This was just a fun summer project that I indulged in with a friend after my 2nd year in school.

The only theory I applied was related to gear ratios and a bit of intuition in the dimensions and shaft sizes relating to its dynamics and structural strength. Nothing too fancy, but a heck of a lot of fun and a good learning experience. It topped out at about 50 km/h given the small 50cc motor, and lasted us nearly 100 rides before the chain eventually deformed and kept falling off of the sprocket. Bearings also moved a bit in their seating over time due to the lateral loads from drifting. It would still work had I replaced the chain, but I figured it was time to put it to bed at that point.
 

Outcome: Built a fun trike that goes upto 50 km/h, is cheap (under $200), drifts, and is safe .