Hey Mick,
This Nordic 17 conversion is running at 36V, so I adjusted his performance statistics for 48V and converted his speed readings to knots (because these are boats after all)
So it looks like he got 3.3kts @ 375W (or 7.5A @ 48V), 4kts @ 750W (15A @ 48V) and 5kts @ 1875W (37.5A @ 48V). So now we've got some observed performance data that we can use for battery performance calculations (going with the assumption that this data is correct and your boat will perform similarly).
Like all known battery LiFePO4 batteries are affected by Peukert's Effect, albeit to a small amount. Luckily, it is not difficult to accurately predict virtually any battery's performance using the rated capacity and an accurate Peukert's Exponent for the battery type. I have been using a Peukert's Exponent of 1.03 for the 8kWh LiFePO4 battery bank that I have been running with since 2010. Real world observations have confirmed this PE value to be correct and that my batteries are still operating above the rated capacity.
We have all heard that lithium batteries can be safely discharged to lower states of charge than L/A batteries, the common assumption is for an 80% depth of discharge is OK for LiFePO4. With your 48V 200Ah battery, you've got about 8000Wh of usable storage. I know that you asked for a 6 hour runtime, 4kts will give you about 10hrs of capacity (40nm) and 5kts will give you about 4 hours of runtime (20nm) . Your 6hr discharge rate is 26A which may be about 4.6kts (27.5nm) (I'm taking an educated guess on the "watts to knots" conversion for 26A, based on the other performance data given here.)
Once you get your project up and running, please take some time to measure your actual performance. First of all, it gives you excellent baseline data that you can use to judge the efficacy of future improvements and to see if your boat is gradually developing any performance issues. I spend a couple of hours once every season to check my boat's performance to make sure that everything is still meeting my original observations.
Your conversion seems like a fun project.
Fair winds and calms seas,
Eric
1964 Bermuda 30, 5kW drive, 8kWh lithium battery bank
Marina del Rey, CA