Experimental Investigation of Biofouled Ship Control Surface Performance

Biofouling remains an ongoing operational challenge in the maritime domain, particularly for modern surface ships. To date, the majority of existing marine biofouling studies have focused on the corresponding effects on overall ship resistance and propulsion, including resulting economic, environmental, and safety impacts [1–11]. Far fewer researchers have considered the relationship between biofouling and ship maneuvering, though several investigations have acknowledged the potential for both practical and operational consequences [12–17].

Effective ship maneuverability and control are predicated on appropriately designed and well-functioning control surfaces, particularly rudders [18–20]. Marine biofouling results in atypical control surface performance. For ship operators, this introduces significant risk: if the ordered rudder angle does not result in predictable ship behavior, then overall ship safety is fundamentally compromised. In a worst-case scenario, an unexpected loss of ship control can result in a collision, allision, grounding, and/or depth excursion.

This paper presents background information on marine biofouling, ship control surfaces, and the experimental characterization of ship control surface performance. The author's approach to investigating biofouling effects, using model-scale wind tunnel testing and sandpaper sheets with varying grits, is discussed in detail. For a selected control surface geometry, resulting lift, drag, and moment coefficients are shown for a variety of scenarios: different model scales; no biofouling/roughness (i.e., the establishment of a “baseline” condition); different roughness locations; different sandpaper grits; and different Reynolds numbers. Ultimately, assuming a lift-to-drag ratio as a measure-of-performance, this paper assesses the statistical significance and relevance of specific experimental results.

Marine biofouling communities are inherently diverse. As shown in Fig. 1, common “soft” and “hard” (calcareous) biofouling species include algae, hydroids, polyzoans, tunicates, worms, sponges, anemones, barnacles, and mussels, all developing as a function of the given ship's operating environment [21,22].

Shipboard biofouling typically begins with “microfouling,” the process by which an immersed surface is colonized by bacteria that coalesce into larger assemblies of biofilms or “slimes” [22]. These biofilms can achieve thicknesses of about 0.50 mm [22], and previous researchers have shown the potential for significant ship resistance (drag) penalties resulting from biofilms of varying thickness and coverage density [7]. However, these biofilms remain difficult to grow/simulate and study, particularly for model-scale physical experiments in a laboratory environment.

Over time, “macrofouling” communities may emerge on the immersed surface, overgrowing the initial biofilm, and “the specific organisms that develop in a fouling community depend on the substratum, geographical location, the season, and factors such as competition and predation” [22]. For surface ships transiting the world's oceans, a vessel's unique mission profile can also impact community diversity. Specifically, organism attachment and/or detachment may be directly influenced by local flow speeds and conditions, including boundary layer thickness and flow separation [23–25]. A vessel with longer in-port periods or a slower-speed operating profile is more likely to experience adverse macrofouling effects.

Historic ship surveys have shown barnacles to be the predominant macrofoulers of record [26,27], and these sessile invertebrates have been extensively studied. For the experimental investigation presented herein, barnacles are assumed to be the exclusive source of control surface biofouling. As shown in Fig. 2, this is a greatly simplifying assumption, as “real-world” control surfaces, such as one of the rudders on a United States Navy Yard Patrol Craft, experience multi-organism/multicommunity biofouling.

“Acorn barnacles,” specifically, have been reported as one of the most common calcareous biofoulers [27]. These particular barnacles are actually members of the Balanomorpha order [28], of which the Balanus genus and two distinct species, Balanus amphitrite and Balanus improvisus, have been most extensively modeled, simulated, and studied [26,29–31]. Figure 3 presents a representative three-dimensional scan of Balanus amphitrite, as provided directly to the author by Schultz and labeled using characteristic measurements detailed by Spivey [31].

For the purposes of this initial experimental investigation, the author further assumed that barnacle-like roughness could be simulated using appropriately selected (high-quality) sandpaper. Precedence exists to introduce artificial roughness to both airfoil and hydrofoil surfaces using sandpaper [32,33] and similar coatings [34]. However, a technical challenge remains converting a representative barnacle biofouling pattern to an equivalent sand-grain roughness (k_S) value and selecting a corresponding sandpaper grit with comparable properties. The author's methodology, for this particular study, is presented in Sec. 3 of this paper.

