How a Sweptback Stern Foil Improves Flat-Hull Ship Efficiency: A CFD-Based Extension of the Hull Vane Concept

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Improving the hydrodynamic efficiency of commercial vessels has become increasingly important as the maritime industry seeks to reduce fuel consumption, greenhouse gas emissions, and operating costs. Stern-mounted energy-saving devices such as the Hull Vane® have demonstrated promising performance in reducing ship resistance through pressure recovery and wake-flow modification. However, most previous investigations have concentrated on conventional straight-foil configurations, leaving the influence of planform geometry largely unexplored. This study investigates the hydrodynamic performance of a sweptback stern foil using Computational Fluid Dynamics (CFD) simulations. By evaluating multiple sweptback angles under medium- to high-speed operating conditions, the research identifies an optimal configuration capable of enhancing wake characteristics and reducing resistance more effectively than the conventional Hull Vane® design.

Bibliographic Information

Item Information
Article Title Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept
Authors Rahmat Azis Nabawi; Budi Syahri; Yogi Dian Alfana; Donny Fernandez
Journal Teknomekanik
Volume & Issue Volume 9, Issue 1
Publication Year 2026
Pages 110–120
DOI https://doi.org/10.24036/teknomekanik.v9i1.54872
Publisher Universitas Negeri Padang
License Creative Commons Attribution 4.0 International (CC BY 4.0)
ISSN e-ISSN: 2621-8720
p-ISSN: 2621-9980
Keywords flat-hull ship; flow simulation; energy-saving device; affordable and clean energy; ship resistance reduction

Research Background

  • Flat-hull ships experience relatively high hydrodynamic resistance. Compared with streamlined hull forms, flat-hull vessels generate greater pressure and wave resistance, requiring higher propulsion power to maintain operational speed. Increased propulsion demand directly contributes to higher fuel consumption, operating costs, and exhaust emissions.
  • Conventional design modifications have practical limitations. Increasing the length-to-beam (L/B) ratio can reduce wave-making resistance, but this approach may also reduce transverse stability, creating potential safety concerns under demanding operating conditions. Consequently, alternative resistance-reduction technologies remain an active area of research.
  • The Hull Vane® concept has demonstrated significant energy-saving potential. Previous investigations have shown that stern-mounted hydrofoils reduce ship resistance by modifying the pressure field around the stern, improving trim, and interacting constructively with stern waves. Experimental studies, CFD analyses, and full-scale trials have reported meaningful reductions in resistance for commercial vessels.
  • Most previous studies have focused on straight-foil configurations. Although the Hull Vane® has been extensively investigated, existing research has largely examined straight planform geometries. The influence of sweptback planform design on stern-mounted lifting surfaces has received comparatively little attention, particularly for flat-hull ships operating in the medium-to-high Froude number range.
  • The role of planform geometry remains insufficiently understood. Limited evidence is available regarding how sweptback stern foils influence wake characteristics, pressure recovery, turbulence development, and overall hydrodynamic efficiency. This knowledge gap restricts the optimization of stern-mounted energy-saving devices for practical marine applications.
  • This study addresses an important design optimization problem. Rather than introducing an entirely new energy-saving device, the research extends the established Hull Vane® concept by systematically modifying its planform geometry into a sweptback configuration and evaluating multiple sweptback angles using Computational Fluid Dynamics simulations.
  • The research emphasizes hydrodynamic optimization through numerical simulation. By combining resistance prediction with velocity contour and turbulence analyses, the study investigates not only whether resistance decreases but also the underlying flow mechanisms responsible for improved hydrodynamic performance.

Research Objective

  • To investigate the influence of sweptback stern foil geometry on the hydrodynamic performance of flat-hull ships using Computational Fluid Dynamics (CFD) simulations.
  • To evaluate the effect of sweptback angles ranging from 5° to 30° on total ship resistance under medium- to high-speed operating conditions.
  • To compare the hydrodynamic performance of sweptback stern foils with both a conventional Hull Vane® configuration and a flat-hull ship without a stern foil.
  • To analyze wake-flow characteristics through velocity contour and turbulence-length visualizations in order to explain the mechanisms responsible for resistance reduction.
  • To identify the sweptback stern foil configuration that provides the most effective pressure recovery and wake-flow modification for improving hydrodynamic efficiency.
  • To demonstrate that planform optimization represents an important design parameter for developing more efficient stern-mounted energy-saving devices for commercial vessels.

