sin and carbon 14 dating?

A little off-topic from dating, but one thing that casts doubt on the shroud to my mind is that it shows the conventional long-haired hippy Jesus of medieval iconography. But St Paul wrote (1 Corinthians 11:14): He would hardly have written that if Jesus had long hair as depicted on the Shroud.Also, the face looks too old, to my eyes anyway. Traditionally, Jesus was 33 at the time of the Crucifixion; but if we ignore that and put his birth as early as possible (4 BC) and his trial under Pilate as late as possible (36 AD) that still doesn't make him as old as the guy on the Shroud looks.