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SFOC Curves: Load, Tuning, and Correction

Contents

The SFOC curve plots specific fuel oil consumption in g/kWh against engine load as a percentage of maximum continuous rating. It is characteristically U-shaped, with a minimum near 70 to 85 percent MCR on an optimised slow-speed two-stroke, rising on both sides. Every engine shop-test certificate carries this curve. The curve’s exact shape, the load at which the minimum falls, and how far SFOC rises at part load all depend on the engine’s tuning point, whether turbochargers are cut out at low load, and the ISO 3046 reference conditions under which the figures are declared. Understanding the curve is the starting point for engine selection, derating decisions, slow-steaming analysis, and CII voyage planning.

The companion article specific fuel oil consumption (SFOC) covers what SFOC is, how it relates to brake thermal efficiency, and its role in the EEXI and CII regulatory indices. This article focuses on the curve itself: why it has the shape it does, how the tuning point moves the minimum, what happens to the curve when the engine is derated or turbochargers are blanked, how the curve is corrected for ambient conditions and fuel calorific value at the ISO 3046 reference, and how operators read it for engine selection and voyage fuel planning. The brake thermal efficiency calculator and the SFOC air-temperature sensitivity calculator apply the corrections described here.

What the SFOC curve represents

An engine running at a fixed load burns a fixed mass of fuel per hour. Power delivered to the shaft is independent of fuel consumed in that instant; it is the product of combustion pressure on the piston and the rotational speed. SFOC ties those two quantities together:

SFOC=m˙fuelPbrake[gkWh] \text{SFOC} = \frac{\dot{m}_{\text{fuel}}}{P_{\text{brake}}} \quad \left[\frac{\text{g}}{\text{kWh}}\right]

where m˙fuel \dot{m}_{\text{fuel}} is the fuel mass flow rate in g/h and Pbrake P_{\text{brake}} is the net shaft power in kW. If the engine runs at 10 MW and burns 1,700 kg/h, SFOC is 1,700,000 / 10,000, which is 170 g/kWh.

The SFOC curve records that ratio across the full load range, from the low-load anchor points near 25 percent MCR through the design optimum to 100 percent and, for overload certification, 110 percent MCR. Engine project guides published by MAN Energy Solutions and WinGD include the SFOC load programme as a standard table, listing values at 25, 50, 75, 85, 100 and 110 percent MCR alongside power, speed, and mean effective pressure. The 85 percent MCR row corresponds to the continuous service rating (CSR), the power most vessels actually hold on the loaded voyage leg.

The curve is not a straight line

A first-principles guess might expect SFOC to be roughly constant: if efficiency were constant, doubling the load would double both power and fuel flow, canceling in the ratio. That is not what happens. Thermal efficiency varies with load because four separate loss mechanisms each have a different load-sensitivity, and their combined effect traces the U shape across the range.

The precise shape is engine-specific. Mechanical two-stroke engines from the 1980s and 1990s showed a steeper low-load rise and a broader high-load shoulder than their electronically controlled successors. Modern ME-series and X-series engines use variable injection timing and variable exhaust-valve closing to actively manage the curve, flattening the part-load end meaningfully, but the U remains.

Why the SFOC curve is U-shaped

The U shape arises because three distinct loss mechanisms dominate at low load and two different mechanisms dominate at high load, with a minimum between them where neither set is severe. The minimum for a tuned slow-speed two-stroke falls characteristically between 70 and 85 percent MCR.

Low-load penalty: turbocharger efficiency collapse

The turbocharger on a large two-stroke is sized to provide the scavenge air pressure needed for full or near-full load. At low load, exhaust-gas energy is low, the turbocharger runs well below its design flow, and its adiabatic efficiency falls sharply, from around 70 to 75 percent at the design point to well under 60 percent at 30 percent load on a fixed-geometry conventional unit. Lower turbocharger efficiency means lower scavenge-air pressure and lower air-mass flow per cycle.

The consequence for SFOC is direct. With less air trapped per cycle, the fuel-air ratio rises toward stoichiometry even at the same fuel injection quantity, combustion temperature falls, and the thermodynamic efficiency of the cycle drops. The marine engine turbocharging article describes the turbocharger characteristics in detail.

