Calculations with context

ITTC-1957 friction-line estimate

Calculate Re, Fr, Cf and friction-line force/effective-power components with explicit reference lengths. Total ship resistance and engine power are not calculated.

ITTC-1957 friction-line estimate

See how water-relative speed, length, wetted area and viscosity determine a friction-only teaching estimate. This is one resistance component; it is not total ship resistance or required engine power.

Re = V LRe / ν · Fr = V / √(g LWL) · Cf = 0.075 / (log₁₀ Re − 2)² · RF = ½ρSV²Cf · PE,F = RF V

Enter a teaching case

Use a decimal point, no thousands separators. Scientific notation is accepted. Bounds are numerical teaching controls, not evidence that a vessel or propeller is validated.

Water-relative speed V chosen unit0–50 m/s after conversion; zero is allowed.

Speed unit

Reynolds characteristic length LRe m0.1–1,000 m. Normally submerged overall length; declare the reference used.

Waterline length LWL m0.1–1,000 m. Used only for the length Froude number.

Wetted reference area S m²0.01–1,000,000 m². User-supplied bare-hull/reference area.

Water density ρ kg/m³100–2,000 kg/m³. Enter the density for the actual fluid condition.

Kinematic viscosity ν cSt0.1–1,000 cSt. This is kinematic, not dynamic viscosity.

Gravity g m/s²1–20 m/s². Default 9.80665 m/s² is the declared reference.

The initial result below is the synthetic/default teaching case.

Calculated example
Quantity	Value	Unit
V	10	m/s
ν	0.000001	m²/s
Re	1000000000	1
Fr	0.31932996	1
ITTC-1957 coefficient Cf	0.0015306122	1
Friction-line force RF	156.88776	kN
Friction-only effective power PE,F	1568.8776	kW

Physical interpretation

Speed points right; the friction-force component points left. Other resistance components are not drawn; this is not a total force balance. Schematic only; arrow lengths and drawing dimensions are not to scale.

Substitution using these inputs

V = 10 m/s
ν = 1 × 10⁻⁶ = 0.000001 m²/s
Re = 10 × 100 / 0.000001 = 1000000000
Fr = 10 / √(9.80665 × 100) = 0.31932996
Cf = 0.075 / (log₁₀(1000000000) − 2)² = 0.0015306122
RF = ½ × 1025 × 2000 × 10² × 0.0015306122 = 156887.76 N
PE,F = 156887.76 × 10 = 1568877.6 W
PE,F − RF V = 0 W

Speed sensitivity

Only V is multiplied by 0.5, 0.75, 1, 1.25 and 1.5. LRe, LWL, S, ρ, ν and g are held fixed. Cf is recalculated at each speed. Unsupported Reynolds/speed points remain unavailable; lines do not bridge them.

Circles show the five computed sensitivity cases, with gaps for unsupported cases. Horizontal axis is speed in metres per second; vertical axis is friction force in kilonewtons. The complete values, including power, are in the following table.

Only V is multiplied by 0.5, 0.75, 1, 1.25 and 1.5. LRe, LWL, S, ρ, ν and g are held fixed. Cf is recalculated at each speed. Unsupported Reynolds/speed points remain unavailable; lines do not bridge them.
V ×	V · m/s	V · m/s	Re	Fr	Cf	RF · kN	PE,F · kW	Status
0.5	5	5	500000000	0.15966498	0.0016712645	42.826154	214.13077	Calculated from the current inputs.
0.75	7.5	7.5	750000000	0.23949747	0.0015867486	91.485973	686.1448	Calculated from the current inputs.
1	10	10	1000000000	0.31932996	0.0015306122	156.88776	1568.8776	Calculated from the current inputs.
1.25	12.5	12.5	1250000000	0.39916245	0.0014890959	238.48801	2981.1002	Calculated from the current inputs.
1.5	15	15	1500000000	0.47899494	0.0014564157	335.88587	5038.2881	Calculated from the current inputs.

The CSV is generated locally and includes inputs, units, assumptions, model version, sources, interpolation details, every supplied curve row and sensitivity rows where applicable. Extra digits describe arithmetic, not experimental accuracy.

Model and equations

Start by declaring what each input represents. V is speed relative to the water, not speed over ground. S is an entered wetted reference area; this page does not reconstruct a hull or change the area with trim, sinkage or speed. The Reynolds and waterline lengths are separate so that their physical meanings are visible.

