Longships were/are built by 'rules'- longships are only one model of the different hulls that could be built by these rules.
There were around 5/6 sizes of boat- 3 main ones (the scandinavian names escape me now) a one man canoe size vessel that was used for single fjord trips between villages, most rowed, some with a sail. Next there were the 30-40ft single sail 6-8 man rowed vessels that were used for inter-fjord trading etc. Last, but by no means least there were the longships- usually around 70ft in length with around 80 rowing.
The different sizes were all 'scaled' because of the planking 'rules' the 'vikings' (in commas because these rules were used alover scandinavia with slight diferences) used, for example the 40ft boats would use a 7 plank design, flat on the curve with a pronounced 'v' to the bottom of the keel to impeed windage, however, the little fjord boat would only use 5 planks with a flat bottom for skimming over the slate and granite beaches of the fjords.
There are a few surviving ships that could be copied- the 'Ostberg' ship being the best preserved, however experts differ on what this ship was really built for- most seem to say she would never have gone to sea and was purely an elaborate burial for a rich lord, however it follows the same rules so could be scaled to whatever size you wished.
Also, the same shipbuilding techiniques are still used in many scandinavian boatyards, using clincher techniques without frames (some of the only boats that are designed to flex with waves as this allows the ship to sit lower in the water through big waves and keeps the COG lower down) and the same planking shape and sizing techniques that the vikings used- literally the scale calculator used cannot be dated as it's just 'always' existed!!!
Good look, I hope you build a decent sized model as there aren't many around, a cheap boat to build though- all pine!
Greg