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Bunker figure: from the gauged volume to tonnes in air

Why it matters Bunkers are paid for by the tonne; a skipped correction means paying for oil that is not on board.

Bunker figure: the gauged volume brought to 15 °C, then weighed in airThe tank is gauged warm: 312.4 m³ at the observed temperature. At 15 °C the same oil takes 312.4 × 0.978 = 305.53 m³, 6.87 m³ less. Weighed in air: 305.53 × (0.985 − 0.0011) = 300.61 t; in vacuum it would be 300.94 t.sounding pipegauged 312.4 m³× VCF 0.978 = 305.53 m³ at 15 °Cmagnified ×10as gauged, warm: 312.4 m³same oil at 15 °C: 305.53 m³6.87 m³ expansionWEIGH IN AIR305.53 m³ × 0.9839 t/m³WCF = 0.985 − 0.0011(air buoyancy)300.61 t in airin vacuum (× 0.985): 300.94 tTank of uniform section · column to scale by volume

Words on this page

Bunkers
the fuel a ship takes on for her own engines.
Gauged volume
the volume found by measuring the fuel level in the tank.
Volume correction factor (VCF)
the multiplier that turns the warm oil's volume into its volume at 15 °C.
Gross standard volume (GSV)
the room the same oil would take up at 15 °C.
Density at 15 °C
how heavy one cubic metre of the oil is at the standard 15 °C.
Weight in air and weight in vacuum
what the oil would weigh on scales in air, and with no air at all; the papers use the weight in air.
Air buoyancy correction
a small fixed figure, 0.0011 t/m³, taken off the density because air holds the oil up a little.
Weight correction factor (WCF)
the density at 15 °C less the air buoyancy correction; the volume times this is the weight in air.
Bunker delivery note (BDN)
the supplier's paper stating how much fuel was delivered and what it is like.
Supplier
the firm that sells and delivers the fuel.

An everyday picture

Look at a thermometer. When it warms up, the liquid inside climbs. There is no more liquid; the same liquid just takes more room.

Fuel oil does the same. Delivered warm, it fills more cubic metres than the same oil would at 15 °C.

So the warm volume is first brought back to 15 °C. Only then is it multiplied by the density at 15 °C.

The rule

  • Bunkers arrive warm, and warm oil takes more room. First bring the gauged volume to 15 °C with the volume correction factor. Gross standard volume = volume × VCF.
  • The density on the bunker delivery note is the density at 15 °C. So it may only multiply the volume at 15 °C.
  • GSV × density at 15 °C is the weight in vacuum (in vacuo). Weighed in air, oil is held up slightly by the air around it. So first take the air buoyancy correction, 0.0011 t/m³, off the density at 15 °C. That gives the weight correction factor (WCF).
  • Heated bunkers are warmer than 15 °C. So each correction lowers the figure, and a skipped one counts in the supplier's favour. Check which of the two the delivery note quotes.

Formula

  • Gross standard volume = volume at the observed temperature × VCF
  • WCF = density at 15 °C − air buoyancy correction
  • Weight in air = GSV × WCF

Worked example

Volume received, at the observed temperature312.4 m³
Volume correction factor to 15 °C0.978
Density at 15 °C from the bunker delivery note0.985 t/m³
  1. Gross standard volume = 312.4 × 0.978 = 305.53 m³ at 15 °CWe bring the warm volume back to what it would fill at the standard temperature.
  2. WCF = 0.985 − 0.0011 = 0.9839 t/m³We take the small air allowance off the density.
  3. Weight in air = 305.53 × 0.9839 = 300.61 tWe multiply the standard volume by that factor; this is the weight in air.

Answer300.61 t

Common mistake

Multiplying the warm volume, 312.4 m³, straight by the density at 15 °C and leaving the VCF out.

The 0.985 belongs to the oil at 15 °C, not at the temperature it was delivered at. Without the VCF the figure comes out 307.37 t, 6.76 t more than she received. And the ship signs for oil she does not have.

Note for mariners The VCF comes from the ASTM tables for that oil's density and temperature; a wrong tank temperature gives a wrong VCF.