Do I understand well?

Hello everyone, two weeks ago, I had a crazy idea to build a propulsion system for my kayak using a custom made electric waterjet system. I'm a mechanical engineer so I started from the base for everything related to the electricity. In fact, a week ago, I didn't knew that it's was possible to build a battery pack from 18650 cells.

I therefore read a lot on the subject and I just wanted to use your knowledge to be sure I understood everything right. Here's my plan for the electric system:

Motor: 130KV, 7000W, 200A Max Amp, 18S max volt (64.8V)
http://alienpowersystem.com/shop/brushless-motors/c80100-sensored-outrunner-brushless-motor-130kv-7000w/

Custom Battery Pack: 308 cells 18650, 10A 2.6Ah, 14S22P for a total of 58.8V and 57.2Ah
If I understood the math, 10A/2.6Ah = 3.84C and 57.2Ah x 3.84C = 220A so I should be good if Amp battery > Amp Max Motor

ESC: Anything above 220A, like 250A or 300A.

Did I said any stupidity?

Thanks for your help!

knowing how fast a fairly fit human can paddle one and your thinking of having something like 20-30X that power ... would be fun but i can see things going bad

Okay, first of all you're asking how you're expected to take that information. So you should view it as "Optimism." Not so much about getting that much performance out of it for a moment as sustaining it. You can't. 64.8 X 130 equals the rpm you can get this up to when it's just running without a load, for as long as it takes to go ahead and burn up. A propeller in the water will be under a much greater strain than a propeller in midair, right? You would need the big controller, yes, people have a way of blowing those out with such motors. One of the longest, strangest threads here was discussing one of their controllers to use on a motor like that.

As to his point about something going wrong: You don't really want a 1hp motor on a kayak, do you? Why consider 9hp?

You might want to check out the thread on hydrofoils if you haven't seen it already:
https://endless-sphere.com/forums/viewtopic.php?f=39&t=88524

Your proposed battery sounds reasonable.

Motors like those have very high peak power ratings, but for continuous use it's better to run them at lower levels.
The ESC or controller will get pretty hot, so some kind of cooling will be needed.

Mr. electric has a kayak he runs with a 12v trolling motor and a lithium battery. It goes faster than anybody can paddle. Not sure what the power rating is, but around 1kW.

Sounds fun

That's a 7000w outrunner, and you're looking to pump ~15,000 watts through it, likely in an enclosed space of the drive box. Cooling will be a problem. an Inrunner would be a better motor choice so you could build a water jacket to fit around it and keep it cool.

Google around, you will find a. Ready made electric jet drive built for model boats that will do this easily.
But, if you want to maximise your run time and keep weight down, you need to do much more research and go with a custom prop drive, low rpm, efficient prop design, etc
You certainly do not need 7kW.

Thanks a lot all for your reply. A lot of your comments were based mainly on the power that I want to reach.

Actually, Fechter has highlighted exactly what I have used in term of comparaison, electric surfboard, like Onean, Waterwolf and Lampuga, and they are all using motor of at least 5000W, reaching 11000W for the Lampuga Boost. Also, compagny like Jetsurf use gaz engine to power the same kind of product producing 15hp (11,000W) so for me, 6000-7000W made sense?

About the cooling, with th eproper water cooling system, should I be good or the heat production will be higher than what the ESC can takes?

A water cooling system would be ideal.