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The Old Bedford River, photographed from the bridge at Welney, Norfolk (2008); the camera is looking downstream, south-west of the bridge. The Bedford Level experiment was a series of observations carried out along a 6-mile (10 km) length of the Old Bedford River on the Bedford Level of the Cambridgeshire Fens in the United Kingdom during the 19th and early 20th centuries to deny the curvature ...
Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere. The concept of a spherical Earth gradually displaced earlier beliefs in a flat Earth during classical antiquity and the Middle Ages .
The curvature is the norm of the derivative of T with respect to s. By using the above formula and the chain rule this derivative and its norm can be expressed in terms of γ′ and γ″ only, with the arc-length parameter s completely eliminated, giving the above formulas for the curvature.
where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second term for the inclination. A further reduction of the above Earth normal section length to the ellipsoidal geodesic length is often ...
For example, when an aeroplane carrying gravimetric reading instruments cruises over one of the poles at constant altitude, the aeroplane's trajectory follows the curvature of the Earth. The first term in the formula is zero then, due to the cosine of the angle being zero, and the second term then represents the centripetal acceleration to ...
A data set which describes the global average of the Earth's surface curvature is called the mean Earth Ellipsoid. It refers to a theoretical coherence between the geographic latitude and the meridional curvature of the geoid. The latter is close to the mean sea level, and therefore an ideal Earth ellipsoid has the same volume as the geoid.
The design of some large structures needs to take the shape of Earth into account. For example, the towers of the Humber Bridge, although both vertical with respect to gravity, are 36 mm (1.4 inches) farther apart at the top than the bottom due to Earth's curvature. [28]
In the 19th century, many astronomers and geodesists were engaged in detailed studies of the Earth's curvature along different meridian arcs. The analyses resulted in a great many model ellipsoids such as Plessis 1817, Airy 1830, Bessel 1841, Everest 1830, and Clarke 1866. [7] A comprehensive list of ellipsoids is given under Earth ellipsoid.