The vertical deflection (VD)  , also known as deflection of the plumb line and astro-geodetic deflection, at a point on the Earth is a measure of how far the gravity direction (plumb line) has been shifted by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith (plumb line) and the line perpendicular to the surface of the reference ellipsoid  chosen to approximate the Earth's sea-level surface  . VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ (flat areas ) or 20–50″ (alpine terrain). The deflection of the vertical has a north-south component ξ (xi) and an east-west component η (eta). The value of ξ is the difference between the astronomic latitude minus the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the astronomic longitude minus the longitude (taking east longitudes to be positive and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will change  too.
The vertical deflection (VD) or deflection of the vertical (DoV) , also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith-nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid ( chosen to approximate the Earth's sea-level surface ) . VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ in flat areas or 20–50″ in mountainous terrain). The deflection of the vertical has a north-south component ξ (xi) and an east-west component η (eta). The value of ξ is the difference between the astronomic latitude and the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the product of cosine of latitude and the difference between the astronomic longitude and the longitude (taking east longitudes to be positive and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will change , too.
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or deflection of the vertical (DoV)
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at a point on the Earth
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(plumb line) has been shifted
at a given point of interest is rotated
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zenith
zenith-nadir curve
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and the line perpendicular
tangent line and the normal vector
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(
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(flat areas )
in flat areas
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(alpine
in mountainous
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minus
and
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astronomic longitude minus
product of cosine of latitude and the difference between the astronomic longitude and
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,