Hi everyone.
I've been having this discussion with a pal regarding what affects the grip of a motorcycle's tires when turning and I was hoping someone in here could enlighten us :)
So, we have a motorcycle that is making a turn at a constant speed and leaned in an angle.
How do you calculate if the bike is able to make the turn or if the tires will skid and the bike fall? Clearly, making everything else constant, there will be a velocity cutoff that the bike will not be able to make it.
From wikipedia I got this equation that gives the lean angle with respect to the velocity and curve radius:
∂ = arctan( v^2 / (gr) )
Because the tires are not spheres, the bike can not lean indefinitely. Assuming the lean is still inside the tire limits, what affects the grip?
To me, this problem is solved as follows:
We have a centripetal force that is causing the bike to turn.
We have the weight of the bike equal to the normal force of the ground.
therefore, let
Fn be Normal force,
Ff be Friction Force,
μ be the static friction of the tire/asphalt
m the mass of the bike
r the radius of the turn
ac centripetal accelaration
v velocity
we have:
ac = v^2/r
(fricion force is the friction coeficient times the normal force) (=) Ff = μ Fn
(on the vertical axis, the resulting force is 0) (=) Fn - mg = 0 (=) Fn = mg
(on the horizontal axis the bike is turning) (=) Ff = m ac (=) μ Fn = m v^2/r
if we solve this for v, we get v=√(μ g r)
So, this means that
a) the mass of the bike is irrelevant
b) the lean angle is irrelevant. The Friction does not increase with the lean angle
However, I've seen in some places people say that the friction actually increases with the lean. How is this possible?
(e.g.
http://genjac.com/BoomerBiker/Two%20...%20Physics.htm
Quote:
A myth exists that leaning a motorcycle reduces the cornering grip (friction) of the tires. Notice that the mass of the vehicle does not changeif it weighed 600 lbs. on a straightaway, it still weighs 600 lbs. in a curve. However, gravity works in corners to help us out. Friction is actually increased when g-forces come into play. Camber thrust and total grip is also affected by centrifugal force as the motorcycle leans when going around a corner. Cornering causes centrifugal force to press the tires downward into the asphalt, compressing both the front and rear suspension springs, reducing ground clearance. (...) Camber thrust literally compresses the motorcycle tire as the rubber tries to roll under the wheel rim. Cars can't do this trick since the inside tires lose as much grip as the outside tires gain. Traditional car suspensions lose camber thrust completely in turns. The faster a motorbike rider goes through the same turn, the more grip he has to work with (until the bike drags). At a 45 degree lean angle, a motorcycle has nearly 50% more "weight" pressing the tires into the pavement, and thus benefits from nearly 50% more grip than it does when it is vertical, thanks to centrifugal force and camber thrust.
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How is this possible?
Thank you!
