In my opinion, a large dinghy, plus outboard, suspended from davits at the stern of a boat of your length, as well as of mine, also 38 ft, spoils the look of the boat. It also affects the trim somewhat. That being said, there are few carry alternatives for a 10-ft inflatable with aluminum hull. That boat weighs probably 120 - 125 lbs. A four-stroke outboard with enough power to plane it w/ just two (adults) aboard, say 10-hp, might weigh another 90 - 100 lb. (With two adults & teen, that might not be even enough.) That, stuck outward from the transom, plus the weight of the davits, is what will be loading your boat at the stern
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FWIW, I have (since May, 2018) a 9.5-ft aluminum hull inflatable & 8-hp Honda four-stroke. Love the boat; outboard has been a disappointment, frankly. I installed a “crane” to my stern-mounted radar post to lift the engine (89#) which rides on the port-side stern rail unless stowed in my (deep) starboard locker. The boat is carried on the foredeck bottom-side up, of course. I lift it with a 6-fold-purchase block and fall that I had made up for the purpose and which hangs from my spinnaker halyard several feet above the deck. I have a lift bridle rigged to the cockpit lift eyes (four point attachment). I basically can lift the dink by it’s transom high enough to spin it over. Then reattach to the lift bridle and haul it up more or less horizontal, and lower over the side, all in but a few minutes. Don’t need any help with this. Control everything from the foredeck. Then, drop on the outboard. Another maybe 8 min. If not going far to another anchorage, or in relatively flat waters, I’ll tow after initial launch, sometimes with outboard still attached. For me, the towing bridle has to be twin warp or the dink slews around too much. For the trip home over open seas, everything is pulled back up and secured.
The whole business is only slight more trouble than with my 8 1/2 ft Achilles with inflatable floor. That one was nearly always stowed deflated in the locker on the outbound. So, had to lug it out of the locker, then to the foredeck; unpack & inflate, then muscle over the lifelines into the water. This was also a one-person job, but more steps and more brute lifting than for the RIB, as I describe above. It usually rode inverted & strapped on the foredeck for the ride home.
Finally, for all of the trouble and expense you’re talking, you might wish to CRITICALLY access your actual need for that particular model of inflatable if you have not already, or any other. It being summer time in FL for nearly another 3 mo, you with a new yacht, where will you be going where you might need that kind of “transportation?” Anchor out locations? Egmont Key? Pt DeSoto? Very hot and humid. Not so great for a pleasant week or weekend out, even with AC below, IMHO. Also, consider where to stow it (inflatable) when in the slip? Answer—on your davits!!! Your yacht will be married to the davit system as long as you have the RIB. In most places, you’ll be charged for that overhang of the davits at the $/ft rate of the hull. Figure two, maybe three, extra feet added to your monthly slippage tab. But, even if you decide to leave the RIB home in the slip, as in just going for a daysail, you’ll still have the davits attached, most likely.
Perhaps, consider a “rubber ducky” for now
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