If the basement-directed duct is going to run both horizontally and down, your concept that the framing is like a window is inaccurate; It will be a "7"-shape gap in the framing. The "sill" of the "window" opening will be interrupted where it turns down, so there will be no continuity of framing there from floor to ceiling. It's like a short/wide window, but with the jack and king studs removed from one end. That makes it an unstable form.
The other problem is duct sizing. An 800 cfm fan may call for an 8" or 10" round duct. I don't think even a 4x16 is an equivalent to an 8" round. So unless you downsize the fan you'll be throttling it with an undersized duct.
I would rethink it.
Casey

The area of a 8" duct is around 50sqin. The area inside a standard wall cavity with 16" centers is around 50 sqin. I think to pull this off you'll need custom ducts and transitions made. I believe that making a narrow rectangular duct like this will cause a LOT of restriction to the air flow. That is, it will not flow like a round 8" pipe.

A basement directed duct would go straight down between studs. I might reposition one or two of the studs. The horizontal option would be just like a window frame high up on the wall, not a "7", but a rectangular area containing a duct that would have the area required. I somewhat misspoke: the duct does not have to go up AND then over. And the load of this wall would strictly be the hood and four feet of wall cabinets on each side of it. Structurally, the cabinets would bridge the frame. The cabinets go flush to the ceiling and are being custom made). The ceiling is the second floor and the wood is 2-1/4 ship-lapped wood with plywood on I am doing the rest of the work...

A 14.25" X 3.5" area (between studs), is equal to an 8" diameter duct's area. Recommendations I have seen call for a 6"-7" diameter duct for 800 CFM airflow. I am thinking of using a 900-1100 CFM variable speed fan.
I'm no expert; that's why I am asking for advice. I appreciate yours. It has made me realize a few things.
I worry about airflow noise as it goes out of the hood, turns and goes into the wall. However, I believe noise is generated from velocity. If I go bigger than I need in the duct area in the wall, and cut a bigger opening in the back of the vent hood to match the area, the velocity should drop in that area. I can neck it back down before it goes into the remote fan. I have some sheet metal working tools to cut the hood with.
Does anyone see a problem with that?
I see Weedmeister is saying the area is as I am saying.I can easily have 24 inches or more between studs. 24" between centers equals a 10" diameter duct.

To clarify, I meant to say, "with plywood over it." It is a "Deck" house. This is the most decent representation of the ceiling (floor for second story), that I can find: http://www.deckhouse.com/deck_house/photo_gallery/default.cfm?showProj=420&viewType=2&viewSet=&viewBy=1
I cannot penetrate the ceiling.
This is basic design. http://share.shutterfly.com/action/welcome?sid=1AZsmLRm0Ys3-g
I would like for all four doors (not just two, as shown), above the hood to be glass and the cabinet space fully functional.
I estimate the horizontal duct run to be 5 feet (no bends), and the vertical down to the basement and out to be 12'. The basement seems better because I won't have a fan hanging off the wall outside. I'm suspecting having the fan in the basement would be quieter.

Supporting your wall cabinets is one challenge, if you have a duct going horizontally through the wall. A challenge, but not a deal breaker. It is true that a rectangular duct is less optimal than a round duct, but it's not a deal breaker. You can make it 4" by 16" or you can make it much larger. Getting someone to bend galvanized sheet metal is not a big challenge. Buying an inline fan is not a challenge. Building a canopy is a design challenge because you have a free hand to do it any way you want. The noise of air moving through a quarter turn bend is not a big noise. Your plan is fine.

I had a rectangular duct built to fit a stud cavity. I left the stud cavity open all the way down to the countertop, so it looks like a big niche in the wall. It's the exhaust opening, but guests don't know it. (Galvanized steel is not the visible surface.)

In my case, the fan made a hum noise when variable speed controls slowed it down, so I put a 3 speed switch on it and put the variable speed control on my bathroom fan (another inline one, much farther from the opening).