The broad term, “control surface,” first appeared in the early 1900s [35], with rudders serving as the primary control surfaces of interest in today's naval architecture community. However, mariners have maneuvered ships using rudders since at least 2500 BCE [36]. Mott [36] presents an excellent history of the design and development of the rudder, documenting that the “change (from a flat quarter-rudder) to a foil shape can be seen in medieval iconography.” Ship control surface shapes have evolved minimally since then, and Liu and Hekkenberg [37] thoroughly detail more recent findings/lessons learned related to rudder design and associated experimentation. As a representative example of a modern ship control surface, Fig. 4 depicts a nuclear-powered aircraft carrier's large stern-mounted rudders.

This study primarily focuses on a rudder-like shape, assuming that the entire control surface can be uniformly rotated about a single stock. The vast majority of today's rudders feature “airfoil” or “hydrofoil” cross-sections that reside within a standard National Advisory Committee for Aeronautics (NACA) series [20,38]. The most common NACA series used for surface ships and uncrewed maritime systems include the symmetrical NACA 0012, NACA 0015, and NACA 0018 shapes [20,37,39], though other variants have been studied and implemented. Interestingly, at least one previous study of rudder performance has suggested that, “a common airfoil section is not appreciably better than an ordinary streamline rudder if the latter is thin, and a thick rudder should be avoided from the point of view of propulsion” [40].

The standard geometry of a nontapered (symmetric) hydrofoil, including traditional parametric nomenclature, is shown in Fig. 5 [20,39]. The control surface's aspect ratio (AR) is particularly important for associated hydrodynamic performance, and both a geometric aspect ratio (AR_G) and an effective aspect ratio (AR_E) can be defined for the given shape [20,36,37]. AR_G can be calculated by dividing the hydrofoil's span (s) by its (mean) chord (c), and AR_E is double AR_G, accounting for the reflection plane formed by the adjacent hull. For most ocean-going vessels, AR_G values range from 1.50 to 3.00 [37]. For preliminary design efforts, “size coefficients” or “rudder area ratios,” typically a function of the ship's immersed lateral area, can be used to size the surface ship's control surfaces [37].

In a moving fluid with a given inflow velocity, lift force (L) and drag force (D) develop as functions of the control surface's angle-of-attack (AoA or α) relative to the incident flow. These forces act through the hydrofoil's varying center-of-pressure, but the rudder's “quarter-chord” location is typically assumed as the center about which a resultant (yaw) moment (M) should be calculated [20,41]. Figure 6 depicts the typical forces acting on a rudder in an incident flow field [20].

For the purposes of this study, a traditional hydrofoil shape was subdivided into three distinct regions: leading-edge (LE), midbody (MB), and trailing-edge (TE). These regions were established by dividing the hydrofoil's contour into thirds using a three-dimensional rhinoceros model, not by an even subdivision of the hydrofoil's chord line. The author could identify no published references that clearly define “standard” boundary definitions for these three distinct regions. Thus, Fig. 7 presents the spatial regions assumed for this investigation.

At model-scale, three primary venues exist to experimentally investigate the hydrodynamic performance of a ship control surface:

• Wind tunnel: In a typical wind tunnel, high-speed air is forced through a test-section using precisely controlled fans. The operator can adjust the air speed to achieve a desired (target) Reynolds number. During testing, the control surface model remains fixed to a force/moment measurement apparatus. This apparatus generally allows for the adjustment of angle-of-attack, within limits, relative to the incoming air. The two most basic classifications of subsonic wind tunnels include “open-circuit” (Eiffel) wind tunnels and “closed-circuit” wind tunnels, each with varying advantages and disadvantages [42]. A “floor-mounting” arrangement, where the model is oriented vertically in the test-section, is most common for ship control surface testing, and the experimenter can further decide whether or not to model specific hull interactions by including removable panels and/or structures in the given test-section [20,42].

• Recirculating water tunnel: A recirculating water tunnel is comparable to a wind tunnel, but the fluid medium is generally temperature-controlled freshwater. The water tunnel features a closed-circuit design, with the ability to carefully fill or drain the system, and a large (operator-controlled) axial-flow impeller (pump) is typically used to change the fluid's speed. Like a wind tunnel, the control surface model remains fixed to a force/moment measurement apparatus as the high-speed water circulates. A water tunnel's test-section is usually much smaller than that of a wind tunnel, though specialized facilities with very large test-sections do exist [43]. Given the smaller size of these facilities; the difficulty pushing large volumes of water at high speeds; and the inherent differences in viscosity between air and water, water tunnel testing may not be able to achieve high Reynolds number conditions, particularly the conditions frequently required for testing the control surfaces of smaller vessels (e.g., uncrewed maritime systems).

