## Elliptical distribution independence,gym equipments to reduce stomach quickly,where can i buy an elliptical trainer jec-4005 - Easy Way

The force distribution across a wing taking an elliptical form is one where the lift Schematic of circulation across the wing span, leading to the loading profile on the rectangular wing.
For a planar wing, the induced drag is at a minimum, for a fixed span, total lift, and equivalent velocity. The effective angle of attack, , and the local lift coefficient, , are constant along the span as a result of the absolute angle of attack, , and the downwash angle, , are constant along the span. Observing that an elliptic planform produces an elliptical lift distribution it could be expected that a rectangular or tapered planform produces a trapezoidal lift distribution.
The Supermarine Spitfire (pictured above), is the classic example of an aircraft with an elliptical planform, Though seen clearly in the picture the planform is not an exact ellipse. My understanding is that the planform does not make a big difference to lift distribution and aerodynamic performance.
Originally Posted by ccg [SIZE=2]My understanding is that the planform does not make a big difference to lift distribution and aerodynamic performance. Originally Posted by Dan Thomas Planform makes a huge difference in stall initiation and progression. Originally Posted by ccg My understanding is that the planform does not make a big difference to lift distribution and aerodynamic performance.
Jamie Thinner profiles stalling before the thicker root can be extrapalated from the existing NACA test data. You better edit the decimal point, (one step to the right) before someone tell you you have made a mistake. From reading the late Professor Strojnik's books (decent aerodynamics theory for political science majors), a tapered wing offer almost the same advantages of a true elliptical wing with just a little more work to build than the Hershey bar.
Originally Posted by kent Ashton From reading the late Professor Strojnik's books (decent aerodynamics theory for political science majors), a tapered wing offer almost the same advantages of a true elliptical wing with just a little more work to build than the Hershey bar. Originally Posted by bmcj But if you look at the stall progression chart posted by Dan Thomas in post #3, you'll see that the rectangular wing has the most desirable stall propogation pattern, starting at the root where it gives you good advanced warning before it moves out to the ailerons, then the tips. I was thinking about increasing the thickness of the airfoil towards the tips to maintain the same wing thickness but this would result in very thick airfoil sections at the wing tips with a much of a taper.
The BD-5 used a tapered wing with thicker airfoil at the tip to accommodate a tubular spar. Originally Posted by durabol But from these post I get the impression I should probably add a few degrees of washout to the wing although if I keep the taper to about .7 I may be able to get by without the wash out.
This is for wings without twist and of constant airfoil section and I assume it's just an approximation. As for tapering the wing more than it takes to get close to an elliptical lift distribution. DESCRIPTION: This highly controversial map has only recently been uncovered (1957) and therefore has only a short history of scholarly analysis. THE MANUSCRIPT: First brought to the publica€™s attention in 1957 by an Italian bookseller, Enzo Ferrajoli from Barcelona, the document now known as the Vinland map was discovered bound in a thin manuscript text entitled Historia Tartarorum (now commonly referred to as the Tartar Relation). The Tartar Relation, in essence, is a shortened version of the more well-known text entitled Ystoria Mongolorum, which relates the mission of Friar John de Plano Carpini, sent by Pope Innocent IV to a€?the King and People of the Tartarsa€™, which left Lyons in April 1245 and which was away for 30 months.
The fate of the Speculum Historiale was very different, for Vincenta€™s work became a standard reference book on the shelves of monastic libraries and was constantly multiplied during the next two centuries in manuscript form. According to these same scholars, the Tartar Relation text does have some significance in its own right as an independent primary source for information on Mongol history and legend not to be found in any other Western source.
That the map and the manuscript were juxtaposed within their binding from a very early date cannot be doubted.
The association of the map with the texts is reinforced by paleographical examination, which has enabled the hands of the map, of its endorsement, and of the texts to be confidently attributed to one and the same scribe. The map depicts, in outline, the three parts of the medieval world: Europe, Africa, and Asia surrounded by ocean, with islands and island-groups in the east and west. In the design of the Old World the map belongs to that class of circular or elliptical world maps in which, during the 14th and 15th centuries, new data were introduced into the traditional mappaemundi of Christian cosmology.
Written in Latin on the face of the map are sixty-two geographical names and seven longer legends. Before proceeding to analyze the geographical delineations of the map in detail, we may briefly survey the antecedent materials, cartographic and textual, to which comparative study of it must refer. As noted above, the representation of Europe, Africa, and Asia in the map plainly derives from a circular or oval prototype. Variations of this basic pattern were introduced to admit new geographical information, ideas, or new cartographic concepts.
The circular form of the medieval world map, in the hands of some 14th and 15th century cartographers, is superseded by an oval or ovoid; and even in the 14th century rectangular world maps begin to appear, mainly under the influence of nautical cartography. Most of these variations in the form and design of world maps were adapted from the practice of nautical charts and, in the 15th century, of the Ptolemaic maps. If the Vinland map was drawn in the second quarter of the 15th century, and perhaps early in the last decade of that quarter, it would take its place after that of Andrea Bianco and would be contemporary with the output of Leardo, whose three maps are dated 1442, 1448, and 1452 or 1453.
As previously noted, the outlines of the three continents form an ellipse or oval, the proportions between the longer horizontal axis and the vertical axis being about 2:1.
It is not necessary to assume that the prototype followed by the cartographer was also oval in form.
If the model for the Vinland map corresponded generally in form and content to Andrea Biancoa€™s world map, then the variations introduced by its author are not less significant than the general concordance.
Comparison of the geographical outlines of the Vinland map with those of Bianco suggests that its author, while generally following his model, was inclined to exaggerate prominent features, such as capes or peninsulas, and to elaborate, by fanciful a€?squigglesa€?, the drawing of a stretch of featureless coast.
EUROPE: With the reservations made in the preceding paragraph, the cartographera€™s representation of the regions embraced by the a€?normala€? portolan chart of the 15th century, the Mediterranean and Black Seas, Western Europe, and the Baltic, closely resembles that of Bianco in his world map, which reflects his own practice in chart making.
