Generate a preliminary calm-water resistance and delivered-power curve across a selected vessel speed range.
A ship speed–power curve shows how delivered propulsion power changes as vessel speed increases. It is useful during preliminary design, machinery selection and early performance checks because a single design-point estimate does not show how quickly power demand rises across the operating range. The curve can also help identify unrealistic assumptions, compare service-speed options and show the effect of applying a sea margin.
This generator evaluates a series of speeds rather than one isolated condition. For each point, it converts knots to metres per second, calculates Froude and Reynolds numbers, applies the ITTC 1957 model-ship correlation line for friction, adds the entered roughness allowance and combines it with the calculator’s simplified Froude-based residuary coefficient. Total resistance is then converted to delivered power using the entered propulsive efficiency. A separate marine-margin power value is included in the table.
The method is intended for transparent preliminary estimates and comparison work. The residuary resistance relation is a simplified trend model, not a substitute for Holtrop–Mennen, model testing, CFD, sea-trial analysis or a vessel-specific resistance database. Results are especially sensitive to wetted surface area, propulsive efficiency and the selected resistance allowances. Use consistent units, enter a realistic speed interval and review the shape of the full curve rather than relying only on the highest-speed result.
Calculated resistance coefficients and power at each speed point.
Enter the vessel inputs and speed range, then generate the table and curve.
| Speed V (kn) | Froude No. Fn | Reynolds No. Re | Friction Cf | Residuary Cr | Resistance RT (kN) | Delivered Power PD (kW) | Power + Margin (kW) |
|---|
Delivered power PD without the separately calculated sea margin.
Generate the curve to display delivered power against speed.
A ship speed–power curve connects vessel speed with the propulsion power required to overcome calm-water resistance. Instead of calculating one operating point, the curve shows how resistance and delivered power change across a selected speed range. This is useful when comparing service-speed options, reviewing machinery margins or checking whether a preliminary power estimate follows a sensible trend.
This speed–power curve calculator combines the ITTC 1957 friction line with a simplified Froude-number-based residuary coefficient. It then converts calculated resistance to delivered power using the entered overall propulsive efficiency. A second table value applies the selected sea margin. The result is a transparent preliminary estimate rather than a vessel-specific powering prediction.
Method limitation: The ITTC friction equation is a recognised friction correlation line. The residuary coefficient used by this particular calculator is a simplified trend equation. It is not an ITTC residuary-resistance method and should not be presented as a replacement for Holtrop–Mennen, model testing, CFD, speed trials or class-approved design calculations.
For every speed between the entered minimum and maximum values, the generator calculates:
The table is useful for inspecting individual values, while the plotted curve makes it easier to see how quickly power demand rises. A smooth increasing curve is normally expected from this simplified method. Unusual jumps, flat sections or extreme results usually indicate an input problem or use outside the intended range.
| Input | Symbol | Unit | Use in the calculation |
|---|---|---|---|
| Waterline length | LWL | m | Used in both Froude and Reynolds number calculations. |
| Beam | B | m | Used only when wetted surface area is estimated. |
| Wetted surface area | S | m² | Scales the calculated frictional and residuary resistance. |
| Water density | ρ | kg/m³ | Appears directly in the total-resistance equation. |
| Propulsive efficiency | ηD | – | Converts effective resistance power to delivered power. |
| Roughness increment | ΔCf | – | Added directly to the ITTC friction coefficient. |
| Sea margin | SM | % | Applied to delivered power as a separate result. |
| Speed range | Vmin, Vmax, ΔV | kn | Defines the generated curve points. |
The entered vessel speed is converted from knots to metres per second before the hydrodynamic calculations are performed.
V (m/s) = V (kn) × 0.514444
Froude number relates vessel speed to waterline length and gravity. It is commonly used when discussing wave-making behaviour and comparing ships of different lengths at dynamically similar speeds.
Fn = V ÷ √(g × LWL)
where g = 9.80665 m/s².
A longer vessel has a lower Froude number than a shorter vessel travelling at the same speed. The value should therefore be interpreted together with waterline length rather than speed alone.
Reynolds number describes the relation between inertial and viscous effects. The calculator uses waterline length as the characteristic length and a fixed kinematic viscosity.
Re = V × LWL ÷ ν
where ν = 1.19 × 10⁻⁶ m²/s.
The water-density field is editable, but kinematic viscosity remains fixed at the value above. Entering freshwater density therefore changes the resistance multiplier but does not constitute a complete temperature-and-viscosity correction.
The base friction coefficient is calculated with the ITTC 1957 model-ship correlation line:
Cf,ITTC = 0.075 ÷ (log10Re − 2)²
The entered roughness allowance is added directly:
Cf,adjusted = Cf,ITTC + ΔCf
This roughness increment is a direct coefficient allowance. It is not a full hull-fouling, coating-age or correlation-allowance model. Values should be selected consistently when comparing alternatives.
The calculator uses the following smooth relation to create a Froude-number-dependent resistance trend:
Cr = 0.004 + 0.0025 × Fn2.5
This equation is specific to the calculator. It does not use block coefficient, prismatic coefficient, displacement, transom geometry, bulbous-bow geometry, appendage area, draught or hull-form details. Consequently, two vessels with the same length, wetted area and input assumptions will receive the same coefficient trend even when their hull forms differ significantly.
