Engine Load Diagram: Layout, Limits, and Propeller Curves

The engine load diagram is the log-log power-versus-speed field that defines where a slow-speed two-stroke marine engine may run, bounded by a torque-limit line, a maximum-speed line, an overload ceiling at 110 percent of the specified MCR, and the propeller demand curves that connect engine output to ship speed. Every operational decision involving a slow-speed main engine, from initial rating selection to slow-steaming dispatch and CII compliance planning, is made by reading this diagram.

The layout diagram, which precedes the load diagram, shows the rectangular L1-L4 field inside which the shipyard or owner places the specified maximum continuous rating (SMCR) at the contract stage. Once SMCR is fixed, the maker draws the load diagram around it. The two diagrams are companion documents in every engine project guide; MAN Energy Solutions has published both in their current form since the introduction of the ME-C electronic engine platform in 2001, and WinGD publishes equivalent diagrams for the X-series. This article covers both diagrams, the propeller curve mathematics, the margin conventions, and the operational and regulatory uses of the envelope.

For the underlying thermodynamic relationships between brake mean effective pressure, power, and speed that the load diagram encodes, see engine power and BMEP relationships. For the fuel-consumption consequences of operating at different positions on the diagram, see SFOC curves: load, tuning, and correction.

The log-log power-speed field

Why logarithmic axes

Both the layout diagram and the load diagram use logarithmic axes: brake power in kW or MW on the vertical axis, rotational speed in rpm on the horizontal axis. This convention, adopted consistently by MAN Energy Solutions and WinGD in their project guides, is not cosmetic.

On log-log axes, a line of constant brake mean effective pressure (BMEP) is a straight line of slope 1. This follows from the two-stroke power equation:

where $V_s$ is per-cylinder swept volume in m³, $N$ is cylinder count, $n$ is speed in rev/s, and $k = 1$ for a two-stroke. At constant BMEP, swept volume, and cylinder count, power is directly proportional to speed, so $\log P = \log n + \text{const}$: a straight line of slope 1 on log-log axes. This means the L1-L2 line (the upper BMEP limit of the layout envelope) and the L3-L4 line (the lower BMEP boundary) are both straight lines on the diagram.

Lines of constant mean piston speed are vertical lines on the diagram because mean piston speed $c_m = 2 \times s \times n$ (with stroke $s$ fixed) is directly proportional to rpm alone, regardless of power. The maximum-speed boundary of the load diagram is therefore a vertical line.

The propeller demand curve, which follows the cubic law, appears as a straight line of slope approximately 3 on log-log axes. All three families of lines, the BMEP iso-lines, the speed boundaries, and the propeller curves, appear as straight lines. This is the geometric payoff of the log-log convention: the entire operating map is a set of intersecting straight lines, readable and interpolatable without computation.

What the axes represent

The vertical axis is the brake power delivered to the propeller shaft. On modern electronically controlled engines this is monitored continuously via shaft torsiometry and shaft speed measurement. The horizontal axis is the engine output shaft speed, which for a direct-coupled slow-speed two-stroke (the standard configuration on ocean-going cargo ships) equals propeller shaft speed.

The two axes together define the engine’s torque at every point, since $T_b = P_b / (2 \pi n)$. Lines of constant torque are therefore lines of constant $P/n$ ratio: on the log-log diagram they are straight lines of slope 1, parallel to the constant-BMEP lines. The torque limit of the engine, which is a material constraint on crankshaft and connecting-rod loading, appears in the load diagram as one of these slope-1 lines.

The layout diagram: L1 to L4

Definition of the four corners

The layout diagram shows a rectangular envelope bounded by four corner points. MAN Energy Solutions labels these L1, L2, L3, and L4; WinGD uses the same designation in their X-series project guides. The table below gives the meaning of each corner in the MAN convention.

The power ratio from L1 to L3 (equivalently L2 to L4) and the speed ratio from L1 to L2 (equivalently L3 to L4) are not fixed percentages: they vary by engine series and are published explicitly in each project guide. For the MAN B&W ME-C family the L2-to-L1 rpm ratio is approximately 0.80 and the L3/L4-to-L1/L2 power ratio is approximately 0.67, giving a layout rectangle that is about 20 percent wide in the speed axis and about 33 percent tall in the power axis, on a linear scale. On the log-log diagram these appear as roughly equal intervals.

