Banking of roads VS leaning of a cyclist inwards

In some textbook, the maximum speed of taking a turn is derived for a banked roads, and a note is mentioned saying, the same works for a cyclist, except that the road doesn't need to be banked.. and cycle banks.. and everything is the same

This is not true right? :O.. the normal forces are not the same in the banked road and a leaning cyclist.. So i wanna know, is there some derivation that i can see.. and then check the final answer? does it turn out to be the same?

i feel it would be difficult, it would depend on the cog of the bike.

Question

Banking of roads VS leaning of a cyclist inwards

In some textbook, the maximum speed of taking a turn is derived for a banked roads, and a note is mentioned saying, the same works for a cyclist, except that the road doesn't need to be banked.. and cycle banks.. and everything is the same

This is not true right? :O.. the normal forces are not the same in the banked road and a leaning cyclist.. So i wanna know, is there some derivation that i can see.. and then check the final answer? does it turn out to be the same? 

i feel it would be difficult, it would depend on the cog of the bike.

anonymous · Answer

@Vincent-Lyon.Fr

anonymous · Answer

@hartnn @ganeshie8

anonymous · Answer

i did the derivation.. get the same result.. but its due to torques :-/

but unlike in banked roads, a cyclist on an unbanked road has to only rely on friction

vincent-lyon.fr · Answer

In banked roads, the normal reaction can contribute to circular motion and the friction force becomes smaller, if not zero, preventing any chance of slipping, thus and allowing a greater speed.