I'm installing a new kitchen, and now need to plumb in the kitchen sink/dishwasher in their new locations. Due to the location of the sink, I need to route the drainpipe under the floor a distance of about 9m, assuming one right-angle bend. I also need to tee into the outside stack lower down than other existing connections, in order to get enough of a fall. Luckily I do have a lot of space under the floor, so I should be able to have a reasonable fall on this long run of drain. In order to have such a long branch, I believe I need to have a ventilation pipe and possibly use a larger diameter pipe than the standard 40mm. I'm also aware that I can't tee into the stack lower than 450mm above invert of the tail of the bend at the foot of the stack . Since the new sink location is by the side wall (drain is on back wall) I could perhaps take the ventilation pipe out the side wall and up that wall, right? This would be an easier to implement routing for the pipe. Are there any other solutions to this long run that don't require a ventilation pipe? I would appreciate any advice/comments.
Here's a diagram (viewable with monospace font)
SIDE OF HOUSE
x--wwwwww-------------- [sink] | . | . | . | . |----- . | . | . | BACK OF HOUSE . | . |----| . |o ...........|.
-| external walls . proposed drain route o existing stack x possible ventilation pipe location? w window