My reading of formation changes on page 21, coupled with the British national differences, p44, suggests to me that this would cost half a move in open terrain and a full move in difficult terrain. Although not specifically shown in the formation changes section, it is a change from line to column so presumably is subject to the same rules.
You've got it. The unit ends the move in a different formation to that it started in, so a formation change has taken place. So half a move to turn into a column, then they can move off half a line move (10cm). Movement during a turn when a formation change takes place is always at line speed.
Note the unit could actually move sideways 15cm (deducting a quarter of a move as per the National Table), whilst still facing to its front. But then on the next move it could only move another 15cm to the side, whereas if it had changed to column it could now move off 25cm. So it depends what you want to do in the longer term.
Of course, it is perfectly arguable that to move sideways some kind of formation change is probably taking place during the movement. The unit wouldn't just sidestep across the table. This is one of those cases where simple movement rules have been prioritised over what some might see as historical accuracy or a strictly logical approach. The point is, it saves a lot of fiddly rules and makes almost no difference to the game. Overall, it is surprising not how cumbersome SYW units were, but actually how well reasonably well-drilled units could move around the battlefield and carry out the various basic evolutions. It was, if you think about it, what most of their training was about.
Thanks for the replies - I just wanted confirmation because it's not explicitly stated in the rules, (it's difficult to cover everything in rule sets). Yes, I appreciate that any movement is at "line speed" when changing formation and that you could move sideways at a reduced rate. However, we've found that when you get to the 'messy' part of a game with units all over the place, carrying out a formation change as I've described is sometimes preferable.