Gravity, Latitude and Why Marine Scales Need Gravity Compensation

A kilogram of fish has the same mass at every latitude, but it does not weigh the same. Gravitational acceleration at sea level is about 9.780 m/s² at the equator and about 9.832 m/s² at the poles. Because a load cell measures force, a scale adjusted at one latitude reads differently at another. For a vessel that is built in one country, commissioned in a second port and fishes hundreds of kilometres further north or south, this is a measurable error. This article quantifies it, explains the European gravity zone system and sets out the practical options.

Why gravity varies with latitude

Gravity at the Earth's surface increases from the equator towards the poles by about 0.53%. Two effects combine. The Earth's rotation produces a centrifugal effect that is largest at the equator, and the Earth is slightly flattened, so a point on the equator is further from the centre of mass than a point at the poles.

Geodesists describe this with a normal gravity model on a reference ellipsoid. The NOAA National Geodetic Survey lists the GRS-80 values as 9.780 326 7715 m/s² for equatorial normal gravity and 9.832 186 3685 m/s² for polar normal gravity. The difference, 0.0519 m/s², is 0.53% of the equatorial value.

Legal metrology in Europe uses a standard model of gravity by latitude and altitude, published in WELMEC Guide 2. WELMEC notes that real local gravity normally deviates from that model by no more than about 0.005%, which is negligible for commercial weighing. The table below is based on it.

Gravity by latitude: reference table

The table gives gravity at sea level from the WELMEC model. Values are the same for northern and southern latitudes; example regions are approximate and only indicate the latitude band.

Latitude	Example region (approximate)	Gravity (m/s²)	Difference vs 52° (Netherlands)
0°	Equator	9.7803	−0.33%
12°	Caribbean, central Peru coast (12° S)	9.7826	−0.31%
36°	Strait of Gibraltar, Malta	9.7982	−0.15%
43°	Northern coast of Spain	9.8044	−0.08%
52°	Netherlands, southern North Sea, Falkland Islands (52° S)	9.8125	0
56°	Denmark, central North Sea	9.8159	+0.04%
60°	Shetland, southern Norway	9.8192	+0.07%
64°	Iceland, central Norway	9.8222	+0.10%
70°	Northern Norway, Barents Sea	9.8261	+0.14%
78°	Svalbard	9.8299	+0.18%
90°	Pole	9.8322	+0.20%

Altitude hardly matters at sea. Gravity drops by about 0.000 003 m/s² for every metre of height, so a scale on a deck 10 metres above the waterline differs by about 3 parts per million from one at the waterline.

Worked example: a scale adjusted in the Netherlands, used off northern Norway

A scale adjusted at 52° N and used at 70° N reads about 0.14% heavy if nothing is corrected. The steps:

1. Gravity where the scale was adjusted (52° N): 9.81247 m/s².
2. Gravity where the scale is used (70° N): 9.82609 m/s².
3. Gravity at 70° N is 0.139% stronger, so the scale over-reads by 0.139%.
4. On a 15 kg load, 0.139% is 20.8 g too heavy.
5. On a 400 kg load, it is 555 g too heavy.

Is 20.8 g significant? For a class III instrument with a maximum capacity of 15 kg and a verification scale interval of 5 g, OIML R 76-1 sets the maximum permissible error on initial verification at one and a half intervals (7.5 g) for loads above 2,000 intervals (10 kg). The gravity error alone is almost three times that limit. The effect also accumulates: over a trip that lands 30 tonnes, a 0.139% bias is about 42 kg.

The reverse happens when a vessel moves towards the equator. A scale adjusted at 52° N and used at 36° reads 0.15% light, which on a 25 kg box is 36 g short, a direct loss where fish is sold by weight.

Gravity zones in European legal metrology

A gravity zone is a band of latitude and altitude within which a gravity-sensitive weighing instrument stays within its tolerances without re-adjustment. WELMEC Guide 2 explains the concept under the EU Non-automatic Weighing Instruments Directive 2014/31/EU:

• If an instrument is verified away from its place of use, it must be finally adjusted to the gravity of that place, or to the reference value at the centre of a specified gravity zone that contains the place of use.
• A zone is bounded by two latitudes (in steps of 1°, exceptionally 0.5°) and two altitudes (in steps of 100 m). Longitude is irrelevant, as PTB notes, because the gravity model is symmetric around the Earth's axis.
• The zone must be narrow enough that the gravity variation within it changes the indication by no more than one-third of the maximum permissible error.
• Zones are identified by a code such as 49-52 0-200: latitudes 49° to 52°, altitudes 0 to 200 m.

The permitted zone width depends on the resolution of the instrument. The WELMEC gravity information page shows, for example, that in Austria no marking of the place of use is needed for class III instruments with up to 1,000 verification scale intervals, one zone is sufficient for more than 1,000 and up to 3,000 intervals, and three zones apply for more than 3,000 and up to 5,000 intervals. The finer the scale, the narrower the zone.

A land-based zone system fits a vessel poorly, because the vessel moves across several zones on a single trip. WELMEC Guide 2 therefore has a separate section for weighing instruments installed in ships, which covers gravity compensation, tilt and dynamic acceleration tests. More on this in the legal metrology hub.

Options for vessels: calibrate where used, or compensate

There are three practical ways to deal with gravity on a vessel, and the right one depends on how far the vessel travels and how fine the scale is.

Approach	What it involves	Suits	Watch out for
Adjust with test weights where used	Span adjusted with certified weights in the home port or on the fishing grounds	Vessels that operate within a narrow latitude band	Must be repeated when the operating area changes; adjusting on a moving deck needs a compensated scale
Gravity value or zone setting	Indicator uses the gravity value of the area of use	Predictable operating areas	Setting must be secured and changed deliberately; a wrong setting gives a silent bias
Automatic gravity compensation	The scale corrects for local gravity itself, wherever the vessel is	Vessels crossing many degrees of latitude	Ask for test results and certificates that show how compensation was verified

OIML R 76-1 permits a gravity-sensitive instrument to have a device that compensates for gravity variations, provided external access to that device is practically impossible after securing (clause 4.1.2.6). What to ask a supplier about motion, tilt and gravity compensation is covered in Motion Compensation in Marine Scales: What It Does and How to Judge It.

Practical checklist for fleets

1. Record the latitude at which each scale was last adjusted or verified.
2. List the latitude range the vessel actually fishes, including seasonal grounds.
3. Look up the gravity difference in the table above and express it in scale divisions at your typical load.
4. If the difference exceeds about one-third of your accuracy requirement, use gravity compensation or re-adjust in the operating area.
5. After any re-adjustment or setting change, check with known test weights and log the result.
6. For regulated weighing, confirm the requirements with the competent authority in the country of use.

Other routine checks at sea are covered in Getting Accurate Weights in Rough Seas.

How WPL approaches this

The M5 Series marine platform scale compensates for gravity change as well as for motion and tilt, which suits vessels that work across a wide range of latitudes. Calibration, capacity and filter parameters for WPL scales are managed with the R10 Configuration Panel. WPL has delivered scales to fishing and research fleets from Greenland and Iceland to the Mediterranean, the Caribbean and the Falkland Islands, which shows how wide the range of operating latitudes can be. See the Weighing at Sea guide for the wider context.