"As the crow flies" is itself becoming archaic, but it has a companion phrase that is even less-frequently heard. "As the fox runs" refers to the distance that a terrestrial creature would have to travel to reach a certain destination.

How far must I travel from here to reach the shire?

It's but a short distance as the crow flies. But between us lies the forest of peril, treachery, and GTKY nodes, so it will be a journey of several days as the fox runs.

Sometimes the fox is replaced with a deer or a wolf.