Ship resistance and powering

In short

Ship resistance is the total fore-and-aft force the water and air exert against a hull moving at steady speed; powering is the chain of calculations that converts that resistance into the engine power to be installed. The subject decides a ship's main engine rating, fuel bill, hull form and propeller — so it drives both the design spiral and the IMO energy-efficiency rules (EEDI, EEXI, CII) that every new Indian-flag and Indian-built ship must satisfy. It is examined heavily in naval architecture degree papers at IIT Kharagpur, IMU, CUSAT, AMET and in GATE NM (resistance components, Froude scaling, model-ship extrapolation, powering definitions). It is used daily at Cochin Shipyard, Mazagon Dock, GRSE, Hindustan Shipyard, L&T Shipbuilding, Goa Shipyard, the Naval Design Directorate, IRS and classification/consultancy design offices, and in towing-tank work at IIT Madras, IIT Kharagpur and NSTL Visakhapatnam.

Explained

Components of resistance

• Total resistance R_T = the towing force needed to move a hull at steady speed V in calm water; the conventional split is R_T = R_F (frictional) + R_R (residuary), which is Froude's split used for model extrapolation.
• The physical split is R_T = R_V (viscous) + R_W (wave) + R_AA (air) + R_APP (appendages); R_V = friction + viscous pressure (form) drag.
• Frictional resistance R_F: tangential shear in the boundary layer over the wetted surface; depends on Reynolds number Rn = VL/ν and on roughness. It is the largest part for slow, full ships (often 70-85% of R_T for tankers and bulk carriers).
• Viscous pressure (form) drag: the boundary layer and any separation prevent full pressure recovery aft; handled through the form factor k, R_V = (1+k) R_F. Typical k ≈ 0.1-0.4, larger for full hulls.
• Wave-making resistance R_W: energy carried away permanently by the wave system (Kelvin pattern — diverging and transverse waves); depends on Froude number Fn = V/√(gL). It grows roughly as the sixth power of speed in the working range and dominates fast, slender ships.
• Wave-breaking and spray resistance: at blunt bows the bow wave breaks, dissipating energy; counted with wave resistance.
• Eddy/separation resistance: vortices at a blunt stern, transom, shaft brackets, rudder horn, apertures.
• Appendage resistance: rudders, bilge keels, bossings, stabiliser fins, sea-chest openings, thruster tunnels — commonly 2-10% of bare-hull resistance.
• Air resistance R_AA: on the above-water hull and superstructure; roughly 2-4% of total in still air, far more with headwind. R_AA = ½ ρ_a C_AA A_T V_rel².
• Added resistance in service: waves, wind, hull and propeller roughness, fouling, shallow and restricted water, steering. Covered by a sea margin (15-25%) and an engine margin (10-15% of MCR).

Humps, hollows and the speed-length relation

• The bow and stern wave systems interfere: when their crests coincide the wave resistance peaks (a hump), when crest meets trough it dips (a hollow).
• The main hump lies near Fn ≈ 0.5 (speed-length ratio V/√L ≈ 1.7 with V in knots and L in feet); significant humps also occur near Fn ≈ 0.3 and 0.24.
• Designers choose a service speed in a hollow, not on a hump; a merchant ship at Fn < 0.2 is "displacement/low-speed" (wave resistance small), 0.2-0.3 moderate, > 0.35 fast (wave resistance dominant).
• Bulbous bow: generates its own wave system in antiphase with the bow wave, cancelling part of it — effective over a narrow design speed and draught band, and can increase resistance off-design or in ballast.
• Other form measures: fine entrance angle, low prismatic coefficient at high Fn, bulbous/immersed transom choice, stern bulb, pre-swirl ducts (e.g. Mewis duct), hull-vane devices.

Dimensional analysis and the laws of similitude

• Dimensional analysis gives R/(½ρSV²) = f(Rn, Fn) — the resistance coefficient depends on both viscous and gravity scaling.
• Both cannot be satisfied at once in a model: Fn equality needs V_m = V_s/√λ, Rn equality needs V_m = λ V_s (λ = L_s/L_m). This clash is the central difficulty of model testing.
• Froude's hypothesis: run the model at the same Fn (corresponding speed), so the residuary coefficient is the same for model and ship; scale friction separately by a friction line at each one's own Rn.
• Froude's law of comparison: at corresponding speeds, residuary resistance scales as the displacement ratio, R_R ∝ Δ (or λ³ for geometrically similar hulls).
• Cavitation number governs propeller tests; Weber number matters only for very small models (surface tension/laminar-flow scale effect) — turbulence stimulators (studs, trip wire, sand strip) are fitted to force a turbulent boundary layer.

