Hull grooming benefit model

What this calculator does

It estimates the annual value, per vessel, of holding the hull at fouling rating FR-0 to FR-1 by grooming it every 10–14 days while underway, compared with what the operator does today. The baseline is not a dirty hull: the saving is the difference between two hull-condition profiles over the docking cycle, one under the current cleaning practice and one groomed. Everything below can be reproduced in a spreadsheet from the formulas given. The model is a best-effort estimate; it is not a performance guarantee, and any contractual terms are those of your CRABI Master Service Agreement.

Live derivation for the current inputs

Symbols

\(P(t)\)	added fuel at constant speed, percentage points	\(F,\ R\)	removable fouling; coating-ageing residual
\(S_{\text{sat}},\ \tau,\ e\)	soft-fouling saturation, time constant, share of its penalty a brush clean removes	\(H_{\text{sat}},\ t_{\text{lag}},\ r_H,\ e_H\)	hard-fouling ceiling, succession lag, logistic rate, share of its penalty a brush clean removes
\(R_{60}\)	ageing residual at month 60	\(H_0\)	hard-fouling seed at the end of the lag
\(D,\ \delta,\ D_{\max}\)	accumulated brush-cleaning roughness; increment per clean; cap
\(k,\ k_G\)	fouling-pressure multiplier, ungroomed / groomed	\(I,\ D\)	cleaning interval, docking cycle (months)
\(\bar P,\ \bar F,\ \bar R\)	cycle means	\(f,\ s\)	frictional share of resistance; scaling to the 0.85 calibration
\(P_b,\ P_g\)	cycle-mean penalty, current practice / groomed (\(P_g^{\text{raw}}(t)\) is the groomed profile before speed scaling)	\(\varphi,\ E\)	fuel saved as fraction of actual burn; penalty removed
\(m\)	annual fuel at sea, MT	\(c\)	share of fuel-side value captured by the owner (1 if owner pays fuel)
\(T_{\text{dock}}\)	docking interval, years	\(V_d = \text{TCE} + Y\)	value of a dock day: earnings plus yard day cost
\(A\)	wetted surface, m²	\(c_{\text{AF}},\ c_{\text{hard}}\)	applied coating cost, $/m²

1. Hull-condition model

Added fuel at constant speed is split into soft fouling and hard fouling, which in-water cleaning removes, and coating ageing, which only a dry-dock recovers:

$$P(t) = S(t) + H(t) + D(t) + R(t)$$ $$\frac{dS}{dt} = \frac{k\,S_{\text{sat}} - S}{\tau / k}, \qquad S \;\to\; (1-e)\,S \ \text{ at each in-water clean}$$ $$\frac{dH}{dt} = \begin{cases} 0 & t - t_{\text{clean}} < t_{\text{lag}} \\[4pt] k\,r_H\,H\left(1 - \dfrac{H}{k\,H_{\text{sat}}}\right) & \text{otherwise} \end{cases}, \qquad H \;\to\; (1-e_H)\,H \ \text{ at each clean}$$ $$D \;\to\; \min(D + \delta,\ D_{\max}) \ \text{ at each brush clean}, \qquad R(t) = R_{60}\,\frac{t}{60}, \qquad k = k_{\text{trade}}\left(1 + \frac{\text{idle days}}{365}\right)k_{\text{coating}}$$

Soft fouling (slime, weed) grows toward a saturation level with an assumed first-order time constant \(\tau = 4.5\) months. Hard fouling (barnacles, tubeworms) follows succession: it establishes \(t_{\text{lag}}\) months after the last clean, seeded at \(H_0\), and then grows logistically toward a ceiling \(H_{\text{sat}}\) that depends on the coating. A diver clean with brushes removes only part of each penalty (\(e\), \(e_H\)) and abrades the coating, adding a permanent roughness penalty \(\delta\) that accumulates with each clean until the hull is recoated — Utama et al. (2021) measured about 7% from abrasive cleaning, while Oliveira & Granhag (2020) found no wear from gentle water jets, which is why the groomed profile carries no \(D\) term. The fouling-pressure multiplier \(k\) raises saturation levels and growth rates together.

The removal fractions and the hard-fouling ceiling were solved against the full event history in Adland et al. (2018), a five-year panel of eight Aframax sister ships: the model is run through each ship's actual delivery, cleaning and docking dates (20 underwater cleanings at 13–55 months after delivery, 8 dry-dockings) and must reproduce the two measured effects, together with an independent anchor for an uncleaned hull:

$$\overline{\Delta C}_{\text{clean}} = 9\%, \qquad \overline{\Delta C}_{\text{dock}} = 17\%, \qquad P_{\text{uncleaned}}(60) = 38\%$$

Those three conditions leave one degree of freedom, which is fixed by setting the soft-fouling saturation at 10 points (heavy slime, Schultz 2007). The brush-damage increment \(\delta\) is set from Utama et al. rather than fitted. The live reproduction of the Adland schedule, and a cross-check against the IMO GloFouling cleaning-strategy model, are in section 5.

