Estimate bare-hull wetted surface area using Holtrop–Mennen or Denny–Mumford.
WSA = — m²
WSA = — m²
Wetted surface area is the area of the ship's immersed external hull surface that is in contact with the water at a stated loading condition. It extends over the underwater shell from one side of the waterline to the other, but it does not include the horizontal waterplane area.
In resistance calculations, wetted surface area is normally represented by the symbol S. It is the reference area used in the frictional-resistance term. The result must be associated with a particular draft, trim and hull condition.
The methods on this page estimate the static bare-hull wetted area. Appendages such as rudders, shafts, brackets, bilge keels and stabilizer fins are not included.
| Method | Main inputs | Intended use |
|---|---|---|
| Holtrop–Mennen | L, B, T, CB, CM, CWP and optional ABT | Preliminary estimate for conventional displacement hulls |
| Denny–Mumford | L, T and ∇ | Simple independent estimate when limited hull-form data are available |
The Holtrop–Mennen regression estimates the bare-hull wetted area from principal dimensions and hull-form coefficients:
S = L(2T + B)√CM [0.453 + 0.4425CB − 0.2862CM − 0.003467(B/T) + 0.3696CWP] + 2.38ABT/CB
| Symbol | Meaning | Usual unit |
|---|---|---|
| S | Estimated bare-hull wetted surface area | m2 |
| L | Waterline length used by the method | m |
| B | Moulded breadth | m |
| T | Mean moulded draft | m |
| CB | Block coefficient based on the same length reference | Dimensionless |
| CM | Midship section coefficient | Dimensionless |
| CWP | Waterplane area coefficient | Dimensionless |
| ABT | Transverse bulb area where the still-water surface intersects the stem | m2 |
When the vessel has no relevant bulb section, or when that area is not being included, enter ABT as zero. This removes the final bulb correction without changing the baseline hull term.
Consider a conventional displacement vessel with:
F = 0.453 + 0.4425(0.750) − 0.2862(0.980) − 0.003467(20/8) + 0.3696(0.850)
F = 0.8098915
Sbase = 120(2 × 8 + 20)√0.980 × 0.8098915
Sbase = 3,463.567 m2
Sbulb = 2.38 × 0 / 0.750 = 0 m2
S = 3,463.567 + 0 = 3,463.567 m2
ABT is not the external surface area of the bulb. It is a transverse sectional area measured at the location specified by the Holtrop–Mennen method.
The correction adjusts the estimated bare-hull wetted area for the presence of the bulb. It does not add rudder, shaft, bracket, bilge-keel or stabilizer areas.
Appendages are separate: appendage wetted areas and appendage resistance factors are handled separately in resistance methods. Do not enter their combined surface area as ABT.
The Denny–Mumford relationship provides a simpler estimate using length, draft and displacement volume:
S = 1.7LT + ∇/T
This method does not use CB, CM or CWP. It is useful as a separate preliminary check, but it cannot reproduce the effect of detailed hull-form differences.
Use the same basic vessel condition:
1.7LT = 1.7 × 120 × 8 = 1,632 m2
∇/T = 14,400 / 8 = 1,800 m2
S = 1,632 + 1,800 = 3,432 m2
For this example, the Denny–Mumford estimate is close to the Holtrop–Mennen result. That agreement should not be assumed for every hull, particularly when proportions or form coefficients differ from conventional displacement ships.
Wetted surface area is a geometric property of the stated static condition. Entering speed does not alter the calculated area.
When speed is entered, this calculator additionally evaluates Reynolds number:
Re = VL / ν
It then applies the ITTC-1957 frictional correlation line:
CF = 0.075 / [log10(Re) − 2]2
The current implementation uses:
For the Holtrop example at 14.5 kn:
V = 14.5 × 0.514444 = 7.459 m/s
Re ≈ 7.522 × 108
CF ≈ 0.001586
Viscosity assumption: kinematic viscosity varies with water temperature and salinity. The displayed Reynolds number and CF use the fixed value stated above and should be recalculated when a different viscosity is required.
Wetted surface area enters the conventional frictional-resistance expression:
RF = 1/2 × ρV2SCF
Increasing S increases the frictional-resistance term when density, speed and CF remain unchanged. This does not mean that total ship resistance is determined by wetted area alone.
Pressure resistance, wave-making resistance, form effects, appendages, transom immersion, bulb behaviour, roughness and air resistance may also contribute to total resistance.
The meaning of a reported wetted area should be stated. Depending on its intended use, a value may refer to:
These values are not automatically interchangeable. Resistance calculations may require separate appendage areas and resistance factors, while coating estimates may require all submerged surfaces that are to be painted.
Wetted surface area changes with loading condition. A deeper draft generally immerses more shell plating, but the rate of change depends on the local hull geometry.
The dimensions and coefficients entered in one calculation must belong to the same draft and trim condition. Combining a loaded-condition block coefficient with ballast dimensions produces an inconsistent estimate.
The formulas estimate geometric wetted area. Surface roughness, coating condition and biofouling do not change the nominal geometric area, but they can materially affect frictional resistance.
Holtrop–Mennen is a regression-based prediction method developed from model and full-scale ship data. Its estimates are most defensible for hulls resembling the conventional displacement forms represented by the underlying data.
Unusual hull forms, multihulls, planing craft, vessels with extensive appendages and hulls with unconventional proportions may require another method or direct surface calculation.
Denny–Mumford is simpler and uses less geometric information. It is suitable as an early comparison estimate rather than a replacement for an actual hull-surface calculation.
Wetted area is useful for frictional-resistance estimates, preliminary powering studies, coating quantities and comparisons between loading conditions.
Wetted surface area alone cannot determine:
Final design check: empirical formulas provide estimates. When hull offsets, a surface model or approved hydrostatic data are available, use the directly calculated bare-hull surface and add appendages according to the intended resistance or coating calculation.
The formulas and terminology used on this page follow established resistance and naval-architecture references:
NauticalSolver calculators are intended for preliminary engineering, study and independent checking. Use vessel-specific geometry, approved hydrostatic data or a suitable surface model for operational, contractual or final resistance calculations.