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Here's how the royal cubit really originated. They took a Nippur cubit and divided it into 28 instead of the normal 30 fingers. That 1/28th of a Nippur cubit then became the Egyptian finger (or digit). Simple as that. 40 of those fingers made the diagonal of a royal cubit square. That's why Petrie found that the Egyptian digit was not evenly divisble into a royal cubit. He correctly deduced that it was 1/40th of the diagonal of a royal cubit square but he still didn't know where it originally came from.

So there is the true origin of the royal cubit. Since the Nippur cubit was 518.5 mm in 2650 BC, known because a copper alloy Nippur cubit rod was found, we know that 1/28th of that would be 18.51785714 mm. Multiplying that by 40 yields 740.7142857, dividing that by sqrt 2 gives the side of the square as 523.7640944 mm, which converts to 20.62063364 inches. This, then, was the true length of the Egyptian royal cubit in the 4th Dynasty. The mean side length of the GP is 9068.8 inches, which would be 439.7924991 true royal cubits.

Here's a quote from Petrie;

"As I have already pointed out (Ind. Met., p. 56), the cubit and digit have no integral relation one to the other; the connection of 28 digits with the cubit being certainly inexact, and merely adopted to avoid fractions. Now these earliest values of the cubit and digit entirely bear out this view; 28 of these digits of .727 is but 20.36 ± .06, in place of the actual cubit 20.62 ± .01. Is there then any simple connection between the digit and cubit? Considering how in the Great Pyramid, the earliest monument in which the cubit is yet found, so much of the design appears to be based on a relation of the squares of linear quantities to one another, or on diagonals of squares, it will not be impossible to entertain the theory of the cubit and digit being reciprocally connected by diagonals.

A square cubit has a diagonal of 40 digits, or 20 digits squared has a diagonal of one cubit; thus a square cubit is the double of a square of 20 digits, so that halves of areas can be readily stated. This relation is true to well within the small uncertainties of our knowledge of the standards; the diagonal of a square cubit of 20.62 being 40 digits of .729, and the actual mean digit being .727 ± .002. This is certainly the only simple connection that can be traced between the cubit and digit; and if this be rejected, we must fall back on the supposition of two independent and incommensurable units." [www.ronaldbirdsall.com]