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Marine & Nautical

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

Hull Speed

NEWIntermediate
v=1.34Lv = 1.34\sqrt{L}

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

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Speed in Knots

NEWBasic
v=dtv = \frac{d}{t}

One knot is one nautical mile per hour.

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Nautical Mile to Kilometres

NEWBasic
dkm=1.852dnmd_{km} = 1.852\, d_{nm}

Convert nautical miles to kilometres.

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Buoyant Force (Archimedes)

NEWIntermediate
Fb=ρgVF_b = \rho g V

Upward force equals the weight of displaced water.

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Ship Displacement

NEWIntermediate
Δ=ρV\Delta = \rho V

A floating ship displaces its own weight in water.

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Draft from Displacement

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

Depth of hull below waterline from displacement and waterplane area.

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Froude Number

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

Ratio of inertia to gravity waves; governs hull resistance.

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Great-Circle Distance

NEWAdvanced
d=Rarccos(sinϕ1sinϕ2+cosϕ1cosϕ2cosΔλ)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.

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Estimated Time of Arrival

NEWBasic
t=dvt = \frac{d}{v}

Voyage time from distance and speed over ground.

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Anchor Scope

NEWIntermediate
S=LdS = \frac{L}{d}

Ratio of anchor rode paid out to water depth.

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Metacentric Height

NEWAdvanced
GM=KMKGGM = KM - KG

Stability measure; positive GM means the ship rights itself.

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Deep-Water Wave Speed

NEWAdvanced
v=gλ2πv = \sqrt{\frac{g\lambda}{2\pi}}

Speed of ocean waves in deep water from wavelength.

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Ship Fuel Consumption

NEWAdvanced
F=cv3F = c\, v^3

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

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Deadweight Tonnage

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

Cargo-carrying capacity: loaded minus empty displacement.

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Distance Along a Meridian

NEWBasic
d=60×Δϕd = 60 \times \Delta\phi

Nautical miles between two latitudes on the same meridian.

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