Scandinavia, as in all maps before the second quarter of the 16th century, lies east-west in both maps; but there is a conspicuous divergence in their treatment of its western end, which both cartographers extend into roughly the longitude of Ireland. In its delineation of the British Isles, the Vinland map again diverges from that in Biancoa€™s world map.
These differences seem too great to fall within the limits of the license in copying which the author of the Vinland map evidently allowed himself in those parts of his design which agree basically with Biancoa€™s rendering and may derive from a common prototype. In the Vinland map, Europe is devoid of rivers, save for a very muddled representation of the hydrography of Eastern Europe. The twelve names on the mainland of Europe are, with two exceptions, those of countries or states. AFRICA: The general shape and proportions of Africa, extending across the lower half of the Vinland map, also correspond to a type followed, with variation, in most circular world maps of the 14th and 15th centuries, and deriving ultimately from much earlier medieval and classical models. Alike in the general form of Africa (with one major variation) and in the detailed outlines of the continent, the Vinland map agrees with Biancoa€™s circular map of 1436 (which itself has, in this part, close affinities with the design of Petrus Vesconte). The hydrographic pattern of the African rivers in the Vinland map is a somewhat simplified version of that drawn by Bianco, with the Nile (unnamed) flowing northward from sources in southern Africa to its mouth on the Mediterranean and forking, a little below its springs, to flow westward to two mouths on the Atlantic; the western branch is named magnus [fluuius].
The African nomenclature of the Vinland map, some fourteen names, is conventional, over half the forms corresponding to those of Bianco.
Africa is the continent in which we have noted some striking links between the Vinland map and Biancoa€™s world map of 1436. The great advance in the knowledge which, from the second half of the 13th century, reached southern Europe about the interior of West Africa and the Sudan was reflected in many maps, from the information collected by merchants on the Saharan trade routes and in the markets of Northwest Africa. ASIA: If we are justified in supposing the cartographera€™s prototype to have been circular, he, or the author of the immediate original copied by him, has adapted the shape of Asia, as of Africa, to the oval framework by vertical compression rather than lateral extension. It is in the outline of East Asia that the maker of the Vinland map introduces his most radical change in the representation of the tripartite world which we find in other surviving mappaemundi and particularly (in view of the affinities noted elsewhere) in that of Andrea Bianco.
This version of East Asian geography is found in no other extant map, and its relationship to the prototype followed for the rest of the Old World is best seen by comparison with Biancoa€™s delineation, which itself descends from an ancient tradition. It is a striking fact, and one which perhaps does credit to his realism, that, in order to admit into his drawing of the Far East a representation derived from a new source under his hand, he has gone so far as to jettison the Earthly Paradise from the design.
The concentration of interest on the Greenland sector has led to the comparative neglect of the Asian section, which has topographical features at least as unusual. The remaining islands of Asia are drawn in the Vinland map very much as by Bianco, with some simplification and generalization, and may be taken to have been in the prototype.
Within the restricted space allowed by his revision of the river-pattern and of the coastal outlines, the author of the Vinland map has grouped the majority of his names in two belts from north to south, on either side of the river which runs from the Caspian to the ocean. For Asia the compiler of the Vinland map shows the same conservatism in his use of sources as for Africa; and, apart from the modifications introduced from his reading of the Tartar Relation, this part of the map could very well have been drawn over a century earlier. To the north of the British Isles, the Vinland map marks two islands, presumably representing either the Orkneys and Shetlands or these two groups and the Faeroes. To the west of Ireland the Vinland map has an isolated island, also in Bianco; and to the southwest of England another, drawn by Bianco as a crescent. Further out, and extending north-south from about the latitude of Brittany to about that of Cape Juby, Biancoa€™s world map shows a chain of about a dozen small islands, drawn in conventional portolan style.
Further south, the Vinland map lays down the Canaries as seven islands lying off Cape Bojador, with the name Beate lsule fortune.
ICELAND, GREENLAND, VINLAND: In the extreme northwest and west of the map are laid down three great islands, named respectively isolanda Ibernica, Gronelada, and Vinlandia Insula a Byarno re et leipho socijis, with a long legend on Bishop Eirik Gnupssona€™s Vinland voyage above the last two.
The three islands are drawn in outline, in the same style as the coasts in the rest of the map; and there can be no doubt that the whole map, including this part of it, was drawn at the same time and by a single hand. The land depicted to the west of Greenland in the northwest Atlantic has the following legend (in translation): Island of Vinland discovered by Bjarni and Lief in company.
The question a€?what kind of map is this?a€? the answer must be: a very simple map, simple both in intention and in execution. In finding cartographic expression for the geography of his texts, the maker of the map has practiced considerable economy of means. Examination of the nomenclature has suggested that the Vinland map, in the form in which it has survived, is the product of a stage of compilation (the work of the author or cartographer) and a subsequent stage of copying or transcription (the work of a scribe who was perhaps not a cartographer). The process of simplification described above was presumably carried out in the compilation stage.
These considerations must govern our judgment of the date and place of origin to be ascribed to the map. The Map was interesting to historians as apparent evidence that Norse voyages of the 11th and 12th centuries were known in the Upper Rhineland in the mid-15th century, and consequently that some continuity of knowledge existed between the early discovery of what we know as America and the rediscovery of western lands in the later 15th century. As a world map the Vinland map does not fit into the framework of medieval cartography as conceived in Western Europe.
SOURCES: Analysis of the nomenclature and of its affinities with other maps or texts suggests some general remarks about the Vinland map and about its mode of compilation. In those parts of the map in which (as noted above) the influence of O1 predominates, there are very few names which cannot be traced to it or to the common stock of toponymy found in contemporary cartography (and therefore perhaps in O1). On this assumption, some other names (if they were not in O1) and all the legends (which can hardly have been in O1) must be attributed to the compiler of the map, i.e.