Why This Research Matters

  • Supports maritime energy efficiency. Reducing hydrodynamic resistance lowers propulsion power requirements, contributing directly to lower fuel consumption and improved operational efficiency.
  • Contributes to cleaner shipping. Improved hydrodynamic performance reduces engine workload, helping decrease greenhouse gas emissions and supporting more sustainable maritime transportation.
  • Extends an established engineering concept. Instead of replacing the Hull Vane®, the research demonstrates how optimizing planform geometry can further improve the effectiveness of an already proven stern-mounted energy-saving device.
  • Provides new understanding of sweptback foil performance. The systematic evaluation of multiple sweptback angles offers valuable insight into how planform geometry influences wake modification, pressure recovery, and turbulence development behind flat-hull ships.
  • Demonstrates the value of CFD-based engineering optimization. Numerical simulations enable detailed investigation of complex flow phenomena that are difficult to observe experimentally, supporting more efficient marine engineering design processes.
  • Offers practical guidance for ship designers. Identifying an optimal sweptback configuration provides useful engineering knowledge for developing future stern-mounted hydrofoils capable of improving the hydrodynamic performance of medium- and high-speed commercial vessels.
  • Supports innovation in sustainable ship design. The findings contribute to ongoing efforts within naval architecture to improve vessel efficiency through relatively simple geometric modifications rather than major structural redesigns.

Research Methodology

  • Research Design

    This study employed a quantitative computational engineering approach to investigate the hydrodynamic performance of a sweptback stern foil developed as an extension of the Hull Vane® concept. The research focused on evaluating how variations in sweptback angle influence ship resistance and wake-flow characteristics through Computational Fluid Dynamics (CFD) simulations. The sweptback stern foil was assessed against both a conventional Hull Vane® configuration and a flat-hull ship without a stern-mounted foil.

  • Ship Model

    The numerical model was based on a previously developed flat-hull ship. The conventional straight Hull Vane® utilizing a NACA 4012 foil served as the reference configuration. The principal innovation consisted of replacing the straight planform with a sweptback stern foil while maintaining comparable installation conditions. Six sweptback angles were investigated: 5°, 10°, 15°, 20°, 25°, and 30°.

  • Computational Fluid Dynamics (CFD) Simulation

    Hydrodynamic performance was evaluated using SolidWorks Flow Simulation under free-surface flow conditions. The simulations modeled two immiscible fluids (air and water), incorporated gravitational effects, and applied no-slip boundary conditions on the hull and stern foil surfaces. External flow analysis was performed to simulate realistic operating conditions for marine vessels.

  • Operating Conditions

    The simulations covered Froude numbers ranging from 0.5 to 1.0, representing medium- to high-speed operating conditions where wave-making resistance and pressure resistance become dominant components of total ship resistance. This operating range enabled evaluation of foil performance under practical commercial vessel conditions.

  • Numerical Model

    The governing flow equations were solved using the Reynolds-Averaged Navier–Stokes (RANS) approach coupled with a two-equation turbulence model commonly applied in ship hydrodynamics. This numerical framework enabled prediction of pressure distribution, viscous flow behavior, wake development, and overall resistance characteristics.

  • Computational Domain and Mesh Strategy

    The computational domain followed International Towing Tank Conference (ITTC) recommendations for ship CFD simulations. Grid independence was evaluated using coarse, medium, and fine meshes. Since the difference between medium and fine meshes remained below 2%, a computational grid containing approximately 3.4 million cells was selected to balance numerical accuracy and computational efficiency. Local mesh refinement was applied around the stern foil to improve prediction of pressure gradients, velocity fields, and wake structures.

  • Model Validation

    The numerical model was validated by comparing the simulated resistance of the baseline configuration and the conventional Hull Vane® with previously published results. The reported deviation remained within the acceptable range for steady-state RANS simulations, confirming that the computational model was suitable for the parametric investigation performed in this study.

  • Performance Evaluation

    Hydrodynamic performance was assessed using three complementary indicators: total ship resistance, velocity contour visualization, and turbulence-length distribution. Resistance measurements quantified overall hydrodynamic efficiency, while CFD visualizations explained how each sweptback angle modified pressure recovery, wake characteristics, and turbulence development behind the vessel.

Key Findings

The 15° Sweptback Stern Foil Produced the Lowest Hydrodynamic Resistance

Among all evaluated configurations, the 15° sweptback stern foil consistently delivered the greatest reduction in ship resistance throughout almost the entire Froude number range. The results indicate that neither smaller nor larger sweptback angles achieved the same level of hydrodynamic efficiency. Smaller angles generated insufficient pressure recovery, whereas larger angles increased pressure resistance and flow separation effects, particularly at higher operating speeds.