• Towing tank: A towing tank features a large (static) body of water, usually (relatively) isothermal freshwater, to support direct hydrodynamic experimentation. A powered towing carriage, traveling above the free-surface along the tank's longitudinal axis, provides an instrumented apparatus to which the control surface model can be rigidly mounted. That is, unlike both a wind tunnel and a water tunnel, the physical model moves and the fluid medium remains stationary. The operator can carefully adjust the towing carriage's speed to achieve the desired Reynolds number. Model geometries in a towing tank can be much larger, as blockage concerns [42,44] are much less significant than for other facilities; however, the model's maximum size is generally limited by loading considerations on the towing carriage and associated force/moment measurement instrumentation. For control surface testing, the experimenter must carefully consider how to accurately model the given hydrofoil's fully submerged performance. This is typically accomplished by affixing the control surface to a large (movable) stock/post, like the rudder stock of a full-scale vessel, and introducing a representative hull-form or “false ceiling” above the assembly [45]. If the control surface is tested too close to the free-surface, ventilation can occur, particularly at higher speeds where the surface effects (e.g., wakes) from the carriage-mounted test assembly are significant.

The primary goal for traditional control surface experimentation is to collect associated force and moment measurements for varying angles-of-attack and inflow speeds (or Reynolds numbers). Depending on the specific facility, precalibrated multi-axis force/moment transducers are commonly used. Other experimental goals may include collecting visual/qualitative data, especially to better understand flow separation effects, and these goals can be accomplished by using smoke (or dye) injection, particle image velocimetry, and other modern imaging techniques [42,46,47]. The process for converting collected lift force, drag force, and moment values into relevant nondimensional coefficients is detailed in Sec. 3 of this paper. Traditionally, experimenters have conveyed overall control surface performance by plotting lift coefficient (C_L), drag coefficient (C_D), and moment coefficient (C_M) values as functions of angle-of-attack [20,38]. A nondimensional lift-to-drag (L/D or C_L/C_D) ratio value can also be used as a valid measure-of-performance for the overall control surface system [20].

Relevant to this particular study, previous research teams have identified the following factors with the potential to significantly influence (or even degrade) a given control surface's physical performance:

• Model-scale (λ): Blockage effects can significantly affect the validity of collected experimental data. The larger the physical model, the more significant the effect, particularly at high angle-of-attack values. Within a given test-section, as the model size increases, the model will behave less like a “finite span” (three-dimensional) hydrofoil and more like an “infinite span” (two-dimensional) control surface, with near-wall interference effects introducing experimental error. Recommended practice in a standard wind tunnel is to limit the “solid blockage,” the ratio of the model's frontal-area to the test-section's cross-sectional area, to less than 10.0%, with 5.0% blockage suggested as a typical value to minimize error [18,42], and these references also provide several other important considerations for model-to-ship data correlation.

• Aspect ratio (AR): Most ship control surfaces feature relatively low aspect ratio values [20,42,48]. For a given angle-of-attack, as aspect ratio is reduced (from that of an infinite span hydrofoil), C_L decreases, C_D increases, and the corresponding L/D ratio decreases [49]. However, the hydrofoil's observed stall-angle increases as aspect ratio is reduced [20,50]. That is, ship control surfaces with lower aspect ratios (i.e., more “square-like” hydrofoils) exhibit worse hydrodynamic performance, with the exception of stall, than those with greater aspect ratios. When designing a ship control surface, a naval architect has to balance this knowledge with practical considerations, like ensuring that the rudder does not significantly protrude below the ship's baseline; ensuring that (hydraulic or electromechanical) control surface actuators can withstand the associated hydrodynamic loading; and ensuring that the given control surface is structurally sound enough for sustained operations in the marine environment.

• Reynolds number (Rn): Control surface performance is highly dependent on inflow speed, and this subject has been extensively studied for both airfoils and hydrofoils [51–54]. In general, performance improves as Reynolds number increases: at a given angle-of-attack, the L/D ratio value steadily increases with an increase in Reynolds number. Specifically, C_L is greater and C_D is lesser, at a single angle-of-attack, as Reynolds number increases [55]. Above a Reynolds number of 1 × 10⁶, however, less dependence on speed has been postulated [54], though additional experimental datasets collected at (very) high Reynolds numbers are still required to assess the validity of this prevailing assumption [56]. Most full-scale ships operate in this “fully turbulent” regime, with control surface (chord) Reynolds numbers on the order of 10⁶, 10⁷, or even greater [18]. Low Reynolds number control surface behaviors are primarily a design consideration for small uncrewed surface vehicles, small-diameter uncrewed underwater vehicles, and mission-dictated slow-speed operations (e.g., mooring, hovering, etc.).

