My advice is to use the lowest weight you can manage with your vane and work upwards if it furls too early, don't use the theoretical figures as it will be too heavy.
Flux covered this well. I refuse to tell you if your calculations are "correct" because my experience has told me I need to know a lot more about your machine to be able to even get close.
The important thing to realize is that there is only, probably, one chance in a thousand you will get it perfect first time on the tower. And if you do it will be pure luck more than attempting to design it with calculations. All the calculations provide is an understanding of how it works, and a basic starting point.
Every new design, that does not follow proven designs that have been adjusted to work, is finalized thru trial and error when it comes to furling. There are too many variables to attempt to arrive at the correct solutions with calculations - some variables you cannot even measure until you get the machine on the tower to see how it acts.
As an example, the machine I showed you the photo of above will furl fine @ 12.5 m/s with the rotor running at 400 rpm and reaches full furl around 15 m/s @ 450 rpm. If I speed the rotor up so it is running at 500+ rpm, the machine refuses to furl at all, even at 20 m/s, and it puts out way excessive levels of power. This is an example of why it is impossible to calculate furling to the last digit. It won't work. You need to arrive at a starting point, and fly it to see what it does, assuming you are working with a new design.
Tail fin area is also not a precise thing. I prefer to use long tail booms on my machines with a small, sleek sexy looking tail. Some folks like to use a shorter boom with a big club of a tail. If you make the tail boom long enough, you don't need a fin at all because aerodynamic drag on the boom structure will steer it. If you want to use 7% of the swept area, I would say that will work fine in probably all cases of boom length.
Turbine diameter is 5.6 m (5 kW output power).
Turbine thrust is 1.626 kN (using BEM Method) at 12 m/s wind speed (speed at which furling should start)
Now, looking at your calcs, @ 5 kW output your generator is running at about 54% efficiency, which I would say is reasonable. I would calculate rotor thrust to be .981 kN using the CO (Chris Olson) method, assuming 36% rotor efficiency @ 5 kW output. I do not know what the BEM method is, but it is wrong in my experience and will yield a tail that is way too heavy.
The second thing is, will your generator actually handle sustained output at 5 kW while dissipating 4,200 watts in the stator winding? I highly doubt it. That means you need to furl it earlier at the power level your stator can handle for heat dissipation. So while I refuse to tell you that your calculations are correct, I will tell you they are NOT correct. I know beyond a shadow of a doubt that if the above machine was built and flown it would burn up the generator in sustained 13 m/s wind. Even if I drop the rotor efficiency to 30% in my calcs, which raises gen efficiency to 65% @ 5 kW, it doesn't figure out very well because you would still be dissipating 2.7 kW in the stator. That could be done with a very elaborate cooling system on the stator in sustained 13 m/s wind. But it would be very questionable.
My point in all this is that the machine cannot be furled at outputs beyond what your generator can handle or you will burn it up. So what are the design details of your generator? What voltage does it operate at? How much surface area does it have to dissipate heat? What is the resistance of the windings in it? All those factors determine how much power it can actually produce, sustained, and therefore affect furling calculations.
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Chris