Low-load penalty: friction becomes proportionally large

A two-stroke main engine’s friction mean effective pressure, the engine’s own mechanical losses from ring-liner friction, crosshead bearings, camshaft drive and scavenge blowers, is roughly constant in absolute terms over a wide speed and load range. At 100 percent MCR it might represent 1 to 2 bar against a brake mean effective pressure of 18 to 21 bar, a mechanical efficiency of 88 to 92 percent. At 25 percent MCR, the same absolute friction acts against a much smaller brake output, and the mechanical efficiency can fall to 80 to 85 percent. Because SFOC is referenced to brake power, the deteriorating mechanical efficiency raises it. The engine power and BMEP relationships article derives the mechanical-efficiency relationship quantitatively.

Low-load penalty: combustion quality and heat loss

Combustion quality degrades at low load for two reasons. First, injection pressure in mechanically timed systems falls with engine speed, reducing atomization quality and extending ignition delay. Second, charge temperatures are lower because less heat is transferred to the incoming air from residual exhaust. Poor atomization raises the fraction of fuel that burns late in the expansion stroke, converting work into waste heat rather than shaft output. Simultaneously, heat losses to the cylinder liner walls and cooling water become a higher proportion of the small energy release per cycle, because the surface-to-volume ratio does not change but the heat added per cycle falls roughly in proportion to load. Together these effects add several grams per kilowatt-hour to the low-load SFOC relative to what a purely thermodynamic cycle model would predict.

At very low load, below about 20 to 25 percent MCR, a further risk arises. Liner temperatures can fall into the sulphuric-acid dew-point range when burning high-sulphur fuel, causing cold corrosion that damages the liner surface and raises SFOC through blowby and increased friction. The cylinder oil base number and fuel sulphur article covers the neutralization requirement.

High-load penalty: air-excess ratio and turbocharger overload

Above the optimum, SFOC rises for the opposite reason. The turbocharger now approaches or exceeds its own design point; its pressure ratio and efficiency peak, then fall. The air-excess ratio, the ratio of actual air supplied to the stoichiometric air required to burn the injected fuel, begins to decline. On a modern two-stroke optimised for about 2.0 to 2.2 excess air at 85 percent MCR, the ratio at 100 percent MCR may fall to 1.8 to 1.9, and at 110 percent overload to 1.6 to 1.7. A lower air excess means hotter combustion, higher peak pressures that are constrained by structural limits, and some incomplete combustion, all of which add to SFOC.

The high-load rise is shallower than the low-load rise for most engines. Going from 85 to 100 percent MCR typically adds 2 to 5 g/kWh; going from 85 to 50 percent MCR adds 5 to 15 g/kWh on a modern electronically controlled engine, and more on older mechanical designs.

Summary: typical SFOC penalties by load

The table below reflects values documented in MAN Energy Solutions and WinGD project guides for modern large-bore slow-speed two-strokes at their design tuning point, at ISO 3046 reference conditions:

Load (% MCR)Typical SFOC (g/kWh)Increment above optimum
25185 to 210+20 to +45
50175 to 190+10 to +25
75162 to 1720 to +7 (near optimum)
85 (CSR)160 to 168reference optimum
100 (MCR)163 to 175+3 to +8
110 (overload)168 to 185+8 to +20

The spread at each load reflects the variation between engine families, bore sizes, and tuning states. The best figures come from large-bore MAN B&W G-type and WinGD X-type engines with optimised tuning; smaller bore engines sit toward the upper end. Older mechanical-camshaft designs add a further 5 to 15 g/kWh across the range, with a steeper low-load gradient because their injection timing is fixed at one setting for all loads.

Tuning points and the movable optimum

What the tuning point is

On an electronically controlled two-stroke, the injection timing, the exhaust-valve-closing timing, and the injection-pressure profile are not mechanically fixed. They are set by control parameters stored in the engine-control system. The tuning point is the load at which these parameters are optimised for minimum SFOC. Below the tuning point, injection timing retards progressively to avoid excessive peak pressures; above it, injection advances toward maximum efficiency. The result is a curve with a distinct minimum at the tuning point and rising SFOC on both sides.

MAN Energy Solutions calls its tuning options high-load tuning (HLT), part-load tuning (PLT), and low-load tuning (LLT). WinGD offers equivalent adjustments through its tuning option packages. Both makers permit the tuning point to be changed during a scheduled maintenance visit, without hardware modification, by uploading revised control parameters, provided the engine’s rating and the agreed guarantee load are adjusted accordingly.

