Understanding the Marine Power Chain: Effective Power, Delivered Power & Brake Power

How hull resistance becomes propeller demand, shaft demand, engine power, and installed power.

When discussing ship propulsion, engineers often mention terms such as Effective Power (PE), Delivered Power (PD), Shaft Power (PS), and Brake Power (PB). These values are closely related, yet they describe different points within the propulsion system. Confusing one for another can lead to significant errors when estimating engine requirements, fuel consumption, or vessel performance.

A common mistake among students and even experienced professionals outside naval architecture is to assume that the power required to overcome hull resistance is the same as the power that must be produced by the main engine. In reality, every component between the engine and the surrounding water introduces losses. By the time useful thrust is generated at the propeller, a portion of the engine's power has already been lost to mechanical inefficiencies and hydrodynamic effects.

This sequence of power transformations is known as the marine power chain. Understanding it is fundamental to ship design, propulsion analysis, machinery selection, speed-power prediction, and fuel consumption estimation.


Why the Marine Power Chain Exists

A ship moving through water experiences resistance. To maintain a constant speed, the propulsion system must generate enough thrust to exactly balance this resistance.

At first glance, the problem appears straightforward. Calculate the resistance, multiply it by speed, and obtain the required power. While this provides an important starting point, it only represents the useful power required at the hull itself.

Between the engine room and the surrounding sea lies a complex system consisting of:

  • The main engine
  • Reduction gearboxes, where fitted
  • Bearings and shafting
  • Stern tube arrangements
  • The propeller
  • Hull-propeller interaction effects
Power chain overview:
Hull resistance -> Effective Power (PE) -> Delivered Power (PD) -> Shaft Power (PS) -> Brake Power (PB) -> Installed Power with service margin.

The Starting Point: Hull Resistance

Every propulsion calculation begins with resistance. Resistance prediction may be performed using the Holtrop-Mennen method, CFD simulations, model testing, empirical resistance methods, or sea trial measurements. The final result is usually expressed as total resistance force, commonly denoted as RT.

Resistance Example
For example, a vessel may have:

RT = 400 kN
at a speed of:
V = 14 knots

Resistance alone does not indicate engine size. It simply tells us how much force opposes the ship's motion. To determine power requirements, speed must also be considered.

Effective Power (PE): The Useful Power Required by the Hull

Effective Power is the first power value in the chain. It represents the useful power required to tow the vessel through the water at a given speed.

Effective Power
PE = RT x V
where:
PE = Effective Power RT = Total Resistance V = Vessel Speed

Effective Power can be visualized as the power that would be required if the vessel were being pulled by an ideal towing cable with no losses whatsoever. For this reason, PE is sometimes referred to as towing power.

PE does not account for:

  • Propeller inefficiencies
  • Shaft losses
  • Mechanical losses
  • Hull-propeller interaction effects
  • Engine losses

This makes Effective Power extremely valuable during hull form development because it allows designers to compare different hull shapes independently of propulsion system details. A hull requiring lower PE at the same speed is generally more hydrodynamically efficient. However, PE alone cannot determine engine size.

You can calculate this value using the Effective Power Calculator.


Why Effective Power Is Not Engine Power

Many newcomers to marine engineering assume that once Effective Power is calculated, the propulsion problem is solved. This assumption can produce major errors.

Important distinction: If a vessel requires PE = 5,000 kW, this does not mean that a 5,000 kW engine is sufficient. The propeller is not perfectly efficient. The shaft line is not perfectly efficient. The interaction between hull and propeller is not perfectly efficient.

As a result, significantly more power must be produced by the engine than is ultimately converted into useful towing power. The difference becomes particularly important on larger vessels, where even a few percentage points of efficiency can represent hundreds or thousands of kilowatts.


Understanding Propeller Efficiency

The propeller is responsible for converting rotational power into thrust. Unfortunately, no propeller converts 100% of incoming power into useful thrust.

Some energy is lost through:

  • Slip
  • Rotational flow in the propeller wake
  • Tip vortices
  • Turbulence
  • Viscous effects

The efficiency measured under ideal open-water conditions is known as open-water propeller efficiency and is commonly denoted as ηO.

EfficiencyTypical RangeMeaning
Open-water propeller efficiency (ηO)0.55 to 0.75Propeller performance under ideal open-water conditions

This means that a substantial portion of power entering the propeller never becomes useful thrust.


Hull Efficiency and Wake Effects

One of the most misunderstood topics in propulsion analysis is hull efficiency. When a propeller operates behind a ship, it does not experience the same flow conditions seen during open-water testing. The hull modifies the inflow reaching the propeller. This phenomenon is known as wake.

At the same time, the propeller changes the pressure distribution around the stern, influencing hull resistance. This interaction creates two important concepts:

  • Wake fraction
  • Thrust deduction
Hull Efficiency
ηH = (1 - t) / (1 - w)
where:
t = thrust deduction fraction w = wake fraction

Hull efficiency is unique because it can exceed unity. This often surprises students, but an efficiency greater than one does not violate physics. Instead, it reflects beneficial hydrodynamic interaction between the hull and propeller.

EfficiencyTypical RangeNotes
Hull efficiency (ηH)1.00 to 1.15Common for many merchant ships, although values outside this range are possible

You can estimate this value with the Hull Efficiency Calculator.


Relative Rotative Efficiency

Another correction factor frequently encountered in propulsion calculations is relative rotative efficiency, denoted ηR. This parameter accounts for differences between propeller performance measured in open-water tests and propeller performance when operating behind the ship.

