Naval Architecture, Maritime Chartering & Propulsion Economics
Admiralty Coefficient, Hull Speed & Slow-Steaming Formula
Calculate Displacement Vessel Froude Hull Speed 1.34*SQRT(LWL_ft), Admiralty-Formula Shaft Power (Disp^(2/3) * V^3) / C_adm, Daily Bunker Consumption (t/day), and Slow-Steaming Voyage Fuel per 1,000 Nautical Miles.
Cut maritime voyage bunker burn by 36% with a 20% slow-steaming speed reduction!
Container lines, bulk charterers, and naval architects size main diesel propulsion using the classical Admiralty Coefficient formula: Shaft_Power_kW = (Displacement_tonnes^(2/3) * Speed_knots^3) / C_adm, where Displacement^(2/3) scales wetted hull surface area and Speed^3 reflects hydrodynamic drag power below the wave-making Froude Hull Speed ceiling V_hull = 1.34 * SQRT(LWL_ft)! Because daily bunker burn scales cubically with speed (V^3) while daily distance steamed scales linearly with speed (V), Voyage Bunker Fuel per 1,000 Nautical Miles scales with Speed SQUARED (V^2)—meaning a 20% slow-steaming reduction from 20 knots to 16 knots slashes daily power by 48.8% (0.8^3 = 0.512) and cuts total fuel burned over a fixed ocean crossing by 36.0% (0.8^2 = 0.64)!
Verify on a Panamax Vessel—Displacement = 64,000 tonnes (B2, so 64,000^(2/3) = 1,600 exact!), Waterline_Length LWL = 625 ft (B3), Service_Speed = 20.0 knots (B4), Admiralty_Coefficient C_adm = 640 (B5), and Two-Stroke_Diesel_SFOC = 175 g/kWh (B6): Wave-Making Hull Speed is 1.34 * SQRT(625) = 33.50 knots (E2); Required Shaft Power is (1,600 * 8,000) / 640 = 20,000.00 kW (E3); Daily Bunker Consumption is (20,000 * 175 * 24) / 1,000,000 = 84.00 tonnes/day (E4); and Distance-Normalized Voyage Fuel is 84 / (20 * 24) * 1,000 = 175.00 tonnes per 1,000 nm (E5)!
| Maritime Propulsion Metric (64,000 t, LWL=625 ft, V=20 kn, Cadm=640, SFOC=175) | Formula | Verified Output |
|---|---|---|
| Froude Hull Speed Ceiling (kn) | 1.34 * SQRT(LWL_ft) | 33.50 knots |
| Required Shaft Power (kW) | (Disp^(2/3) * Speed_kn^3) / C_adm | 20,000.00 kW (10,240 kW @ 16 kn) |
| Daily Bunker Consumption (t/d) | (Shaft_kW * SFOC * 24) / 10^6 | 84.00 t/day (43.01 t/d @ 16 kn) |
| Fuel per 1,000 Nautical Miles | (Shaft_kW * SFOC) / (Speed_kn * 1000) | 175.00 t/1000nm (112.00 @ 16 kn) |
Admiralty Propulsion Shaft Power Formula
Validate positive Displacement, LWL_ft, Vessel_Speed, Admiralty_Coefficient, and Engine_SFOC!
=LET(dp_t, B2, lw_f, B3, v_kn, B4, c_ad, B5, sf_c, B6, IF(OR(dp_t <= 0, lw_f <= 0, v_kn <= 0, c_ad <= 0, sf_c <= 0), "Invalid Vessel Propulsion Input", ROUND(((dp_t ^ (2 / 3)) * (v_kn ^ 3)) / c_ad, 2)))16-Knot Slow-Steaming Charter Sensitivity Check
Reduce Service_Speed B4 from 20 knots to 16 knots: Shaft Power E3 drops to 10,240.00 kW, Daily Bunker Burn E4 falls to 43.01 t/day, and Voyage Fuel per 1,000 nm E5 drops 36% from 175.00 to 112.00 tonnes!
=IF(ISTEXT(E3), E3, ROUND((E3 * B6) / (B4 * 1000), 2))Try the example
Use the original values or change them to test your understanding.