If it is like the picture Billman posted, then you have your answer -- it's a sun plane (US nomenclature) or topping plane (UK nomenclature). "Topping plane" gives the clearest idea of its use. Once the cask has been fully raised, this plane evens up the tops of the staves so the surface around the cask end is perfect, hence the curve of the body of the plane.
There are also planes that are radiused from end to end. These are used by some (few) coopering traditions, but find greater use among other types of wood workers -- like carriage makers, wheelwrights, and come cabinet makers. These woodworkers would need several different radii for their work, and were supplanted by the adjustable radius plane in the photos (courtesy Billman).