L1 is not the same as the specified MCR. L1 is the maximum rating that the engine model can physically offer. The SMCR chosen by the shipyard will in almost all cases be at or below L1.

What constrains the four corners

L1 defines the engine’s type-approval ceiling. The upper-power boundary (the L1-L2 line) corresponds to the maximum certified BMEP for that engine model and marks the limit of the engine’s combustion and structural design. Exceeding it would violate the combustion pressure limit documented in the classification society type-approval certificate and invalidate the maker’s warranty.

The maximum-speed boundary (the L1-L3 vertical line) is set by the mechanical and tribological limits on mean piston speed. For MAN B&W G-type engines the maximum rated speed is in the range of 84 to 95 rpm depending on bore; at a stroke of 3,200 to 3,730 mm, this gives mean piston speeds of 8.9 to 9.5 m/s, close to the practical limit for ring-liner wear life. WinGD X-series engines of equivalent bore sit in a similar range.

The minimum-speed boundary (the L2-L4 vertical line) is set by turbocharger performance at low load: below roughly 80 percent of rated rpm, scavenge air pressure falls and combustion quality deteriorates. Engines operated continuously below this limit risk cylinder fouling, exhaust valve coking, and cold corrosion on the liner walls.

The lower-power boundary (L3-L4) is a commercial rather than a physical constraint: it marks the lowest specific output the maker supports for continuous-service rating. Engines specified at or near L3-L4 are large relative to their output but offer the lowest mechanical stress and the longest overhaul intervals.

Placing the SMCR within the layout field

The shipyard places the SMCR somewhere within the L1-L4 rectangle based on four inputs: the required shaft power at the design speed (from model tests or resistance calculations), the propeller matching, the desired margins, and the engine availability from the maker’s order book.

Most practical SMCRs sit in the upper portion of the layout rectangle, near the L1-L2 line, because owners prefer a compact engine with a high specific output rather than a large engine with headroom to spare. A 10 percent gap between SMCR power and L1 power is common: it means the engine could theoretically be rated 10 percent higher, but the shipyard has chosen a lower rating as the specified maximum. That headroom is not normally usable in service without a new type-approval, but it does signal that the engine’s thermal design is not fully loaded.

For very large propellers on tankers and bulk carriers with design speeds below 14 knots, the SMCR tends toward the L2 corner (high power, low rpm) to match the propeller’s optimal speed. For container ships with design speeds of 20 to 24 knots and smaller propellers running at 90 to 102 rpm, SMCR shifts toward L1 or between L1 and L3.

The load diagram: limit lines and operating area

Once the SMCR is fixed, the maker constructs the load diagram around it. The load diagram shows the limit lines that govern where the engine may operate in service. It is the document that the chief engineer or performance officer consults when the propeller is fouled, when the ship is trading in heavy weather, or when a derating for slow steaming is being planned.

The engine theoretical propeller curve

The starting reference in the load diagram is the engine theoretical propeller curve (ETPC), sometimes called the engine layout propeller curve. This is a cubic curve passing through the SMCR point, defined by the propeller power law:

where $P_{\text{SMCR}}$ and $n_{\text{SMCR}}$ are the power and speed at the specified MCR. On the log-log diagram, this is a straight line of slope 3 passing through the SMCR point.

The exponent is ideally 3 for a propeller in geometrically similar flow conditions, derived from dimensional analysis: thrust and torque of a propeller scale with the square of diameter times the square of speed (for thrust) and diameter squared times speed squared times another speed factor (for torque), and at similar advance ratios, power scales as the cube of speed. In practice, the exponent for real ship-propeller combinations ranges from about 2.7 to 3.2 due to changes in propeller efficiency across the speed range and hull wake non-uniformity. The value 3.0 is the standard used in the load diagram.

The ETPC is a reference line, not an operating constraint. The actual propeller curves in service fall to the left or right of the ETPC depending on hull and propeller condition and weather.

The propeller curves in service: light and heavy running

The load diagram overlays two operational propeller curves on the ETPC.