The constant term also means that the calculated residuary coefficient does not approach zero at low Froude number. It is therefore inaccurate to state that friction must dominate every low-speed result produced by this implementation.
The adjusted friction coefficient and simplified residuary coefficient are added and used with dynamic pressure and wetted surface area.
RT = 0.5 × ρ × V² × S × (Cf,adjusted + Cr)
Resistance is calculated in newtons and displayed in kilonewtons. Wetted surface area has a direct linear effect in this equation. A 10 percent increase in entered area produces a 10 percent increase in calculated resistance when all other values remain unchanged.
Resistance power is converted to delivered power using the entered overall propulsive efficiency.
PD = RT × V ÷ ηD
A lower propulsive efficiency produces a higher delivered-power result. The input should represent an overall power-conversion assumption suitable for the intended preliminary comparison. It should not be confused with propeller open-water efficiency alone.
PD,margin = PD × (1 + SM ÷ 100)
The plotted curve shows delivered power before sea margin. The table shows both delivered power and power after the entered margin. The margin is a direct percentage addition and does not calculate added resistance from a specific wind, wave, fouling or weather condition.
Consider a preliminary displacement-vessel estimate with these inputs:
S = 1.7 × 100 × 15
S = 2,550 m²
V = 12 × 0.514444 = 6.173 m/s
Fn = 6.173 ÷ √(9.80665 × 100) = 0.197
Re = 6.173 × 100 ÷ 1.19 × 10⁻⁶ = 5.188 × 10⁸
Cf,ITTC = 0.001663
Cf,adjusted = 0.001663 + 0.0004 = 0.002063
Cr = 0.004 + 0.0025 × 0.1972.5 = 0.004043
RT = 0.5 × 1025 × 6.173² × 2550 × (0.002063 + 0.004043)
RT = 304.13 kN
PD = 304,131 × 6.173 ÷ 0.65 = 2,888.5 kW
PD,margin = 2,888.5 × 1.15 = 3,321.7 kW
Repeating the calculation at each selected speed creates the table and plotted curve.
| Speed | Fn | Resistance | Delivered power | Power with 15% margin |
|---|---|---|---|---|
| 8 kn | 0.131 | 136.57 kN | 864.7 kW | 994.4 kW |
| 12 kn | 0.197 | 304.13 kN | 2,888.5 kW | 3,321.7 kW |
| 16 kn | 0.263 | 539.37 kN | 6,830.1 kW | 7,854.7 kW |
| 20 kn | 0.329 | 845.76 kN | 13,387.6 kW | 15,395.7 kW |
These values demonstrate the implemented equations only. They must not be used as a reference curve for a real 100 m vessel without vessel-specific hull-form, displacement, draught and propulsion data.
Delivered power rises more rapidly than resistance because power includes an additional multiplication by speed. Even when the total resistance coefficient changes only gradually, increasing speed raises dynamic pressure through the V² term and then raises power again through RT × V.
For this reason, an approximately cubic speed–power relationship is often used as an initial rule of thumb. The exact slope is not fixed. Friction coefficient, residuary coefficient, propulsive efficiency, hull form and operating condition all influence the curve.
The generated plot should be used to compare trends rather than to find a single supposedly exact engine rating. Useful checks include:
Use dimensions for the same loading condition. Mixing waterline length from one draught with beam or wetted area from another condition reduces the usefulness of the comparison.
Beam does not enter the resistance equation directly when a wetted area is supplied. It is used only by the fallback area estimate.
A known wetted surface area from hydrostatics, a hull model or a lines-plan calculation is preferable. The fallback relation S = 1.7 × LWL × B is intentionally simple and does not account for draught, fullness, appendages or hull-form differences.
Since resistance is directly proportional to area in the implemented equation, an unrealistic area produces a proportional resistance and power error.
The entered efficiency represents the overall relationship between effective resistance power and delivered propulsion power. A value that is too high will understate delivered power, while a low value will increase it. For a real design, the value should be derived from propulsion calculations or suitable comparable-vessel data.
The roughness increment is added directly to the friction coefficient at every speed. It is therefore a broad allowance, not a speed-dependent fouling model. Keep the same assumption when comparing alternative hulls or operating speeds.
Sea margin is applied after delivered power has been calculated. It does not change the resistance coefficients or the plotted un-margined curve. It is best treated as a separate planning allowance rather than a correction for a defined weather condition.
Select a range that covers the expected operating speeds without extending far beyond the method’s intended preliminary use. A very small interval produces a larger table but does not improve the underlying accuracy. Intervals of 0.5 or 1 knot are often sufficient for an initial curve.
The calculator does not include:
High-speed craft, planing vessels, multihulls and vessels with unusual hull forms require methods developed for those configurations. For a conventional displacement vessel, a method such as Holtrop–Mennen provides a more detailed empirical breakdown when the required hull particulars are available.
Contractual speed and power should be supported by appropriate model tests, numerical analysis, propulsion prediction and properly corrected sea trials. This page is intended for preliminary exploration and consistency checking.
The following primary references provide further information on friction, resistance prediction and measured ship speed–power performance:
NauticalSolver provides this calculator for preliminary engineering, education and comparison work. Verify important design decisions using suitable vessel-specific methods and source data.