High-load tuning

With high-load tuning, the injection timing is optimised near full MCR. SFOC at 85 to 100 percent MCR is minimised; SFOC at 50 percent MCR may be 2 to 4 g/kWh higher than it would be with part-load tuning. This setting suits ships that routinely run at or near full speed, such as a container ship on a fixed-schedule route where the schedule and charter terms make slow steaming impractical.

Part-load tuning

Part-load tuning shifts the minimum to around 50 to 85 percent MCR, accepting a small penalty of 1 to 3 g/kWh at full power in exchange for 2 to 6 g/kWh lower SFOC in the mid-load band where most ships actually operate. MAN’s project guides document that PLT is the default for most bulk-carrier and tanker orders, where vessels rarely run at 100 percent MCR but frequently hold 70 to 80 percent MCR on laden voyages.

Low-load tuning

Low-load tuning moves the optimum further down, toward 25 to 70 percent MCR, for ships committed to extended slow steaming. The SFOC gain at 30 to 50 percent MCR over the standard setting is typically 3 to 8 g/kWh. The trade-off is a higher SFOC at 85 to 100 percent MCR, and LLT requires care that the NOx tuning remains within the engine’s Tier II or Tier III certification, because altering injection timing affects combustion temperature and therefore NOx formation. Class society approval is required before a tuning change is applied to the NOx technical file.

Guarantee load and the SFOC certificate

The engine’s shop-test certificate records the guaranteed SFOC at one specific load, the guarantee load. The guarantee load can be anywhere from 50 to 100 percent MCR; it must be stated and is fixed at the time of order. ISO 3046-1 allows a tolerance of up to five percent above the guaranteed SFOC at high load, widening to about six percent at 65 to 84 percent MCR and seven percent at 50 to 64 percent, before a guarantee exceedance is triggered. Purchase contracts routinely tighten this to three to five percent with liquidated damages, so the choice of guarantee load and the tuning state at shop test are financial decisions, not just technical ones.

Derating and the SFOC curve

What derating does to the curve

Derating is a formal, class-approved reduction in the engine’s rated MCR to a lower maximum power. The physical engine is unchanged; only the rating plate and the approved operating limits are modified. The effect on the SFOC curve is a horizontal rescaling: the original curve still exists as a physical reality, but the new 100 percent MCR point is defined at what was previously, say, 75 percent of the original rating. If the original SFOC minimum was at 75 percent of original MCR and the derating is to 75 percent of original MCR, the new 100 percent MCR sits at the bottom of the original SFOC curve. The engine derating for slow steaming article covers the process, the propeller rematching, and the cold-corrosion constraint in detail.

The economic logic is straightforward. A large-bore slow-speed two-stroke sized for 22 knots operates at perhaps 25 to 30 percent of its original MCR when slow-steaming at 12 knots, deep in the high-SFOC region of the curve. Derating to 40 percent of the original MCR, with a rematched propeller, moves the 12-knot operating point to 75 percent of the new MCR, near the SFOC minimum, and eliminates both the fuel penalty and the cold-corrosion risk.

Derating and the engine load diagram

Derating always involves checking the new operating points against the engine’s load diagram. The load diagram defines the permissible combinations of power and speed; derating moves the rating point and shifts all load lines. The propeller curve, the maximum continuous rating line, and the light-propeller limit must all be checked against the derated configuration before the class society will approve the change.

Turbocharger matching and cut-out at low load

Turbocharger matching to the SFOC optimum

A turbocharger is designed around a target efficiency at a specific air-flow rate and pressure ratio. When the engine runs at its SFOC optimum, the turbocharger should be working near its own peak efficiency, the two optima are matched. When a new engine order specifies low-load or part-load tuning, the turbocharger selection is adjusted to ensure its efficiency peak aligns with the expected operating load range. MAN’s engine-selection tools and WinGD’s project guides both show the turbocharger operating line against the compressor map, and an acceptable match means the operating line passes through the high-efficiency island across the intended speed range.

