I did end up taking off the tent canvas last night and I got a good night’s sleep as a result despite the wind. The strong winds and rain continued today and will carry on through the night tonight. This gave me time to check the geometry of the roof and work out the point at which the principal rafters should hit the tie beam and the height of the king post.
These calculations took me a couple of hours as I needed to dredge up my O Level maths. The calculation sequence is shown below. If you want to know the actual calculations involved please ask in a comment to this blog post and I will post them. The key thing to note is that in order to achieve the 45mm gap between the underside of the softwood rafter and the top face of the green oak principal rafter, the top face of the green oak principal rafter needs to hit the top surface of the tie beam 182mm in from the outside shoulder of the cog joint.
I used this information, together with the actual distance between the outside edges of the cog joints on the tie beam (4306mm) to calculate the height of the tie beam. The calculation sequence shown below indicate that the distance between the top of the tie beam and the top of the king post should be 1654mm.
The next job will be to lay up all these elements of the truss using these calculated values to check it all works.
[Addendum. This is how things worked out: Shaping the Roof]