Calm-water resistance estimation for displacement ships using a transparent, simplified Holtrop–Mennen formulation. Step-by-step educational trace included.
Each numbered step mirrors the physical derivation — useful for learning or cross-checking results.
Fill inputs and run calculation.
The Holtrop–Mennen method is a semi-empirical regression model for predicting the calm-water resistance of conventional displacement ships. It combines Froude's classical decomposition of resistance into physical components with regression coefficients derived from a large database of model test results at MARIN (Netherlands). The method is universally taught in naval architecture programmes and used in early-stage ship design for speed–power estimation before model tests or CFD become available.
In this calculator, total resistance is decomposed as:
RT = RV + RAPP + RA + RAIR + RW
where RV = (1 + k)·RF is the viscous component, RAPP is appendage drag, RA is the correlation allowance, RAIR is air drag on the above-water hull, and RW is wave-making resistance.
The method was developed by Jan Holtrop and G. G. J. Mennen at the Netherlands Ship Model Basin (NSMB, later renamed MARIN) in the late 1970s and early 1980s. The key publications are:
The regression was fitted to the results of model tests for over 300 ships spanning tankers, bulk carriers, general cargo ships, container ships, frigates, and fishing vessels. Since publication it has become the most widely cited resistance prediction method in preliminary naval architecture, and is embedded in commercial tools such as NAPA, AVEVA FORAN, and Maxsurf Resistance.
Frictional resistance arises from viscous shear stress acting on the wetted hull surface as water flows past it. It is calculated using the ITTC-1957 friction line:
CF = 0.075 / (log10 Re − 2)²
The ITTC-57 line was adopted internationally at the 8th International Towing Tank Conference to standardise the extrapolation of model test results to full scale. Frictional resistance is always the dominant component at low Froude numbers, typically contributing 60–80% of total resistance for slow cargo ships.
The hull is not a flat plate — its curvature creates pressure gradients that thicken the boundary layer and increase the effective viscous resistance above the ITTC baseline. The form factor (1 + k) corrects for this. Slender, fine-entry vessels have k ≈ 0.05–0.10; full-form tankers and bulk carriers may have k = 0.20–0.30. In the Holtrop–Mennen regression, k is expressed as a function of B/T, L/B, and the volumetric Froude number.
As a ship moves through water it generates a wave system — primarily a bow wave and a stern wave. Energy is continuously transferred from the ship into these waves, creating wave-making resistance. This component is highly sensitive to Froude number: it rises steeply near the wave-making hump at Fn ≈ 0.27–0.30, where the bow and stern wave systems interfere constructively.
In the full Holtrop–Mennen formulation, RW is expressed as a complex polynomial in CP, L/B, B/T, and Fn. This calculator uses a Gaussian heuristic centred at Fn = 0.27 as an approximation — adequate for educational comparison but not for final design. For accurate RW in the 0.20–0.35 Fn range, use the complete 1982/1984 regression or towing tank tests.
Appendages are all underwater structures attached to the hull outside the main moulded form: rudder(s), bilge keels, shaft brackets, propeller bossings, stabiliser fins, and sonar domes. Each appendage generates both frictional and pressure drag. In Holtrop–Mennen this is treated as:
RAPP = ½ · ρ · V² · Σ(Cd · A)
Typical appendage drag on a well-designed single-screw merchant ship adds 2–5% to bare hull resistance. Twin-screw or multi-appendage arrangements can add 10–15%.
When resistance is predicted from model tests, a correlation allowance CA bridges the gap between the smooth model surface and the rougher real ship hull. It accounts for:
ITTC recommends CA in the range 0.00025–0.0006 depending on ship length and surface condition. This calculator uses the Holtrop correlation formula as a function of Lpp.
