Speed–Power Curve Generator

Speed–Power Curve Generation in Preliminary Ship Design

A speed–power curve represents the fundamental relationship between a vessel’s operating speed and the power required to maintain that speed in calm water. It is one of the most important tools in preliminary ship design, performance evaluation, and machinery sizing. By sweeping through a range of speeds and computing resistance and power at each point, designers can visualize trends, identify operating sweet spots, and assess engine margins.

This calculator generates a continuous speed–power table and curve using ITTC ’57 friction scaling combined with a Froude-number-based residuary resistance approximation. While not a replacement for model testing or full empirical methods, it provides a fast and transparent framework for early-stage analysis and consistency checks.

What a speed–power curve tells you

A speed–power curve shows how required delivered power increases nonlinearly with speed. At low speeds, frictional resistance dominates and power grows roughly with the cube of speed. As speed increases, wave-making effects become more significant, steepening the curve and rapidly increasing power demand.

Engineers use speed–power curves to:

• Select appropriate main engine power ratings.
• Check whether contractual or service speeds are realistically achievable.
• Estimate fuel consumption trends across the operating envelope.
• Apply sea margins and operational allowances consistently.

Resistance components used in this calculator

The total calm-water resistance in this tool is assembled from two main components:

• Frictional resistance, computed using the ITTC ’57 friction line as a function of Reynolds number.
• Residuary resistance, represented here by a smooth Froude-number-based approximation to capture wave-making trends.

This separation reflects standard naval architecture practice, where viscous and wave-related effects are treated independently in early design stages.

ITTC ’57 friction line

The ITTC ’57 friction formulation is widely adopted for estimating flat-plate frictional resistance: C_f = 0.075 / (log₁₀Re − 2)². It provides a practical and consistent way to evaluate friction over a wide range of Reynolds numbers encountered in ship-scale flows.

An optional roughness increment ΔC_f can be added to reflect hull condition, coating quality, or service deterioration.

Role of the Froude number

Wave-making resistance is primarily governed by the Froude number: F_n = V / √(gL). As F_n increases, wave patterns grow in amplitude and length, leading to a rapid rise in residuary resistance.

The smooth C_R(F_n) representation used here allows the calculator to generate realistic resistance trends across a speed range without introducing abrupt discontinuities that would distort the power curve.

Delivered power and sea margin

Once total resistance is computed, delivered power is obtained by accounting for overall propulsive efficiency: P_D = R_T · V / η_D. This links hydrodynamic resistance directly to machinery requirements.

A sea margin is then applied to the delivered power to represent added resistance from wind, waves, fouling, aging, and operational uncertainty. Typical preliminary margins range from 10% to 20%, depending on vessel type and service profile.

How to use this tool effectively

• Use realistic wetted surface areas; power predictions are very sensitive to S.
• Choose a speed range that brackets the expected service speed.
• Apply a reasonable sea margin rather than oversizing the base resistance model.
• Compare curve shape against empirical methods or past vessels for sanity checks.

Limitations and scope

• This is a calm-water estimator; it does not include added resistance in waves.
• Not intended for final contractual power predictions.
• High-speed craft, planing hulls, and multihulls require specialized methods.
• Accuracy depends on input consistency and realistic efficiency assumptions.

Related calculators

• Holtrop–Mennen Resistance – detailed empirical resistance prediction for displacement vessels.
• Froude Estimator – quick friction + residuary trend checks.
• Telfer Method – semi-displacement resistance estimation.
• Savitsky Method – planing craft resistance prediction.
• Delivered Power (PD) – converts resistance into delivered power requirements.

Tip: A well-shaped speed–power curve is often more informative than a single design-point estimate. Sudden curvature changes usually indicate unrealistic inputs or operation outside the assumed resistance regime.