Model testing and extrapolation (ITTC procedure)

Step-by-step, as examined:

1. Build a geometrically similar wax or GRP/wooden model (typically 4-9 m long), fit turbulence stimulators, ballast to the correct displacement and trim.
2. Tow it in a towing tank at corresponding speeds; measure resistance with a dynamometer, plus sinkage and trim; record water temperature.
3. Compute C_Tm = R_Tm/(½ρ_m S_m V_m²).
4. Get C_Fm from the ITTC 1957 correlation line, C_F = 0.075/(log₁₀Rn − 2)².
5. Two-dimensional (Froude) method: C_R = C_Tm − C_Fm, then C_Ts = C_Fs + C_R + C_A. Three-dimensional (ITTC 1978) method: C_W = C_Tm − (1+k)C_Fm, then C_Ts = (1+k)C_Fs + C_W + C_A + C_AAS, with k from a low-speed (Prohaska) run.
6. Add a roughness/correlation allowance C_A (order 0.0002-0.0005, from the tank's correlation database) and air drag.
7. R_Ts = C_Ts × ½ρ_s S_s V_s² at ship scale; then P_E = R_Ts V_s.
8. A geosim series (same hull, several scales) isolates scale effect; a methodical series (Taylor-Gertler, Series 60, SSPA, BSRA, NPL, Series 64, Holtrop-Mennen regression) gives resistance without a test.
9. Open-water and self-propulsion tests supply wake fraction w, thrust deduction t and relative rotative efficiency η_R; skin-friction correction force (FD) is applied in the self-propulsion test.
10. CFD (RANS/potential-flow) is now standard alongside tanks: cheaper for form variants, but validated against model data; ITTC publishes verification and validation guidelines.

Powering chain and efficiencies

• Effective power P_E (EHP) = R_T V — power to tow the bare ship (naked EHP) or with appendages.
• Thrust power P_T = T × V_A, where V_A = V(1 − w) is the speed of advance and T the propeller thrust.
• Delivered power P_D (DHP) = power at the propeller behind the stern tube.
• Shaft power P_S (SHP) = measured by torsionmeter at the shaft after the gearbox; brake power P_B (BHP) at the engine coupling; indicated power P_I inside the cylinders.
• Chain of efficiencies: P_E → (η_H) → P_T → (η_O η_R) → P_D → (η_S shafting, η_G gearing) → P_S/P_B.
• Hull efficiency η_H = (1 − t)/(1 − w), usually 0.95-1.10 (can exceed 1 because the wake gives the propeller slower water to work in).
• Open-water efficiency η_O = 0.5-0.75 for well-designed propellers; relative rotative efficiency η_R ≈ 0.95-1.05.
• Quasi-propulsive coefficient (QPC) η_D = P_E/P_D = η_H η_O η_R, typically 0.60-0.75.
• Propulsive coefficient PC = P_E/P_S = η_D × η_S (shaft/transmission efficiency 0.96-0.99 for direct drive; a gearbox loses another 2-3%).
• Trial and service allowances: trial power = P_E/PC with a small trial allowance; service power adds the sea margin for weather and fouling; installed MCR adds the engine margin so the engine runs near its best BSFC (often ~85-90% MCR as NCR).
• Admiralty coefficient is a quick first estimate from a similar ship; fuel coefficient and Froude's circular notation (© ®, K etc.) appear in older syllabi and texts.

Estimation methods, trials and standards

• Preliminary estimates: Admiralty coefficient, Holtrop-Mennen statistical method, Guldhammer-Harvald charts, Taylor's and Series 60 data, Savitsky's method for planing craft, slender-body theory for high-speed catamarans.
• Speed trials: run in deep, calm water over measured runs in reciprocal directions to cancel current (double or "mean of means" runs); ISO 15016 (current edition is the 2015 revision) prescribes correcting trial data for wind, waves, current, shallow water and displacement — this is the IMO-accepted basis for EEDI verification.
• IMO/statutory: EEDI for new ships (MARPOL Annex VI Reg. 21 series, phased reduction factors), EEXI for existing ships and the operational CII rating (A-E) in force since 2023 — these push minimum propulsion power rules (so a ship stays manoeuvrable in bad weather despite low installed power) and devices such as shaft power limitation. The reduction-factor schedule and CII correction factors are revised periodically, so check the current MARPOL Annex VI text.
• Indian practice: the Merchant Shipping Act, 2025 (replaced the 1958 Act from 15 March 2026) is the governing statute, administered by the Directorate General of Maritime Administration (formerly DG Shipping), which issues statutory circulars adopting MARPOL Annex VI; Indian Register of Shipping (IRS) Rules for the Classification of Ships cover powering, shafting and propulsion machinery approval. Model tests for Indian yards and the Navy are done at NSTL Visakhapatnam, IIT Kharagpur and IIT Madras towing tanks; inland vessels follow the Inland Vessels Act, 2021 and IRS inland rules.
• ITTC recommended procedures (7.5-02 series) are the de facto international standard for tank testing and extrapolation; they are voluntary guidance adopted by the member tanks.

