I want to understand this better so please explain.
Obviously the cornering forces themselves did not change in value.
What changed is the amount of cornering forces your bike can handle has been increased by hanging off.
I did not say the cornering forces are reduced, what I said was "In effect, reducing the cornering forces on the bike because you have increased your bikes ability to handle more cornering forces."
I'll clarify as best I can, but am first going to establish what you really did say, which has a lot to do with why I jumped in:
In a simple example, if moving your body to the inside of the curve moved the combind center of gravity of bike and rider 5 degrees to the inside, then the bike could go around the corner with about 5 degrees less lean angle at the same speed. Thus gains ground clearance because the bike is 5 degrees more vertical AND, it increases the forces of gravity downward through the contact patch of the tire and reduces the lateral forces on the tire contact patch saving a little traction.
In the bolded part above, you are saying hanging off:
- increases the force of gravity downward
- reduces the lateral forces on the contact patch
Those are unambiguous statements. They may or may not be what you intended to say, but as written, they mean what they mean and they're not correct.
The only ways you can "increase the force of gravity downward" are to make the bike heavier or increase the mass of the planet. As far as I know, hanging off doesn't accomplish that.
The lateral force is a function of velocity and turn radius. Change either of those things and you can affect the lateral force. Hanging off doesn't change lateral force.
But it's true that riders can go faster if they hang off...
Maybe I misunderstand it but, in a simple example: if your bike has the ability to handle 1.0x cornering forces with you not hanging off and it can handle 1.1X cornering forces if you do hang off (thus allowing you to go faster through the same corner), have you not, in effect reduced the cornering forces on the bike since without hanging off the bike it required 100% of your bike's ability to handle the cornering forces and with hanging off the bike only requires about 91% of your bikes ability to handle the cornering forces?
You haven't reduced the cornering forces, you have increased the amount of cornering force the bike can support. Sometimes.
People will say the suspension works better when it's more vertical. This can be true, though sometimes when people hang off they aren't doing it to bring the bike more vertical, they're doing it because they want to go faster and the bike is out of cornering clearance. In that case, the tires and suspension were always able to support a higher lateral load, but if the rider cornered harder, he would drag something hard and pry the tires off the ground. He hangs off as a substitute for leaning the bike more.
Sometimes the road surface is bumpy. This can be a case where relaxing the lean angle (bringing the bike more toward vertical) can increase traction by allowing the suspension to work better. This can increase the amount of available grip.
It's debatable whether relaxing the lean angle presents a better contact patch to the ground. There was a time where this was generally true, but if we are using a modern race tire, the part of the tire you're on when the bike is leaned to the paint is as good as it gets. They make them that way in order to support the highest lateral loads possible.
One last benefit of hanging off that comes to mind is this: Sometimes traction is quite poor and hanging off won't really improve it. Think of a wet, gravelly road where you can't lean the bike over very far. Hanging off can get the bike closer to vertical and in this case, if the bike has a big slide, you have a little more time to recover the slide before the bike hits the ground.