Constant	Value	Basis
\(\tau\)	4.5 months	Assumed
\(S_{\text{sat}}\)	10 pts	Heavy-slime penalty, Schultz (2007)
\(e\)	0.50	Calibrated: share of the soft-fouling penalty a brush clean removes
\(e_H\)	0.78	Calibrated: share of the hard-fouling penalty a brush clean removes
\(\delta,\ D_{\max}\)	1 pt per clean, 6 pts	Brush abrasion, scaled to the ≈ 7% measured by Utama et al. (2021); zero for non-contact grooming
\(H_{\text{sat}}\)	SPC 23 · FR 16 · hard coat 46 pts	SPC calibrated; FR and hard coat scaled by the same ratios as the growth multipliers
\(t_{\text{lag}},\ H_0,\ r_H\)	6 months, 0.5 pts, 0.20 /month	Assumed succession timing: hard fouling reaches half its ceiling about two years after the lag
\(R_{60}\)	5.0 pts	Set so coating ageing contributes 2.5 points averaged over a five-year cycle

A consequence worth noting: because brush cleaning restores only half of the slime penalty and roughens the coating each time, diver cleaning reaches a floor it cannot get below — monthly cleaning still leaves roughly a 10% penalty on a tanker hull, and cleaning more often than twice a year buys almost nothing. Grooming, which removes biofilm before it matures and never contacts the coating abrasively, sits near 3% including coating ageing. That gap, not cleaning frequency alone, is where the value of grooming comes from.

The groomed profile is evaluated over the same cycle as the sum of three terms, each exposed as an input:

$$P_g^{\text{raw}}(t) = \underbrace{R(t)}_{\text{coating ageing, if retained}} \;+\; \underbrace{0.4\,k_G}_{\text{residual biofilm}} \;+\; \underbrace{\tfrac{\text{niche}\,\%}{100}\,F_{\text{current}}(t)}_{\text{ungroomed niche area}}$$

The groomed line is therefore not flat. It rises through the docking cycle because the coating ages whether or not it is groomed: harbour water quality, suspended debris, abrasion and the coating's own leaching roughen the surface and build up a leached layer that only recoating removes. Grooming keeps fouling off the coating; it does not change the coating's condition, and the ageing ramp \(R(t)\) is identical in both profiles. Niche areas (sea chests, thruster tunnels, gratings) follow the current diver schedule and so carry the current-practice sawtooth at reduced amplitude.

0.4 points is the mean biofilm penalty at a 12-day interval, from a first-order regrowth curve fitted to the biofilm drag measurements of Schultz et al. (2015) and scaled to a mid-size hull. It is extrapolated from 3- and 6-month test-panel data and can be adjusted.

2. Multipliers

Input	Effect	Values	Status
Trade area	Scales \(S_{\text{sat}}\), \(H_{\text{sat}}\) and both growth rates	Cold 0.7 · Mixed 1.0 · Warm 1.35	Assumed; CRABI's regional regrowth programme is replacing these with measured values
Idle days	Each idle day at twice the sea rate	\(1 + \text{idle}/365\)	Assumed
Coating	Growth multiplier (ungroomed) / hard-fouling ceiling / residual-biofilm multiplier (groomed)	SPC 1.0 / 23 / 1.0 · FR 0.8 / 16 / 0.8 · Hard 1.3 / 46 / 1.0	Assumed; CRABI's coating-compatibility programme is measuring these
Speed and hull form	Percentage penalty scaled by frictional share relative to the Aframax calibration	see below	Engineering approximation

The calibration data is from Aframax tankers at about 13 kn, where friction is roughly 85% of total resistance; a container ship at 20 kn is nearer 65%. The same roughness therefore costs a smaller percentage of fuel on the faster, finer hull. Residuary resistance grows steeply with speed in the service range, so the share is taken to vary as the square root of the speed ratio:

$$f = \operatorname{clamp}\!\left(f_{\text{preset}}\sqrt{\frac{v_{\text{preset}}}{v}},\ 0.50,\ 0.92\right), \qquad s = \frac{f}{0.85}$$ $$P_b = s\,\bar P_{\text{current}}, \qquad P_g = s\,\bar P_g^{\text{raw}}$$

At lower speed the frictional share rises, so slow-steaming raises the percentage saving while reducing absolute fuel — enter actual fuel/day at the operating speed.

3. Fuel saving

$$\varphi = 1 - \frac{1 + P_g/100}{1 + P_b/100}, \qquad E = \frac{P_b - P_g}{P_b}$$ $$\Delta m = m\,\varphi, \qquad S_{\text{bunker}} = \Delta m \cdot p_{\text{bunker}} \cdot c$$

The consumption entered is treated as today's fouled consumption, so the saving is multiplicative rather than \(m \cdot P \cdot E\). The IMO DCS annual figure can be entered directly as \(m\). On time charter \(c\) defaults to zero: the charterer buys the fuel.