Key points

• Total resistance - R_T = R_F + R_R (Froude split, used for scaling) = R_V + R_W + R_AA (physical split).
• Reynolds number - Rn = VL/ν, governs friction; Froude number Fn = V/√(gL), governs wave making.
• Scaling clash - a model cannot match Rn and Fn together; Froude's hypothesis resolves it by scaling only R_R.
• Corresponding speed - V_m = V_s/√λ, the speed at which model and ship have the same Fn.
• Froude's law of comparison - at corresponding speeds R_R scales as displacement (λ³ for similar hulls).
• ITTC 1957 line - C_F = 0.075/(log₁₀Rn − 2)²; a correlation line, not pure flat-plate friction.
• Form factor - R_V = (1+k)R_F; the basis of the 3-D (ITTC 1978) extrapolation.
• Correlation allowance C_A - covers roughness and model-ship correlation, typically 0.0002-0.0005.
• Wetted surface - S from Denny-Mumford or Taylor's formula when the lines are not yet faired; R_F is directly proportional to S.
• Humps and hollows - interference of bow and stern wave systems; main hump near Fn ≈ 0.5.
• Bulbous bow - cancels part of the bow wave, effective only near its design speed and draught.
• Effective power - P_E = R_T V; the yardstick for comparing hull forms.
• Wake fraction and thrust deduction - V_A = V(1−w), T = R/(1−t); together they give η_H = (1−t)/(1−w).
• QPC - η_D = η_H η_O η_R = P_E/P_D, typically 0.60-0.75.
• Propulsive coefficient - PC = P_E/P_S; power chain order P_E ≈ P_T < P_D < P_S < P_B < P_I (P_T is slightly *below* P_E whenever η_H > 1, since P_T = P_E/η_H).
• Margins - sea margin 15-25% for weather and fouling, engine margin 10-15%; installed MCR follows from both.
• Admiralty coefficient - A_c = Δ^2/3 V³/P; constant for similar ships at similar Fn — a first-cut power estimate.
• Fouling and roughness - can add 0.5-1% power per month out of dock; the cheapest resistance saving is a clean, smooth hull.

Formulas and examples

Example 1 — Full model-to-ship extrapolation (2-D Froude method). A ship of L = 150 m, S = 4,500 m², service speed 18 knots. A λ = 25 model (L_m = 6 m, S_m = 4,500/625 = 7.2 m²) is tested in fresh water at 15 °C; at the corresponding speed the measured resistance is 38 N. Take C_A = 0.0004.

1. Ship speed V_s = 18 × 0.5144 = 9.26 m/s. Corresponding model speed V_m = 9.26/√25 = 1.852 m/s.
2. Model Rn = 1.852 × 6/1.14 × 10⁻⁶ = 9.75 × 10⁶ → log₁₀Rn = 6.989; C_Fm = 0.075/(4.989)² = 0.003014.
3. C_Tm = 38/(0.5 × 1,000 × 7.2 × 1.852²) = 38/12,347 = 0.003078.
4. C_R = 0.003078 − 0.003014 = 0.000064 (a slow, friction-dominated hull: Fn = 9.26/√(9.81×150) = 0.241).
5. Ship Rn = 9.26 × 150/1.19 × 10⁻⁶ = 1.167 × 10⁹ → log₁₀Rn = 9.067; C_Fs = 0.075/(7.067)² = 0.001502.
6. C_Ts = 0.001502 + 0.000064 + 0.0004 = 0.001966.
7. R_Ts = 0.001966 × 0.5 × 1,025 × 4,500 × 9.26² = 0.001966 × 0.5 × 1,025 × 4,500 × 85.75 ≈ 388.9 kN.
8. P_E = 388.9 × 9.26 ≈ 3,601 kW.

