about the ship art of the bayeux tapestry, it should be noted that the tapestry is an example of early medieval representational art. it was an early attempt at 'realistic'' art, which includes foreshadowing. the quality of such art, at the time, was very poor. much like MS I.33, which often shows hands on backwards, the art of the tapestry shows a lack of understanding of the techniques that show perspective. if you look at the art that you posted, you will note that it is supposed to depict ships running before the wind, which 'shortens' the appearance of the width of the yard because of perspective. thus, if viewed straight on, the yard would appear longer.
secondly, look at the sail, it was this very art that made some speculate that the vikings may have used lateen sails because the artist's attempts to depict perspective in the sail ( seen from the edge of the sail ) reduces the foot of the sail to nearly a point, making it look as if it might be some sort of a three sided sail. furthermore, if you wish to use this art as a realistic indicator of dimensional proportions, the sail, itself must have hung down a few yards below the water line, when there was no wind in it. look how long it is, like a bridal train. this is about the worst period representation of viking ships that you could have found. it is totally unreliable as a gauge of proportions.
now, compare this actual viking age art.
notice that the sail, in each representation, from the crudest to the most intricate, indicates a sail that is longer than it is tall. in fact, in each image, the yard is nearly the length of the ship. for all of this art, from different sources, to depict similar proportions can not be a coincidence. in none of these images, is a tall narrow sail depicted.
beyond the evidence supporting the sail used on the reproduction, from the site i linked to, there is the unarguable performance evidence of replicas built with the usual tall, square sail that is attributed to the vikings ( the unsupported sail shape you are willing to accept as historically accurate ). the sailing performance of these vessels, with even this type of sail, far exceeds what you claim could have been possible.
note that, in the following video, depicting smaller versions of longships being tested for the qualities of various hull and sail variations, that the yards are all, to some extent, angled down in the front, much like a dipping lug, when sailing to wind. we know that lug sails can sail efficiently to wind. notice the tight luff on these sails; nothing like the loose luffs you often see in the tall ships of later periods. the way the vikings set their sails, including the use of the beitas, gave them much better control over sail shape.
watching that video, it is interesting to note that the sailing qualities demonstrated by these boats is not at all primitive or crude.
this next video shows the beitas, up close, and shows how the vessel was tacked. you get a really good view of the sail shape. the sail, on this boat, was woven using techniques evident from sail fragments that have been found. it still has the tall, narrow shape because only fragments of sail have been found; nothing to indicate actual shape. good informational video. pay attention to the steering oar. i will mention that later.
i apologize for the link instead of the video. despite my best attempts, i can't get this video to post like the others. it's worth the effort, to watch, though.
this next video shows, again, the beitas and the control over sail shape that was achieved using viking age methods, even with the tall, square sail. at one point, while it is sailing, you can clearly see the flag, which is blowing in the apparent wind. it is obvious that it is sailing close hauled and not on a reach.
this last video clearly shows the ship sailing close hauled. at 4:22, look at the wind vane on the prow. it is clearly indicating that the boat is not on a reach, but is close hauled.
now, compare the angle of sail trim to a 'modern' square rigger.
at 1:00 in the video, you see the ship sailing 'close hauled'. note that the square sails are not trimmed in nearly as tight as on the viking ships, showing that the vessel is not pointing as high. it can't because the sail shape is not as controlled as on the norse ships, which also have hulls that are far more efficient, on the wind.
finally, the under water 'foils'. it should be noted that the viking keel is not straight from stem to stern, as many think. it is deeper in the middle and is shallower at the ends, to help in turning.
also, although they knew nothing about lift, they carved their steering oars in a foil shape. what's more, they understood enough to know that the steering oar being off center would effect the handling, so the foil shape, of the 'rudder' is asymmetrical, to account for this.
the viking ships were far more sophisticated than most people believe, and had/have far greater performance than modern sailors will be comfortable to admit. already, replicas have circumnavigated the globe numerous times and the seafaring accomplishments of the vikings wouldn't be equaled for a few hundred years. the first european born on this continent was Norwegian, hundreds of years before columbus set sail.
if you look on any sailing blog, you will see someone who wants to bash the sailing qualities of these boats. i have seen it a lot; not just in this thread. it must be remembered that much of what the general public 'knows' about the people and technology from these earlier times is wrong; little more than urban myth, much like the idea that vikings wore horned helmets and crude animal furs or the idea that their swords were heavy, poor quality bashing weapons.
if you mention the weatherly quallities of viking age vessels, you often get jokes about '40 vikings rowing up wind'. however, viking war ships, which often had 80 men or more, didn't use their oars due to lack of windward ability. they used them for stealth. a big sail is very visible when you are doing a quick surprise raid. during such activities, the sail and mast would be lowered and they would row in to shore. in comparison, the knarrs/knorrs that were the work horses of the viking age, boats that were used to cross oceans, had only 4 oars even though these were not small vessels. they didn't row up wind. they sailed up wind. the oars were only for moving around the dock. such vessels were lightly manned and had no use for stealth, so they didn't need a lot of oars.