Sorry, this should be a the electrical board. K

I assume this is an exterior wall, being 2x6. What climate? Why not just terminate at rimjoist level?

The reason I ask is I wouldn't want to remove 4" of insulation from the building envelope to accomodate a bath fan. I would also be concerned the moisture in the air would condense before reaching the roof.

I agree.
Terminate as close as possible using 4" round duct. If you like, insulate the duct with an insulation sleeve that's sold for dryer vents.

It is an interior non-load-bearing wall. It is a short section of wall, about 28 inches wide, with a hall closet on the other side. The DWV main stack already passes through one cavity. The adjacent cavity is wide open with no basement or attic obstructions. It is very close to the location for the basement bath.

I prefer to go through the roof because passing through the rimjoist would put the exhaust either near the front porch or under main-floor windows. Because of existing plumbing and ductwork, routing to a better spot along the rim would be more difficult than going up through the roof.

The house is in warm and sunny southern Michigan (a whopping 30 degrees F today, and bound to be warmer by next July).

Since you're in Michigan it will probably change to snow before it leaves the attic.

Why not use insulated flexible duct for the cold attic portion, at least? Then use either 3" or 4" round duct in the lower portion. Hold it up with pipe collars. If you did use pvc, you might want to mark it up a lot with a Sharpie so it's not confused with a plumbing vent down the road.

Before you run the vent up to the roof consider the down sides to this idea.

When your taking a shower the bathroom atmosphere will typically be 75 to 80degF with 80 or 90% humidity. As that moisture laden air is forced through the duct the moisture will condense to liquid on the duct wall and run back down to the bathroom ceiling, flooding your fan and dripping through the ceiling causing untold damage. Now you could attempt to prevent the condensation by installing insulation on the pipe but that is is fools errand as well. Keep in mind that when the fan is not running the top of the vent is open to atmosphere, therefore the cold outside air will settle down the interior of the pipe and cool the pipe wall, which would further increase the rate of condensation when the fan runs. (Insulated ducts are used to prevent the air surrounding the outside of the pipe from condensing on the pipe wall then allowing the condensate to drip to the ceiling, but it will not prevent condensate from occurring inside the pipe.)

Now what are the downsides of running the pipe horizontal and terminating under the window or near the porch? Aside from the fact that the vent would be visible from the outside and occassionally a bit of steam while someone is taking a shower? Do you honestly think anyone observing your house from the street would really care? The upside of running the duct horizontal is that the horizontal section can be pitched downward toward the termination point so any condensate that might develop will be harmlessly discharged outside.

I like the logic,LazyPup. Also I hate putting any holes in the roof is there is any possible way to avoid them. I'm in the northern part of the country too and last year there was enough snow on my roof that the 2 vents were buried.

In the past I have had many homeowners ask me to vent run there bathroom and laundry dryer vents through the roof and I politely explain to them that i will only do so it they will sign a waver of liability for condensate moisture damage.

Good idea.

Would the basement bath really be significantly worse that 1st floor baths vented to the roof?

I was in the attic of a townhome (10 yrs old, very large development in South Riding, VA). Their bath vent ducts were extended (no insulation) up to just under the ridge, presumably so the moist air would travel out the ridge vent. Just an observation. Wonder how typical that is.

Around here one can buy a newly built house with this set-up, but home inspectors identify flag them as issues to remedy for the resale.

Thanks for the suggestions.

Text communication being what it is, I may have been misunderstood on a couple of points. The reason for not wanting to vent near the porch or under windows has nothing to do with appearance from the street, but rather what I thought was a more obvious objection to moisture and odor wafting in through open windows during the warmer months, or making the porch a less enticing place to relax or entertain when the bath is in use. I confess to being a bit fussy about details, so if I did go through the roof, I wanted the vent to be in the same line as the other two bath vents, which are a couple feet apart in the same shingle row, thus the offset in the attic.

Another Q/A site suggests that the worst two places to vent a bath is 1) into the attic, even if under a ridge vent, and 2) under a vented soffit. The site "expert" instead recommends going through the roof, though the bath in this case is on the highest floor.

The two existing baths have vented through the roof for many years with no apparent issues. The runs are relatively short, the duct is insulated and the vents themselves have dampers. Enough warmth seems to escape to keep snow clear around the vents.

The clothes dryer also vents through the roof as the alternative would be to vent directly out to the front porch, which would create a nice steamy fog on cool days, not to mention the moisture rising up through the porch ceiling vents. Again, no apparent issues after years of use.

Having said all of this, I appreciate the concern about running a duct from the basement to the roof. If I can find a path to an acceptable point along the rimjoist, I'll take it.