For ships that regularly slow-steam but were designed before slow steaming became routine, the turbocharger may be mismatched: sized for full-load air supply, it operates in a low-efficiency region when the ship is at 30 to 50 percent MCR. Turbocharger retrofits, replacing an original unit with a smaller-flow model, have been carried out on large container ships for exactly this reason. The turbocharger manufacturer’s compressor-efficiency contour map is the reference for evaluating whether a mismatch exists.

Turbocharger cut-out

Many large two-stroke engines are fitted with two or three turbochargers. At low load, all three running means all three are operating far off-design. Blanking one turbocharger, closing its air and exhaust connections and taking it out of service, concentrates the available exhaust energy through the remaining units. Each remaining unit then operates at a higher fraction of its design flow and achieves higher efficiency, raising scavenge pressure and air-mass flow per cycle even though total exhaust energy is low.

MAN Energy Solutions documents typical SFOC savings from turbocharger cut-out in its project guides. For an engine with two turbochargers, cut-out of one unit at loads below 40 to 50 percent MCR saves approximately four to six g/kWh. The gain depends on engine size and the specific turbocharger characteristics; some installations show savings as high as eight g/kWh in the 20 to 35 percent MCR band. The tradeoff is that the remaining turbocharger must be capable of supplying adequate scavenge air at the intended low loads without pushing its compressor into surge. Turbocharger maps are checked against the reduced-airflow operating line before cut-out is approved.

Auxiliary blowers, electrically driven fans that supplement the turbocharger scavenge supply at low load, serve a related function: they keep scavenge pressure above the minimum needed for adequate liner cooling and combustion quality when the main-engine turbocharger cannot sustain it alone. Most large two-strokes start auxiliary blowers automatically when load falls below about 35 to 40 percent MCR.

ISO 3046 reference conditions and the correction equations

Why a reference is necessary

An SFOC reading taken in the tropics at 45 degrees Celsius ambient and 30 degrees charge-air coolant temperature will differ from one taken in the North Sea at 5 degrees ambient, even if the engine and load are identical. The denser cold air produces a better charge, better combustion, and a lower fuel burn per kilowatt-hour. Without a common reference, shop-test figures from different test sites and different seasons would be incomparable.

ISO 3046-1 fixes the reference at:

  • Ambient (turbocharger inlet) air temperature: 25 degrees Celsius (298 K)
  • Barometric pressure: 100 kPa (1,000 mbar)
  • Relative humidity: 30 percent
  • Charge-air coolant temperature (at the air cooler inlet): 25 degrees Celsius
  • Reference fuel lower calorific value (LCV): 42,700 kJ/kg

Every SFOC value on a shop-test certificate is declared at these conditions. Departures from the reference shift SFOC in predictable ways, and ISO 3046-1 provides the correction method.

Ambient air temperature correction

Warmer inlet air is less dense. Less air mass enters the cylinder per scavenge stroke, so less fuel can be burned for a given air-fuel ratio limit, and the combustion quality is slightly worse. The practical effect is that SFOC rises with ambient air temperature above the reference.

ISO 3046-1 expresses the correction through the engine’s power-output sensitivity to inlet conditions. For a turbocharged engine the relationship, simplified to the air-temperature correction alone, is approximately:

SFOCISOSFOCmeas×TrefTmeas \text{SFOC}_{\text{ISO}} \approx \text{SFOC}_{\text{meas}} \times \sqrt{\frac{T_{\text{ref}}}{T_{\text{meas}}}}

where temperatures are in Kelvin and the square-root factor comes from the turbocharger’s response to inlet conditions. For practical purposes engine project guides state this as a linear sensitivity. MAN’s project guides give approximately 0.5 g/kWh per 10-degree Celsius rise above 25 degrees for a typical large two-stroke. At 45 degrees ambient, common in the Persian Gulf summer, the correction is about 1.0 g/kWh, modest in isolation.

The SFOC air-temperature sensitivity calculator applies this correction for given ambient conditions.

Charge-air coolant temperature correction

The air cooler cools the compressed air between the turbocharger compressor outlet and the engine scavenge ports. The colder the coolant entering the cooler, the denser the charge delivered to the cylinder and the more fuel can be burned efficiently. Seawater is the usual coolant, so charge-air coolant temperature tracks sea-surface temperature, which ranges from about 5 degrees Celsius in high-latitude winter to 32 to 35 degrees in tropical shallow-water ports.

