And when it was decided that we should sail for Italy, they delivered Paul and some other prisoners to a centurion of the Augustan Cohort named Julius. 2 And embarking in a ship of Adramyttium, which was about to sail to the ports along the coast of Asia, we put to sea, accompanied by Aristarchus, a Macedonian from Thessalonica. 3 The next day we put in at Sidon. And Julius treated Paul kindly and gave him leave to go to his friends and be cared for. 4 And putting out to sea from there we sailed under the lee of Cyprus, because the winds were against us. 5 And when we had sailed across the open sea along the coast of Cilicia and Pamphylia, we came to Myra in Lycia. 6 There the centurion found a ship of Alexandria sailing for Italy and put us on board. 7 We sailed slowly for a number of days and arrived with difficulty off Cnidus, and as the wind did not allow us to go farther, we sailed under the lee of Crete off Salmone. 8 Coasting along it with difficulty, we came to a place called Fair Havens, near which was the city of Lasea.
9 Since much time had passed, and the voyage was now dangerous because even the Fast  was already over, Paul advised them, 10 saying, “Sirs, I perceive that the voyage will be with injury and much loss, not only of the cargo and the ship, but also of our lives.” 11 But the centurion paid more attention to the pilot and to the owner of the ship than to what Paul said. 12 And because the harbor was not suitable to spend the winter in, the majority decided to put out to sea from there, on the chance that somehow they could reach Phoenix, a harbor of Crete, facing both southwest and northwest, and spend the winter there. (Acts 27:1-12 (ESV)
Paul advises that the voyage will not be a good one, but the centurion doesn’t pay attention to him. Paul wasn’t inexperienced in travel and does note that he himself had suffered shipwreck three times. Yet it would make sense to listen to the ship owner and pilot.
I don’t know what to read into Paul’s perception. The truth is that the sea was rough on boats at that time of year, and everyone knew it. Yom kippur falling in October, there are many storms. So Paul could just be going off of common knowledge and knowing that travelling at this time of year wasn’t a good idea. But no one wanted to stay in Fair Haven. On the other hand, it could be Paul prophesying. In any case they go and Paul proves prescient.