Whether the novelties in the nomenclature of the Atlantic island groups were in O1 or were introduced by the compiler of O2 cannot be determined; the affinities between their delineation in the Vinland map and in surviving charts suggest that the names also may have been found by the compiler in maps which have not survived. At each stage of derivation, from O1 to O2, and (less probably) from O2 to the Vinland map in its present form, there must have been a process of selection or thinning out of names. The representation of the Atlantic, with Iceland, Greenland, and Vinland, was almost certainly not in the prototype used for the tripartite world, but was added to it by the cartographer from another source or other sources.
The world picture of the 14th century, which was taken over into the mappaemundi of the next century, including the prototype used in the Vinland map, owed its general form and plan to geographical concepts of classical origin, confirmed and modified by the authority of the Christian Fathers. On this pattern were to be grafted geographical facts derived from experience and unknown to the creators of the model. As a result the induced drag is a minimum when compared to a planar wing of equal span, total lift and velocity. The main advantages would be a larger wing stub (about 10%) for more room for fuel and retractable gear. The lift distribution with a 0.4 taper wing is only 1% or so different from the optimal elliptical planform. 99 of his book that the results of the NACA tests indicating tip stall are due to a reduction in the tip airfoil's thickness ratio?
Has anyone ever heard about using a higher taper ratio than what is equivalent to an elliptical wing or is this not a good idea?
This fact not withstanding, it may also claim, during this rather short period, to have undergone more intensive scrutiny and examination in both technical and academic terms than any other single cartographic document in history. This manuscript text and map were copied about the year 1440 by an unknown scribe from earlier originals, since lost.
Whereas Carpinia€™s Ystoria is not considered a rare text, no manuscript or printed version of the Tartar Relation has survived, save the one bound with the Vinland map.
It is because the Tartar Relation, one, had the good fortune to become embodied in a manuscript of this popular work (possibly a substitute for, or an addition to, Books XXX-XXXII, which also contained an abridgement of Carpinia€™s own account) and, two, because, in general, a bulky manuscript like the Speculum Historiale had a better chance of physical survival than a slender one like Tartar Relation bound separately. Additionally the Tartar Relation does act, partially, as one of the chief sources for some textual legends on the Vinland map with regards to Asia.
As part of Vincenta€™s encyclopedia of human knowledge entitled Speculum Majus, Speculum Historiale was included as a chronicle of world history from the time of mana€™s creation to the 13th century, in 32 sections or books.
The physical analysis, together with the endorsement of the map, points with a high degree of probability to the further conclusions that the map was drawn immediately after the copying of the texts was completed, and in the same workshop or scriptorium, and that it was designed to illustrate the texts which it accompanied. Further evidence on their relationship and on its character must be sought in the content of the map. The derivation of the map, in this respect, from a circular or oval prototype is betrayed by the general form of Europe, Africa, and Asia, which are rounded off (or beveled) at the four oblique cardinal points, although the artist had a rectangle to fill with his design. The whole design is drawn in a coarse inked line, with evident generalization in some parts and considerable elaboration in others.
The features named are seas and gulfs, islands and archipelagos, rivers, kingdoms, regions, peoples, and cities. It is, of course, not to be supposed that its anonymous maker had direct access to all surviving earlier works with which his shows any affinity in substance or design; but identification of common elements will help us to reconstruct the source or sources upon which he drew. Even when the world maps of the late Middle Ages, drawn for the most part in the scriptoria of monasteries, attempted a faithful delineation of known geographical facts (outlines of coasts, courses of rivers, location of places), they still respected the conventional pattern which Christian cosmography had in part inherited from the Romans, and, in part, created.

The traditional orientation, with east to the top, came to be abandoned by more progressive cartographers, who drew their maps with north to the top (following the fashion of the chart makers) or south to the top (perhaps under the influence of Arab maps). While the work of Leardo is considerably more sophisticated in compilation and more a€?learneda€? in its incorporation of varied geographical materials than that of Bianco, the world maps of both these Venetian cartographers plainly depend for their general design on models of the 14th century.
Since the map is oriented with north to the top, the longer axis lies east-west, and the two greater arcs at top and bottom are formed by the north coasts of Europe and Asia and by the coasts of Africa respectively. In fact his map has striking affinities of outline and nomenclature with the circular world map in Andrea Biancoa€™s atlas of 1436 (#241). His personal style of drawing, save perhaps in the outlines of certain large islands, shows no sign of the idiosyncrasies of the draftsmen of the portolan charts, although these have left a clear mark on the execution of Biancoa€™s world map. The orientation and outline of the Mediterranean agree exactly in the two maps, although in the Vinland map it has a considerably greater extension in longitude, in proportion to the overall width of Eurasia. Bianco shows Scandinavia as terminating in an indented coast projecting westward with a large unnamed island off-shore, divided from it by a strait; but the author of the Vinland map has altered the island to a peninsula and the strait into a deep gulf by drawing an isthmus across the south end of the strait. In both, Ireland has the same shape and coastal features, derived from the representation in contemporary Italian charts; and Biancoa€™s version of Great Britain also is that of the portolan chart makers, with the English coasts deeply indented by the Severn and Thames estuaries and the Wash, with a channel or strait separating England and Scotland, and with Scotland drawn as a rough square with little indentation. In view of the novel elements in the northwest part of the map, we must reckon with the possibility, but no more, that its author found this version of the British Isles in a map of the North Atlantic which may have served him as a model for this part of his work and from which may stem not only his representations of Iceland, Greenland, and Vinland, but also his revisions of Scandinavia and Great Britain and of the islands between. The lower course of the Danube is correctly drawn as falling into the Black Sea; but the copyist or compiler appears to have erroneously identified it with the Don (which debouches on the Sea of Azov), for the name Tanais is boldly written just above the river, with a legend about the Russians. The only European city named in the Vinland map is Rome, while Biancoa€™s world map marks only Paris.
The northwest coast was by this date known as far as Cape Bojador, and this section is traced with precision in both maps. Errors made by the anonymous cartographer in common with Bianco, or derived from their common prototype, are the transference of Sinicus mons [Mount Sinai] to the African side of the Red Sea and the location of Imperits Basora [Basra] in the eastern horn of Africa (Bianco also incorrectly places the Old Man of the Mountain (el ueio dala montagna; not in the Vinland map) in Africa instead of Asia). It also seems, although no doubt deceptively, to provide the latest terminus post quem for dating both. The wealth of detail for this region recorded by Carignano, the Pizzigani, and the Catalan cartographers is wholly absent from Biancoa€™s world map and from the Vinland map. Thus, in place of the steeply arched northern coast of Eurasia shown by Bianco, we have a flattened curve which abridges the north-south width of the land mass.
