The link claims a silent motot so i doubt a gearbox is used, in any case having a custom one of those made is an expensive proposition.
From the stated weight of the battery i assume a capacity of approx 1 KWh.
Link states a duration of one hour i assume at dawdling pace this implies a consumption of 20 A.
If you can find out how long it lasts on the foils you can better estimate the size of motor you need.
10 KW seems high to me but i just do not know.
From this picture of liftfoils.com we can count 196 Li-Ion cells. Assuming a 14S14P arrangement and a modest cell capacity of 3000mAh, we can assume a capacity of 42000mAh, a voltage of 51.8 (nominal) and a power of 2.175kW if they are in fact getting one hour ride times. Hydrofoils produce very low hydrodynamic drag and this is the attraction...great performance on low power.
As this is something that already is meant to carry a person, there must be some form of throttle control in place. Any good reason to mess with this?
I am building this from scratch so there is no throttle control already in place. I could buy one of these but they are being marketed at $12,500!!! I don't want one that bad but if I can build it <$2,000, I'd like to try.
Sounds like a fun project! But it looks like you might be jumping in at the deep end (ObPun), I think most of those 7 items would be a decent task by themselves.
I would start with a wired throttle control, once you have that nailed you can add bluetooth, etc. It doesn't look like CPU speed will be a problem, depends on how often you want stuff updated. Probably Flash size will exceed a small AVR once you add all the features, you could relatively easily move to a Mega.
If you need to move to a faster CPU, it is doable but a lot of code depends on AVR features so porting might not be trivial. To see if you are in the right ball park, I would take the most intensive CPU feature and run a benchmark.
I doubt you will find off the shelf boards that perform all the functions you require, either way you will end up with a nest of boards. It doesn't look like there will be a huge amount of space available. You might need to think in terms of creating a custom PCB.
You also have the fun problem of making things watertight. I'm not sure how far radio propagates underwater, radio antennas for GPS etc might need to be located above the water line.
I plan on keeping all the electronics either integrated into the board or on top of the board in some sort of pelican case. Either way, the electronics won't be underwater (except for the motor of course).
I should probably clear up the GPS, I know it seems like unnecessary complexity. From a standpoint of safety there is a very real chance the batteries could discharge before I get to shore. I want the Arduino to use the GPS to measure my current distance from my starting point, monitor the state of charge/amp draw of the battery and alert me when I'm in danger of falling below the electrical energy to get back. Also, I could determine the optimal speed/power (best range) and have the Arduino common that throttle setting automatically.
So if I used my Mega, and attached a GPS and Datalogging shield, would the code get too complicated if I tried to manage those inputs and outputs while monitoring the voltage/amperage, sending PWM to the motor, and perhaps lighting up a few LEDs? For the sake of argument lets say I abandon the bluetooth for the immediate future.
For further discussion on the mechanics of this DIY project check out Endless Sphere Forum
Also, there is a great guy documenting his attempt at this same project Here