-only selection would choose configuration 3.

Torque reveals that low speed is not a sufficient efficiency measure. At 4N, configuration 3 requires 5100 rpm but 0.066N m, whereas configuration 2 requires 6400 rpm but only 0.056N m. The APC blade produces thrust through stronger loading at a larger effective radius, increasing the torque arm. Nevertheless, its favourable C l / C d keeps configuration 3 at the highest efficiency. This separation among thrust, speed, torque, and efficiency supports the multi-metric treatment advocated in recent comprehensive propeller studies (Hu et al., 2025; Rajendran et al., 2025).

Radial loading mechanism

At 4.5N, normal load is small at the root, rises strongly across the mid-span, peaks around 0.7 R – 0.8 R, and collapses near the tip. For configuration 3, it reaches 35.87 Nm − 1 at 0.8 R; configuration 6 reaches 36.93 Nm − 1 at the same station. Tangential load is lower in magnitude but extends across a broad region. Configuration 6 peaks at 7.30 Nm − 1 near 0.6 R, explaining its relatively high torque.

The C l / C d distributions clarify why configuration 3 is efficient. Its value rises to 41.83 at 0.5 R and remains 39.71 at 0.6 R, exceeding the corresponding configuration-6 values of 28.84 and 32.31. The advantage is not uniform: configuration 6 slightly exceeds configuration 3 around 0.4 R, and both lose efficiency at the tip. Hence the global ranking is the integral of local performance weighted by speed, chord, and moment arm, not a single airfoil datum.

Structural screening and constraint-driven selection

Figure 4 changes the ranking. All maximum stresses, 7.48–16.76MPa, are below the 40 MPa allowable value. Stress alone would therefore accept every design with safety factors from 2.39 to 5.35. The displacement constraint is decisive: configurations 1–3 deflect 9.00, 5.97, and 5.81 mm, all exceeding 3.6 mm; configurations 4–6 deflect 3.32, 2.12, and 1.89 mm and pass. Fukui and Nishida (2019) emphasized the importance of centrifugal stress in high-speed small propellers. Möhren et al. (2023) showed that blade elasticity can alter propeller behaviour. The distinctive result here is that the stiffness limit, rather than the stress limit, overturns the purely aerodynamic ranking and selects a different blade family for subsequent optimization.

The result is not a simple “thicker is stronger” statement. Configurations 4–6 are heavier (approximately 4.95, 4.97, and 4.93 g) than configurations 1–3 (2.90, 2.60, and 2.44 g), so their centrifugal forces are higher. Configuration 5 reaches 142N and the largest stress, 16.76 MPa. Yet the thicker section raises bending rigidity sufficiently to reduce displacement. Moreover, configuration 6 places its normalized centre of mass furthest outward (R cm / R = 0.52), producing both a larger inertial moment and stronger centrifugal stiffening. This is consistent with the rotating-blade mechanism described by Algolfat et al. (2022).

Table 2, Panel A, makes the selection logic explicit. Configurations 3 and 1 occupy the first two aerodynamic positions but are infeasible. Configuration 6, with 65.30% efficiency at the design point, is the most efficient design satisfying both constraints and therefore becomes the optimization baseline. Relative to configuration 3, it sacrifices 2.96 percentage points of efficiency to reduce deflection from 5.81 to 1.89 mm. This is the central distinction between an aerodynamic best and an engineering optimum.

Aerodynamic-only versus constraint-balanced endurance case

Table 2, Panel B, converts the hover FoM into a transparent endurance proxy. At 4.5N per rotor, ρ = 1.225 kg.m − 3, and the present disk area, the ideal induced power is 28.82W per rotor. Equation 5 then gives rotor shaft power. The illustrative duration assumes 100 Wh of usable energy shared by four identical rotors and excludes motor, controller, battery, and vehicle-interaction losses; it is therefore a normalized aerodynamic comparison, not a flight-time prediction.

The aerodynamic-only blade has a nominal 0.47-min (1.33%) duration advantage over the locally improved constraint-balanced blade in this idealized 100-Wh case, but it exceeds the deflection limit by 61.4%. Local twist redesign recovers 1.07 min relative to the feasible baseline while retaining stress and displacement compliance. The small residual endurance gap is therefore the quantified aerodynamic price of structural feasibility under the assumed PETG model.

