Need help designing wireless charging coil

[Gladius]

I am planning on building a bit of a special bike light.
Basicaly im tired of having to constantley change batteries and remembering to charge my bikes light.
There are existing wireless solutions that work by having magnets mountet to the spokes of the wheel and a pickupcoil inside the bikes light. When the wheels turn the magnets move over the coil causing a current to flow and lighthing up some LEDs. Sadley those LEDs are nowhere near powerfull enought to be actualy usefull to see at night so I thought id desing my own solution. Same concept just a bit better. Mainley I'm thinking of using a 1W-3W LED and a backup battery that gets charged whenever you use the bike so the light output is stable and independent of speed.
For the magnets I thought some strong neodymiums from aliexpress but I am not shure how I should aproach the coil.

It should deliver about:
 4.5-5V @  400-500mA
@15Kmh. -> 115 rpm=2rps => v(magnet@0.3m from middle)=3.57m/s

I was hoping to use industry standart parts such as coils for QI chargers to avoid having to make or order custom parts.
If anyone could help me by pointing out:

- Formulas
- Things to know about designing such coils and associater electronics
- Of the shelf parts I can use

It would be greatley apreciatet.

Thanks for all the help.

[SiliconWizard]

Are you sure you don't want to buy a dynamo hub instead? https://www.cyclingabout.com/best-dynamo-hub-bicycle-touring-bikepacking/
 

[Gladius]

Haha yeah I know it would be much easier but since this is a joined venture with a buddy of mine who is a designer he turned down this exact question for lack of sex appeal and ease of use. So sadley not an option.