The vent has to go through the roof at some point. Period. It cannot run through a gable vent (Vent on side of house at the top where the two flat sections of roof form the peak). It can either go through the roof straight up, or, for aesthetic reasons, can be ducted over slightly (For instance so the vent protrusion is on the rear of the roof rather than the front face). Your gable vents are sized so that your attic receives proper ventilation and remains at ambient temperature. Decreasing the attic ventilation by running a 10" vent through the gable vent will result in higher attic temperatures during summer (higher utility bills for you), shorter lifespan of your shingles, and a warmer than needed attic during winter leading to possible ice dams that will damage your roof.

can you run the duct work to an outside wall inbetween the joists? the motor you pick (along with the recommended duct size) will result in a "maximum recommended duct length" per the manufac. Also, addding 90 bends to the duct will "add" a variable amount of resistance (equiv. to 10 feet of duct length for my 7" installation). again, you might ask a contractor about running the duct between floor joist in the ceiling, to an exterior wall. you would probably need some drywall work on the ceiling, some messing with the cross members between the joists, but it might be easier than running something up to the roof..depends on your layout

Assuming that you build a system capable of 1000 to 2000 ft/min air velocity up the stack, there should be minimal condensation. Certainly grease particles and steam won't slow down and reverse direction. Residences tend not to condense much grease anyway because they are not cooking greasy foods for hours as a restaurant might be. Also, even with a cold attic, the stack will warm up once the blower has run for a bit. Establish an air flow rate (CFM) to achieve an actual 90 CFM per square foot of hood entry aperture, then size the stack diameter to achieve a velocity in the range noted in the paragraph above. Keep in mind that the blower rating must be higher than the CFM calculated on the basis of the sentence above to counteract pressure losses in the air flow circuit. (The air flow circuit may be considered to start at the cooking zone, pass through the hood baffles, continue out of the hood into the stack, go up the stack, flow past the roof blower or cap to the outside, and thence return from the outside back into the kitchen via one or many make-up air paths. No matter where one starts, it is the sum of the pressure losses in this circuit that determines how much lower the blower flow rate is relative to its rating. The relationship is given by the blower's fan curve; see Broan example below.) I would also plan on a damper at the hood and one at the roof. Most down-slope roof blower housings include dampers. Use of a roof blower allows use of a silencer in the attic to reduce noise, depending on space. This may also apply to using an in-line blower with a silencer. In this latter case, it may be necessary to jog the duct to have enough room for both in the attic. With respect to directional changes in the duct, the dominant causes of pressure loss are not jogs in the duct, particularly if they are 45-degrees or less, but rather the MUA path and the hood baffles. So it is not particularly inefficient to angle the duct in the attic to mate to the faux chimney placed where it best meets whatever considerations apply. kas

"The manufacturers of Vent Hoods are miseducating the consumers." Yes. Somewhat. Not really. They are in business to make money and they do that by making hoods as inexpensively as possible and then selling as many as they can for as much money as they can. Their goal is NOT your health or the IAQ of your home - that is up to you. Telling consumers that they'll also need to spend money on MUA if they buy hood X will negatively impact their sales (ignorant consumer will just go buy a hood from brand Y instead because it doesn't say you need MUA even though it has an identical need for MUA) so they do not want to do that. MUA is also not something that fits well within consumer hood manufacturers world except to the extent that they might offer a hood w/ integrated front curtain ducting. It is much more of a pure HVAC thing. It can be supplied to the return ducts of an HVAC system, the supply ducts or ducted directly to appropriate locations. Incoming air can be heated by gas, electric or hydronic. Incoming air may need to be humidified or dehumidified. It often needs to be electrically integrated with the HVAC system controllers to function properly. Consumer hood manufacturers - ARE NOT IAQ or HVAC people or engineers - they make something decorative that by nature must include air movement so they reluctantly include air movement in their product. Commercial hood manufacturers - ARE IAQ and HVAC people and engineers. Their customers are much more educated than consumers. The one singular purpose of the product they are selling is IAQ - so they design and sell systems that provide good IAQ. Aesthetics is quite secondary for them. Residential HVAC companies in the U.S. - ARE NOT IAQ people (they should be though). A tiny few, less than about 1%, know it well and a few more know it a very little but the vast majority know just enough, based on what they've been told at a 4 hr CEU course, to sound like they know what they're talking about but they don't really understand it. Most residential HVAC people do not understand air movement or why things are done the way they are - they only know how to use tables that tell them to do this or that and as soon as something is outside of defined parameters they're totally lost (though sometimes don't even realize that they're lost). Licensed Professional Engineers do (or most do, some don't) understand air movement and other elements. They are the people who create the tables that HVAC people use. They can think independently. Defined parameters for them are not tables but the physics of air - it's movement, temperature and components. Unfortunately, most U.S. engineers do not have a good understanding of human physiology (except perhaps for biomedical engineers). They do not, for instance, understand how CO2 functions in our bodies and how high levels of CO2 due to poor ventilation affect us. Or how poor ventilation resulting in high levels of VOC's, PM, Carcinogens and Pathogens affect us.