The light-running propeller curve is the curve that applies in the best-case operating condition: calm sea, clean hull, clean propeller, design draught. In this condition the propeller is least loaded and demands the least power for a given shaft speed. The light-running curve sits to the right of the ETPC on the log-log diagram, meaning that for a given engine speed, the propeller demands less power than the theoretical curve predicts. Equivalently, for a given power, the engine runs at a slightly higher rpm than the ETPC would predict. This is the condition in which the engine runs “light.”

The heavy-running propeller curve applies when the hull is fouled, the propeller has marine growth, the ship is in adverse sea states, or the ship is operating at a draught deeper than design. In all these cases the propeller demands more power for a given shaft speed; the curve shifts to the left. For a given power delivery, the engine runs at a lower rpm: it runs “heavy.” Heavy running is the dangerous side of the diagram because it drives the operating point toward the torque limit line.

The separation between the light-running and heavy-running curves at the SMCR power level is typically 5 to 10 percent of rpm. That is the practical width of the “propeller corridor” inside which normal operation takes place.

The light-running margin

The light-running margin (also called the sea margin or weather margin in different maker documents, although these are not strictly the same thing, as discussed below) is the deliberate offset applied when matching the propeller. The propeller designer pitches the propeller so that its design point (where it absorbs SMCR power at SMCR speed) is not the ETPC but the light-running curve, which sits to the right of the ETPC by approximately 3 to 7 percent of rated rpm.

This offset means that in calm water with a clean hull, the propeller runs at a higher rpm than the ETPC predicts for the same power. The operating point in this condition sits to the right of the ETPC, inside the safe part of the load diagram, away from the torque limit. As the hull fouls over months of service, the propeller demand shifts left, and the operating point tracks back toward the ETPC and eventually toward the heavy-running region.

The size of the light-running margin is a design choice. A large margin (7 percent) gives more room for fouling before the engine hits the torque limit, but it means that in calm clean conditions the engine is slightly over-sped for a given power, which shifts the operating point toward the maximum-speed line. A small margin (3 percent) is chosen for ships with aggressive hull coating programs and frequent drydocking.

The limit lines of the load diagram

The load diagram boundary is defined by five lines. In the MAN Energy Solutions convention, these are numbered in their project guide publications:

Line 1: the maximum-speed line. A vertical line at the maximum permissible continuous rpm, typically 105 percent of SMCR speed. This is set by the governor’s maximum speed setting and by the mechanical overspeed protection. Sustained operation beyond this line risks crankshaft bearing fatigue and main bearing overlay damage.

Line 2: the maximum-power line. A horizontal line at 100 percent SMCR power. This is the contractual MCR ceiling. Brief excursions above it are permitted by the overload provision (Line 5), but sustained operation above Line 2 exceeds the certified BMEP limit.

Line 3: the engine theoretical propeller curve. Not a limit in itself, but the reference cubic from which the other lines are derived. It appears as a slope-3 line on the log-log diagram.

Line 4: the torque or BMEP limit line. This is the critical safety boundary on the left-hand side of the operating area. It runs parallel to the constant-BMEP lines (slope 1 on log-log axes) and limits the maximum permissible torque at any speed. It defines the heavy-running boundary: if the propeller demand shifts far enough to the left (due to severe fouling or storm seas), the operating point hits Line 4 and the engine governor must reduce fuel injection to prevent over-torquing. The engine cannot be allowed to run continuously above Line 4 without risk of crankshaft fatigue and bearing damage.

Line 5: the overload line. A horizontal line at 110 percent of SMCR power, valid only for short periods, typically defined as no more than one hour in any twelve-hour period. Sea trials are conducted at 100 percent and sometimes at 110 percent SMCR. The overload region above Line 2 and below Line 5 exists to allow brief maximum-effort passages and sea trial verification without requiring a permanent type-approval revision, but it cannot be used for sustained propulsion.

The operating area approved for continuous sea service is the region bounded by Lines 1, 2, 4, and the lower power boundary (which is not a fixed line but the low-load limit set by turbocharger surge and minimum scavenge pressure, typically around 25 to 30 percent MCR).