The prototype is, in this region, not wholly set aside for traces of it remain but rather adapted to admit a new geographical concept which, significantly enough, can be considered a gloss on the Tartar Relation.
The most prominent of these is the Magnum mare Tartarorum [the Great Sea of the Tartars] set between the eastern shores of the mainland and the three large islands on the margin, and occupying an area approximately one-third of that of continental Asia. Again, the northernmost of these islands on the Map has the inscription, Insule Sub aquilone zamogedorum, while the text states that the Samoyeds are a€?poverty stricken men who dwell in forestsa€™ on the mainland of Asia.
The three small islands in the Persian Gulf appear in both, though Biancoa€™s crescent outline for them (of portolan type) is not reproduced by the anonymous cartographer; the large archipelago depicted by Bianco (again in portolan style) in the Indian Ocean is reduced to four islands, and the two bigger oblong islands to the east of them are in both maps.
Instead of Biancoa€™s representation of the Arctic zones of Eurasia (with two zonal chords, delineations of skin-clad inhabitants and coniferous trees, and a descriptive legend), the Vinland map has only the two names frigida pars and Thule ultima.
The nomenclature for Asia, with twenty-three names, is richer than that for the other two continents; some names come from the common stock found in other mappaemundi, but the greater number are associated with the information on the Tartars and Central Asia brought back by the Carpini mission. The cartographera€™s neglect to use any information from Marco Polo or from the travelers in his footsteps, notably Odoric of Pordenone, is common to all maps before the Catalan Atlas of 1375 (in which East Asia is drawn entirely from Marco Polo) and to most maps of the first half of the 15th century.
His delineation of them, indeed, closely resembles that in Biancoa€™s world map, which is in turn a generalization, with nomenclature omitted, from the fourth and fifth charts (or fifth and sixth leaves) in his atlas of 1436.
The two islands appear, in exactly the same relative positions, in Biancoa€™s world map, although they are absent from the charts of his atlas.
These islands, the Azores of 15th century cartography and the Madeira group, are represented in the Vinland map, in more generalized form and without Biancoa€™s characteristic geometrical outlines, by seven islands, having the same orientation and relative position as in Biancoa€™s map, and with the name Desiderate insule. Their agreement in outline with the two large islands laid down in exactly the same positions at the western edge of Biancoa€™s world map is striking: in particular, the indentation of the east coast of the more northerly island and the peninsular form of its southern end, the squarish northern end of the other (and larger island) and its forked southern end, are common to both maps.
That they lie outside the oval framework of the map suggests that they were not in the model, apparently a circular or elliptical mappamundi, which the cartographer followed in his representation of Europe, Africa, and Asia. For this part of the map there are no earlier or contemporary prototypes of kindred character for comparison, and indeed (except in respect of Iceland) no representations with much apparent analogy can be cited before the late 16th century. It is drawn as a rough rectangle, with a prominent west-pointing peninsula in the northwest, the EW axis being considerably longer than the N-S axis.
The northernmost point of Vinland is shown in about the same latitude as the south coast of Iceland and somewhat lower than the north coast of Greenland; and its southernmost point in about the latitude of Brittany.
Residual from the representation described under the previous name, the large elliptical island being suppressed. Buyslaua = Breslau (Bratislava), where Carpinia€™s party stopped on the outward journey and was joined by Friar Benedict.
Ayran (NE of the Caspian) Perhaps Sairam in Turkestan, a station on the old highway, east of Chimkent and N.E.
Vinlanda Insula a Byarno re pa et leipho socijs [Island of Vinland, discovered by Bjarni and Leif in company]. The links between the map and the surviving texts which accompany it strongly suggest that it was designed to illustrate C. There is a decided incongruity between, on the one hand, the care and finish which characterize the writing of the names and legends, with their generally correct Latinity, and, on the other hand, the occurrence of onomastic errors which knowledge of current maps and geographical texts or reference to the prototype used by the compiler would have corrected. If we are justified in supposing the scribe who made the surviving transcript of the map to have been ignorant or naive in matters of geography, the draft which he had before him for copying must have been the product of selection and combination already exercised by the compiler. The evidence, internal and external, which indicates that the manuscripts were produced in the Upper Rhineland in the second quarter of the 15th century can only apply to the map included in the codex. In its representation of Europe, Africa, and Asia it can be referred to, and collated with, not only extant cartographic works of similar character and design, but also a text which is bound in the same volume and to which its content is clearly related. This information was limited in its scholarly impact by the failure of historians to find any other evidence of continuity or to discover that the evidence contained in the Map had ever been known to anyone concerned with exploration either before Columbusa€™s voyage or after. In respect of toponymy, as of outline and design, the correspondences between this map and Biancoa€™s world map of 1436 are almost certainly too extensive to be explained by coincidence. Some of these anomalies (Aipusia, aben, Maori) are plainly the product of truncation or corruption in transcription, and indicate that the draftsman lacked the knowledge to correct his own errors in copying. In Asia however, while a number of names and the basic geographical design derive from O1, the authority of the Tartar Relation of other Carpini information generally prevails in the toponymy. The names for Iceland and Greenland may point to literary sources, perhaps of Norse origin (these names, however may have been in cartographic sources used by the compiler); so, with more certainty, do the name and legends relating to Vinland.
