Acts 27:4

And putting to sea from thence, we sailed under the lee of Cyprus, because the winds were contrary. And when we had sailed across the sea which is off Cilicia and Pamphylia, we came to Myra, a city of Lycia.

The winds were contrary ... The route to Rome lay in a westerly direction, but the winds coming from almost exactly the direction they wished to go forced them to sail northward. It was late August or early September, approaching the time when navigation of the Mediterranean would no longer have been safe for ancient sailing vessels. It was urgency from this consideration that probably influenced Julius to take passage with his company on a ship going only part of the way.

Myra ... was "important as one of the great harbors in the corn (wheat) trade between Egypt and Rome,"[12] and Julius' probable anticipation of finding a ship sailing directly to Rome was quickly fulfilled at Myra.