A rhumbline network (or windrose network) is a navigational aid consisting in multiple lines in a web-like grid drawn on

portolan chart Portolan charts are nautical charts, first made in the 13th century in the Mediterranean basin and later expanded to include other regions. The word ''portolan'' comes from the Italian ''portulano'', meaning "related to ports or harbors", and whi ...

s (and other early

map A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...

s). These

nautical chart A nautical chart is a graphic representation of a sea area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land (topographic map), natural features of the seabed, details of the coa ...

s were used in the

medieval age In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire an ...

and

age of exploration The Age of Discovery (or the Age of Exploration), also known as the early modern period, was a period largely overlapping with the Age of Sail, approximately from the 15th century to the 17th century in European history, during which seafari ...

marine navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

. Since the invention of the

Mercator projection The Mercator projection () is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and sou ...

c. 1600, the term ''

rhumb line In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb li ...

'' (or ''loxodrome'') has been redefined to mean a mathematically precise curve of constant bearing on the Earth's surface. To avoid confusion, the lines on earlier sailing charts can be unambiguously called ''windrose lines'', since they are not true rhumb lines by the modern definition. A rhumb line in the modern sense is only straight on a chart drawn with the Mercator projection, but not on charts from the 13th–16th centuries. Older windrose lines were a close approximation on charts of the

Mediterranean Sea The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western and Southern Europe and Anatolia, on the south by North Africa, and on the ea ...

and surrounding areas, but the rhumb lines on small-scale maps such as the

Teixeira planisphere The Planisphere of Domingos Teixeira is a hand-painted parchment map of the world made by a Portuguese cartographer in 1573, during the reign of Sebastian of Portugal. It is conserved in the Bibliothèque nationale de France. Datasheet * Date: 1 ...

were highly inaccurate. The grid can be easily spotted (as parchment is quite translucent) by observing a chart from its rear face, with a light source illuminating the other side. The hole in the center of the circle, origin of the whole network, is also clearly visible from the rear.

Use of windrose lines on a rhumbline network

To calculate on a

the course to follow from a point of origin to a point of destination, one should transfer — using a parallel rule — the "line of course" drawn from the point of origin to the point of destination, on top of the ''windrose line'' on the ''

compass rose A compass rose, sometimes called a wind rose, rose of the winds or compass star, is a figure on a compass, map, nautical chart, or monument used to display the orientation of the cardinal directions (north, east, south, and west) and their int ...

'' closest to the ship's position, obtaining on it the theoretical course to be followed when sailing towards the destination. This theoretical course may have to be modified (as many times as needed) when tacking if the wind is right ahead of you, or to correct the effects of

leeway Leeway is the amount of drift motion to leeward of an object floating in the water caused by the component of the wind vector that is perpendicular to the object’s forward motion.Bowditch. (1995). The American Practical Navigator. Pub. No. 9. ...

currents Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...

, etc. that a sailor with experience should be able to calculate empirically.

Rhumblines vs. windrose lines

Before modern accurate surveying, there was no method for measuring longitude at sea so maps used to have 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. All

portolan map Portolan charts are nautical charts, first made in the 13th century in the Mediterranean Sea, Mediterranean basin and later expanded to include other regions. The word ''portolan'' comes from the Italian language, Italian ''portulano'', meaning " ...

s share these characteristic "windrose networks", which emanate from

s located at various points on the map (or mapamundi). These better called "windrose lines" are generated "by observation and the compass", and are designated today as "lines of course" or "lines of rhumb" ("rhumb lines" in the fourteenth century, traced on portolan's particular projection, though not to be confused with modern

s, meridians or

isoazimuthal The isoazimuth is the locus of the points on the Earth's surface whose initial orthodromic course with respect to a fixed point is constant. That is, if the initial orthodromic course Z from the starting point ''S'' to the fixed point ''X'' is 8 ...

s). To understand that those lines should be better called "windrose lines", one has to know that

s are characterized by the lack of

map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...

, for cartometric investigation has revealed that no projection was used in portolans, and those straight lines they could be

loxodrome In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb li ...

s only if the chart was drawn on a suitable projection. As

Leo Bagrow Leo Bagrow (1881 Saint Petersburg – 9 August 1957 The Hague The Hague ( ; nl, Den Haag or ) is a city and municipality of the Netherlands, situated on the west coast facing the North Sea. The Hague is the country's administrative centre ...

states: ''"The word ("Rhumbline") is wrongly applied to the sea-charts of this period (

Middle Age In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...