What the diagram looks like

The load diagram, centered on the SMCR point, looks like a roughly trapezoidal region on the log-log plot. To the right is the maximum-speed vertical line. Above is the horizontal maximum-power line. To the upper-left is the slope-1 torque-limit line, cutting off the high-power-low-speed corner of the envelope. The ETPC runs diagonally (slope 3) through the SMCR point. The light-running propeller curve (LRC) runs parallel to and slightly to the right of the ETPC, the heavy-running curve slightly to the left.

In calm clean conditions the engine’s operating point tracks along the LRC, moving up and down as ship speed varies. As the hull fouls, the operating point migrates left, crossing the ETPC and heading toward the heavy-running curve. In storm seas, the instantaneous operating point can cross the heavy-running line and touch the torque limit; the governor responds by shedding load (reducing fuel injection, dropping rpm) until the torque drops below Line 4.

Sea margin and engine margin

Sea margin

Sea margin is the power allowance for the difference between calm-water model-test performance and average service conditions. It covers wave resistance, wind resistance, and the loss of propulsive efficiency in irregular seas. Standard practice places sea margin at 15 percent of calm-water design-speed power, though 10 to 25 percent is the documented range depending on trade route (North Atlantic routes use larger margins than Pacific container routes).

Sea margin is built into the propeller design, not the engine rating. The propeller is pitched to absorb SMCR power at SMCR speed only in a defined sea state (typically Beaufort 3 to 4, corresponding to significant wave height around 1 to 2 metres). In calmer conditions the propeller is under-loaded; in heavier conditions it is over-loaded. The light-running margin accommodates the under-loaded side; the engine’s torque limit accommodates the over-loaded side.

Engine margin

Engine margin is the intentional gap between SMCR and the continuous service rating (CSR): the power level at which the ship is actually dispatched. It is typically 10 to 15 percent of SMCR. The CSR sits on the ETPC below the SMCR, at approximately 85 to 90 percent of MCR power. At CSR, the SFOC curve for most modern slow-speed two-strokes is near its minimum (around 70 to 85 percent MCR), which is one reason CSR is chosen where it is: the engine burns less fuel per kilowatt-hour than at full power.

Engine margin serves three purposes. First, it reserves headroom for occasional high-demand situations without exceeding the certified SMCR. Second, it reduces thermal and mechanical stress at the typical operating point, extending overhaul intervals. Third, as the engine ages and its performance degrades (rising SFOC, higher exhaust temperatures), the margin absorbs some of that degradation before the engine can no longer maintain the design CSR.

Combined margins and SMCR calculation

The relationship between the calm-water service power and the SMCR is:

For typical values of 15 percent sea margin and 10 percent engine margin:

So the SMCR is about 28 percent above the calm-water service power. A container ship requiring 36,000 kW in calm water at design speed would be specified with an SMCR around 46,000 kW. This SMCR must fall within the L1-L4 layout rectangle of the chosen engine model.

Propeller curves and the cubic law

The n-cubed power law

The cubic relationship between propeller power and shaft speed is the single most important operating characteristic of a fixed-pitch propeller drive system. For a geometrically similar propeller operating at similar advance ratio on a displacement hull:

Equivalently, propeller thrust $T \propto n^2$ and torque $Q \propto n^2$, so power $P = 2\pi n Q \propto n^3$.

The physical basis: thrust coefficient $K_T$ and torque coefficient $K_Q$ are approximately constant across the operating range at similar advance ratios. Thrust is $T = \rho n^2 D^4 K_T$ and torque is $Q = \rho n^2 D^5 K_Q$, where $\rho$ is water density and $D$ is propeller diameter. Power is:

So at fixed diameter, density, and hydrodynamic similarity, $P \propto n^3$.

The practical implication for ship operations: halving shaft speed reduces propeller power demand to one-eighth of its full-load value. A ship at 10 knots instead of 20 knots (half speed) does not need half the engine power. It needs roughly one-eighth. The strong sensitivity of power to speed is why slow steaming delivers such large fuel savings.

Deviation from the ideal cubic

Real propeller-hull systems deviate from the ideal cubic exponent of 3. At very low speeds, the wake fraction changes and the advance coefficient changes, altering $K_T$ and $K_Q$ more than the similarity assumption predicts. The actual exponent for most displacement cargo ships is between 2.7 and 3.2, with the range depending on hull form, propeller design, and loading condition.

