Sereno, the OP stated it's a 2004 logan straight load, if that helps.
OP - what is he scraping his knee on? Any idea? Is he tied during transport? How wide is the trailer/stall?
If it's a double trailer, then he doesn't have a wall on the right side of him to scrap against, hence only the left side scrape. This may not have anything to do with turning at all. Regardless it's still a concern -- possible that turns are made sharply and quickly throwing him off balance? Or starting and stopping too quickly? Are the roads very rough?
I agree -- pics of the trailer interior might be helpful.