), since a loxodrome gives an accurate course only when the chart is drawn on a suitable projection. Cartometric investigation has revealed that no projection was used in the early charts, for which we therefore retain the name 'portolan'."''

Network design

Atlantic map from Pietro Vesconte 1325 atlas

Pujades in his book "Les cartes portolanes" has a chapter with all known theories and, with the aim to clarify the controversial arguments, he shows an image of Petrus Vesconte drawing a

portolan Portolan charts are nautical charts, first made in the 13th century in the Mediterranean basin and later expanded to include other regions. The word ''portolan'' comes from the Italian ''portulano'', meaning "related to ports or harbors", and whi ...

chart in which it is visible how he started by drawing first the rhumbline grid. Some authors call it "winds network" instead of using the term "rhumbline network" or "network of rhumblines". The

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

is divided into sixteen equal parts defining a hexadecagon, then the network of sailing directions is drawn "for a set of 16 wind roses", placed in the 16 vertex of an hexadecagon, in groups of 16 "straight lines" called "rhumblines" (on 13th-century charts). From each

vertex Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

, 7 rhumblines are projected towards the hexadecagon's interior connecting "in an alternated pace: skipping 1 of every 2 vertex", that means => to 7 of the vertex opposite to it, but without routing any line to connect that vertex to the other 8 intermixed vertex (keep in mind: 7+8+itself=16 vertex). The remaining 9 rhumblines (to complete the 16 winds) are projected from each vertex towards the exterior of the hexadecagon, although in some portolans those 9 lines do not appear. The lines of the courses for the eight main directions (or winds) are drawn with black ink (or sometimes

gold Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...

); the eight intermediate directions (half-winds) are drawn in green; and in the case of a 32 winds rose, the sixteen remaining (quarter-winds) are drawn in red. The intersection of this set of "rhumblines" determine on the portolans a varied pattern of symmetrical squares, parallelograms, trapezoids and triangles.

Vellum map creation process

The process for a vellum chart creation used to be as follows: * They prepared a

vellum Vellum is prepared animal skin or membrane, typically used as writing material. Parchment is another term for this material, from which vellum is sometimes distinguished, when it is made from calfskin, as opposed to that made from other anima ...

of good size, or several pieces of vellum glued together. * They drew a well-centered hexadecagon (or two linked by a vertex) with a network of 16 lines per vertex (with the different colors mentioned above: black, green and red). * They copied on top of the grid the

coast The coast, also known as the coastline or seashore, is defined as the area where land meets the ocean, or as a line that forms the boundary between the land and the coastline. The Earth has around of coastline. Coasts are important zones in n ...

s lines trying to let the 16 vertex in visible places, as shown in Vescomte's portolan picture with its rhumbline network drawing a 16 vertex regular polygon (hexadecagon) that is perfectly centered on the parchment. * In the case of the

Mediterranean The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western and Southern Europe and Anatolia, on the south by North Africa, and on the e ...

sometimes contained two hexadecagons and has the two opposite corners matching what is called the "portolan diaphragm " (axis of the Mediterranean .. or parallel of

Rhodes Rhodes (; el, Ρόδος , translit=Ródos ) is the largest and the historical capital of the Dodecanese islands of Greece. Administratively, the island forms a separate municipality within the Rhodes regional unit, which is part of the So ...

). * Finally they labeled and decorated the whole

with more or less profusion.

Planispheres with double hexadecagon

In large planispheres, especially those containing the oceans (

World Map A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of map projection, projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensiona ...

), the cartographer used to draw two hexadecagons with the two opposite corners superimposed in the center of the vellum. There are plenty of mappae mundi that use the double-hexadecagon rhumbline networks but they can not be considered portolan charts since they do not have any ports indicated on them. In the Cresques planisphere one is able to read the names of those lines which were winds: tramontana, levante, ponente, mezzogiorno, greco, sirocco, and lebegio. When limited to small seas, planispheres approximately follow both rhumb lines and great circles. But on big oceans they do not follow either of them, due to the imprecision of the map making of that time, corresponding more or less accurately to

rhumb lines In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb li ...

only in the Mediterranean

s and deviating greatly in the Texeira planisfere (among others).