The Admiralty Coefficient method, which relates speed, displacement, and power through the empirical relationship:

where $\Delta$ is displacement, $V$ is ship speed, and $P$ is shaft power, encodes an exponent of 3 for speed and 2/3 for displacement. The admiralty power coefficient calculator implements this for quick power estimates without model test data.

Light running and heavy running in terms of the cubic law

On the log-log load diagram, every propeller curve is a straight line of slope equal to the propeller exponent. The ETPC has a slope of exactly 3.0. The light-running propeller curve (LRC) is a parallel line shifted to the right, representing the same slope-3 relationship but offset by the light-running margin in rpm.

Heavy running doesn’t change the slope of the propeller curve; it shifts the curve to the left. When the hull fouls, the effective advance coefficient decreases for a given speed through water, and the propeller needs more torque to drive the ship at the same speed. The propeller demand curve shifts left on the log-log diagram. If the ship tries to maintain the same shaft speed (same rpm), the power demand rises along the new (left-shifted) propeller curve, and the engine runs at higher BMEP than it would with a clean hull. If the ship tries to maintain the same power, the rpm drops (moves down and to the left along the new propeller curve), increasing the risk of touching the torque limit line (Line 4).

Derating for slow steaming

What derating means on the load diagram

Slow steaming, defined operationally as sustained operation at 40 to 70 percent of design speed, places the engine’s continuous operating point well below the CSR on the ETPC. At 60 percent of design speed, propeller power demand is approximately $0.6^3 = 21.6$ percent of design power. For an engine with an SMCR of 45,000 kW, this corresponds to roughly 9,700 kW, or about 22 percent MCR.

At 22 percent MCR, the engine is far from its design point. Scavenge air pressure is low (the turbocharger is far below its design operating point), exhaust temperatures at the exhaust-gas receiver are reduced, and the cylinder liner temperature may fall below the sulfuric acid dew point, causing cold corrosion of the liner bore. The load diagram’s lower boundary (approximately 25 to 30 percent MCR) reflects exactly this: below about 25 percent MCR, sustained operation is not recommended without specific countermeasures.

Derating addresses this by formally reducing the SMCR to a lower value, typically 55 to 75 percent of the original SMCR, using power limitation (EPL) in the ME-C engine control system or a physical stop on the fuel pump rack. After derating, the engine’s new 100 percent corresponds to the old 55 to 75 percent, and the operating point in service (at 85 to 90 percent of the new SMCR) sits in a much healthier part of the original engine performance map: in the 50 to 65 percent MCR range of the original rating, where combustion temperatures are adequate and the SFOC is near its minimum.

On the load diagram, derating shifts the SMCR point down and to the left. The new ETPC is a cubic through the new SMCR, parallel to the original but lower. The load diagram limit lines (Lines 1 through 5) are redrawn around the new SMCR.

MAN Energy Solutions documents the derating procedure for ME-C engines in their project guides for each model. For the MAN B&W 6G80ME-C10.5, a derating from 30,420 kW (original SMCR) to 18,250 kW (60 percent) using EPL is a documented option. The engine derating for slow steaming article covers the full procedure, the cold-corrosion risk at low BMEP, and the cylinder cut-out strategy.

The low-load operating guidance area

For electronically controlled engines operating below 25 percent MCR without formal derating, MAN and WinGD define a low-load operating guidance area (LLOGA) or equivalent. This is not a fixed boundary but a region requiring specific attention and countermeasures. Inside the LLOGA, auxiliary blowers must be in continuous operation, cylinder lubrication feed rates must be increased above the normal load-proportional schedule, and exhaust temperatures must be monitored closely. Some vessels conducting anchorage or waiting operations at very low power (ship hotel load only) run in this region for days, which requires a formal engine management plan agreed with the classification society.

The diagram and CII compliance

How CII connects to the load diagram

The IMO Carbon Intensity Indicator framework under MARPOL Annex VI Regulation 28 (applying from 2023) rates ships on a scale of A to E based on the ratio of CO₂ emitted to transport work done. Transport work is tonnes of cargo times nautical miles sailed. For a given cargo and route, CII rating depends directly on fuel consumption, which depends on SFOC and on where the engine operates on the load diagram.