The findings demonstrate that planform geometry possesses an optimal operating condition rather than exhibiting continuously improving performance with increasing sweptback angle.

Sweptback Geometry Outperformed the Conventional Hull Vane®

Comparison with the baseline ship and the conventional straight Hull Vane® revealed that the optimized sweptback stern foil provided greater resistance reduction, especially at higher Froude numbers between 0.8 and 1.0. The improved performance confirms that modifying planform geometry can enhance the hydrodynamic effectiveness of an established stern-mounted energy-saving device.

Rather than replacing the Hull Vane® concept, the sweptback configuration extends its design by improving pressure recovery and stern-flow interaction.

Wake Characteristics Became More Efficient with the 15° Configuration

Velocity contour analysis demonstrated substantial differences in wake development among the tested configurations. Ships without stern foils generated a broad wake characterized by an extended velocity-deficit region behind the stern. Installing the conventional Hull Vane® narrowed this wake, while the 15° sweptback stern foil produced the most focused and stable wake structure.

The narrower wake indicates improved pressure recovery, smoother velocity-gradient distribution, and more efficient interaction between the stern foil and the surrounding flow field.

The Optimized Foil Improved Turbulence Control

CFD turbulence-length visualizations revealed that the optimized 15° sweptback configuration localized turbulence close to the trailing edge of the foil while reducing the development of large turbulent structures behind the vessel. Compared with ships without foils, the optimized configuration generated a narrower and more rapidly dissipating wake.

This behavior suggests improved control of turbulence development, contributing to reduced pressure resistance and enhanced overall hydrodynamic efficiency.

Resistance Reduction Was Primarily Achieved Through Pressure Recovery

The numerical results support the established working principle of the Hull Vane®, indicating that resistance reduction originates primarily from improved pressure distribution and wake-flow modification rather than from direct thrust generation. The sweptback geometry strengthened these mechanisms by producing more effective interaction between the stern foil and the surrounding flow.

Consequently, pressure recovery emerged as the dominant mechanism responsible for the observed improvement in ship performance.

Planform Optimization Is a Critical Stern Foil Design Parameter

A principal outcome of the research is the demonstration that sweptback angle should be considered a key hydrodynamic design variable for stern-mounted lifting surfaces. The systematic comparison of six sweptback angles shows that relatively small geometric modifications can significantly influence resistance, wake characteristics, and turbulence behavior.

These findings establish planform optimization as an important consideration for developing future energy-saving devices intended for medium- and high-speed commercial vessels.

Scientific Contribution

  • Introduces a sweptback extension of the Hull Vane® concept by systematically investigating the influence of planform geometry on hydrodynamic performance rather than relying on the conventional straight-foil configuration.
  • Provides one of the first detailed CFD investigations evaluating multiple sweptback stern foil angles for flat-hull ships operating within the medium- to high-Froude-number range.
  • Demonstrates that planform geometry directly affects resistance reduction mechanisms through pressure recovery, wake modification, and turbulence control, thereby expanding current understanding of stern-mounted lifting surfaces.
  • Integrates quantitative resistance analysis with qualitative flow visualization by combining resistance measurements, velocity contours, and turbulence-length distributions to explain the physical mechanisms underlying hydrodynamic improvement.
  • Identifies 15° as the optimum sweptback angle among the investigated configurations, providing practical engineering evidence for stern foil optimization.
  • Strengthens the application of CFD as a marine design tool by demonstrating how numerical simulations can efficiently evaluate geometric modifications before prototype fabrication or experimental testing.

Industrial Implications

  • Supports the development of energy-efficient commercial vessels. Optimized stern foil geometry offers a practical strategy for reducing ship resistance and improving propulsion efficiency without requiring major hull redesign.
  • Reduces operational fuel consumption. Lower hydrodynamic resistance decreases engine power demand, helping ship operators reduce fuel costs during long-term operation.
  • Contributes to maritime decarbonization. Improved propulsion efficiency can reduce greenhouse gas emissions and support international efforts toward cleaner and more sustainable shipping.
  • Provides practical guidance for naval architects. The identified optimum sweptback configuration offers useful design information for engineers developing future stern-mounted energy-saving devices.
  • Promotes CFD-driven engineering optimization. The study illustrates how numerical simulation can accelerate marine design processes while reducing dependence on expensive towing-tank experiments during early-stage development.
  • Supports innovation in retrofit technologies. Because stern-mounted foils can potentially be installed on existing vessels, optimized sweptback designs may offer cost-effective opportunities for improving the efficiency of operational commercial fleets.
  • Enhances competitiveness in ship design. Incorporating optimized stern foil geometry into future vessel designs may improve overall transport efficiency while lowering lifecycle operating costs for the maritime industry.