Convert units before using the equations: 1 kn = 1 nautical mile per hour = 1852/3600 m/s exactly; 1 cSt = 10⁻⁶ m²/s exactly. Re compares inertial and viscous scales; Fr compares speed with √(gLWL). Both are dimensionless. They describe different aspects of similarity and are not interchangeable.

For a positive speed in the declared numerical window, evaluate the base-10 logarithm in the ITTC-1957 model–ship correlation line. Multiply Cf by dynamic pressure ½ρV² and wetted area to obtain RF. Multiplying that component by V gives the effective power associated with that component only.

Dimensional check: (kg/m³)(m²/s²)(m²) = kg·m/s² = N; N·m/s = W. At fixed geometry, density and viscosity, force is not exactly proportional to V² because Cf also changes with Re. Friction power is correspondingly not exactly proportional to V³.

The 1957 correlation line is not a universal flat-plate truth. Its historical formulation includes a correction relative to the Hughes line. No additional form factor k is fitted or applied here. A separately justified viscous form-factor model would require an explicit (1+k) term and still would not supply the missing wave, appendage or air contributions.

Symbols and units

Symbols and units
Symbol	Quantity	Unit
V	Water-relative speed	m/s
LRe / LWL	Reynolds reference length / waterline length	m
S	Entered wetted area	m²
ρ / ν	Density / kinematic viscosity	kg/m³ / m²/s
g	Gravitational acceleration	m/s²
Re / Fr / Cf	Reynolds number / length Froude number / correlation coefficient	1
RF	Friction-line resistance component	N
PE,F	Effective power for RF only	W

Worked example

Load the 10 m/s example to reproduce every number: V = 10 m/s, LRe = LWL = 100 m, S = 2000 m², ρ = 1025 kg/m³, ν = 1 cSt = 10⁻⁶ m²/s and g = 9.80665 m/s². These are illustrative inputs, not measurements of a named vessel.

Re = 10 × 100 / 10⁻⁶ = 10⁹. Fr = 10 / √(9.80665 × 100) ≈ 0.319330. Because log₁₀(10⁹) = 9, Cf = 0.075/(9−2)² = 0.001530612245.

RF = ½ × 1025 × 2000 × 10² × 0.001530612245 ≈ 156887.755 N = 156.887755 kN. PE,F = 156887.755 × 10 ≈ 1568877.551 W = 1568.877551 kW. The engine rating cannot be inferred from this friction component.

Try doubling only S: RF and PE,F double, while Re, Fr and Cf do not change. Then double only LRe: Re doubles and Cf decreases, while Fr does not change. Changing only LWL affects Fr and leaves the friction calculation unchanged. These checks expose accidental mixing of the two length definitions.

Assumptions and limits

Positive-speed calculations require 10⁶ ≤ Re ≤ 10¹⁰. This is a deliberately bounded teaching window, not an ITTC-certified validity interval. A scale-aware allowance of four machine epsilons handles floating-point rounding at these guard edges; the calculated Re is not clipped. Turbulent boundary-layer applicability must be justified independently; a large Reynolds number alone does not establish it.
At V = 0, Re = Fr = 0 and RF = PE,F = 0 by the explicit stationary case. Cf is undefined and is not evaluated. Positive-speed cases below the window, including the singularity at Re = 100, are rejected rather than assigned a laminar or transitional formula.
For Fr > 0.45 the output carries a scope warning. The cited resistance procedure addresses conventional displacement vessels; a friction-line number does not make this a planing or high-speed resistance method. Fr ≤ 0.45 also does not validate the missing physics.
No wave-making, viscous-pressure/form-factor addition, appendage, air, roughness/fouling, shallow-water, acceleration, trim or sea-state resistance is included. No propulsive, hull, relative-rotative, shaft or transmission efficiency is assumed.
The result cannot size an engine, establish available thrust, predict a sea trial or certify performance. Measured geometry, operating condition and appropriate resistance/propulsion methods are required for those tasks.

Primary sources

Public ITTC equations checked on 9 October 2026. This simplified workspace does not implement the complete test or extrapolation procedures.

propulsion-teaching-1.0.1

Related context

The method explanation and worked example are on this page. The articles below provide additional context.

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