Now that's interesting, because both I and the joiner who will be building the structure had the impression that all the load was carried at the front, in that fashion. Our original design had no new purlin at all, but simply interleaved the new dormer rafters through from the back to the front of the roof. However, *two* structural engineers have told me that this is *not* the case, and that the load will also tend to push the other side of the roof out if a new purlin is not inserted. Hence the revised design with the new purlins.
I note the wikipedia definition of purlin, linked to above:
"In timber roof construction prior to the introduction of trusses, under purlins were used to support rafters over longer spans than the rafters alone could span. Under purlins were typically propped off internal walls. For example, an 8"x 4" under purlin would support the center of a row of 6"x 2" rafters that in turn would support 3"x 2" roof purlins to which the roof cladding was fixed."
So perhaps we have a difference of terminology. My existing 8 x 3 purlins ("under purlins") support 3 x 2 rafters at 400 centres, iI.e. they "support rafters over longer spans than the rafters alone could span" The rafters span nearly 5 metres, at a 45 degree pitch. The purlins are clearly taking a considerably load, as they have bowed. Perhaps if you had considerably more substantial rafters, you wouldn't need purlins in this role. As it is, my purlins support the rafters at just below the mid-point of their span, and transmit load to the gable end walls, and to load-bearing built-up ground floor walls in the middle of the house. As I'm cutting through these purlins, they need to be replaced with new purlins to take that load. They'll be higher up, where the dormer roof joins the existing roof.
I agree that you should work out your design before taking it to an engineer. I had four different plans, and after discussion I settled on the one that was technically easier to achieve. I'm sure the actual dimension of the purlins is over-specified, but the need for them in the first place is not.
So my advice would be to get a structural engineer in - you'll need Building Control in order to convert your loft, and if you don't come armed with professional calculations, they're likely to insist on a certain amount of over-engineering in any case. But your question concerned design, and the first thing you need to know is what is feasible.
Regards Richard