• Surface roughness: At higher speeds, increased surface roughness has been observed to degrade (or “penalize”) the hydrodynamic performance of a ship control surface. In general, at a single angle-of-attack value, the introduction of roughness dramatically reduces C_L, increases C_D, and reduces the L/D ratio. This behavior has been observed for airfoils experiencing icing [57,58]; hydrofoils covered with biofilms [13]; and (marine) tidal turbines featuring various biofouling communities [34,59,60]. The overall density and characteristic height of the tested roughness pattern further appear to influence resulting performance. The majority of these past studies compared entirely “fouled” surfaces to completely “clean” (smooth) baselines. Less well-studied (and the primary focus of this paper) have been the spatially dependent effects of introduced roughness; however, several previous research teams have considered singular regions, including the effects of leading-edge roughness [61]; a (near) midbody patch of sandpaper roughness [32]; and barnacle-like roughness on the upper (suction) surface of a turbine blade [60]. At model-scale, at least two research teams have used sandpaper-like roughness/grit to simulate the effects of biofouling along the length of a ship's hull-form, recognizing the adverse impacts of spatiality from a larger (total ship resistance) perspective [62,63]. Of important note, however, is the fact that surface roughness may actually introduce some hydrodynamic benefits, particularly if fully turbulent flows have not been developed: rougher surfaces can delay flow separation at higher angles-of-attack and change the control surface's stall characteristics [17,34]. Several studies have also considered how artificial tubercules, introduced at particular locations along an immersed surface, can yield beneficial drag reduction [64]. However, these benefits may not be operationally realized by full-scale ships operating at high Reynolds numbers and with average (commanded) rudder angles within the range of ±15 deg [37].

Appropriate scale factors were selected to minimize wind tunnel blockage effects at high angle-of-attack values. Full-scale and model-scale control surface geometries are defined in Table 1. All developed model-scale control surfaces represent hydrofoils with “finite” span (s) values.

All physical experimentation was performed in USNA's Eiffel Wind Tunnel, shown in Fig. 8, with each control surface mounted vertically. This open-circuit wind tunnel features a test-section with the following approximate dimensions: 78.74 cm width, 111.76 cm height, and 304.80 cm length. The maximum inflow velocity of the wind tunnel is 91.44 m/s. A precalibrated pyramidal balance is used to measure resultant forces and moments for all six degrees-of-freedom, and both inflow velocity and AoA can be directly controlled by the operator. The primary (model-scale) experimental outputs of interest include measured AoA (α_M), measured lift force (L_M), measured drag force (D_M), and measured moment (M_M) about the pyramidal balance's center. For each operator-selected AoA value, 30 samples were collected (with a 250 ms delay between samples), and a complete “data run” was established as a manual “sweep” through multiple AoA values while manually maintaining a constant inflow velocity.

For this study, the full-scale inflow-of-interest corresponded to a (chord) Reynolds number on the order of 10⁷. Given the physical limitations of USNA's Eiffel Wind Tunnel, particularly limiting moments on the pyramidal balance, this full-scale value cannot be reached. During pre-experimentation planning/preparation, the author assessed that a (chord) Reynolds number of 1.00 × 10⁶ could be most consistently achieved, for all desired test conditions, without risking potential damage to the wind tunnel.

Standard practice suggests that this coefficient should also be reported as the quarter-chord moment coefficient (C_M,QUARTER) [20,42,65]. Calculating the quarter-chord moment coefficient requires a geometric correction that accounts for the measured distance between the balance center and the given hydrofoil's quarter-chord point (Δx). For each tested hydrofoil, this measured offset distance is reported in Table 2.

Ultimately, as detailed, three experimental properties are corrected/adjusted appropriately: AoA, drag coefficient, and moment coefficient. The experimental lift coefficient is not adjusted for this paper as additional investigation is required to better understand appropriate correction factors for USNA's Eiffel Wind Tunnel.