The correction follows the same direction as the air-temperature correction, roughly 0.6 to 0.7 g/kWh per 10-degree Celsius rise above the 25-degree reference. A ship cooling with 30-degree seawater carries a combined air-temperature plus charge-air correction of about 1.5 to 2 g/kWh against the ISO reference. In practice, these corrections are applied together to the measured SFOC before comparing to the shop-test baseline:

SFOCISOSFOCmeaskT(Tinlet25)kC(Tcoolant25) \text{SFOC}_{\text{ISO}} \approx \text{SFOC}_{\text{meas}} - k_T \,(T_{\text{inlet}} - 25) - k_C \,(T_{\text{coolant}} - 25)

with kT0.05g/kWh per °C k_T \approx 0.05\,\text{g/kWh per °C} and kC0.07g/kWh per °C k_C \approx 0.07\,\text{g/kWh per °C} , all in degrees Celsius. These coefficients are indicative; the exact values for a specific engine family are stated in its project guide.

Fuel LCV correction

Fuel lower calorific value varies between bunker deliveries. A high-LCV fuel releases more energy per gram burned, so the engine needs fewer grams per kilowatt-hour of output. The correction scales SFOC inversely with LCV:

SFOCISO=SFOCmeas×LCVrefLCVactual \text{SFOC}_{\text{ISO}} = \text{SFOC}_{\text{meas}} \times \frac{\text{LCV}_{\text{ref}}}{\text{LCV}_{\text{actual}}}

where LCVref=42,700kJ/kg \text{LCV}_{\text{ref}} = 42{,}700\,\text{kJ/kg} . Residual heavy fuel oil typically delivers around 40,200 to 40,900 kJ/kg; very-low-sulphur fuel oil (VLSFO) tends toward 40,500 to 41,500 kJ/kg. For heavy fuel at 40,200 kJ/kg, the correction factor is 42,700 / 40,200, about 1.062, raising the ISO-corrected SFOC by approximately 6 percent relative to the reading on the flow meter. For marine gas oil at about 42,700 kJ/kg the correction is near unity. The bunker delivery note states the density and the ISO 8217 grade; the LCV must be measured or estimated from the fuel certificate and applied before any comparison to the shop-test table. The LCV from ISO 8217 analysis calculator performs the estimation.

Barometric pressure correction

At sea level, barometric pressure is close enough to the reference 100 kPa that the pressure correction is negligible for practical SFOC comparison. The correction matters at altitude, for shore-based power plants, and for engine performance at unusually low atmospheric pressures during storm conditions, where the pressure can fall to 96 to 97 kPa. For marine operations, this correction is rarely more than 0.3 g/kWh and is often omitted from operational monitoring without material error.

The combined correction in service use

In practice, service engineers compute a corrected SFOC from the daily noon report data, applying all corrections in sequence:

  1. Read measured SFOC from flow meter and shaft-power meter or indicator readings.
  2. Apply the LCV correction from the fuel certificate.
  3. Apply the ambient air temperature correction from the engine-room log.
  4. Apply the charge-air coolant temperature correction from the central cooling-water temperature log.
  5. Compare the result to the certified shop-test SFOC at the same load fraction.

A consistent positive deviation, the corrected SFOC running above the baseline, indicates engine deterioration: worn cylinder liners, fouled turbocharger, degraded fuel injectors, or air-cooler fouling. The engine performance monitoring (PMI) article covers how class societies and performance-monitoring systems structure this comparison.

The SFOC curve and efficiency

The SFOC curve is the inverse image of the brake thermal efficiency curve. Because brake thermal efficiency is:

ηBTE=3600SFOC×LHV \eta_{\text{BTE}} = \frac{3600}{\text{SFOC} \times \text{LHV}}

with SFOC in g/kWh and LHV in MJ/kg, wherever SFOC is at its minimum, efficiency is at its maximum, and vice versa. The 3,600 in the numerator is the kilowatt-hour expressed in kilojoules. At 165 g/kWh on the 42.7 MJ/kg reference, efficiency is 3,600 / (165 × 42.7), about 51.1 percent. At 190 g/kWh, it falls to 44.3 percent. The best large-bore two-strokes at their optimum reach 52 to 54 percent, the highest of any commercial heat engine.