For Europe and Africa, Biancoa€™s world map has considerably more names than the Vinland map; in Asia the balance is redressed by the introduction of names from the Tartar Relation. The lucky accident that his sources for the Old World can be easily identified or reconstructed allows us to hazard some inferences about his treatment of his sources for the Atlantic part of his map. Patristic geography, as formulated in the Etymologiae of Isidore of Seville (7th century, #205), envisaged the habitable world as a disc, the orbis terrarum of the Romans encircled by the Ocean and divided into three unequal parts, Europe and Africa occupying one half and Asia the other half of the orbis, with the Earthly Paradise in the east. One problem is that I want to use a laminar airfoil but may be too hard to make with elliptical wing. The wing would be a bit lighter for the area but this isn't much of a problem with pulruded carbon spars. Interest has been virtually international in scope and has covered every aspect pertinent to a document purported to be of seminal historical significance: its historical context, linguistics, paleography, cartography, paper, ink, binding, a€?worminga€?, provenance or pedigree, etc.
The Tartar Relation itself was initially bound as part of a series of volumes containing 32 books of Vincent of Beauvaisa€™ (1190-1264) Speculum Historiale [Mirror of History].
Clearly, Painter points out, any circulation that the Tartar Relation may have had in separate form was too limited, in view of the normal wastage of medieval manuscripts, to ensure its transmission to the present day.
Based upon various internal and external evidence, it is likely that the juxtaposition of the Speculum Historiale and Tartar Relation first occurred prior to the drafting of the Yale manuscript of 1440, but sometime after the 1255 date of the original production of the Speculum, so that the Yale manuscript is itself a copy of an earlier manuscript, now unknown, in which the Speculum Historiale, Tartar Relation and Vinland map were already conjoined. The Yale manuscript contains only Books XXI-XXIV, and comparative calculations indicate that 65 leaves are missing that could account for the table and text of Book XX (these four Books cover the history from 411 A.D. The physical association of the map with the manuscript is demonstrated beyond question by three pairs of wormholes which penetrate its two leaves and are in precise register with those in the opening text leaves of the Speculum. These texts may have included, in addition to the surviving books (XXI-XXIV) of the Speculum and the Tartar Relation, other books of the Speculum conjectured to have formed the missing quires and a lost final volume of the original codex. The nomenclature is densest in Asia, where it is largely borrowed from the Tartar Relation or a similar text. Moreover, in the light thrown on the cartographera€™s work-methods and professional personality by his treatment of sources which are to some extent known, we may visualize his mode of compilation or construction from materials which have not come down to us. The elliptical outline is interrupted, in its western quadrant, by the Atlantic Ocean and by the gulfs or seas of Western Europe, and in its eastern by a great gulf named Magnum mare Tartarorum; the curvilinear outline is however continued southeastward from Northern Asia by the coasts of the large islands at the outer edge of this gulf. The features common to both maps, and in some cases peculiar to them, are sufficiently numerous and marked (as their detailed analysis will demonstrate) to place it beyond reasonable doubt that the author of the Vinland map had under his eyes, if not Biancoa€™s world map, one which was very similar to it or which served as a common original for both maps. Some apparent differences in the rendering of particular major regions in the Vinland map, which may be due to the use of a different cartographic prototype or simply to negligence by the copyist, are discussed in the detailed analysis which follows.
The distinctive shapes in which Bianco draws the Adriatic, Aegean, and Black Seas reappear in the Vinland map. This seems a more probable explanation of the feature than to suppose that it represents the gulf of the northern ocean supposed by medieval geographers to cut into the Scandinavian coast and drawn in various forms by cartographers of the 14th and 15th centuries, from Vesconte to Fra Mauro. The a€?Danubea€? is shown as rising just south of the Baltic and turning eastward in about the position of Poland; at this point it forks, and a branch flows in a general southeasterly direction to fall into the Aegean. Beyond it the coast line, conventionally drawn, trends southeastward with two estuaries or bays similarly shown by both cartographers, although the anonymous map has a slight difference in the river pattern. They have in common the precise tracing of the northwest coast as far south as Cape Bojador, and if they shared a common prototype, this (it might be supposed) could not have been executed before the voyage of Gil Eannes in 1434.
The latter repeats Biancoa€™s anachronistic reference to the Beni-Marin and his erroneous location of two names; but these aberrations, which appear to be peculiar to Bianco, do not help in dating. This concept is the Magnum mare Tartarorum with, lying beyond it and within the encircling ocean, three large islands which appear to derive from the cartographera€™s interpretation of passages in C.
This great sea is connected in the north with the world ocean by a passage named as mare Occeanum Orientale [the eastern ocean sea]. The Tartar Relation also states that the Tartars have one city called a€?Caracarona€™ (Karakorum) but this city does not appear on the Vinland map. The elimination of East Asia by the western shoreline of the Sea of the Tartars has affected the distribution of place names in the Vinland map and its delineation of the hydrography. The location and arrangement of the names cannot, in general, be connected with Carpinia€™s itinerary (or any other itinerary order), nor with any systematic conception of Central Asian geography.
The affinity between the two world maps, in this respect, is so marked as to distinguish them from all other surviving 15th century maps and to confirm the hypothesis that one has been copied from the other or that both go back to a common model for their drawing of the Atlantic islands. These islands (unnamed in the two world maps) are Satanaxes and Antillia, which make their first appearance in a map of 1424 and have been the subject of extensive discussion by historians of cartography. Greenland, somewhat larger than Iceland, is dog-legged in shape, with its greatest extension from north to south.
Between these points Vinland is drawn as an elongated island, the greatest width being roughly a third of the overall length; the somewhat wavy details of the outline, if compared with this cartographera€™s technique in other parts of his map, seem to be conventional rather than realistic. To facilitate location of the name and legends on the original map, numbers have been added, keying them to the reproduction at the end of this section.
Presumably intended for the Orkneys and Shetlands, or one of these groups and the Faeroes]. The form (for Dania) common in mediaeval cartography, and found in many charts and world maps.
Mediaeval world maps commonly show a pair of such legends, indicating the regions, outside the oikoumene, too cold or too hot for human habitation. Although the second word is truncated, no trace of further letters can be seen in ultraviolet light. The name is, however, placed too far inland and too far east for Mauretania, and this may be a corruption of another name in the prototype, e.g.
