http://www.theenglishwarbowsociety.com/tudor-livery-arrow.htmlThat's the Society spec for the Livery arrow. The Livery arrow is an exact replication of the arrows found onboard the Mary Rose. The head comes from a find at Portchester Castle from the same period, and the fletchings are the most efficient shape and size when restricted to the 7.5" length that was determined via the whipping on the MR arrows.
Essentially, if you had to pigeon-hole a "medieval" arrow into one set of dimensions/materials, I think it would be roughly as follows:
Half inch tapered shaft of poplar, ash or birch - half inch at the shoulder of the arrowhead, with either a straight taper ("bobtailed") or late taper ("torpedo") to 3/8" at the nock end.
1mm thick cow horn insert at the nock end, inserted against the grain and reinforcing 2" of the shaft.
1/8" wide nock
7.5" fletchings cut in a straight triangle, or with the edge trailing "as nature intended", and cut around 1/2" high. Some arrows are fletched with 5/8", some with 3/4"
The fletchings should ideally be bound on with silk (or very fine linen if you have to) at between 4 and 6 turns per inch.
The head is the most variable element - you've got short stubby swaged Tudor bodkins for the later period, or Type 10 bodkins or lozenge-shaped plate cutters for slightly earlier (14thC onwards) periods. Avoid the fancy Hollywood hunting heads, with swept out barbs or swallowtails, and avoid the long needle-shaped bodkins as they were for a much earlier period.
That's a really basic, rough idea - each type of arrow has it's own specific details and dimensions, but if you were to make an arrow using the above guidelines, it would be quite clearly accepted as a "medieval war arrow."