Brake mean effective pressure and SFOC are connected through the engine’s mechanical efficiency and the thermodynamic cycle. At the SFOC optimum, mechanical efficiency is highest, the combustion process is at its best match to the expansion ratio, and peak pressures are within structural limits. The engine power and BMEP relationships article shows that:

Pb=BMEP×Vs×n/k P_b = \text{BMEP} \times V_s \times n / k

where Vs V_s is total swept volume, n n is shaft speed in rev/s, and k k is 1 for a two-stroke and 2 for a four-stroke. As load falls, BMEP falls roughly in proportion; friction FMEP does not fall proportionally, so the ratio BMEP/IMEP, the mechanical efficiency, decreases. That mechanical efficiency drop at low load is one of the mechanisms driving up SFOC.

Running the engine at its SFOC optimum means running at the load where BMEP is high enough that friction is a small fraction of indicated work, where combustion temperatures sustain good efficiency, and where the turbocharger operates near its compressor-map efficiency island. All three conditions are met simultaneously in the 70 to 85 percent MCR band for a well-matched modern two-stroke.

Comparing engine types: SFOC curves by technology

SFOC curve shape differs across engine types, and the differences matter for selection.

Engine typeOptimum SFOC (g/kWh)Optimum load (% MCR)Low-load SFOC at 50% (g/kWh)
Modern slow-speed two-stroke (large bore, electronic)155 to 16570 to 85170 to 185
Modern slow-speed two-stroke (smaller bore)165 to 17570 to 85178 to 195
Older mechanical slow-speed two-stroke175 to 19580 to 90195 to 220
Medium-speed four-stroke (propulsion)175 to 19580 to 85190 to 210
Dual-fuel two-stroke (gas mode, energy basis ~6,500 kJ/kWh)n/a75 to 85n/a
Marine gas turbine230 to 26090 to 100270 to 320

The older mechanical two-stroke shows a steeper low-load gradient because its injection timing is fixed at one point for all loads. Going from 85 to 50 percent MCR might add 20 to 30 g/kWh on a 1980s camshaft-controlled engine, versus 8 to 15 g/kWh on a modern ME or X-series engine with variable timing. This gap, compounded across an entire voyage at slow speed, is one of the main reasons operators of older tonnage have fitted electronic control retrofits.

Medium-speed four-stroke engines have flatter SFOC curves than might be expected from their lower peak efficiency. The four-stroke cycle’s charge exchange is less sensitive to turbocharger efficiency at low load than the uniflow two-stroke, partly offsetting the two-stroke’s advantage in mechanical efficiency.

How the SFOC curve is used in engine selection

Matching the curve to the ship’s operating profile

The SFOC curve is most useful when laid beside the ship’s actual load distribution. A container ship running most of the year at 80 to 90 percent MCR wants a tuning point at 85 percent and a high-BMEP engine with a flat curve in that region. A bulk carrier ordered in a period of high fuel prices and oversupply of ships, expecting to slow-steam at 50 to 60 percent MCR indefinitely, wants part-load tuning, turbocharger cut-out capability, and an engine whose SFOC at 55 percent MCR is documented rather than interpolated.

Engine makers publish SFOC load programmes for each engine variant and each tuning state. A side-by-side comparison of two candidate engines, both at the same shaft power and the expected operating load, on their ISO-corrected SFOC tables, gives the expected fuel difference in g/kWh. Multiplying by the annual shaft energy in kWh yields an annual fuel-mass difference; at the bunker price, that is the lifecycle fuel-cost differential that, discounted, competes against the capital cost difference between the two engines.

Derating decisions during selection

When the design speed and cargo volume require a power output well below the minimum rating of standard engine designs, or when the owner expects to slow-steam from delivery, derating can be specified from the outset. A new-build order specifying a derated engine matches the propeller pitch and diameter to the lower rated speed, so the propeller absorbs the power at the intended service speed without being over-pitched. The SFOC curve is then shifted such that the service operating points align with the tuned optimum, avoiding the twin penalties of high SFOC and cold-corrosion risk that come from running a full-rated engine at sustained low load.