The concept of the Western Nile, or a€?Nile of the Negroesa€?, represented in mediaeval cartography arose from the identification of the Niger, by some classical writers, as a western branch of the Nile and from subsequent confusion of the Niger, the Senegal, and the Rio do Ouro (south of C. Although of diverse languages it is said that they believe in one God and in our Lord Jesus Christ and have churches in which they can pray]. The remaining children of Israel also, admonished by God, crossed toward the mountains of Hemmodi, which they could not surmount]. This name is placed in the approximate position of India media of Andrea Bianco, who (like most medieval geographers) distinguished three Indiasa€”minor, media, and superior. According to Carpini, one of the nations of the Mongols: a€?a€¦ Su-Mongal, or Water-Mongols, though they called themselves Tartars from a certain river which flows through their country and which is called Tatar (or Tartar)a€?. The Khitai, who ruled in China for three centuries before the Mongol conquests under Ogedei and Kublai, a€?originated the name of Khitai, Khata or Cathay, by which for nearly 1,000 years China has been known to the nations of Inner Asiaa€?.
Carpinia€™s statement that a€?they called themselves Tartars from a certain river which flowed through their countrya€? (see above, under Zumoal) reflects the opinion of other 13th century writers, such as Matthew Paris.
In medieval cartography generally Thule is represented as an island north or NW of Great Britain; some writers identified it as Iceland. The name and delineation probably embody the mapmakera€™s interpretation of what he had read or been told of the Caspian Sea. The last phrase of the legend is inconsistent with the geographical ideas of the Mongols, contrasting with those of the Franks, as reported by Rubruck: a€?as to the ocean sea they [the Tartars] were quite unable to understand that it was endless, without boundsa€?. These islands, and the Postreme Insule, are associated with the cartographic concepts in the two preceding legends (see notes on Magnum mare Tartarorum and on Tartari a rmant .
This is written in the center (between the fourth and fifth, counting from the north) of the chain of seven unnamed islands extending in a line N-S from the latitude of Brittany to that of C.
The name is placed westward of, and between, two large unnamed islands, to which it plainly refers. In no other map or text is the form Isolanda found, or the epithet Ibernica annexed to the name for Iceland. The Icelandic name Groenland, in variant forms (including the latinization Terra viridis), is used in all early textual sources. 1001 rest on the sole authority of the a€?Tale of the Greenlandersa€? in the 14th-century Flatey Book.

What other undetected changes or corruptions the copyist may have introduced into the final draft we cannot tell, since his original, the compilera€™s preliminary draft, is lost. For its delineation of lands in the north and west Atlantic, the cartographic prototypes (if it had any) either have not survived or have been so transformed as to be difficult to identify; and if the codex once included a text relating to these lands, this too has now disappeared. Finally, the inscriptions on Greenland and Vinland in the Map offered a few scraps of information which differed somewhat from what was commonly accepted.
1440 on the argument that it is in the same hand as the Tartar Relation, of which the Map is held to be an integral part. It seems to be an inescapable inference that the author of the Vinland map (or of its immediate original) employed no eclectic method of selection and compilation from a variety of sources, but was content to draw on a single map, which must have been very like Biancoa€™s, for the majority of the names, as well as the outlines, in Europe, Africa, and part of Asia. Thus, in Europe, Ierlanda insula may perhaps arise from his misinterpretation of O1 or of some other map in which the names for Ireland and for the islands north of Scotland misled him; and Buyslava may come from the reports of the Carpini mission.
The degradation of names from this source points again to carelessness or ignorance in the copyist, although in one instance - Gogus, Magog - he, or the compiler of O2, has emended the debased form (moagog) in the Tartar Relation by reference to O1. In the absence of the prototype O1, we cannot say whether its author or the compiler of the Vinland map was responsible for introducing the few names in the Old World which must have come from classical or medieval literary sources and the nomenclature for the Atlantic islands.
His apparent preference for the simple solution or the single source admits the possibility that the western part of his map also derives, in the main, from one prototype rather than that it combines features from several; it may have been modified by interpolation or correction from another source (as is the representation of Asia from the Tartar Relation), and this too must be taken into account. This theoretical and schematic construction did not necessarily imply belief in a a€?flat eartha€?, although it is uncertain whether Isidore himself admitted the sphericity of the earth. Some of the other advantages would be less induced drag due to smaller wing tips so more efficient slow speed flight but not much effect on cruise speed. The choice of the name Vinland and the appearance of this Norse discovery prominently displayed on the map was what attracted such immense popular and scholarly attention. All indications (paper, binding, paleography, etc.) point to an Upper Rhineland (Basle?) source of origin for the present three-part manuscript. This foregoing explanation or scenario has been the one put forward by the a€?believersa€™. The sources of all of the names and each of the legends are examined in great detail in Skelton, et ala€™s The Vinland Map and the Tartar Relation. We may even catch a glimpse of these materials, as they are reflected in the Vinland map, and of the channels by which they could have reached a workshop in Southern Europe (this assumes that the ascription of the manuscript to a scriptorium of the Upper Rhineland is valid).
The only parts of the design which fall outside the elliptical framework are the representations of Iceland, Greenland, and Vinland, in the west, and (less certainly) the outermost Atlantic islands and the northwest-pointing peninsular extension of Scandinavia. If this original was circular, the anonymous cartographera€™s elongation of the outline to form an ellipse may be explained by his choice of a pattern into which elements not in the original, notably his delineation of Greenland and Vinland and his elaboration of the geography of Asia, could be conveniently fitted, perhaps also, or alternatively, by the need to fill the rectangular space provided by the opening of a codex.
The Peloponnese and the peninsula in the southwest of Asia Minor are treated with the anonymous cartographera€™s customary exaggeration.