The inflow reaching the propeller behind a hull is non-uniform and often significantly different from ideal test conditions. Relative rotative efficiency compensates for this difference.

EfficiencyTypical RangeMeaning
Relative rotative efficiency (ηR)0.95 to 1.05Correction for behind-hull propeller operation

Although its numerical effect may appear small, ηR remains an important component of accurate propulsion analysis.


Quasi-Propulsive Efficiency

The combined influence of propeller efficiency, hull efficiency, and relative rotative efficiency is commonly expressed through quasi-propulsive efficiency. This efficiency links Effective Power and Delivered Power.

Quasi-Propulsive Efficiency
ηD = ηO x ηH x ηR
where:
ηO = open-water propeller efficiency ηH = hull efficiency ηR = relative rotative efficiency

For many conventional displacement ships, ηD often falls within the range 0.55 to 0.75. The exact value depends on hull form, propeller design, loading condition, and operating speed.

Improving ηD is one of the most effective ways to reduce fuel consumption without reducing vessel speed. You can calculate it directly using the Propulsive Efficiency Calculator.


Delivered Power (PD)

Delivered Power represents the power actually delivered to the propeller. This is the power that arrives at the propeller shaft and becomes available for thrust generation.

Delivered Power
PD = PE / ηD
Since ηD is less than one in practical calculations, Delivered Power is greater than Effective Power.
Delivered Power Example
Consider a vessel requiring PE = 5,000 kW. Assume ηD = 0.65.

Delivered PowerPD = 5,000 / 0.65
ResultPD = 7,692 kW
Although the hull requires only 5,000 kW of useful towing power, nearly 7,700 kW must reach the propeller.

You can run this calculation with the Delivered Power Calculator.


Shaft Power and Mechanical Losses

Before power reaches the propeller, it must travel through the shafting system. Mechanical losses occur due to bearings, seals, gearboxes, shaft generators, and couplings.

Although these losses are generally small compared to hydrodynamic losses, they still affect overall propulsion efficiency. Shaft efficiency is commonly represented by ηS.

EfficiencyTypical RangeComment
Shaft efficiency (ηS)0.97 to 0.99Modern propulsion systems
Scale matters: Even with high efficiency, the effect becomes significant when dealing with large power levels. A 1% loss in a propulsion plant transmitting 20 MW still represents 200 kW of lost power.

Brake Power (PB)

Brake Power is the power produced by the main engine at its output flange. This is the value most directly associated with engine ratings. Brake Power must be sufficient to overcome propeller losses, hull interaction effects, and shaft losses.

Brake Power
PB = PD / ηS PB = PE / (ηD x ηS)
This equation forms the backbone of many preliminary propulsion calculations.

You can calculate Brake Power using the Brake Power Calculator.


Worked Example

Input Values
Effective Power PE6,000 kW
Quasi-propulsive efficiency ηD0.68
Shaft efficiency ηS0.98
Power Chain Calculation
Delivered PowerPD = 6,000 / 0.68 = 8,824 kW
Brake PowerPB = 8,824 / 0.98 = 9,004 kW
Although the hull itself requires only 6 MW of useful power, the engine must produce approximately 9 MW. This represents a difference of roughly 50%. Such differences are entirely normal in marine propulsion systems.

Service Margin and Sea Margin

The calculation is still not complete. Ships rarely operate in ideal calm-water conditions. Real vessels encounter wind, waves, current, hull fouling, propeller fouling, aging machinery, and variable loading conditions.

To account for these uncertainties, designers apply margins. A service margin of 10% to 20% is commonly used during preliminary design.

Installed Power with Margin
Applying a 15% service margin to the previous example gives:

Brake Power9,004 kW
Service margin15%
Required installed power9,004 x 1.15 = 10,355 kW
This final value begins to resemble the power level that may ultimately be selected during machinery design.

Why the Marine Power Chain Matters

Understanding the marine power chain affects far more than engine selection. It directly influences:

Fuel Consumption

Higher brake power requirements generally result in higher fuel consumption.

Emissions

Every additional kilowatt generated by the engine contributes to fuel burn and CO2 production.

Propeller Design

A more efficient propeller reduces Delivered Power requirements.

Hull Optimization

Reducing Effective Power through better hull design lowers every subsequent power value in the chain.

Operating Costs

Small efficiency improvements can save thousands of tonnes of fuel over a vessel's lifetime.


Common Mistakes in Power Chain Calculations

MistakeWhy It Matters
Treating PE as engine powerEffective Power is useful power at the hull, not engine output.
Ignoring hull efficiencyMany simplified calculations neglect hull-propeller interaction entirely.
Forgetting mechanical lossesEven highly efficient shaft systems are not loss-free.
Applying margins multiple timesService margins should be applied carefully and consistently.
Mixing trial conditions and service conditionsSea trial power and operational power are not necessarily the same.

Final Thoughts

The marine power chain provides the link between hydrodynamic resistance and machinery selection. Effective Power describes the useful power required by the hull. Delivered Power accounts for propeller and hull interaction effects. Brake Power represents the power that must be generated by the engine. Additional margins then account for the realities of operating at sea.

Understanding the distinction between these power values is essential for anyone involved in naval architecture, marine engineering, propulsion analysis, fuel consumption estimation, or ship performance assessment. While the equations themselves may appear straightforward, the engineering significance behind each step is what transforms a resistance prediction into a practical propulsion system.

A successful ship design is not simply one that minimizes resistance. It is one that efficiently converts engine output into useful thrust while maintaining acceptable fuel consumption, emissions, reliability, and operating costs throughout the vessel's service life.