As previously depicted in Fig. 7, the primary focus of experimentation was the introduction of artificial surface roughness to three distinct hydrofoil regions: LE, MB, and TE. Accordingly, a major methodological assumption for this study was how to select sandpaper grits that reasonably reflect real-world barnacle-like biofouling. First, the author considered existing field studies of measured acorn barnacle characteristics [2,28,30,66–69] and a series of barnacle scans provided by Schultz to derive average barnacle basal diameter and diameter-to-height values. On average, a basal diameter (D_BASAL) of 10.00 mm and a diameter-to-height ratio of 2.22 appear to serve as relevant parametric values.

Next, the author created a “composite” barnacle geometry, in the form of a truncated cone, significantly influenced by the published work of Womack et al. [70]. This representative shape, as modeled in rhinoceros, is shown in Fig. 9 and features a basal diameter (D_BASAL) of 10.00 mm, a diameter-to-height ratio of 2.22, a maximum geometric height (k_BARNACLE) of 4.50 mm, an interior conical angle of 56 deg, and a cone-top diameter of 3.93 mm.

The author then considered two major findings from Womack et al. [70] to develop a “worst-case” roughness pattern: (1) “Important turbulent boundary layer parameters […] showed only minor differences between the staggered and random arrangements when determined using well-resolved spatial-averaged profiles,” and the observation that (2) “peak roughness length occurred at approximately 40% planform density.” rhinoceros was used to develop a square-staggered pattern featuring the conical shapes shown in Fig. 9 and covering 40% of the given surface-of-interest. This baseline surface pattern was then geometrically scaled as a function of D_BASAL, using the scale factors presented in Table 1.

Finally, to convert all geometric height (k_BARNACLE) values to corresponding equivalent sand-grain roughness height (k_S) values, data from Womack et al. [70] were again considered. This past research suggests that, for a 40% density square-staggered pattern with truncated cones, the ratio between k_S and the height of an individual “barnacle” (k_BARNACLE) is approximately 2.45, and the ratio between k_S and the mean surface height (k_MEAN) is approximately 12.06. Table 3 summarizes the results of these associated calculations and conversions. For each model-scale roughness pattern, k_MEAN was calculated using rhinoceros; this k_MEAN value would change if the pattern density was varied by the experimenter.

Relating a calculated k_S value to a corresponding sandpaper grit remains an ongoing research challenge, and very few works could be identified that summarize major practical findings related to this experimentally relevant task [71,72]. Specifically, Flack and Schultz [71] found that k_S for sandpaper is “observed to be several times larger than the median grain size of the grit,” on the order of about 2.00 to 2.50 times larger. Using this guidance and relevant vendor data [73–75], Table 4 presents the closest equivalent Coated Abrasives Manufacturers Institute (CAMI) sandpaper grits that effectively model the desired worst-case biofouling/roughness patterns-of-interest. Ultimately, for this initial experimental study, the author procured rolls of 36-grit (310X), 40-grit (310XF), and 50-grit (310XF) cloth-backed, closed-coat, aluminum oxide sandpaper from Klingspor Abrasives (Hickory, NC). The backing thickness on each roll was approximately 0.80 mm.

The three control surface model scales (9.29, 10.68, and 13.11) correspond to 10.0%, 7.5%, and 5.0% solid blockage values, respectively, at a 20 deg angle-of-attack value. As detailed in Sec. 2.3, the model with the least blockage (λ = 13.11) is hypothesized to exhibit the most representative performance, as this model-scale minimizes adverse blockage and wall interference effects. However, the smallest model also makes it less likely to achieve desired (full-scale) chord Reynolds number values.

To assess potential model scaling effects, all three (smooth/unfouled) models were tested at (chord) Reynolds number values of 1.00 × 10⁶ and 1.50 × 10⁶, with the higher Reynolds number representing the physical limit of the wind tunnel and pyramidal balance for this particular experiment. Figure 10 presents faired C_L,INITIAL, C_D,CORRECTED, and C_M,QUARTER values, all as a function of α_TRUE, for testing at Rn_EFFECTIVE equal to 1.00 × 10⁶. Figure 11 presents these same faired nondimensional coefficients for testing at Rn_EFFECTIVE equal to 1.50 × 10⁶.

The most observed variation occurs with the C_L,INITIAL values for each different model-scale. Lift coefficient results for the largest model (λ = 9.29) appear as the largest values and the most impacted by Reynolds number. Corresponding results for the smallest model (λ = 13.11) appear to be more consistent (i.e., nearly linear) and the most independent of Reynolds number. Additional study is needed to better understand these scaling effects, particularly any/all corresponding wind tunnel interferences, but the author elected to proceed with experimentation exclusively using the smallest model (λ = 13.11) at an effective (chord) Reynolds number of 1.00 × 10⁶.