On the source of this farrago, which is in marked contrast with the relatively correct river pattern drawn in Central Europe by Bianco and the chart makers, it is perhaps idle to speculate; it seems to involve a confusion of the Oder, the lower Danube, and the Struma. Yet this section of coast had been laid down in very similar form on earlier maps; as Kimble puts it, a€?Cape Non ceased to be a€?Caput finis Africaa€™ about the middle of the 14th centurya€?, and a€?the ocean coast as far as Cape Bojador (more correctly, as far as the cove on its southern side) was known and mapped from the time of the Pizzigani portolan chart (1367)a€™a€™. Nor was the transference of the Prester John legend to Africa a novelty in the middle of the 15th century. Against the most northerly island is inscribed Insule Sub aquilone zamogedorum [Northern islands of the Samoyeds]; then in the center Magnum mare Tartarorum. It may be recalled here that there is nothing in the Tartar Relation referring to Greenland and Vinland. The four streams issuing from Eden, shown by Bianco as the headwaters of two rivers flowing west and falling into the Caspian Sea from the northeast and south, have disappeared from the Vinland map, in which we see only the two truncated rivers entering the Caspian from the east and south respectively. They appear, rather, to be dictated by the cartographera€™s need to lay down names where the design of the map allowed room for them. In point of date, Biancoa€™s atlas of 1436 is the third known work to show the Antillia group, and the fourth chart of the atlas names the two major islands y de la man satanaxio and y de antillia.
Its outline, on the east side, is deeply indented and in the form of a bow, the northeast coast trending generally NW-SE to the most easterly point, and the southeast coast trending NNE-SSW to a conspicuous southernmost promontory, in about the latitude of north Denmark; from this point the west coast runs due north, again with many bays, to an angle (opposite the easternmost point) after which it turns NW and is drawn in a smooth unaccidented line to its furthest north, turning east to form a short section lying WE. The island is divided into three great peninsulas by deep inlets penetrating the east coast and extending almost to the west coast.
This legend, the first part of it seems to be distilled from references to the defeat of a€?Nestoriansa€? by Genghis Khan and their diffusion in Asia.
The course of the river of the Tartars, as depicted in the Vinland Map, recalls Rubrucka€™s statement that the Etilia (i.e.
The Vinland Mapa€™s location of the name, in the extreme north of Eurasia, places Thule (as Ptolemy and other classical authors did) under the Arctic Circle. The name Magnum Mare was applied by Carpini and Friar Benedict to the Black Sea while Rubruck called it Mare maius. As the examples already cited show, the name Insulee Sancti Brandani (in variant forms) is commonly ascribed by chart makers to the Azores-Madeira chain.
Medieval mapmakers, from the 10th century (Cottonian map, Book II, #210) onward called the Island or Ysland (v.l.
This legend on Vinland Map, if it faithfully reproduces a genuine record, accordingly authenticates Bjarnia€™s association with the discovery of Vinland and adds the significant information that he sailed with Leif.
They also prompt the suspicion that missing sections of the original codex may have been illustrated by the other novel part of the map, namely its representation of the lands of Norse discovery and settlement in the north and west of the Atlantic. In a map of this form, drawn like the circular mappaemundi, on no systematic projection, we do not of course expect to find graduation for latitude and longitude, even if the quantitative cartography of Ptolemy had been known to its author. If Biancoa€™s world map be assumed to have resembled, in form and content, the model followed by the compiler for the tripartite world, we can however assess the performance of the final copyist by comparison of his work with Biancoa€™s map, so far as it takes us.
Bjarni, it was implied, had accompanied Lief on his first discovery of Vinland; Bishop Henricus, the Eirik of the annals, who was said there to have gone to look for Vinland, was stated to have found it, and at a different date. Some students have been reluctant to accept these propositions; the provenance of the Map had not been established, the nomenclature also presents difficulties, as does the representation of certain topographical features, in particular the accurate delineation of Greenland, a point heavily stressed by the editors of The Vinland Map and the Tartar Relation. For convenience of reference, this Bianco-type original, which has not survived, will be cited as O.
In Africa, Phazania must have been taken by the author of O1 or from Pliny or Ptolemy; and magnus fluuius (if not a coinage of the cartographer) perhaps from a geographical text of the 14th or early 15th century. The names for Iceland, Greenland, and Vinland, with the legend on Vinland, must, like their delineations, be held not to have been in O1. It must be noted that the textual content of these Books show no relationship with either the Vinland map or the Tartar Relation, but, instead, are to be seen within the context of all 32 Books of the Speculum Historiale.
These two explanations, taken together, may account for a further modification probably made by the cartographer to his prototype.
The outline of Spain is depicted with slight variation from Biancoa€™s, the Atlantic coast trending NNW (instead of northerly) and the north coast being a little more arched. Some have concluded that, if authentic, the Vinland map was not drawn primarily to illustrate the Tartar Relation.
The four longer legends written in Asia or off its coasts are all related, by wording or substance, with the Tartar Relation. Since the outline given to these two islands both in the world map and in the fourth chart of Biancoa€™s atlas is easily distinguishable from that in any 15th century representation of them, the concordance with the Vinland map in this respect is significant. Here we have at once the most arresting feature and the most exacting problem presented by this singular map. The approximation of the east coast and of the southern section of the west coast to the outline in modern maps leaps to the eye. The more northerly inlet is a narrow channel trending ENE-SSW and terminating in a large lake; the more southerly and wider inlet lies roughly parallel to it. The second part of the legend relates to the medieval belief that the Ten Tribes of Israel who forsook the law of Moses and followed the Golden Calf were shut up by Alexander the Great in the Caspian mountains and were unable to cross his rampart. The first to cross into this land were brothers of our order, when journeying to the Tartars, Mongols, Samoyedes, and Indians, along with us, in obedience and submission to our most holy father Pope Innocent, given both in duty and in devotion, and through all the west and in the remaining part [of the land] as far as the eastern ocean sea]. The cartographer has perhaps confused the Great Khan (Kuyuk) with Batu, Khan of Kipchak, whom the Carpini mission encountered on the Volga. Hence their identification with the Tartars and their location by Marco Polo in Tenduc, with a probable reference to the Great Wall of China.