A ship with a C or D CII rating faces regulatory pressure (a mandatory corrective action plan) and commercial exposure (charterers discriminating on CII grade). The most direct lever to improve CII is to reduce speed: because power scales as the cube of speed and fuel consumption is proportional to power times SFOC, a 10 percent speed reduction reduces fuel consumption by roughly 27 percent (the cube-law saving, partially offset by SFOC change at the new load point).

On the load diagram, the CII-driven operating point is typically well below the CSR: ships on slow steaming at 12 to 15 knots instead of 18 to 22 knots operate at 30 to 60 percent of design power. The CII and slow steaming article covers the regulatory mechanics. The key load-diagram implication is that CII compliance has moved the fleet-average engine operating point into the lower half of the load diagram, where cold corrosion, turbocharger surge margin, and auxiliary blower management have become everyday concerns rather than occasional emergencies.

Shaft power limitation and the EEXI

The Energy Efficiency eXisting-ship Index (EEXI), which applies from 2023 under MARPOL Annex VI Regulation 23, sets a maximum CO₂-per-transport-work threshold for existing ships. Many ships cannot meet this threshold at their original SMCR. The compliance pathway is Engine Power Limitation (EPL), which restricts the fuel pump stroke via the engine management system, preventing the engine from exceeding a set fraction of original SMCR. EPL is equivalent to a permanent derating: it moves Line 2 (the maximum-power line) down to a new level on the load diagram and prohibits operation above it.

For ships applying EPL, the effective SMCR on the load diagram is the EPL-limited power, not the original contractual SMCR. The propeller curves remain unchanged (the propeller didn’t change), but the maximum-power ceiling is lower. A ship with an original SMCR of 45,000 kW and an EPL limit of 36,000 kW operates with a 20 percent effective derating: at its previous service speed, the engine would hit the new Line 2 before reaching the original CSR. Operators must either reduce speed or accept the new ceiling as the operating maximum, which the EEXI EPL and ShaPoLi article covers in detail.

Tier III operation and dual-fuel envelopes

Tier III sub-envelope

IMO NOx Tier III limits (MARPOL Annex VI Regulation 13) apply to ships built after 2016 operating in Emission Control Areas (ECAs). Compliance for slow-speed two-strokes is achieved by Exhaust Gas Recirculation (EGR) or by Selective Catalytic Reduction (SCR). Both systems impose additional constraints on the engine’s operating envelope.

With EGR, a portion of exhaust gas is recirculated into the scavenge air. This changes the combustion dynamics and requires the engine management system to compensate with injection timing adjustments. The Tier III operating mode has a slightly different SFOC characteristic and a different exhaust temperature profile than Tier II mode. MAN Energy Solutions publishes separate SFOC tables for Tier II and Tier III operation in their ME-GI and ME-C engine project guides. On the load diagram, the Tier III sub-envelope is the region where EGR can be operated stably: typically from about 40 percent MCR upward. Below 40 percent MCR the exhaust gas enthalpy is insufficient to maintain stable EGR operation.

With SCR, the constraint is the SCR inlet temperature: the catalyst requires exhaust temperatures above approximately 320°C to operate efficiently. This sets a minimum load for ECA compliance. Below that load threshold the SCR efficiency drops sharply, and the engine must either exit the ECA or accept higher NOx.

Dual-fuel envelopes

LNG-fuelled two-stroke engines (the MAN B&W ME-GI series and WinGD X-DF series) have separate load diagrams for gas mode and diesel pilot mode. The gas-mode envelope is generally similar in shape to the diesel-mode envelope but the absolute power ceiling may differ (typically 95 to 100 percent of diesel-mode SMCR in gas mode). Gas-mode SFOC equivalents (in LNG mass flow per kWh) are lower on a CO₂ basis but the methane slip at low load adds greenhouse-gas complexity. The gas-mode propeller curves are the same physical cubic because the propeller doesn’t change; what changes is the engine’s fuel system response and the SFOC map.

Practical engine selection using the layout diagram

Matching engine and propeller at the design stage

The engine selection process starts with the propeller. Given the hull resistance at design speed (from towing tank tests or computational fluid dynamics), the naval architect determines the required shaft power at design speed. The propeller designer then selects diameter, pitch, and rpm for peak propulsive efficiency. The rpm at the propeller design point is the SMCR speed; the shaft power plus margins is the SMCR power.

