We have all seen artist’s paintings or movies of the crucifixion. These usually draw on traditional art. The thing I notice about them is that they tend to put Jesus up very high on the cross. This is probably a devotional interpretation that sees the crucifixion in light of his later exaltation.
But the cross was a common Roman means of execution. From both ancient texts and archeology (we have found the bones of people who were crucified), we can today reconstruct what it might have looked like. The vertical piece was not very high. The condemned carried the crossbar to the scene and then they dropped it into place.