Optimized twist and local aerodynamic state

Figure 5 shows that the redesign is concentrated in the outer half. The initial and optimized twists differ by only 0.41 ° at 0.2 R and − 0.20 ° at 0.3 R, but the increment grows from 2.41 ° at 0.5 R to 4.91 ° at the tip. The resulting distribution is smoother and decays less sharply: 26.42 ° at 0.2 R, 18.41 ° at 0.6 R, and 13.00 ° at R. Sun et al. (2023) reported that blade twist materially changes both aerodynamic performance and noise. Tang et al. (2023) optimized chord and twist through a broader data-driven search. In contrast, the present redesign retains the selected manufacturable planform and exposes the stationwise aerodynamic reason for each change, which makes the resulting load transfer directly traceable.

The local response confirms that maximizing every station independently is neither necessary nor achieved after the coupled BEMT iteration. At 0.3 R, C l / C d falls from 8.399 to 7.397 (− 11.93 %); at 0.4 R, it falls from 24.885 to 21.948 (− 11.80 %). Conversely, it rises from 32.312 to 36.618 at 0.6 R (+ 13.33 %), from 30.848 to 40.956 at 0.7 R (+ 32.77 %), and from 29.293 to 40.146 at 0.8 R (+ 37.05 %). The outer-span gains dominate because W, local dynamic pressure, and torque arm are larger there. This mechanism agrees with the broad conclusion of twist studies (Sun et al., 2023) and (Zhu et al., 2021), but the present station data identify where the gain is produced.

Performance over the operating range

Figures 6A–C demonstrates that the benefit persists across the tested thrust range. Required speed falls from 3850 to 3450 rpm at 2N, 4600 to 4100 rpm at 3N, 5200 to 4600 rpm at 4N, and 5700 to 5055 rpm at 5N. Relative reductions are tightly grouped between 10.39% and 11.54%, showing that the optimized twist does not create a narrow single-point solution.

Torque rises by 10.17% at 2N, 8.88% at 3N, 8.11% at 4N, and 9.47% at 5N. This is the cost of moving useful loading outward. Efficiency nevertheless rises from 57.57% to 58.31% at 2N, from 60.30% to 62.13% at 3N, from 63.28% to 66.17% at 4N, and from 66.54% to 68.54% at 5N. The largest relative gain, 4.56%, occurs at 4N; the gain at 5N is 3.00%. Thus the optimized blade converts mechanical input more effectively even though its torque is higher, because the angular speed reduction and improved section efficiency alter the overall balance.

Table 3 resolves that balance using P = Q Ω. The torque values are rounded to four significant digits from the BEMT output, so the displayed power changes differ slightly from changes computed from unrounded FoM values.

Although torque rises, the larger reduction in angular speed lowers shaft power by approximately 1.2%–4.4% across the assessed range. This is the direct energetic basis for the FoM and idealized-endurance improvements.

Compared with optimization studies that search larger design spaces (Hoyos et al., 2022; Gao et al., 2026; Sedelnikov et al., 2024), the absolute efficiency gain is modest. That modesty is meaningful: only twist is changed, the candidate had already survived a structural screen, and the response is required to remain feasible. The result should be read as a low-risk refinement of a manufacturable baseline, not as a global optimum over diameter, chord, airfoil, blade count, noise, and motor matching.

Radial redistribution of load

Figures 6D,E shows the aerodynamic mechanism. Up to approximately 0.6 R, both normal and tangential loads are lower after optimization because the rotor turns more slowly and twist changes are small. At 0.5 R, normal load falls from 23.92 to 21.39 Nm − 1 (− 10.59 %); at 0.6 R, it changes only from 31.65 to 30.57 Nm − 1. Beyond 0.6 R, increased twist compensates for lower speed: normal load rises from 35.34 to 36.89 Nm − 1 at 0.7 R and from 36.93 to 39.89 Nm − 1 at 0.8 R.

Tangential load makes the torque penalty still clearer. It falls by 19.68% at 0.4 R but rises by 13.89% at 0.7 R, 19.10% at 0.8 R, and 23.16% at 0.9 R. Because torque integrates r d F t, the same force increment has more leverage at large radius. The load shift is therefore not a secondary plot detail; it is the direct explanation for the 8%–10% increase in rotor torque.