Research Limitations

  • The investigation was conducted entirely through Computational Fluid Dynamics (CFD) simulations. Although the numerical model was validated against previously published results, the study did not include towing-tank experiments or full-scale sea trials to further verify the predicted hydrodynamic performance of the sweptback stern foil.
  • The numerical simulations assumed steady-state operating conditions using the Reynolds-Averaged Navier–Stokes (RANS) approach. Dynamic phenomena such as ship motions, transient wave interactions, and unsteady flow behavior were beyond the scope of the present investigation.
  • The simulations were performed under static trim and sinkage conditions. Consequently, the influence of free-to-trim behavior, dynamic sinkage, and their interaction with the sweptback stern foil were not evaluated and may influence hydrodynamic performance under actual operating conditions.
  • The study investigated only six sweptback angles ranging from 5° to 30°. Other geometric parameters that may affect stern foil performance, including foil span, aspect ratio, chord length, camber distribution, angle of attack, installation height, and foil profile, were not examined.
  • The numerical analysis focused on a single flat-hull ship configuration. Therefore, the reported hydrodynamic trends cannot automatically be generalized to other vessel types, hull forms, displacement characteristics, or operating conditions without additional investigation.
  • Wake characteristics were evaluated using velocity contours and turbulence-length distributions. However, detailed analyses of vortex structures, vortex shedding, pressure fluctuations, and other advanced flow phenomena were outside the scope of this study.
  • The research concentrated exclusively on hydrodynamic resistance reduction. Structural performance, manufacturing feasibility, installation complexity, maintenance requirements, fatigue behavior, and economic cost-benefit considerations were not addressed.

Future Research Opportunities

  • Conduct experimental validation through towing-tank testing and full-scale sea trials to verify the hydrodynamic performance predicted by the CFD simulations.
  • Evaluate sweptback stern foils under free-to-trim and dynamic sinkage conditions to better represent realistic vessel operating behavior.
  • Investigate additional geometric design variables, including foil span, aspect ratio, chord length, airfoil profile, camber distribution, installation height, and angle of attack to establish a more comprehensive stern foil optimization framework.
  • Apply higher-fidelity numerical approaches such as Large Eddy Simulation (LES), Detached Eddy Simulation (DES), or hybrid turbulence models to obtain deeper insight into complex wake structures and vortex dynamics.
  • Assess the hydrodynamic performance of sweptback stern foils on different ship types, including cargo vessels, passenger ferries, patrol boats, fishing vessels, and high-speed commercial ships.
  • Investigate the interaction between sweptback stern foils and alternative energy-saving devices to determine whether combined technologies can produce greater resistance reduction.
  • Incorporate optimization algorithms, machine learning techniques, or artificial intelligence into stern foil design to automatically identify optimal geometric configurations under multiple operating conditions.
  • Perform lifecycle assessments that integrate hydrodynamic performance with fuel savings, carbon emission reduction, manufacturing costs, structural integrity, and maintenance requirements to evaluate the practical feasibility of large-scale implementation.
  • Examine the long-term operational performance of optimized stern foils under varying sea states, wave conditions, loading scenarios, and environmental disturbances to improve confidence in real-world applications.

Potential for Public Policy Citation (Overton)

This article demonstrates meaningful potential for citation in public policy and maritime engineering guidance because it addresses one of the central challenges facing modern shipping: improving vessel energy efficiency while reducing fuel consumption and environmental impacts. By presenting a computationally validated optimization of a stern-mounted energy-saving device, the study provides engineering evidence that can support technical recommendations for improving ship hydrodynamic performance.

The findings are relevant to government agencies, maritime authorities, and organizations responsible for developing standards and strategies related to sustainable shipping, energy efficiency, and marine transportation. The demonstrated improvement achieved through relatively modest geometric modification may inform future engineering guidelines concerning retrofit technologies and energy-saving devices for commercial vessels.

The research also aligns with broader international efforts to improve maritime sustainability by reducing fuel consumption and associated greenhouse gas emissions through technological innovation. Although the study focuses on numerical simulation rather than regulatory implementation, its engineering evidence provides a valuable scientific foundation for future technical reports, maritime efficiency programs, and policy documents promoting cleaner and more energy-efficient shipping.

Who Should Read This Paper?

