Thinking about it and in the name of aesthetics, it would look best if the fascias were level.
This would mean that the joists would sit at the same level as the fascia and not up by the existing wall plate. It would still involve lay boards up the roof in order to take the flat roof material up the slope.
No matter how you tackle this the water run off will be considerable and that a lot of care will need to be taken when building the roof.
Your image shows the deck of the roof actually higher than needs be.
The (horizontal) part of the deck only need to be in line with the fascia top, but lay boards (up the roof pitch) will need to be fixed so that they weather the lower part of the rafters.
You will need the roofer to take great care when fitting the roof light.
The flat roof will slow the water down before it discharges into the continuous gutter.
A flat roof is not flat, so done properly there is no ponding
Depending on where the existing fascias are in terms of frame heights, you could end up with a low ceiling and it looking cramped and "wrong", unless the roof is raised above the fascia level
yes flat roof -im no builder or anything just ive a flat roof on my bungalow in a traingular shape - it recieves rainwater from the eaves if you will from both sides and the gutterings lie on top of the roof - needless to say in the heavy rains i seem to have a full gutter refusing to drain resting on the roof - ive really bad leaks and a big bucket in the poorch
not sure if the guttering can be more sloped to minimise hope this helps a liitle bit
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