The SFOC curve in CII and voyage planning

CII and why the operating load matters

The Carbon Intensity Indicator (CII) introduced under MARPOL Annex VI Resolution MEPC.337(76) rates ships A to E annually against a tightening reference line. The CII metric is CO2 emitted per transport work done, roughly grams of CO2 per nautical mile for a loaded vessel of a given deadweight. Since CO2 mass equals fuel mass times the fuel’s carbon factor, and fuel mass per day equals shaft power times SFOC times operating hours, every gram per kilowatt-hour of operational SFOC feeds directly into the CII numerator.

A ship that holds 70 percent MCR, near its SFOC minimum, for the full laden voyage emits less CO2 per mile than the same ship at 90 percent MCR, even though its fuel burn per hour is lower in absolute terms at 70 percent. The reason is that the slower speed at 70 percent MCR reduces passage fuel burn relative to distance covered. The cube relationship between speed and power reinforces this: halving the speed penalty in power is roughly an eighth, which outweighs any modest SFOC rise at part load. The slow-steaming and CII article works through the trade-off numerically.

The practical implication for CII compliance is that knowing the ship’s SFOC curve well matters as much as knowing the fuel price. A ship rated D or E that can shift its operating point from 95 percent MCR to 70 percent MCR, keeping the same schedule by departing slightly earlier, may recover a full CII rating class without any physical modification. That shift is only identifiable if the operator has the actual SFOC curve and applies the ISO corrections correctly to the daily noon-report data.

Voyage speed optimisation

The optimum voyage speed minimises the fuel cost per ton-mile of cargo carried. Setting up the optimisation requires the SFOC curve, the propulsion-power versus speed curve for the loaded vessel in representative conditions, and the bunker price. The propulsion-power curve scales approximately with V3 V^3 for a displacement vessel; the SFOC curve shows how fuel efficiency changes with the load that V3 V^3 implies. Multiplying the two gives a fuel-burn-per-mile curve, and dividing by cargo mass gives fuel per ton-mile. The minimum of that curve is the optimum voyage speed.

This calculation shows that the optimum voyage speed is not the speed corresponding to the SFOC minimum. Because power scales as V3 V^3 and fuel-per-hour scales as power times SFOC, fuel-per-mile scales as power times SFOC divided by speed, which is V2×SFOC(V3/MCR) V^2 \times \text{SFOC}(V^3 / \text{MCR}). As speed falls the SFOC rises only modestly (the curve is shallow near the optimum), but the V2 V^2 term falls steeply, so fuel per mile continues to decrease with speed until the SFOC rise becomes steep enough to offset it. The cube-law fuel calculator and the slow-steaming savings calculator perform this optimisation with a vessel-specific power curve.

SFOC monitoring and the baseline comparison

The shop-test SFOC curve is the baseline against which service performance is evaluated throughout the engine’s life. In service, shaft power is measured by a torsion meter or estimated from cylinder-indicator data; fuel mass is measured by Coriolis meters in the supply line. The resulting operational SFOC, corrected to ISO conditions by the method in the previous section, is compared to the certified baseline at the same load fraction.

A sustained deviation of more than two to three percent above the ISO baseline indicates a degradation source: turbocharger fouling, air-cooler fouling, worn or damaged fuel injectors, cylinder liner wear, or exhaust-valve seat erosion. The cylinder peak pressure analysis article shows how indicator data are used to localize the degradation to a specific cylinder. Major operators integrate the SFOC trend with turbocharger inlet and outlet temperatures, exhaust gas temperatures, and cylinder peak pressures to build a health record that informs overhaul timing. DNV, Lloyd’s Register, Bureau Veritas and other class societies offer performance-monitoring notations that require continuous shaft-power and fuel-flow metering calibrated to a stated accuracy, verified by a surveyor.

Over a multi-year service life, SFOC typically degrades at 0.5 to 2 g/kWh per year in well-maintained service, accelerating in the years before a major overhaul and recovering sharply after one. The planned-maintenance cycle is therefore the main lever on long-term SFOC: connecting-rod bearings, piston rings, cylinder liners, fuel injectors, turbocharger inserts, and exhaust-valve seats all have SFOC implications when they reach the end of their service interval.

Limitations

SFOC curve figures published in engine project guides are declared at ISO 3046-1 reference conditions using a reference LCV of 42,700 kJ/kg, not the actual conditions or fuel on any specific voyage. Comparisons across engines and across measurements are only valid when both sets of figures are at the same reference. A direct comparison of a shop-test SFOC to a sea-trial SFOC, or of two sea-trial figures from ships in different seasons, requires applying the full ISO correction procedure to both before drawing conclusions.