Structural consequence of the redesign

The speed reduction lowers centrifugal force from 102 to 81N, a 20.59% decrease. Maximum centrifugal stress falls from 11.60 to 8.44MPa; combined stress falls from 14.80 to 11.22MPa, a 24.19% reduction. The optimized stress corresponds to a nominal safety factor of 40 / 11.22 = 3.57, compared with 40 / 14.80 = 2.70 initially. This result supports earlier observations that centrifugal loading dominates small high-speed propeller stress (Fukui and Nishida, 2019): the combined-stress reduction closely tracks the inertial relief.

The displacement response moves in the opposite direction. Maximum displacement rises from 1.89 to 2.75mm, an increase of 45.50%, although it remains 23.61% below the 3.6 mm limit. Two effects contribute. First, moving aerodynamic load outward increases the bending moment. Second, the 20.59% reduction in centrifugal force weakens rotation-induced stiffening. This response is consistent with established centrifugal-stiffening behaviour (Algolfat et al., 2022) and with the sensitivity of propeller performance to elasticity (Möhren et al., 2023).

Table 4 exposes why reporting only stress would be misleading. Optimization increases the stress safety factor by 31.91%, but halves the available displacement margin. The final blade remains feasible, yet its robustness to lower print modulus, thermal softening, or dimensional error is reduced. In a production design, the deflection margin should therefore be verified using measured coupon properties and an as-built blade test.

Mesh quality and grid independence

The final polyhedral grid contains 686,913 cells. Figure 7 groups the global, rotating-region, and near-wall discretizations. Conversion from the initial tetrahedral mesh reduces cell count while improving numerical connectivity; inflation layers resolve strong gradients around the airfoil. Arafat et al. (2024) highlighted the sensitivity of small-UAV propeller predictions to numerical modelling choices. Choayb (2024) also demonstrated the value of resolving the near-blade and wake regions when evaluating propeller flow. The present mesh strategy therefore links the final design check to an explicit grid-convergence test rather than relying on a single discretization.

Table 5, Panel A, shows monotonic convergence. Refining from 562,766 to 622,505 cells changes thrust by 0.62% and torque by 0.57%; the next refinement changes them by only 0.53% and 0.32%. The final values, 4.50952N and 0.08835N m, differ from the design thrust by + 0.2116 %. Because both monitored outputs change by less than 1%, the final grid is adequate for the present mean-load comparison. This dual-output check is more informative than checking thrust alone, since structural loading and power depend on torque as well.

At the 4.5N design condition, BEMT gives Q ≈ 0.0841 N m and P ≈ 42.5 W at approximately 4828 rpm. CFD gives 0.08835N m and 44.7W at the same angular speed. Thus, in addition to the + 0.21 % thrust difference, CFD predicts approximately 5.1% higher torque and shaft power. The radial comparison is qualitative because sectional CFD force exports were not retained: BEMT places the dominant normal and tangential loads over 0.6 R – 0.9 R, and the CFD pressure field independently shows its strongest pressure difference over the same outer-span region. The 6.83% stress difference is physically consistent with spatial load redistribution: the BEMT-strip representation concentrates resultant forces at discrete spanwise locations, whereas mapped CFD pressure spreads them continuously over both blade surfaces. The mapped field therefore produces a slightly smaller root stress but a slightly larger effective bending moment and tip displacement. This agreement supports the load-migration mechanism, while the absence of a sectional CFD force table is retained as a limitation rather than inferred from total loads.

The MRF solution represents a steady mean operating state. It is computationally efficient and appropriate for the isolated-hover comparison, but it does not capture blade-passing transients, wake ageing, or inter-rotor interaction. That scope is consistent with CFD assessments of isolated small rotors (Arafat et al., 2024) and (Choayb, 2024); it should not be regarded as a complete vehicle-level unsteady simulation.

Pressure, velocity, and streamlines

Figure 8 combines the flow diagnostics. The pressure field shows positive pressure over the pressure side and suction over the opposite surface, with the largest magnitude near the leading edge. This is the expected distribution for a cambered section at positive incidence and agrees qualitatively with prior UAV propeller CFD (Kutty and Rajendran, 2017; Choayb, 2024; Arafat et al., 2024). Importantly, the distribution is not uniform along the radius: the stronger outer-span loading seen in BEMT appears as a more pronounced pressure difference where local speed is higher.

