I think you misread the specs - I went to the Capital web site and it looks like all their hoods are 25" deep. I would have been really surprised it was only 15" - that would not have been sufficient.

Ideally, the hood should be wider than the width of the pan surfaces that would be used on the burners. For a 48-inch range a nominal 54-inch minimum aperture hood would be desirable. (Or only boil water on the outer burners.)

Plan on installing a monster hood before installing the counterpart monster range. Large hoods are awkward enough to install without having a range in the way. If a team of weightlifters is not available, a hydraulic sheet rock jack for installing sheet rock on ceilings may prove indispensable in holding the hood while it is carefully aligned and attached to suitable framing. I suggest downloading and reviewing the instructions as soon as possible to plan for this exercise. Framing is usually necessary before finishing the ceiling.

kas

Try to look at a Capital hood before you buy one. The interior geometry is shallow and the styling of the lamps is high key. It's the first thing people will see in your kitchen.

I believe that steeply angled baffles exhaust the smoke with less airflow than a flat underside. If you get a 54" hood with 1200cfm airflow the velocity will be low and drafts may blow the plume away from the hood.

The dealer that sold me a 24" BS stove had a Capital 24" hood with built in blower for sale for $285. A customer had canceled an order and the dealer couldn't return it. I decided to buy a 30" BS hood for $1400 plus a BS roof blower for $750. I never heard the Capital blower but the looks alone dissuaded me.

Early in the renovation I visited a local Ferguson's which has several installed high end hoods with built in blowers. I remember Miele, Wolf, maybe Viking and DCS. They all sounded wretched. Tinny, buzzy and shrill. That taught me that I would be getting a roof blower to get it out of the house.

Unless you installation is simpler than mine your total cost will be several times the price of the hood so I'd choose carefully.