I thought the noise, or lack of noise, was because 3 speed switches are able to match power factor completely (phase of AC), but variable controls might not. I gave up trying to understand it when I received an email saying the fan I got was ".... PSC. Our speed controls are voltage reducing, thus causing hum from slowing the fan down. ...."

hth

This is a case where availability of the often unavailable fan curves would help. (Fan curves show, among other things, the flow rate versus pressure drop across the fan.) What is needed to keep flow up through a more restrictive path than typical is a fan that can meet the desired flow at a higher pressure loss. Often, this can be obtained from a higher overall flow fan, but this is not a "given." Some blade designs can yield high flow when unrestricted but not with modest pressure loss.

Fan curves are available from several suppliers, including Broan, Fantech, Soler & Paleu, and, with some effort, Wolf (some spellings here may be off base). It would seem best to choose a fan that can meet your baseline flow at "several" tenths of an inch of water pressure drop. With inline being an option, it should be easier to meet this requirement. Fantech may provide useful advice here.

"Several" is difficult to remotely guess at and should be evaluated using HVAC tables established for the purpose. Very very roughly (and mainly illustratively), you might need a tenth for negative house pressure unless you have a make-up air system, a tenth for the hood baffles, a tenth for adequate area ducting, a tenth for rectangular over circular duct, and maybe a tenth for every abrupt direction change. This would compare to only the first three tenths if one had a simple straight shot to the the roof configuration.

kas

Can't you vent straight out a wall after taking a 90° bend at the top of your cabinets? Surely there's an exterior wall closer than venting down through a basement! Post a diagram of your kitchen with the exterior walls indicated and we'll see what else can be figured out. The vent could also take a bend or two to run through an upper floor closet and out the roof. Both scenarios would be MUCH more preferable than the convoluted and expensive setup you are contemplating. This is the point you get the professional HVAC person out there and let HIM make the suggestions as to how to vent externally!

Perhaps this will help clarify my first choice of solutions.
http://share.shutterfly.com/action/welcome?sid=1AZsmLRm0Ys2EF
OR http://share.shutterfly.com/action/welcome?sid=1AZsmLRm0Ys2EU See the descriptions! I can't go out the back of the wall because there is a hallway there. Again, there is no way I can go vertically.

I think the final transition could be a stock piece of duct. I anticipate using 8" for that, into one of these wall mount fans: http://www.fantech.net/kitchen2.htm OR http://www.greenheck.com/media/pdf/catalogs/SeriesC_catalog.pdf (model CW-095G or D).

I really appreciate all the opinions I am getting and thank you all for the help.

You can find some excellent HVAC calculators at the link below.

A metal duct in the rectangular stud bay space of 3.5" x 14.5" has the airflow equivalent resistance per foot of a 7.35" round duct (assuming both are made of the same material).

According to the calculator, if you try to push 800 CFM of air through this duct it will need to move at a velocity of 2752 feet per minute (fpm) and the friction rate would be 1.5 WC/100ft. That is way to fast. Your blower would not be able to maintain such a high flow rate against this much friction, and even if it could, it would be very noisy.

If you must go with this size duct, your best bet is to take the shortest path possible. You will probably be ok up to about 450 CFM, which will result in an air speed of just over 1500 fpm.

Here is a link that might be useful: duct speed calculators

I now understand your layout. Still, the bends you are asking the air to make incur a lethal restriction to the flow. Essentially, your 800 CFM fan maybe will be able to pull 400 CFM at best through that obstacle course of plumbing. The worst offender is where it enters the wall, and is met with, well, a _wall_.

Casey

To the OP: scargod i hope you are still encouraged by my post and not put off by sombreuil_mongrel's posts.

No, I do not believe, from all my calculations that the CFM would drop in half. There is only the back outlet of the vent hood that must be navigated and the air bend around once. I used an Excel calculator (Air Duct Calculator - Hart & Cooley Brand Website), and with "two 90 degree bends" it still gives me 2293 FPM and a friction loss of .29 with an 8" round pipe.
The opening at the back of the hood can be very large... and the rectangular duct in the wall can also be quite large.

Have you thought of changing the wall studs to 2x6" rather than 2x4"? You would gain a bit of, er, breathing room.

"Have you thought of changing the wall studs to 2x6" rather than 2x4"?"