The velocity field shows an accelerated stream passing through and below the rotor disk. Air is drawn from the surrounding upper region, redirected through the blades, and discharged into a contracted downward wake. At section scale, the higher suction-side speed corresponds to the lower pressure region. The streamlines remain attached over most of the shown section, although a steady RANS image cannot establish the absence of transient separation at all azimuthal and radial locations.

These fields provide a mechanistic check rather than a second optimization. BEMT predicts the integral thrust and radial force distribution efficiently; CFD confirms that those loads emerge from physically consistent pressure and velocity structures. The agreement of final thrust with Equation 1 to 0.21% also shows that the CFD case represents the intended structural loading point.

Pressure-mapped structural response

Figure 9 shows the final mechanical fields. Maximum von Mises stress is concentrated at the blade root, particularly near the trailing-edge side of the attachment where bending and inertial load transfer into the hub. Maximum displacement occurs at the tip and increases from root to tip, as expected for a cantilever-like rotating blade. The CFD-pressure model predicts 12.27 MPa and 2.83 mm; both remain below the specified limits. Sourirajan et al. (2025) combined aerodynamic and structural considerations in UAV propeller design. Rajendran et al. (2025) likewise emphasized multi-domain evaluation. The added value of the present final check is the direct numerical comparison between a reduced-order BEMT load route and a mapped three-dimensional CFD pressure route on the same optimized blade.

The BEMT-loaded model predicts 13.17 MPa and 2.75 mm. Relative to that model, CFD pressure reduces maximum stress by 6.83% and increases displacement by 2.91%. Table 5, Panel B, summarizes the comparison. The difference is small despite fundamentally different aerodynamic load representations: BEMT applies a spanwise force decomposition, whereas CFD supplies a three-dimensional pressure map. The lower peak stress with CFD implies that the simplified load is slightly more concentrated near the root or less spatially distributed; the slightly higher CFD displacement indicates a modestly larger effective bending moment over the span.

The 13.17 MPa value should not be compared directly with the 11.22 MPa screening value as though both came from one unchanged finite-element model. The screening stage applies stationwise BEMT resultants to a rapid curvature-based mesh and is used for candidate ranking and the initial/optimized relative change. The final ANSYS model uses a refined hub/root representation, a different tetrahedral discretization, and a load-transfer setup shared by both the BEMT-force and mapped-pressure cases. Those changes alter the local peak stress while leaving the BEMT-predicted tip displacement at 2.75 mm. Accordingly, within-stage comparisons are used for the 24.19% stress reduction, while the final model is used for the 6.83% BEMT/CFD load-route comparison. The two numbers answer different questions and are not pooled.

The agreement supports the use of BEMT-loaded FEA during rapid screening, provided that the final candidate is checked with a higher-fidelity pressure field. It does not prove full fluid–structure interaction (FSI), because deformation was not fed back into the CFD geometry. At 2.83mm, the maximum deflection is 2.37% of radius; this is small enough for a one-way coupling assumption to be plausible, but not negligible enough to eliminate experimental validation.

Contribution relative to existing work

Table 6 places the present study in the context of representative prior work. Brandt and Selig (2011) established a widely used low-Reynolds-number experimental basis. Deters et al. (2017) extended static measurements to multirotor propulsion systems. Kutty and Rajendran (2017) demonstrated the usefulness of CFD supported by experiment. Arafat et al. (2024) examined numerical choices affecting small-UAV propeller prediction. Sun et al. (2023) quantified the sensitivity to twist. Hoyos et al. (2022) and Gao et al. (2026) showed the potential of constrained and multi-objective optimization. Sourirajan et al. (2025), Rajendran et al. (2025) moved toward combined aerodynamic–structural assessment. Building on these directions, the present work contributes a single, closed engineering chain in which an aerodynamically attractive candidate can be rejected by stiffness, the surviving blade is locally redesigned, the resulting radial load migration is quantified, the centrifugal-stress/stiffness trade-off is measured, and the final structural response is independently checked with mapped CFD pressure. This continuity between design decision and physical consequence is the principal feature of the study.

Three conclusions sharpen the contribution.

