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A rhumbline network, more properly called, a windrose network, or sometimes also called harbour-finding chart, compass chart, or rhumb chart, is a navigational aid drawn on early portolan charts dating from the medieval to early modern period. This network is like a web forming a grid on the map.
Before accurate surveying there was no method for measuring longitude at sea so maps possessed many distortions especially in the east west direction. There was also distortion due to the curvature of the Earth's surface. The multitude of compass roses with straight lines extending outwards across the map derived from how the maps were then made by compiling empirical observations from navigators who attempted to follow a constant bearing at sea.
To calculate a course to follow from a ship's position to a point of desired destination, one would identify the windrose thought to be closest to the ship's position. Then, using a parallel rule, the "line of course" taken from the rose to the point of destination would be transferred to the ship's known position.
The lines are not true rhumb lines in the modern sense, since these can only be drawn on modern map projections and not on 13th-century charts. They were close to true rhumb lines in the Mediterranean area but highly inaccurate in the Teixeira planisphere and the other planispheres drawn in any pre-Mercator projection.