Marine & Nautical

Ships and the sea: hull speed, buoyancy, draft, knots and great-circle navigation

From hull speed and buoyancy to draft, metacentric height, and great-circle navigation, this category brings together the core formulas used to understand how ships move, float, and stay stable at sea. It’s useful for students, exam revision, and practical work in marine engineering, navigation, and seamanship, where accurate calculations can affect performance, safety, and route planning.

Hull Speed

NEWIntermediate

v = 1.34\sqrt{L}

Theoretical top displacement speed in knots from waterline length in feet.

Speed in Knots

v = \frac{d}{t}

One knot is one nautical mile per hour.

Nautical Mile to Kilometres

d_{km} = 1.852\, d_{nm}

Convert nautical miles to kilometres.

Buoyant Force (Archimedes)

NEWIntermediate

F_b = \rho g V

Upward force equals the weight of displaced water.

Ship Displacement

NEWIntermediate

\Delta = \rho V

A floating ship displaces its own weight in water.

Draft from Displacement

T = \frac{\Delta}{\rho\, A_w}

Depth of hull below waterline from displacement and waterplane area.

Froude Number

Fr = \frac{v}{\sqrt{gL}}

Ratio of inertia to gravity waves; governs hull resistance.

Great-Circle Distance

d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the globe.

Estimated Time of Arrival

t = \frac{d}{v}

Voyage time from distance and speed over ground.

Anchor Scope

NEWIntermediate

S = \frac{L}{d}

Ratio of anchor rode paid out to water depth.

Metacentric Height

GM = KM - KG

Stability measure; positive GM means the ship rights itself.

Deep-Water Wave Speed

v = \sqrt{\frac{g\lambda}{2\pi}}

Speed of ocean waves in deep water from wavelength.

Ship Fuel Consumption

F = c\, v^3

Fuel burn rises with the cube of speed for a ship.

Deadweight Tonnage

NEWIntermediate

DWT = \Delta_{loaded} - \Delta_{light}

Cargo-carrying capacity: loaded minus empty displacement.

Distance Along a Meridian

d = 60 \times \Delta\phi

Nautical miles between two latitudes on the same meridian.