First, airfoil and geometry effects cannot be assessed independently. The E63 airfoil improves efficiency by approximately 4.6–5.4 percentage points at 4N for a fixed planform, but every E63 candidate violates the stiffness constraint. The E216 penalty is therefore the price of feasibility under the assumed PETG modulus and print architecture. In contrast to purely aerodynamic studies, the relevant comparison is not E63 versus E216 at equal geometry; it is the best feasible member of the combined geometry–material system.

Second, the speed reduction is not a free benefit. The optimized blade rotates about 11% more slowly, which reduces centrifugal force and stress, but it transfers tangential load outward and increases torque. The decrease in centrifugal force also reduces stiffness. As a result, stress falls 24.19% while tip displacement rises 45.50%. These simultaneous changes unify the aerodynamic twist mechanism discussed by Sun et al. (2023) with the centrifugal-stiffening mechanism discussed by Algolfat et al. (2022).

Third, the two structural load routes are close enough to justify a tiered engineering workflow. Screening hundreds of candidates with fully mapped CFD pressure would be expensive. Here, simplified BEMT loading and CFD pressure differ by 6.83% in maximum stress and 2.91% in maximum displacement for the final blade. This supports BEMT/FEA for ranking and RANS-CFD/FEA for final verification, a division of labour also consistent with validated reduced-order design programs (Schmähl and Hornung, 2026).

Scope of the optimization claim

The final APC/E216 blade is a structurally feasible, locally improved design, not a demonstrated global optimum. The stationwise procedure searches twist within a fixed planform after the six-candidate gate. Chord, airfoil family, diameter, blade number, hub, material model, motor matching, acoustic emission, and vehicle-level interaction remain fixed or outside the objective. The term “optimization” therefore refers to constrained local twist improvement under the stated model and operating range. Establishing a global or Pareto-optimal rotor would require simultaneous exploration of those additional variables and uncertainty in as-built material and surface properties.

Design implications

For a designer, the results suggest four practical rules. The first is to state a deformation limit before optimization. Had selection used only stress and efficiency, configuration 3 would have been chosen despite a tip displacement 61.4% above the allowable value. The second is to inspect load distributions rather than only global thrust: the torque penalty is visible as a tangential-load increase at 0.7 R – 0.9 R. The third is to preserve a stiffness margin after speed reduction. The optimized design passes, but only 0.85 mm remains before the assumed limit. The fourth is to match the rotor with the motor and electronic speed controller using both speed and torque; a lower rpm requirement does not imply lower current at every point.

Manufacturing sensitivity

FDM PETG modulus and strength vary with raster direction, layer orientation, temperature, infill, void content, and inter-bead bonding (Özen et al., 2021; Ramos et al., 2025). For a blade printed flat in the x y plane, continuous rasters and perimeter paths should preferentially follow the spanwise principal-load direction and remain uninterrupted through the root transition; stacking the weakest interlayer direction across the root bending path should be avoided. The root should use continuous perimeter shells, high local consolidation, and a gradual thickness transition, followed by static proof loading and dynamic balance inspection. Leading-edge sanding or coating must be controlled because geometric smoothing can improve surface fidelity while also changing section thickness and balance.

A first-order linear-elastic sensitivity illustrates the narrow stiffness reserve. For fixed load and geometry, bending displacement scales approximately as δ ∝ E bend − 1. A 20% reduction in effective bending modulus would therefore increase the screening displacement from 2.75 mm to approximately 3.44mm, leaving only 0.16 mm below the 3.6 mm limit; applied to the mapped-pressure result, it gives approximately 3.54 mm. A 25% modulus reduction would raise the mapped estimate to approximately 3.77 mm and violate the limit. Likewise, centrifugal force scales linearly with effective density at fixed speed, so a 10% density deviation produces an approximately 10% inertial-force change before secondary deformation effects. These are bounding analytical estimates, not measured process statistics. Coupon tests and printed-blade modal/static tests are therefore required to identify the actual effective modulus, density, and allowable scatter before flight use.

Limitations

The principal limitations, their numerical indications, and the corresponding remedies are as follows. The published-data comparison validates a related reference propeller, not the optimized printed blade. Its MAPE is 11.25%, with bias improving from − 29.62 % at 2000 rpm to − 1.47 % at 7000 rpm. A dedicated thrust/torque stand test of the printed baseline and optimized blades is required.

Low-Reynolds-number polar uncertainty is largest at the lowest speed, where laminar separation is most sensitive to transition and surface roughness. The remedy is to measure section or rotor performance at the actual print roughness and recalibrate transition settings before extrapolating below the present design range.