The smallest NACA 0018 control surface model (λ = 13.11) was repeatedly tested in the “smooth” (unfouled) condition. Five complete datasets (“sweeps”) were collected during Summer 2022, Winter 2022, and Summer 2023, including after extended periods where the model was removed from the wind tunnel and subsequently re-installed. Figure 12 shows the results of this repeatability verification process for both C_L,INITIAL and C_D,CORRECTED, where error bars represent corresponding mean and (single) standard deviation values. The error bars were derived using data from all five datasets, where 30 samples were collected for each AoA value (in a given sweep). These experimental data are compared to Prandtl's fundamental lifting-line theory for an elliptic planform [76].

The strong agreement with Prandtl's lifting-line theory was somewhat unexpected, as the control surface model has a particularly low aspect ratio (AR_G = 1.08 and AR_E = 2.17). Newman [76] suggests that the lift coefficient should be significantly overpredicted using Prandtl's approximation. Accordingly, the author considered two other empirical estimates, labeled as Timmer [77] and Molland and Turnock [20], as shown in Fig. 13.

Timmer [77] experimentally determined two-dimensional C_L and C_D values for a NACA 0018 model at a Reynolds number of 1.00 × 10⁶. These two-dimensional coefficients were converted by the author to (approximate) three-dimensional coefficient values using established transformation functions [20,39,76]. An Oswald efficiency factor (e) of 1.00 was assumed for this conversion. Molland and Turnock [20] present a series of equations that also appear in Ref. [18] for marine rudders. These equations, derived from experimental data for (all-movable) low aspect ratio rudders, were intended to improve upon Prandtl's approximation [48,50]. An efficiency factor of 1.00 was again assumed. The author used calculated parameters for a square-tipped hydrofoil with no taper and assumed a “minimum section drag coefficient” of 0.0080, as derived from the Timmer [77] dataset.

When compared to Prandtl's initial lifting-line theory, both of these approaches demonstrate greater variability for C_L but less for C_D. Calculated root-mean-square error (RMSE) values are shown in Table 5. Experimental data for C_L most closely follow Prandtl's approximation, whereas experimental data for C_D most closely follow the Timmer [77] approach. The Molland and Turnock [20] estimation fares poorly for this particular control surface model. As Whicker and Fehlner [50] experimented with model geometries featuring both sweep-angle and taper, one can assess that their resulting empirical formulas may not be as valid for the geometry tested by the author. In general, however, the collected experimental data for the smooth NACA 0018 at a Reynolds number of 1.00 × 10⁶ appear to be reasonable. Accordingly, these data were established as the baseline for all subsequent assessments of simulated biofouling effects.

To investigate the spatially dependent effects of biofouling, 36-grit sandpaper was applied to the leading-edge, midbody (both port and starboard sides), and trailing-edge of the baseline control surface model (λ = 13.11). The 36-grit sandpaper was selected to simulate the most discernable (adverse) impact on overall control surface performance. As shown in Fig. 14, the sandpaper was attached with 3M VHB double-sided tape, and a series of angular sweeps (−2 deg to +25 deg) were performed at a constant chord Reynolds number of 1.00 × 10⁶. Only data for “positive” sweeps (i.e., increasing AoA values) were collected to avoid expected hysteresis effects.

Figure 15 shows the results of these wind tunnel tests, as compared to the baseline (unfouled) control surface model. For clarity, C_L,INITIAL, C_D,CORRECTED, and C_M,QUARTER values are all presented using faired trendlines for each condition. Leading-edge roughness appears to result in the worst control surface performance: compared to the baseline (unfouled) model, average lift was reduced by 39%, and average drag was increased by 65%. Midbody roughness resulted in an average lift reduction of 6% and an average drag increase of 15%. Trailing-edge roughness resulted in an average lift increase of 1% and an average drag increase of 15%. The statistical significance of these results is assessed in Sec. 4.6. Negative moment coefficient values are omitted for the clarity of analysis and subsequent visual presentation.

After identifying leading-edge biofouling as the worst-case condition, sandpapers of varying grits were tested on the leading-edge of the smallest control surface model. These grits were previously specified in Table 4, and Fig. 16 shows resulting (faired) C_L,INITIAL, C_L,CORRECTED, and C_M,QUARTER values at a constant chord Reynolds number of 1.00 × 10⁶. With the exception of the measured C_M,QUARTER values, little variability appears between the different leading-edge conditions. The statistical significance of these results is also assessed in Sec. 4.6. Again, negative moment coefficient values are omitted.

