When I built my Scot’s I researched this and found no real information for the Scottish army spear or pike lengths in the 14th century but did for the 15th. Most research articles seem to think somewhere between 12 and 18ft with no prescribed length according to Carrick until 1471.
Looking at historical research in books the first mention of a long spear being referred to as a pike is from 1290 in the county of Zeeland . This law states that whoever carries een speere of een pieck (a spear or a pike) without a 'spear-iron' (spearhead) of 6 thumbs (6 inches = 15,24 cm) in length, shall have to pay a fine and will have his spear or pike confiscated. The two weapons evidently were very alike, very long sticks that both were equipped with the same kind of spearhead. This means their difference can only be explained by differing lengths.
We have two sources that prescribe pike lengths in the 14th century. The first can be found in an article by Müller-Hickler from 1906 where he writes that the citizens of Turin in the north of Italy had to have pikes of 18 feet in 1327. The second is a law of 1390 from Bremen in the north of Germany, summing up what armour and weapons the inhabitants of the rural area around the city were obliged to own at all times. It says their pikes should be at least 16 feet tall.
In comparison, the prescribed pike length for the Scots in 1471 was 6 ells, or 18 ft 6 inches (parliament act 44p) . The Breton and Burgundian troops in 1473 ordonnance was 16 feet plus the pike point, while the city militia of Utrecht in 1521 had to have 18 feet, just like the length prescribed a hundred years later in the Dutch Republic.
With the above information we now know that pikes measured in between 12 and 18ft (4 and 5 meters, but mostly between 4,5 and 5 meters in length) and contained pike heads of ideally 15 cm in length.
So converting
12ft to scale is 6,5cm
14ft to scale 1/56 is 7.6
16ft to scale 1/56 is 8cm
18ft to scale 1/56th is 9.7cm
18.6ft to scale is 10.1cm
Hope that helps
Cheers
Matt