This SMCR point (power, rpm) must fall within the L1-L4 layout rectangle of the chosen engine model. If the required SMCR falls outside the layout rectangle, the engine model is wrong: either the bore is too small (limiting L1 power), the speed is too low for the layout rectangle, or some other mismatch exists. The shipyard must then either select a different engine model or adjust the propeller design.

In practice, the process is iterative. The propeller designer and the engine maker agree on a range of shaft speeds, and the shipyard selects the engine model and SMCR combination that minimizes fuel cost over the ship’s life. For a VLCC running at 15 knots with a propeller diameter of 9.5 metres and a design rpm of 78, the SMCR might be 28,000 kW at 78 rpm, which would fall near L2 on a MAN B&W 6S80ME-C9.2 (L1: 26,040 kW at 78 rpm) or more comfortably within the layout rectangle of a 7S80ME-C9.2 (L1: 30,380 kW at 78 rpm).

The matched propeller design point

The propeller design point is the pitch and rpm combination at which the propeller achieves its design advance coefficient and design efficiency. This point is matched to the ETPC in the load diagram by placing it on the light-running propeller curve, slightly to the right of the ETPC.

The advance coefficient $J = V_A / (n D)$, where $V_A$ is the advance velocity (ship speed through water minus the wake fraction), governs the propeller’s efficiency. Design efficiency for a well-matched propeller is typically 68 to 74 percent for large cargo ships. Mismatching the propeller (wrong pitch for the engine’s rated rpm) means the propeller operates at the wrong advance coefficient, reducing efficiency by 2 to 5 percentage points and shifting the propeller curve away from the ETPC. The marine propeller: pitch and construction article covers propeller design in detail.

Container ship versus bulk carrier example

The difference between a container ship and a bulk carrier shows how the same layout diagram framework produces very different SMCR placements.

A Panamax bulk carrier at design speed of 14 knots might need 9,500 kW of shaft power in calm water. With a 15 percent sea margin and 10 percent engine margin, the SMCR is approximately 12,100 kW. A large slow propeller (diameter 7.5 m) running at 95 rpm places this near the L2 region of a MAN B&W 5S50ME-C engine. The propeller is large and slow, giving high propulsive efficiency at low design speed.

A 14,000 TEU containership at 22 knots in design trim needs roughly 52,000 kW calm-water shaft power. With the same margin structure, SMCR is approximately 66,000 kW. A smaller, faster propeller (diameter 9.6 m, 80 rpm) is needed for the higher design speed. This places SMCR near L1 on a MAN B&W 12G80ME-C10.5 (L1: 66,600 kW at 80 rpm). The containership’s SMCR is near the maximum of the layout rectangle; the bulker’s is nearer L2. Both are within their respective layout rectangles, but they represent very different points on the design trade-off spectrum.

The load diagram in engine-room operations

Reading the operating point from instrumentation

In the engine control room, the load diagram is displayed in real time on the engine monitoring system (the MAN Alpha Lubricator / ME-C control system, or the WinGD iCER system). The current operating point is shown as a dot on the log-log diagram; it moves continuously as ship speed, trim, and weather change.

The chief engineer uses the displayed operating point to assess the propeller condition. An operating point that has migrated 5 percent of rpm to the left of its normal position relative to three months ago suggests that hull and propeller fouling are adding 5 percent resistance. That migration, combined with a rising exhaust gas temperature at constant load and a rising SFOC versus the baseline from the last drydock, diagnoses fouling with reasonable confidence.

The two-stroke marine diesel engine fundamentals article covers the engine monitoring systems and alarm management. The indicator diagram analysis article covers how indicator diagrams, taken when the operating point is in an unusual location on the load diagram, diagnose the cylinder-level cause.

The overload region in heavy weather

In severe head seas the propeller can be over-loaded momentarily as wave action changes the effective advance velocity. The operating point can spike into the overload region (above Line 2, toward Line 5) during a wave encounter and then drop back. Modern ME-C and X-series engine governors handle this by temporary torque limiting: if the torque limit line (Line 4) is approached, the governor sheds load (reduces fuel injection) rather than allow over-torquing. This protection is automatic and acts faster than any manual intervention.

