I have yet to construct one of these, but have tried to think about the process. These types of trusses look awesome in my opinion. It seems that they are very strong (the arch) and provide more open space among second levels.

Where I get stuck brainstorming these is during lay-out. Supposing that you have not had a computer design program give you all your neccessary information, how do you find it. I guess if you have naturally curved trees or timbers this would help and you could scribe the truss (and cutting curves out of straight pieces would work as well). On the other hand, how could you lay-out with a different method (maybe mill rule).

Would you find the properties of an ellipse and transfer to your plans and lay-out? The properties of an ellipse seem complicated when finding an arcs length. Furthermore, would a elliptic arch withstand forces other than downward compression? Instead could you only use a semi-circular arch? It seems that if you could only use the semi-circular arch you would constantly battle with apex, span, and pitch.

Could you use the straight edge of your timbers (outside and top faces) to lay-out say.... mortises for the rafters? Where should your reference lie, (lye?)?

I'll stop because that's a lot of questions and my head hurts good. Anyone with any experience on these that care to share their thoughts?