Even in calm conditions, a ship moving forward must displace air around its superstructure. Air resistance is typically small (1–2% of total resistance at moderate speed) but becomes more significant for large container ships, car carriers, and ro-ro vessels with large windage areas. It is estimated as:
RAIR = ½ · V² · (ρair · Cd · Aabove-water)
The Froude number is the most important non-dimensional parameter in ship hydrodynamics. It expresses the ratio of inertial to gravitational forces:
Fn = V / √(g · Lpp)
Ships operating at the same Froude number produce geometrically similar wave patterns (Froude's law of similitude). This underpins all model testing: a scale model is tested at the same Froude number as the full-scale ship to capture correct wave behaviour.
| Fn range | Ship type / regime | Dominant resistance |
|---|---|---|
| 0.10–0.18 | Slow cargo ships, VLCCs, bulk carriers | Viscous (80–90%) |
| 0.18–0.25 | General cargo, Panamax container | Viscous + rising wave |
| 0.25–0.32 | Fast container ships, RoPax, frigates | Wave-making significant |
| 0.32–0.45 | High-speed ferries, patrol vessels | Wave-making dominant |
| > 0.45 | Planing craft, hydrofoils | Outside H-M validity |
The Reynolds number governs the character of the boundary layer flow:
Re = V · Lpp / ν
For full-scale ships (e.g. Lpp = 180 m, V = 7 m/s), Re ≈ 10⁹. The boundary layer is fully turbulent over essentially the entire hull length at ship scale, justifying use of the turbulent ITTC-57 friction line. This contrasts with small models, where laminar– turbulent transition must be deliberately tripped using turbulence stimulators.
CB = ∇ / (L · B · T) is the fundamental measure of hull fullness. It has a direct relationship to commercial efficiency (more cargo per unit length) but also increases resistance. Typical values:
CP = ∇ / (AM · L) describes the longitudinal distribution of displacement volume. For a given CB, a higher CP means more volume is concentrated in the ends of the ship, reducing the prominence of the midship section. At each design speed there is an optimal CP that minimises wave-making resistance — this optimal value increases with Froude number.
The complete 1984 Holtrop–Mennen method expresses each resistance component as a regression polynomial. The wave resistance formula in the full method is:
RW / (ρ·g·∇) = c1·c2·c5·exp[m1·Fnd + m2·cos(λ/Fn²)]
where the coefficients c1, c2, c5, m1, m2, d, and λ are all functions of hull dimensions and form coefficients. This formulation captures interference between bow and stern wave systems across the design Fn range.
The form factor (1+k) in the full formulation is:
1 + k = 0.93 + 0.487118 · c14 · (B/L)1.06806 · (T/L)0.46106 · (L/LR)0.121563 · (L³/∇)0.36486 · (1 − CP)−0.604247
This calculator implements a simplified version of this expression. For a complete implementation with all interaction terms and appendage sub-formulas, consult the original papers or Maxsurf Resistance.
If you do not supply a wetted surface area, this calculator uses the Denny–Mumford approximation:
S ≈ Lpp · (2T + B) · √CM + 0.85 · ATR
This approximation is accurate to within ≈ 3–5% for conventional hull forms. More accurate formulas (Schneekluth, Holtrop's own regression) may be used when available. You can also compute S precisely from the hull offset table or 3-D model using your CAD tool and paste the result directly into this calculator.
Wetted surface has a linear effect on both RF and RA — an error of 5% in S produces approximately 5% error in those components.
Effective power PE is the power needed to tow the bare hull at speed V in calm water — it is the starting point for propulsion system sizing, not the end point. To estimate required installed power, several further steps are needed:
As a rough guide: PB,installed ≈ PE × 1.20 (sea margin) / 0.65 (ηD) / 0.97 (shaft) / 0.88 (engine margin) ≈ PE × 2.15. This multiplier varies significantly with vessel type and propulsion arrangement.