A persistent operating point above the ETPC (toward the heavy-running region) in conditions that don’t justify it (moderate seas, reasonable draught) signals that the hull or propeller needs inspection. The fouling threshold that triggers drydocking is typically defined as a sustained 4 to 5 percent rpm loss at constant power, which corresponds to a leftward shift of the propeller curve by that amount on the load diagram.

Turbocharger cut-out and the load diagram

On multi-turbocharger installations, MAN Energy Solutions recommends turbocharger cut-out (blanking) at low loads: at 40 to 50 percent MCR on a two-turbocharger installation, blanking one unit concentrates exhaust energy through the remaining turbocharger, raising scavenge air pressure and restoring combustion quality. The fuel savings at 40 percent MCR can be 4 to 6 g/kWh according to MAN project guide data.

On the load diagram, turbocharger cut-out effectively shifts the low-load SFOC contour downward without changing the boundary lines. The operating point location on the load diagram doesn’t change, but the engine’s efficiency at that point improves because the turbocharger is better matched to the lower flow rate.

Limitations

The load diagram framework has four documented limitations that practitioners must keep in mind.

Static representation of a dynamic system. The load diagram shows steady-state limits. In waves, the propeller experiences cyclic thrust and torque variations at 0.1 to 1.0 Hz, which are not visible on the diagram. Peak instantaneous torques can exceed the steady-state Line 4 limit for a fraction of a second without triggering damage; the governor’s response time of roughly 1 to 2 seconds acts on these short transients differently than on sustained over-torque. Designers use separate torsional vibration and propeller loading studies to account for this; the load diagram does not substitute for them.

Fixed-pitch propeller assumption. The cubic propeller law and the propeller-curve framework apply directly only to fixed-pitch propellers on displacement vessels. Controllable-pitch propellers (CPP) change pitch rather than speed to vary thrust, and their power-speed relationship follows a different path on the load diagram: the engine may run at or near a constant speed (particularly in CPP installations used with shaft generators) while power varies. The load diagram applies to CPP installations but must be reinterpreted; the propeller curve is no longer a cubic through SMCR but a set of constant-pitch curves at different pitch angles.

Hull and propeller interaction not captured in detail. The load diagram’s heavy-running propeller curve accounts for increased resistance in aggregate, but it doesn’t distinguish between hull fouling, propeller pitch change due to mechanical damage, and increased sea state. All three shift the propeller curve left, but they have different causes and remedies. The operator must combine the load diagram evidence with other performance data (shaft power, SFOC, exhaust temperatures, drydock inspection records) to distinguish the cause.

Does not show thermal and emission constraints at low load. The load diagram shows the power-speed boundary but does not directly show the minimum exhaust temperature contour relevant for SCR catalyst activity, the cold-corrosion risk boundary for cylinder liner temperature, or the turbocharger surge line. These depend on engine loading, fuel type, and scavenge conditions as well as on the power-speed position. Operators relying on the load diagram alone for low-load management risk misinterpreting a position within the envelope as safe when specific thermal or emission parameters are actually out of range. Detailed performance monitoring data is required alongside the load diagram at low loads.

Exponent varies in practice. The cubic exponent of 3.0 used in the ETPC and the propeller curves is an approximation. For wave-laden conditions, shallow water, or partial loading of a ship not at its design trim, the effective exponent can deviate by ±0.3 or more. Engineers who use the cubic law to project fuel consumption at speeds remote from the design point should expect errors of 10 to 20 percent unless they use verified model-test or sea-trial data specific to the vessel.

See also

• Engine Power and BMEP Relationships
• SFOC Curves: Load, Tuning, and Correction
• Engine Derating for Slow Steaming
• Two-Stroke Marine Diesel Engine Fundamentals
• Indicator Diagram Analysis
• Marine Engine Turbocharging
• Marine Propeller: Pitch and Construction
• Propeller Theory Deep Dive
• Slow Steaming and CII
• EEXI: EPL and ShaPoLi
• Cylinder Bore and Stroke Selection Criteria
• BMEP Calculator
• BMEP from Output Data
• Mean Piston Speed Calculator
• Admiralty Power Coefficient Calculator