Example 2 — Powering chain and installed power. For the same ship take w = 0.28, t = 0.22, η_O = 0.65, η_R = 1.01, shafting η_S = 0.98, sea margin 20%, engine margin 10%.

1. η_H = (1 − 0.22)/(1 − 0.28) = 0.78/0.72 = 1.083.
2. η_D = 1.083 × 0.65 × 1.01 = 0.711.
3. P_D = 3,601/0.711 ≈ 5,065 kW; P_S = 5,065/0.98 ≈ 5,169 kW (trial condition).
4. Service power = 5,169 × 1.20 ≈ 6,203 kW.
5. Installed MCR = 6,203/0.90 ≈ 6,892 kW → select an engine of about 7,000 kW.
6. Check: PC = P_E/P_S = 3,601/5,169 = 0.697.

Example 3 — Froude's law of comparison (quick scaling). A 5 m model of a 125 m ship (λ = 25) shows R_Tm = 50 N at 1.6 m/s in sea water; C_Fm = 0.0032, C_Fs = 0.0016, S_m = 6.0 m², C_A = 0.

1. C_Tm = 50/(0.5 × 1,025 × 6.0 × 1.6²) = 50/7,872 = 0.006352; C_R = 0.006352 − 0.0032 = 0.003152.
2. C_Ts = 0.0016 + 0.003152 = 0.004752. Ship speed = 1.6 × √25 = 8.0 m/s (15.6 knots); S_s = 6.0 × 625 = 3,750 m².
3. R_Ts = 0.004752 × 0.5 × 1,025 × 3,750 × 64 = 584.5 kN; P_E = 584.5 × 8.0 ≈ 4,676 kW.
4. Note the residuary part is 66% of C_T here (Fn = 8.0/√(9.81×125) = 0.228 but the model was chosen with high C_R to show the arithmetic); in design, never scale total resistance by λ³ — only the residuary part follows Froude's law.

Example 4 — Admiralty coefficient estimate and the speed-cubed rule. A bulk carrier of Δ = 52,000 t needs 7,800 kW at 14.5 knots.

1. A_c = 52,000^2/3 × 14.5³/7,800. 52,000^2/3: 52,000^1/3 = 37.33, squared = 1,393.5. 14.5³ = 3,048.6.
2. A_c = 1,393.5 × 3,048.6/7,800 = 4,248,200/7,800 ≈ 545 (tonnes, knots, kW set).
3. A sister ship of Δ = 60,000 t at 14 knots: P = 60,000^2/3 × 14³/545. 60,000^1/3 = 39.15 → ^2/3 = 1,532.5; 14³ = 2,744. P = 1,532.5 × 2,744/545 ≈ 7,717 kW.
4. Speed-cubed rule at constant Δ: dropping speed from 14.5 to 13 knots cuts power by (13/14.5)³ = 0.72 — a 28% saving, which is why slow steaming works. In reality the exponent is 3-4 because resistance itself rises faster than V².

Example 5 — Wake, thrust deduction and hull efficiency from a self-propulsion test. Ship speed 8.0 m/s, measured V_A = 6.0 m/s, bare-hull resistance 500 kN, propeller thrust 640 kN.

1. w = (8.0 − 6.0)/8.0 = 0.25; t = (640 − 500)/640 = 0.219.
2. η_H = (1 − 0.219)/(1 − 0.25) = 0.781/0.75 = 1.041.
3. P_E = 500 × 8.0 = 4,000 kW; P_T = 640 × 6.0 = 3,840 kW (P_T < P_E only because η_H > 1).
4. With η_O = 0.60 and η_R = 1.0: η_D = 1.041 × 0.60 = 0.625; P_D = 4,000/0.625 = 6,400 kW.

Where it is used

• Shipyard design offices: Cochin Shipyard, Mazagon Dock, GRSE, Goa Shipyard, Hindustan Shipyard and L&T Kattupalli fix main engine rating, propeller and hull form from resistance estimates and tank/CFD results.
• Hydrodynamics labs: NSTL Visakhapatnam (naval vessels), IIT Kharagpur and IIT Madras towing tanks, CSIR-NIOT — model resistance, self-propulsion and seakeeping tests for Indian yards and the Navy.
• Classification and regulation: IRS, DNV, LR, ABS and the Directorate General of Maritime Administration review powering, minimum propulsion power, EEDI/EEXI files and ISO 15016 trial reports.
• Shipping operators and energy teams: Shipping Corporation of India, Great Eastern Shipping, trim optimisation and hull-cleaning schedules, slow steaming and CII rating management.
• Job roles: hull form/hydrodynamics engineer, CFD engineer (OpenFOAM, STAR-CCM+, Shipflow), basic design engineer, trials engineer, energy-efficiency and performance monitoring analyst, naval architect in offshore and defence design.
• Beyond ships: inland vessels under the Inland Vessels Act, 2021, high-speed ferries and catamarans, offshore platforms and tow resistance, submarine and AUV drag estimation, dredger and tug bollard-pull design.

