Speed–Power Cubic Fit

Project delivered shaft power at any speed from a single reference speed–power point using the Rayleigh cube law, corrected with an adjustable exponent (typically 2.8 – 3.3).

VoyageSpeed–power

Reference point

Reference speedknUsually the design service speed or a recent sea-trial speed.Reference delivered powerkW

Target point

Target speedknSpeed exponent n–Cube law n = 3. Tankers 2.8 – 3.0, container ships 3.1 – 3.3 depending on hull form and resistance regime.

Power at target speed: 5,120kW

Fuel ratio: 0.512× ref

Saves 48.8 % vs ref at same hours.

Changing the inputs requires JavaScript. The calculator above shows its default inputs and result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

P_\text{new} = P_\text{ref} \cdot \left(\frac{V_\text{new}}{V_\text{ref}}\right)^n

Symbol	Meaning	Unit
$P_\text{new}$	Projected delivered power at target speed	kW
$P_\text{ref}$	Delivered power at reference speed	kW
$V_\text{ref}$	Reference speed	kn
$V_\text{new}$	Target speed	kn
$n$	Speed exponent - cube law $n = 3$ , tankers 2.8–3.0, container ships 3.1–3.3

Source: MAN Energy Solutions - *Basic Principles of Ship Propulsion*; Holtrop & Mennen (1982) - ship resistance regressions

In short

Project delivered shaft power at any speed from a single reference point using the Rayleigh cube law with an adjustable exponent.

Learn the theory Voyage Estimation: TCE, Bunkers, and Canal Economics