Introduction
A ship in shallow water sinks deeper, pushes its return flow through a smaller cross-section and feels more friction, so a speed trial run in 30 m of water needs more power than the same run in the open ocean. ISO 15016:2025 replaced the old Lackenby speed correction by Raven's method, which splits the effect into a viscous resistance increase that scales with (T/h)^1.79 and a sinkage term treated as extra displacement. This calculator checks the run against the minimum trial depth, evaluates every step of Annex G from the depth Froude numbers to the deep-water power, and shows the Lackenby result beside it for anyone still working to the 2015 edition.
It is for trial engineers, naval architects verifying a sea-trial report, performance analysts correcting service data in coastal waters, and students of ship hydrodynamics.
Formulas
h_min = max(2.5 T_M, 2.4 V_S²/g) Formula (7)
Fr_h = V_S/√(g h), Fr_hd = V_S/√(0.3 g L_PP) G.13
d = 1.46 ∇/L_PP² [Fr_h²/√(1−Fr_h²) − Fr_hd²/√(1−Fr_hd²)] ≥ 0 G.12
δ = d A_W/∇ (≤ 0.05), r_sink = (1 + δ)^(2/3) G.10–G.11
(1+k) = 1.017 + 20 C_B (B/L_PP)² (T_M/B)^0.5 G.9
C_V' = 1.06 C_F (1+k) + ΔC_F, R_Vdeep = C_V' ½ρV_S²S G.4–G.8
R_SHV = R_Vdeep × 0.57 (T_M/h)^1.79 G.3
P_Ddeep = (P_Dmsc − R_SHV V_S/η_Did)/r_sink, P_SH = P_Dmsc − P_Ddeep G.1–G.2
Lackenby: ΔV/V = 0.1242 (A_M/h² − 0.05) + 1 − √tanh(g h/V²), V_deep = V (1 + ΔV/V)Assumptions and limitations
- The trial power must already be corrected for wind, waves and water temperature; the propulsive efficiency is assumed unchanged in shallow water.
- Valid above the minimum trial depth and for sub-critical depth Froude numbers; the sinkage term vanishes at and beyond 0.3 L_PP depth by construction.
- Displacement and waterplane area from the block and waterplane coefficients unless hydrostatics are entered.
- Lackenby applies for A_M/h² ≥ 0.05 and is a speed correction, not a power one.
Worked example
A 180 × 32 × 11 m bulk carrier (C_B 0.80, C_WP 0.88, S 7 000 m²) running 12 kn in 30 m of 15 °C water, 5 000 kW delivered, η_Did 0.70.
- Minimum depth max(27.5, 9.3) = 27.5 m: the run is acceptable.
- Fr_h = 0.360, Fr_hd = 0.268 → d = 1.46 × 50 688/180² × (0.1388 − 0.0747) = 0.146 m; δ = 0.0146; r_sink = 1.0097.
- Re 9.35 × 10⁸, C_F 1.543 × 10⁻³, ΔC_F 0.89 × 10⁻⁴, (1+k) 1.313 → C_V' 2.238 × 10⁻³, R_Vdeep 306 kN.
- R_SHV = 306 × 0.57 × (11/30)^1.79 = 29.0 kN → P_Ddeep = (5 000 − 29.0 × 6.17/0.70)/1.0097 = 4 699 kW; P_SH = 301 kW, 6.0 % of the trial power.
- Lackenby: A_M/h² = 0.383 → ΔV/V = 4.1 %, deep-water speed 12.50 kn at the same power.
Six per cent of power is roughly two per cent of speed by the cubic law, so the two methods differ by a factor of two in the speed they imply: Raven's method was calibrated on modern CFD and full-scale data and is the normative one.
FAQ
Why was Lackenby replaced?
It was derived from 1960s model data for a limited hull range and applies one speed correction regardless of hull form; Raven's method separates the physical causes and uses the actual ship coefficients.
Why 0.3 L_PP as the reference depth?
Raven defines "deep water" for sinkage as h = 0.3 L_PP; the additional sinkage is measured relative to that depth, which is why the term is zero when the water is that deep.
What does the exponent 1.79 mean?
The viscous resistance increase rises steeply as the gap under the keel closes; at h = 2 T the increase is 17 % of the deep-water viscous resistance, at h = 1.5 T 28 %.
Is this the same as squat?
The sinkage term is squat, but handled as extra displacement; the ship-squat calculator gives the under-keel clearance consequences instead.
Can I use it for service data in coastal waters?
In principle, with the same caveats: the power must be corrected for weather first, and the depth along the track must be known.
What if the depth Froude number is near 1?
The formula diverges at the critical speed; trials must not be run there and the page refuses supercritical cases.
Related calculators
- Ship squat — under-keel clearance in shallow water.
- Added resistance in waves (STAwave-1) — the wave correction applied before this one.
- Water temperature and density correction — ISO 15016 Annex E.
- Hull roughness and fouling penalty — the roughness allowance used here.
- Holtrop–Mennen resistance — deep-water resistance estimate.