The final two CFD refinements change thrust and torque by 0.53% and 0.32%, respectively, so discretization uncertainty is small relative to the low-speed BEMT bias. Model-form error remains unquantified because steady MRF RANS omits blade-wake transients, rotor interference, forward flight, ground effect, gusts, and body blockage; sliding-mesh and vehicle-level tests are required.

Coupling is one-way: the mapped 2.83 mm displacement (0.0237 R) is not returned to the flow solver. Two-way fluid–structure interaction must determine whether deformed twist materially changes thrust, torque, or separation.

Material properties are representative rather than measured for the exact printer, filament lot, raster, temperature, and post-processing route. The first-order modulus sensitivity above shows that a 20%–25% reduction can nearly consume or exceed the deflection margin; process-specific coupon and blade tests are required.

The search changes twist only. Chord, airfoil, diameter, blade count, acoustics, mass imbalance, fatigue, motor efficiency, and print supports remain outside the objective, so no numerical global-optimality error can be assigned. A broader uncertainty-aware Pareto search is the appropriate remedy.

The reported y + interval of approximately 0.6–2.8 is a pre-mesh estimate, not a retained area-weighted solver statistic. A surface y + histogram and extrema should be exported in the CFD rerun.

Intermediate structural meshes and sectional CFD force exports were not retained. The 6.83% stress and 2.91% displacement differences between load routes provide a cross-check but are not substitutes for a three-grid root-stress study and pointwise radial-force comparison.

These limitations bound the claim: the work establishes a numerically cross-verified design methodology and a feasible candidate, not flight certification or fatigue life.

Future work

Four directions follow directly from the present limitations. Prototype and endurance testing. Print blades using a frozen process specification; measure coupon anisotropy, density, dimensions, balance, thrust, torque, shaft power, strain, tip displacement, fatigue life, and hover endurance. High-speed imaging or digital image correlation should verify the predicted loss of centrifugal stiffening, following the material-to-blade validation logic demonstrated by Malim et al. (2024).

Two-way fluid–structure interaction. Couple transient sliding-mesh CFD to the deformed orthotropic blade, return displacement and twist to the flow domain, and assess whether the current one-way result remains valid under gusts, off-axis inflow, rotor interaction, and thermal softening.

Acoustic multi-objective optimization. Extend the variables to chord, twist, section thickness, tip shape, and rotational speed, and construct a Pareto problem balancing FoM, shaft power, tonal/broadband noise, stress, deflection, and manufacturability rather than treating acoustics as a post-processing quantity.

Low-density-atmosphere extension. Regenerate transition-sensitive polars and rescale disk loading, motor matching, thermal limits, and structural margins for high-altitude terrestrial and low-atmosphere rotorcraft. The hierarchy can then be tested against the low-density rotor-design strategies reported for Mars applications (Zhao et al., 2019; Tang et al., 2023; Wang et al., 2024).

Aerodynamic screening alone selected the thin E63 family, but all three E63 candidates exceeded the 0.03 R tip-deflection limit despite satisfying the stress allowable. The thicker APC/E216 configuration was therefore retained as the most efficient feasible baseline, demonstrating that stiffness, rather than strength, controlled the printed-blade selection.

Constrained twist redesign reduced required speed by approximately 11% and improved hover FoM by up to 4.6% over 2–5N. The improvement arose from a radial crossover near 0.6 R: reduced inner-span loading was exchanged for stronger outer-span loading, increasing the torque arm. At the design point, combined stress fell by 24.19%, whereas tip displacement rose by 45.50% because lower centrifugal force weakened rotational stiffening; the final blade nevertheless remained below the displacement limit.

The tiered workflow reserves RANS-CFD and pressure-mapped FEA for the selected geometry after low-cost BEMT/FEA screening. The final load routes differed by 6.83% in peak stress and 2.91% in displacement, supporting this hierarchy for engineering screening while not constituting prototype certification or a global optimum. Prototype testing, two-way fluid–structure interaction, acoustic Pareto optimization, and low-density-atmosphere extension are the next validation stages. The unique contribution is the explicit quantitative connection between constrained twist change, spanwise load migration, torque demand, centrifugal-stress relief, and loss of centrifugal stiffening in a 3D-printed propeller.