"... why the steep angle on the yard?"
Andrew keeps asking interesting questions. The jaunty and dashing look of Arne’s high-peaked sail designs has a practical reason, as well as its good looks. Two practical reasons, actually.
The first is the harmony between yard angle and mast balance (that is, the percentage of sail area ahead of the mast). There is quite an interesting relationship between the yard angle and the amount of balance given to a sail, that is, if we are considering “conventional” western junk sails, with conventional soft mast parrels and conventional halyard arrangements. (There are some exceptions). Again, it is a matter of geometry, and it is better to leave sail design to people with experience such as Arne, Slieve, Paul Th, David T etc and I will venture into this area only to answer the question from a merely geometric perspective.
Paul Th once gave us a diagram which shows that relationship between balance and yard angle, and here it is again.
For a given mast height: the greater the balance, the lower the yard angle should be. The lower the balance, the greater the yard angle should be.
Arne summed it up in a reverse way: it all comes down to what he calls “halyard angle”, that is, the angle made between the mast and the halyard (the line which runs from the masthead to the sling point, approximately half way along the yard). If the yard angle is wrong for the balance given to the sail, then the halyard angle will be too great. Why should the halyard angle matter? If it is too great, then the effort required to raise the last metre or two of sail will be much greater, seriously, and I know that from experience. Another issue will be (for a similar reason) that the sail will require more effort on the part of extra hauling parrels etc to get it to sit and set nicely. Harmonising sail balance (the amount of sail ahead of the mast) - and yard angle - in theory, because of simple geometry, should result in a better-behaved sail.
You will note the low yard angle of the high balance SJR sail (at least, the beautifully behaved Amiina SJR created by Slieve). Not as pretty as the Johanna sail, but exceptionally well-behaved, (and the look is an acquired taste, if you ever get to try one).
There are always exceptions. David Tyler’s Weaverbird wingsail has a moderately low yard angle and yet very low balance, but that sail follows a different set of rules and the sail does not rely on the usual soft mast parrels. Another rule-breaker is Steve Dawe’s dazzling Serenity sail.
This has a very high halyard angle – but it has slippery, rigid mast parrels, and is thereby able to break a number of rules. In the upcoming magazine you will see some sails with horizontal yards – but they have different halyard arrangements.
But the general rule, for most western type junk sails with soft mast parrels and a conventional halyard arrangement is: the higher the balance, the lower the yard angle and vice versa.
The other reason: there may be some aerodynamic advantages in the low yard angle and my own preference is the high balance/low yard-angle Amiina type of sail because of certain behavioural characteristics, which can be argued. But the lower balance, high peaked sail has its advantages too – one of them being more sail area for a given mast height, and that's the other advantage of the Johanna sail type. At the end of the day, a cruising boat should carry the greatest sail area possible, combined with the simplest and quickest ability to reef. The high peaked Johanna sail gives the greatest amount of sail area, and being a junk sail, it is easy to reef too.
(Arne, would you consider moving that mast back aft another six inches, and bolstering the cabin front in way of partners? Or, failing that, while it is still legal to dream, or imagine, what about having a little sailing dinghy as a tender, and when the dinghy is being towed or carried on deck, plonk its simple little free-standing mast into a socket right behind (or right beside) the rudder stock, and sheet its little mains'l to the stern quarters, try to do away with that boomkin. There wouldn't be much more than a day's work in that, using a second-hand Optimist rig or something even simpler.)