The value of g

A wide variety of engineering calculations in the cement industry make use of the acceleration due to gravity, g. The value used in these calculations is generally a "text-book" value, and may differ substantially from the actual value. Particularly in Great Britain, a vast number of actual accurately-determined values of g have been measured all over the country at a high geographical frequency, so it is possible to obtain a reliable value at any desired location.

Newton's Law of Gravitation as applied to the Earth is F = G m M / r2, where F is the gravitational force acting on a body of mass m, G is the universal gravitational constant, M is the mass of the Earth, and r is the distance of the body from the centre of the earth. g is the factor in the equation F = m g, so g is given by:

g = G M / r2

Both G and M are empirical constants, and g has an inverse-square relationship to r, the distance from the centre of mass of the earth.

The measured value of g is affected by three major factors:

Latitude. This has two effects:

These two effects conspire to produce an increase of g with latitude. Their magnitudes are readily calculated by simple geometry.

Altitude. The latitude effect is calculated on the basis of the standard surface of the geoid, which is the spheroid at sea level. Points above sea level are progressively further from the centre of the earth, so g diminishes with altitude in a predictable manner.

Gravity Anomaly. In practice the value of g varies somewhat from the value predicted geometrically from latitude and altitude. Positive variation is caused by:

The components of the Earth's structure have a variety of densities. The geometrical model of gravity conceives of the Earth as a series of onion-skin layers, each with uniform density (and this is nearly the case). An individual layer, because it is of uniform density, has its centre of mass coincident with that of the Earth. However, if a layer has a small patch of higher density rock, then the centre of mass is displaced towards the patch, reducing r, and so increasing g.

The geometric effects are calculated by a standard equation: the equation recommended by the UK National Physical Laboratory is that used currently (2017) by the International Union of Geodesy and Geophysics. The equation is:

g = 9.780 327 (1 + 0.005 302 4 sin2φ - 0.000 005 8 sin22φ - 0.000 003 088 H

where φ is the latitude and H is the altitude in metres.

The effect of latitude is around +0.000 85 m.s-2 per degree in mainland Great Britain.

The effect of altitude is -0.000 308 8 m.s-2 per 100 metres.

The value of the gravity anomaly in Great Britain varies from -0.00055 to +0.00137 m.s-2, but most values are much nearer zero.

The effect of latitude is therefore dominant.

Values at cement plants

Values have been calculated using the open-source database provided by the British Geological Survey, which covers Great Britain and offshore waters. Anomaly values for Ireland are not open-source (Note 1), and values have been estimated from various third party graphical sources.

The values given (m.s-2) are for plants with rotary kilns, at ground level at the hot ends of the kilns.

Aberthaw9.8119
Arlesey9.8123
Ballyconnell9.8136
Barnstone9.8131
Barrington9.8125
Barton9.8138
Beddington9.8117
Bevans9.8118
Billingham9.8146
British Standard9.8118
Burham9.8117
Cauldon9.8131
Chinnor9.8118
Cliffe9.8118
Coltness9.8154
Cookstown9.8141
Crosfield's9.8137
Crown & Quarry9.8118
Derrylin9.8136
Drogheda9.8141
Dunbar9.8158
Dunstable9.8120
Ellesmere Port9.8137
Gillingham9.8118
Harbury9.8124
Harefield9.8119
Holborough9.8117
Hope9.8134
Humber9.8138
Jarrow9.8152
Johnsons9.8118
Kent9.8118
Ketton9.8129
Kinnegad9.8130
Kirtlington9.8121
Kirton Lindsey9.8136
Lewes9.8112
Limerick9.8130
Lyme Regis9.8114
Magheramorne9.8149
Martin Earles9.8118
Masons9.8125
Metropolitan9.8119
Mitcheldean9.8119
Newhaven9.8112
Norman9.8125
Northfleet9.8118
Oxford9.8121
Padeswood9.8134
Penarth9.8119
Peters9.8117
Pitstone9.8120
Platin9.8136
Plymstock9.8111
Premier9.8125
Rhoose9.8119
Ribblesdale9.8140
Rochester9.8117
Rodmell9.8112
Rugby9.8126
Shoreham9.8112
Sittingbourne9.8118
South Ferriby9.8138
Southam9.8125
Stockton9.8125
Stoneferry9.8138
Sundon9.8121
Swanscombe9.8118
Tunstead9.8132
Vectis9.8111
Warren9.8147
Weardale9.8141
West Kent9.8117
West Thurrock9.8118
Westbury9.8115
Whitehaven9.8147
Widnes9.8137
Wilmington9.8138
Wishaw9.8155
Wouldham9.8118

NOTES

Note 1. In fact the Irish data, held by the Dublin Institute for Advanced Studies, is charged at €0.30 per point, so the BGS database, if charged in the same way, would cost €50,000. The market for this data probably has a high demand flexibility.