The Holtrop–Mennen regression is valid within the following ranges:
| Parameter | Valid range | Note |
|---|---|---|
| Froude number Fn | 0.15 – 0.35 | Most accurate; use with caution beyond 0.32 |
| Block coefficient CB | 0.55 – 0.85 | Extended to 0.90 for very full forms with care |
| Prismatic coefficient CP | 0.55 – 0.80 | — |
| L/B ratio | 3.9 – 9.5 | Extreme slenderness reduces accuracy |
| B/T ratio | 2.1 – 4.0 | — |
| Ship type | Displacement monohulls | Not for catamarans, planing craft, hydrofoils |
The method is not suitable for planing craft (Fn > 0.5), multihulls, high-speed vessels with dynamic lift, slender SWATH forms, or ships with extreme bow flare. For these vessel types, use dedicated regression methods (e.g. van Oossanen for planing hulls, Savitsky method) or CFD.
The 1984 version of Holtrop–Mennen achieves standard deviations of:
These errors are typical for semi-empirical methods at the concept design stage. They are acceptable for comparing hull variants and evaluating sensitivity to speed or loading but should not be relied on for final machinery sizing. Independent validation against towing tank tests or RANS CFD should always be performed before procurement decisions.
The Holtrop–Mennen calculator is most powerful when used comparatively — testing the resistance sensitivity to individual hull parameters. Practical design guidance:
| Method | Type | Speed | Accuracy | Best used for |
|---|---|---|---|---|
| Holtrop–Mennen (1984) | Semi-empirical regression | Seconds | ±5–10% | Concept & preliminary design |
| Series 60 / BSRA series | Systematic model test series | Minutes | ±5–8% | Cargo ships within series range |
| Savitsky method | Semi-empirical | Seconds | ±10–15% | Planing hulls Fn > 0.5 |
| Towing tank model test | Physical experiment | Weeks | ±2–3% | Contract design & optimisation |
| RANS CFD | Numerical simulation | Hours–days | ±2–5% | Detail design, innovative hull forms |
The full Holtrop–Mennen wave resistance formula involves over 20 regression coefficients and multiple conditional sub-cases based on Froude number. Implementing it faithfully requires careful handling of the transition between the low-Fn and high-Fn regimes. This lite calculator substitutes a Gaussian heuristic for clarity and transparency. For design-quality wave resistance, use a full implementation.
PE = RT × V is the power that would be required to tow a bare hull at speed V against calm-water resistance — conceptually, the power input at the towline. It is sometimes called tow-rope power. It excludes all propulsion losses and represents the minimum theoretical power requirement for the hull alone.
The Denny formula used here typically gives results within ±3–5% of the true wetted surface for conventional monohulls. For hulls with complex stern configurations, bulbous bows, or unusual proportions, the error can be larger. When precision matters, compute S from the hull lines or 3-D model and enter it directly.
The Holtrop–Mennen method was calibrated on ships ranging roughly 50–500 m in length. Applying it to small craft (under ~30 m) is not recommended. The Reynolds number dependency and the regression coefficients are not reliable at small scale. For small displacement boats, the Delft Systematic Yacht Hull Series or Savitsky method are more appropriate.
Block coefficient CB relates displaced volume to the overall bounding box (L × B × T). Prismatic coefficient CP relates displaced volume to the midship section area times length — it describes how volume is distributed longitudinally. They are related by CB = CP × CM. A ship can have the same CB with different CP/CM combinations, producing different resistance characteristics.
Model tests are conducted on geometrically scaled but hydraulically smooth models. The ITTC-57 friction line, strictly, applies to a smooth flat plate. Real ships have rougher surfaces, and there are also uncertainties in the model-to-ship extrapolation procedure. CA compensates for these effects. ITTC recommends values from 0.00025 (large, newly painted ships) to 0.0006 (smaller or older vessels).
The Holtrop–Mennen method is part of a broader workflow in preliminary ship design. These calculators are commonly used alongside it:
Tip: For consistent results, ensure that all geometric coefficients refer to the same loading condition and draft. The relationship CB ≈ CP × CM is a useful internal consistency check before running the calculation.