The tuning-point values and load penalties in this article are representative of current-generation MAN B&W ME-series and WinGD X-series engines. Individual engines within those families, and engines from other builders, will show different numbers depending on bore, stroke-to-bore ratio, turbocharger selection, and tuning state. The authoritative figures for any specific engine are in its project guide and shop-test certificate, not in generic tables.

Turbocharger cut-out savings and low-load SFOC values are sensitive to the specific turbocharger model and compressor-map characteristics, which vary between installations. Before specifying a cut-out arrangement or a major tuning change, the operating line must be checked against the turbocharger manufacturer’s compressor map to confirm surge margin is maintained across the intended operating range.

SFOC correction factors for ambient temperature and charge-air coolant temperature are linear approximations valid over a moderate range around the reference conditions. At extreme ambient temperatures, well above 45 degrees or below 0 degrees Celsius, the linear coefficients may understate the correction; the full ISO 3046-1 procedure should be used. The barometric-pressure correction is negligible at sea level and is often justifiably omitted from operational monitoring.

The EEXI and CII provisions cited in this article reflect the MARPOL Annex VI text and IMO guidelines current through mid-2026. The CII reference-line tightening schedule, the default SFC values used when no certified figure is available, and the well-to-wake framework that may supersede the current tank-to-wake metric are subject to revision at successive MEPC sessions; live compliance calculations should be run against the current IMO text and the engine’s own certified data.

See also

Calculators

Related wiki articles

Frequently asked questions

Why is the SFOC curve U-shaped?
At low load, turbocharger efficiency falls, scavenge-air pressure drops, combustion temperatures decrease, and friction losses become a larger share of a smaller output, all of which raise fuel consumption per kilowatt-hour. At high load, the air-excess ratio falls and the turbocharger passes its peak efficiency point, again raising SFOC. The minimum sits between those two zones, typically at 70 to 85 percent MCR for a modern slow-speed two-stroke.
What is a tuning point on an SFOC curve?
The tuning point is the load at which a maker sets the injection timing and other variable control parameters to achieve minimum SFOC. On electronically controlled engines such as the MAN ME series and WinGD X series, the tuning point can be shifted anywhere from about 25 to 100 percent MCR without hardware changes. High-load tuning places the minimum near full power; part-load and low-load tuning shift it down toward 50 to 75 percent MCR for slow-steaming ships.
What are the ISO 3046 reference conditions for SFOC?
ISO 3046-1 sets the ambient (turbocharger inlet) air temperature at 25 degrees Celsius, barometric pressure at 100 kPa, relative humidity at 30 percent, charge-air coolant temperature at 25 degrees Celsius, and the reference fuel lower calorific value at 42,700 kJ/kg. Every SFOC figure on a shop-test certificate or engine project guide is declared at these conditions so engines can be compared on a common basis.
How does engine derating change the SFOC curve?
Derating reduces the rated MCR to a lower power level, which effectively shifts the engine's 100 percent load point down the original SFOC curve. If the original optimum was at 75 percent and the engine is derated by 25 percent, the new 100 percent MCR sits at roughly the old 75 percent, putting the engine near its SFOC minimum at the new full rating. Derating is therefore a standard way to make slow-steaming efficient rather than penalized.
What does turbocharger cut-out do to the SFOC curve?
At low load with multiple turbochargers, each unit operates far from its efficiency peak and scavenge pressure is poor. Blanking one or more turbochargers concentrates the exhaust energy through the remaining units, restoring scavenge pressure and combustion quality. Savings of four to six g/kWh in the 20 to 50 percent MCR band are documented in MAN Energy Solutions' project guides.
How is SFOC corrected for actual fuel LCV?
SFOC scales inversely with the fuel's lower calorific value. The correction is SFOC_corrected equals SFOC_measured multiplied by LCV_reference divided by LCV_actual, where the reference is 42,700 kJ/kg. Heavy fuel oil at around 40,200 kJ/kg requires the measured SFOC to be divided by 0.942, raising the ISO-corrected figure by about 6 percent relative to what the meter reads.