Assuming 36-grit sandpaper on the leading-edge of the smallest control surface, a brief study of Reynolds number dependence was also performed. Figure 17 presents the corresponding control surface performance results, comparing the leading-edge biofouling condition to baseline (unfouled) data. Negative moment coefficient values are omitted. Chord Reynolds number was varied from a maximum of 1.00 × 10⁶ to a minimum of 0.25 × 10⁶. The lowest Reynolds number value was limited by the ability to (accurately) measure force and moment values via the pyramidal balance, and a micromanometer was used to maintain constant inflow velocity.

Previous systematic studies suggest that, at a given angle-of-attack value for a two-dimensional airfoil, C_L should increase and C_D should decrease as Reynolds number increases [38]. In Fig. 17, this behavior holds true for the experimental C_D,CORRECTED values for both the unfouled and fouled conditions; however, the C_L,INITIAL values do not trend as expected.

The unique behavior of the calculated lift coefficient values can likely be attributed to the combined effects of a low aspect ratio hydrofoil, relatively low Reynolds number values, and the introduction of surface roughness. For the biofouled control surface, at least one past work [55] supports the author's findings: for a roughened control surface, C_L will actually decrease as Reynolds number increases (for a given AoA). Roughness impacts the characteristics of the boundary layer and the nature of flow separation, with corresponding effects on the control surface's ability to generate lift. However, another past study of a roughened airfoil [78] shows the opposite (and more typical) behavior, though this particular study was performed for a two-dimensional control surface.

The lift coefficient data for the smooth (unfouled) control surface demonstrate the most unexpected results. For these data, the predicted trend (i.e., increasing C_L with increasing Reynolds number) is shown for the Reynolds number values of 0.50 × 10⁶, 0.75 × 10⁶, and 1.00 × 10⁶. However, for the three lower Reynolds numbers (0.25 × 10⁶, 0.30 × 10⁶, and 0.40 × 10⁶), C_L decreases with increasing Reynolds number for low-to-moderate AoA values. At least one past study [79] shows comparable trends, particularly when lower aspect ratio values are considered, and such behaviors are expected for Reynolds number values in the transitional flow regime.

Additional experimentation is necessary to fully confirm and understand these Reynolds number dependencies, particularly the resulting lift coefficient data for (very) low aspect ratio ship control surfaces. Any follow-on work should, foremost, verify the repeatability of the results shown in Fig. 17.

The author considered both analysis of variance and Kruskal–Wallis (KW) hypothesis testing to assess the impact of biofouling/roughness on control surface performance. Given the non-normal distributions of the collected experimental data, KW testing was decided to be more appropriate for this particular study. For comparison, all experimental data (collected at a chord Reynolds number of 1.00 × 10⁶) were converted into lift-to-drag (L/D) ratios and compiled into six major groups: no biofouling (baseline or BL), leading-edge 36-grit roughness (LE G36), midbody 36-grit roughness (MB G36), trailing-edge 36-grit roughness (TE G36), leading-edge 40-grit roughness (LE G40), and leading-edge 50-grit roughness (LE G50). Figure 18 visually summarizes the results of KW hypothesis testing, performed using matlab. Each individual group is compared to all others to determine whether the calculated differences between mean ranks are statistically significant.

Subsequently, matlab's “multcompare” function was used to perform pairwise hypothesis testing. Major findings from this analysis process are summarized in Table 6. Calculated p-values are provided in parentheses and compared to a standard alpha value (0.05). “Y” indicates that the results are statistically significant, and “N” indicates that the results are not.

Assuming the control surface's lift-to-drag (L/D) ratio as a valid measure of hydrodynamic performance, simulated biofouling results in the following statistically significant results (at a constant chord Reynolds number of 1.00 × 10⁶):

• Leading-edge (36-grit) roughness degrades average performance by 63%.

• Leading-edge (40-grit) roughness degrades average performance by 60%.

• Leading-edge (50-grit) roughness degrades average performance by 57%.

• Midbody roughness degrades average performance by 29%.

• Trailing-edge roughness degrades average performance by 20%.

The coarsest sandpaper grit was hypothesized to result in the worst performance degradation, as the characteristic height of such roughness has the most impactful interaction with the surrounding freestream environment. This hypothesis was directly confirmed by wind tunnel experimentation. Overall, these results suggest that the impact of biofouling on ship control surface performance and associated maneuverability merit additional investigation.