Interview questions

• Q: Why can a model test not satisfy Reynolds and Froude similarity at the same time? A: Equal Fn needs the model speed reduced by √λ while equal Rn needs it increased by λ; both cannot hold for the same model in the same fluid, so Froude's hypothesis scales only the residuary part and friction is computed separately.
• Q: What exactly is the ITTC 1957 line? A: An empirical correlation line, C_F = 0.075/(log₁₀Rn − 2)², used consistently for model and ship; it is slightly above a true flat-plate line to absorb some three-dimensional effect, so it is a convention, not a physical law.
• Q: Difference between the 2-D and 3-D extrapolation methods? A: The 2-D (Froude) method lumps form drag into the residuary coefficient, so R_R is wrongly scaled by Froude's law; the 3-D (ITTC 1978) method separates it using a form factor k, scaling viscous resistance by Rn and only the wave part by Fn.
• Q: Why does a bulbous bow sometimes increase resistance? A: It works by wave cancellation that is tuned to one speed and draught; off-design, especially in ballast or at low speed, its own wave system no longer cancels the bow wave and its extra wetted surface and immersion add resistance.
• Q: Can hull efficiency exceed unity, and why? A: Yes — η_H = (1−t)/(1−w); the propeller works in the hull's wake where the water is already moving with the ship, so if the wake gain (w) outweighs the thrust deduction (t), η_H is greater than 1.
• Q: What is thrust deduction and where does it come from? A: The propeller's suction lowers pressure at the stern and increases the hull's resistance, so the required thrust exceeds towed resistance: t = (T − R)/T, typically 0.10-0.25.
• Q: Order the powers from largest to smallest and say why. A: P_I > P_B > P_S > P_D > P_T ≈ P_E; each step loses something — mechanical friction in the engine, gearing, shafting and stern tube, then propeller and hull interaction losses.
• Q: Why do we add a sea margin, and what does it cover? A: Trial power is measured on a clean hull in calm deep water; in service, waves, wind, fouling and roughness raise resistance, so 15-25% extra power is specified so the ship holds its service speed between dry dockings.
• Q: At what Froude number does wave resistance become a design driver? A: Broadly above Fn ≈ 0.25; the main interference hump is near Fn ≈ 0.5, so designers keep the service speed in a hollow rather than on a hump.
• Q: How is current removed from a speed trial? A: By running reciprocal courses over the same measured stretch and taking a mean of means of consecutive runs, with corrections for wind, waves, shallow water and displacement per ISO 15016.
• Q: If a ship's speed is reduced by 10%, how much power is saved? A: Roughly 27% by the cube law (0.9³ = 0.729); more in practice because the resistance coefficient itself falls, which is the basis of slow steaming and CII compliance.
• Q: Why are turbulence stimulators fitted on models? A: At model Reynolds numbers the boundary layer may stay partly laminar, giving too low a measured resistance; studs or a trip wire force early transition so the friction line used in extrapolation is valid.

Common mistakes

• Scaling total resistance by λ³ instead of only the residuary part — Froude's law applies to R_R, never to R_F or R_T.
• Using the same Reynolds number for model and ship, or forgetting to use each one's own C_F; also using the wrong ν for fresh versus sea water.
• Mixing units: knots left unconverted (1 knot = 0.5144 m/s), S in m² with V in knots, or quoting an Admiralty coefficient without stating whether P is in kW or hp.
• Forgetting the correlation allowance C_A and air resistance, then wondering why the predicted power is below trial results.
• Confusing wake fraction with slip, or P_D with P_S, and dividing by the wrong efficiency in the power chain.
• Reporting trial power as installed power — omitting the sea and engine margins, so the engine has no reserve.
• Assuming a bulbous bow, a longer hull or a lower block coefficient always reduces resistance, without checking the design Froude number.

Related topics

Marine propellers and propulsion · Ship geometry, lines plan and hydrostatics · Seakeeping and manoeuvring · Marine engines and powering plant selection · Computational fluid dynamics for ship flows · Ship design spiral and EEDI compliance