  • Naval architects and ship designers.
  • Marine hydrodynamics researchers.
  • Computational Fluid Dynamics (CFD) specialists.
  • Mechanical and ocean engineering researchers.
  • Graduate students studying naval architecture, marine engineering, and fluid mechanics.
  • Researchers developing marine energy-saving devices.
  • Shipbuilding companies interested in hydrodynamic optimization.
  • Commercial shipping operators seeking fuel-efficiency improvements.
  • Maritime consultants involved in vessel performance analysis.
  • Government agencies and maritime organizations working on sustainable shipping initiatives.

Final Thoughts

This study presents a valuable extension of the established Hull Vane® concept by demonstrating that relatively simple modifications to planform geometry can produce measurable improvements in hydrodynamic efficiency. Through systematic CFD simulations, the authors show that a sweptback stern foil with a 15° angle consistently delivers the greatest resistance reduction among the investigated configurations while simultaneously improving wake characteristics and turbulence control.

One of the principal strengths of the research lies in its integration of quantitative resistance analysis with detailed flow visualization. Rather than reporting only numerical reductions in resistance, the study explains the underlying hydrodynamic mechanisms through pressure recovery, wake modification, and turbulence distribution. This comprehensive interpretation strengthens confidence in the proposed design optimization and provides useful engineering insight for future stern-mounted energy-saving devices.

The research also illustrates the growing importance of Computational Fluid Dynamics as a practical engineering tool for marine design optimization. By enabling systematic evaluation of multiple geometric configurations before physical prototyping, CFD significantly accelerates design development while reducing experimental costs.

Although additional experimental validation and broader parametric studies are still required, the findings clearly demonstrate that planform optimization represents an important direction for future hydrodynamic research. The proposed sweptback stern foil offers a promising approach for improving ship efficiency, supporting sustainable maritime transportation, and advancing the development of next-generation energy-saving technologies for commercial vessels.

Suggested Citations

UNP–Teknomekanik Style

Nabawi, R. A., Syahri, B., Alfana, Y. D., & Fernandez, D. (2026). Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept. Teknomekanik, 9(1), 110–120. https://doi.org/10.24036/teknomekanik.v9i1.54872

APA (7th Edition)

Nabawi, R. A., Syahri, B., Alfana, Y. D., & Fernandez, D. (2026). Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept. Teknomekanik, 9(1), 110–120. https://doi.org/10.24036/teknomekanik.v9i1.54872

IEEE Style

R. A. Nabawi, B. Syahri, Y. D. Alfana, and D. Fernandez, "Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept," Teknomekanik, vol. 9, no. 1, pp. 110–120, 2026, doi: 10.24036/teknomekanik.v9i1.54872.

Harvard Style

Nabawi, R.A., Syahri, B., Alfana, Y.D. & Fernandez, D., 2026. Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept. Teknomekanik, 9(1), pp.110–120. Available at: https://doi.org/10.24036/teknomekanik.v9i1.54872.

Vancouver Style

Nabawi RA, Syahri B, Alfana YD, Fernandez D. Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept. Teknomekanik. 2026;9(1):110–120. doi:10.24036/teknomekanik.v9i1.54872.

Chicago (Author–Date)

Nabawi, Rahmat Azis, Budi Syahri, Yogi Dian Alfana, and Donny Fernandez. 2026. "Hydrodynamic optimization of a Sweptback Stern Foil for resistance reduction in flat-hull ships: A CFD-based extension of the Hull Vane concept." Teknomekanik 9 (1): 110–120. https://doi.org/10.24036/teknomekanik.v9i1.54872.

MLA (9th Edition)

Nabawi, Rahmat Azis, et al. "Hydrodynamic Optimization of a Sweptback Stern Foil for Resistance Reduction in Flat-Hull Ships: A CFD-Based Extension of the Hull Vane Concept." Teknomekanik, vol. 9, no. 1, 2026, pp. 110–120. Crossref, https://doi.org/10.24036/teknomekanik.v9i1.54872.

Editorial Note

This article review has been prepared for Engineering Research Insights as an independent scholarly review based exclusively on the scientific content presented in the original research article. All bibliographic metadata were verified against the official article webpage published by Teknomekanik, while the scientific analysis was developed solely from the published article itself. The review aims to provide researchers, engineers, educators, industry practitioners, and policy stakeholders with an accessible overview of the study's objectives, methodology, principal findings, scientific contributions, practical implications, research limitations, and future research opportunities. This review is intended for educational and scientific communication purposes and does not replace the original peer-reviewed publication.

SEO Meta Description

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SEO Keywords

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