I don't wish to destroy the wall on the far side. I have a large map wallpapered to the other side. I could build out with a false wall for some additional distance, but I don't see that as necessary since I can do at least 3-1/2"x14" (almost equivalent to a 8" round duct). Plus, I found a standard "Straight Register Boot" to transition to 8" diameter. I believe 3-1/2x14" equates to about .05 friction loss for five feet). I just don't know what 2200-2500 FPM will equate to in sound level at the hood. I foresee cutting a 4x15 opening (or bigger), at the back of the hood. I am re-reading rjpjnk's post and I remind you I only have five straight feet till it feeds straight into the fan venturi.

I found this is an engineering handbook:

Duct velocity should be between 1500 and 4000 FPM
 Hood velocities (not less than 50 FPM over face area between hood and cooking surface)
 Wall Type - 80 CFM/ft2
 Island Type - 125 CFM/ft2
 Extend hood beyond cook surface 0.4 x distance between hood and cooking surface Filters  Select ï¬lter velocity between 100 - 400 FPM  Determine number of ï¬lters required from a manufacturerÂs data (usually 2 CFM exhaust for each sq. in. of ï¬lter area maximum)
 Install filters at 45 - 60°to horizontal, never horizontal

Using this as a guide I think an average 400 CFM for general-purpose venting @ 1500 FPM means that I am well covered with a variable speed 1000 CFM external fan and 8" duct area. I'm guessing that at 1500 FPM it will be pretty quiet.
The old Vent-a-Hood units are supposed to deliver 300 CFM each and I usually only use one. They are super noisy at near my ear level and 18 inches away. The air passes through a 3-1/2" x 4-1/2" rectangular opening! That's small and seems to equate to almost 3000 FPM! I guess it's no wonder they're so noisy...
Am I missing anything? Bad calculations or asumptions?

To the OP:

I have seen commentary where the duct velocity was recommended to be on the low side of 1000 to 2000 fpm. I cannot say who is right in this argument. Obviously, grease precipitation on the duct wall will be less with higher and higher velocities, but the noise and pressure drop may be intolerable. You are not building a commercial kitchen, I presume, and hence the total grease load remaining after the baffles will be modest in any case.

The problem is that duct velocity is a later stage of design following the determination of the cfm needed to keep all the captured effluent contained in the ventilation system. Determine the cfm first, then the duct size needed to keep the velocity at least 1000 fpm at full power.

kas

It makes sense that you need to capture more than steam and smoke with the ventilation. We've been in this house for four years and because I wanted to know what was "under the hood" I dismantled the two old blowers. It was easy with the side latches. One was full of grease to the point of overflowing into the cover. As I mentioned above, The exit is small and rectangular and equates to 3000 FPM. If I'm at the cooktop, I can't tell what people are saying if one is on, let alone both! Yet they seem to be capturing the grease because of the centrifugal (squirrel-cage) style of fan.

I have not picked a hood yet. Obviously, it will only have grease removal baffles (or mesh filters), and lights. I am trying to find a nine inch tall one; hopefully, that's not an insert.
I'm straying slightly from the topic's question, but I will have 36" counters and I want two horizontal shelving areas above the hood (see the Shutterfly URL link). Custom made, they can be any height, but I am hoping for 12" each. This leaves me with 36 inches for the hood to cooktop gap. A nine inch tall hood leaves 27". Width is designed at 42" and I'm thinking a 24"depth from the wall. Using the design guide, 560 CFM accomplishes minimal/adequate flow and I can crank the external fan up to a theoretical 1000 CFM. With my BTU's I supposedly only need 330 CFM, but I know that is dependent on the height from the source (and perhaps a few other factors). I wish this didn't have subjective elements, like I am 6' tall and I'm used to the old built-in which protrudes only 14"!
I'm counting on the variable speed fan to compensate and still not get too loud.

Here is a link that might be useful: Shutterfly images: three views

I can add some additional info. Range hood requirements differ between gas and induction. The hood for a gas cooktop must remove combustion bi-products and significant heat. Steam, smoke and other cooking vapors would be common to both. Less flow will do the job over an induction unit.
To increase the wall cavity size without affecting the wall on the other side remove the kitchen drywall and screw a spacer to the existing studs. You can rip down 2x4s to the width necessary.