Old Hickory Dam is just east of Mile 216 on the Cumberland and the canal connecting Kentucky and Barkley is at Mile 33, then another mile through the canal to Kentucky Lake. It is a nice trip and the time you take depends on how fast you want to cruise. A number of sailors have made the trip that sail out of Harbor Island Yacht Club. They race in many of our regattas at Kentucky Lake sponsored by Kentucky Lake Sailing Club. I have personally gone from Clarksville to downtown Nashville in a power boat and in my Hunter 356 from Kentucky Lake to Clarksville (Mile 128). Current for most of the year would be a knot or less unless there have been recent storms and flooding, in which case it can be 2 to 3 knots and you will see lots of tree limbs and floating debris that you have to be careful around.
Look at Activecaptain.com for information about services along the route for fuel, marinas, potential anchorages etc. there is a new Full service marina in Clarksville, and I have personally anchored at Dover Island and it is a nice quiet place. it would be a very fun trip if you properly plan it and do it at a comfortable time of the year. Be sure to understand your fuel consumption and needs. You won't be able to do much sailing until you get to Kentucky. There are some broad open places on Barkley Lake that are very shallow, so have good charts and pay attention to where you are or you will potentially run aground.
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