Volga) flowed from Bulgaria Major, on the Middle Volga, southward, a€?emptying into a certain lake or sea . Members of the Carpini party were somewhat confused about the courses of the rivers flowing into the two seas, supposing the Volga to enter the Black Sea. These are the Azores, laid down in charts with this position and orientation from the middle of the 14th century to the end of the 15th, and the Madeira group. The Vinland Map is the earliest known map to move the name further out into the ocean and apply it to the Antillia group, the word magnce being added to justify the attribution and make a clear distinction from the smaller islands to the east. It might be said that the dominant interest of the compiler or cartographer lay in the periphery of geographical knowledge, to which indeed the accompanying texts relate; and such a polarization of interest is exemplified in the themes of the seven legends on the map. He emerges from this test on the whole creditably, for the outlines of the two maps are (as we have seen) in general agreement. Much argument has centered around the possibility that Norse voyagers might have circumnavigated and charted its coasts, or provided a written description of them.
The fact that, in regard to a few names or delineations, the Vinland map seems to show affinities with charts in Biancoa€™s atlas of 1436, rather than with his world map, may suggest that O1 was of Biancoa€™s, or at any rate of Venetian authorship. Sinus Ethiopicus could have been deduced from Ptolemya€™s text; Andrea Biancoa€™s connection with Fra Mauro, in whose map this very name is found, and his conjectural association with O1 lend substance to the possibility that this name stood in O1, although corrupted in Biancoa€™s own world map. This hypothesis indeed, while it must be tested by collation of other extant maps from which the prototype may be reconstructed, has (prima facie) some support both from the analogy of the cartographera€™s treatment of the tripartite world and also from the uniformity of style which characterizes all parts of the drawing, alike in the east and in the west, in those parts where we know, and in those where we suspect, a cartographic model to have been followed. Therefore, no proverbial rock has been left unturned in subjecting these manuscripts to all of the state-of-the-art technology and worldwide scholarly debate.
The Vinland map and Tartar Relation had become physically separated from the 15th century Vincent text and were later re-bound together as a separate volume in their present 19th century (Spanish) binding.
Some authorities speculate that possibly the link or actual reference to the Vinland portion of the map could be supplied in the missing 65 leaves. The northerly orientation of the map should perhaps be attributed to expediency rather than to the adoption of a specific cartographic model, for it enabled the names and legends to be written and read in the same sense as the texts which followed the map in the codex.
The latter, however, deserves credit for originality in his removal of the Earthly Paradise, an almost constant component of the mappamundi; for, as Kimble observes, a€?the vitality of the tradition was so great that this Garden of Delights, with its four westward flowing rivers, was still being located in the Far East long after the travels of Odoric and the Polos had demonstrated the impossibility of any such hydrographical anomaly, and the moral difficulties in the way of the identification of Cathay with Paradisea€?.
Here again we have plain testimony to the derivation of the Vinland map from a cartographic prototype, and to the character of this prototype. The a€?shut-up nationsa€? were also identified with Gog and Magog and with the Tartars, who were held to be descended from the Ten Tribes. In many 15th century charts the chain has (usually written in larger lettering to the north of Madeira) the general name Insule Fortunate Sancti Brandani, or variants. The alternative form Branzilio (or Branzilia), suggesting an association with the name of the legendary island of Brasil, is not found in any other surviving map. The chart-forms characteristic of Biancoa€™s style of drawing are not reproduced in the Vinland map; at what stage these disappeared we do not know, and they were not necessarily in the original model followed by the compiler. The historical statements about Vinland contained in the map, on the other hand, doubtless come from a textual source, as those in Asia and Africa can be shown to do. The result has been a polarization of many prominent authorities from many disciplines into three camps: the a€?believersa€™, the a€?nonbelieversa€™, and the a€?undecideda€™. Only through extremely fortunate circumstances did the ultimate reunion with this particular copy of Vincenta€™s manuscript occur, also in 1957, in Connecticut. The classical Insulae Fortunatae were the Canaries, the only group known in antiquity, and the association with St. The name Brasil, in many variants, was generally applied by cartographers of the 14th and 15th centuries (a) to a circular island off the coast of Ireland, and (b) to one of the Azores, perhaps Terceira; the variant forms of the name include Brasil, Bersil, Brazir, Bracir, Brazilli. Eric [Henricus], legate of the Apostolic See and bishop of Greenland and the neighboring regions, arrived in this truly vast and very rich land, in the name of Almighty God, in the last year of our most blessed father Pascal, remained a long time in both summer and winter, and later returned northeastward toward Greenland and then proceeded [i.e. All the major divergences, in the geographical elements of the Vinland map, from the representation in Bianco can be traced to its compilera€™s reading of the Tartar Relation or to changes forced upon him by the design adopted. These instances suggest that the draftsman of the Vinland map, as we have it, may not have been its compiler, but that the map may have been copied from an immediate original or preliminary draft (having the same content) by a clerk or scribe who was no geographer and did not have access to the compilation materials. Kemmodi) montes, where a borrowing from a classical text (such as Pomponius Mela), in which the rendering of the initial aspirate was retained, may be suspected; the form in the Vinland map could hardly have been derived from Ptolemya€™s. While the coupling of this name, in the Vinland map, with one from the Tartar Relation (Nimsini) may however mean that Hemmodi too came from a Carpini source, it is more likely that the cartographer was here trying to integrate his two sources. The general name Desiderate insule given in Vinland Map to these islands is not found in any other map; the only explanation we can hazard is that it may allude to the Portuguese attempts at discovery and colonization of the Azores from, probably, 1427 onward.
However, according to my reference book, even the Spitfire used 1.5 degrees wing twist to obtain good stall characteristics. The handwriting is similar in character to that of the manuscript and shows the same idiosyncrasies in individual letters.a€™a€™ The map was therefore probably prepared by the scribe who copied the texts of the Speculum and the Tartar Relation. The inner or western coasts of the three islands and the eastern coast of the mainland, fringing the Sea of the Tartars, have no counterpart in any known cartographic document, but are drawn with elaborate detail of capes and bays.
This river has many other very large branches, besides that of Senega, and they are great rivers on this coast of Ethiopiaa€?. Considering that this sea represents (so far as we know) the cartographera€™s interpretation of a textual source, it may be suspected that the outline of its shores was seen by him in his minda€™s eye and not in any map. I am using a modest taper ratio around 0.7 on the tip sections as I wish to avoid the need for wing twist. With this section, the 12% thickness has a slightly higher stall angle than 15% for the same Reynolds Number.

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