Control surface biofouling has the potential to adversely impact ship safety by degrading expected hydrodynamic performance. Spatially, leading-edge biofouling appears to represent the worst-case scenario, followed by midbody biofouling, then trailing-edge biofouling. For leading-edge biofouling, varying roughness by changing sandpaper grits yielded mixed results: statistically significant performance differences were only observed between the 36-grit roughness and the 50-grit roughness, suggesting that experimental limitations exist for the selected model-scale and experimental setup.

Future (related) work must consider and address the identified limitations of this paper. Foremost, Reynolds number dependencies should be characterized over a wider range. Second, the resulting performance effects of different sandpaper grits, including both coarser and finer grits, should be assessed. A wider range of introduced roughness, using high-quality sandpaper, offers the potential to better understand the similitude between laboratory-based findings and real-world (open-ocean) effects. Third, the resulting performance effects of more representative biofouling patterns (e.g., additively manufactured barnacle patterns instead of sandpaper) should also be investigated. Fourth, flow behaviors, particularly flow separation, should be qualitatively characterized using various (experimental) visualization techniques. Fifth, all derived experimental results should be translated into expected effects on shiphandling behaviors for real-world ships, as supported by computational fluid dynamics. The author's findings can likely inform existing ship control/maneuvering algorithms and coefficient-based estimations. However, computational fluid dynamics practitioners may also be interested in these experimental results to support ongoing verification and validation (V&V) efforts. Finally, the nature of long-term biofouling community development (and retention) on ship control surfaces must be better explored and documented. Historic naval architecture references suggest that a ship's roughness will increase over the given vessel's service life [80]. Additional studies, to include longitudinal investigations that account for a given ship's distinct maintenance/overhaul periods, are necessary to better understand the magnitude and rate of this roughness increase for representative control surfaces. These investigations would require methodical (in-water) visual inspections by divers and/or deployable robotic systems.

From a practical (shiphandler's and ship maintainer's) perspective, several recommendations are offered as a result of the experimental findings presented in this paper. First, crews should be better trained to recognize a loss of ship maneuverability due to control surface biofouling. This is a challenging endeavor, as such degradation will not be an immediate effect (given the time required for biofouling communities to develop and mature). However, the longer that a ship is underway, the more likely that larger (commanded) rudder angles will be necessary to execute desired course changes. Second, automated ship control systems, such as those for uncrewed surface vehicles and uncrewed underwater vehicles, should be developed and tested to account for biofouling effects. Such efforts will require the integration of experimental test data into established modeling/simulation environments. Algorithmically, biofouling will have a direct impact on a ship's estimated (or programmed) maneuvering coefficients. Third, given limited time, funding, and diver support for hull inspections and cleanings, key decision-makers should prioritize the removal of leading-edge biofouling on any ship control surfaces. Prescribed guidance for partial hull cleanings [81] should be updated to reflect this recommendation.

The author is grateful for the generous technical support provided by Naval Sea Systems Command (NAVSEA), Naval Surface Warfare Center Carderock Division (NSWCCD), the Naval Academy Hydromechanics Laboratory (NAHL), USNA's Technical Support Department (TSD), USNA's Aerospace Engineering Laboratory, and USNA's Project Support Branch (PSB). Particular gratitude is extended to Professor Michael Schultz, Ph.D., PE; Professor David Miklosovic, Ph.D.; Mr. Daniel Rodgerson; Mr. Brandon Stanley; and Mr. Charlie Swanton. The author is also thankful for the excellent customer support provided by Mr. Gabe Ellis (Klingspor Abrasives) during the experiment planning/preparation process.

The research presented herein was conducted while the author served as a civilian faculty member at the United States Naval Academy, and subsequent paper revisions were completed as an employee of The Johns Hopkins University Applied Physics Laboratory. The views expressed in this paper are those of the author and do not reflect on the official policy or position of the United States Naval Academy, the Department of Defense, the United States Government, and/or The Johns Hopkins University Applied Physics Laboratory. References within this paper to any specific commercial products, websites, services, companies, or trademarks do not constitute the author's endorsement or recommendation of such items/entities. The appearance of U.S. Department of Defense (DoD) visual information does not imply or constitute DoD endorsement.

• Naval Sea Systems Command (NAVSEA; Funder ID: 10.13039/100010465).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.