4. Other benefit lines

Line	Formula	Default (4,000 TEU)	Confidence
In-water cleaning reduced	\(S_{\text{iwc}} = \dfrac{12}{I}\,C_{\text{clean}}\,(1 - \rho)\)	$18k × 1/yr × (1 − 0.35)	High — a cost you already pay. \(\rho\) is the share of each visit (propeller polish, sea chests, niches) that grooming does not replace; those continue on their current schedule.
Dry-dock days	\(S_{\text{days}} = \dfrac{(d_{\text{insp}} + d_{\text{paint}})\,V_d}{T_{\text{dock}}}\)	(1 + 1.5) × ($25k + $12k) / 5	Medium. Inspection day follows from the per-pass condition record; paint days depend on the coating supplier accepting a lighter scheme.
Paint scope	\(S_{\text{paint}} = \dfrac{A\,(r_0 - r_1)\,c_{\text{AF}}}{T_{\text{dock}}}\)	11,000 m² × 40% × $25 / 5	Low–medium. \(r_0, r_1\) = recoat share today / groomed. An assumption until your coating supplier confirms it.
EU ETS	\(S_{\text{ETS}} = \Delta m\;\text{EF}\;x_{\text{ETS}}\;p_{\text{EUA}}\;c\)	3.151 × 25% × $75	High once \(x_{\text{ETS}}\) is set from the MRV report. Compliance cost avoided, not a credit.
CII compliance	\(S_{\text{CII}} = D_{\text{sea}}\,\dfrac{\min(g,\ 100\varphi)}{200}\,\text{TCE}\)	\(g = 0 \Rightarrow 0\)	Zero by default; only meaningful for D/E vessels.

The CII term follows from how emissions scale with speed. Fuel per day goes as \(v^3\) and days per voyage as \(1/v\), so

$$\frac{\text{CO}_2}{\text{nm}} \propto v^2 \quad\Longrightarrow\quad \frac{\Delta v}{v} \approx \frac{g}{2}, \qquad \Delta D_{\text{sea}} \approx D_{\text{sea}}\,\frac{g}{2}$$

Closing an attained-CII gap of \(g\) percent by speed alone costs about \(g/2\) percent more sea days; a hull improvement of \(\varphi\) removes up to \(g\) of that, and the days kept are valued at the TCE.

Hard-coat strategy (opt-in)

One hard-coat life \(L\) against repeated full antifouling recoats, with \(n = \operatorname{round}(L / T_{\text{dock}})\) dockings including year 0 and \(\theta\) the touch-up share per subsequent dock:

$$S_{\text{hard}} = \frac{\overbrace{n\left(A\,c_{\text{AF}} + d_{\text{full}}\,V_d\right)}^{\text{antifouling path}} \;-\; \overbrace{A\,c_{\text{hard}} + (n-1)\left(A\,\theta\,c_{\text{hard}} + d_{\text{touch}}\,V_d\right)}^{\text{hard-coat path}}}{L}$$

When on, the paint-scope line and the paint-days term are zeroed so nothing is counted twice; inspection days remain. Contingent on continuous grooming and on the coating supplier qualifying waterjet grooming.

5. Checks against published measurements

Sources

• Adland, R.; Cariou, P.; Jia, H.; Wolff, F.-C. (2018). The energy efficiency effects of periodic ship hull cleaning. J. Cleaner Production 178, 1–13.
• GEF-UNDP-IMO GloFouling Partnerships (2022). Analysing the Impact of Marine Biofouling on the Energy Efficiency of Ships and the GHG Abatement Potential of Biofouling Management Measures.
• Gundermann, D.; Dirksen, T. (2016). A statistical study of propulsion performance of ships and the effect of dry dockings, hull cleanings and propeller polishes on performance. HullPIC 2016, 282–291.
• Krapp, A.; Vranakis, G. (2013). A practical way to evaluate the in-service performance of antifouling coatings. SNAME Athens.
• Schultz, M.P. (2007). Effects of coating roughness and biofouling on ship resistance and powering. Biofouling 23, 331–341.
• Schultz, M.P.; Walker, J.M.; Steppe, C.N.; Flack, K.A. (2015). Impact of diatomaceous biofilms on the frictional drag of fouling-release coatings. Biofouling 31, 759–773.
• Oliveira, D.R.; Granhag, L. (2020). Ship hull in-water cleaning and its effects on fouling-control coatings. Biofouling 36, 332–350.
• Tribou, M.; Swain, G. (2010). The use of proactive in-water grooming to improve the performance of ship hull antifouling coatings. Biofouling 26, 47–56.
• CRABI Robotics (2026). Beyond the Berth: Autonomous In-Transit Hull Grooming and Inspection. PortPIC 2026 — derivation of the cycle-mean penalty and the grooming-interval model used here.
• Utama, I.K.A.P. et al. (2021). The effect of cleaning and repainting on the ship drag penalty. Biofouling 37, 372–386.
• IMO Resolution MEPC.378(80), 2023 Biofouling Guidelines; ISO 6319:2026; ISO 19030:2016; IMO DCS emission factors.