Factors affecting motorcycle grip when turning

theproject

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
How is this possible?

Thank you!

jbriggs444

The quoted passage appears to use the idea that the coefficient of static friction is the ratio of frictional force to total force. As such, it is flatly wrong.

If that sort of notion were supportable then a coefficient of static friction above 1.0 would ensure that a tire could never detach from the pavement under any cornering speed or lean angle.

Lsos

Wouldn't the motorcycle's centrifugal force push sideways: parallel to the ground? I don't see how it would add to the weight and thus the grip in the tire.

Unless the road was banked.

theproject

That is my idea.
The leaning is irrelevant to the friction. The weight of the bike does not change because it is leaning, therefore the Friction force must remain the same.
I might be missing something though..

Thank you for your answers

pgardn

The way this problem is stated it appears we are dealing with centripetal force. I dont see anything to indicate we are using a rotating frame of reference.

Imo these types of questions are not meant to play around with the fact that the tire might flatten and change shape or adhere with a diff. part of the tread to change the μ.

Imo this is a classic physics problem that requires you to have a good grip on forces involved in uniform circular motion. If they had banked the pavement as well they would have required you to have a very good grip on forces and angles and how to reconcile them so the net force was always in towards the center of the circular path taken. But they were nice.

Notice that the mass of the vehicle does not change—if it weighed 600 lbs. on a straightaway, it still weighs 600 lbs. in a curve.........?

The sentence above gives me a hint that the source of this quote is not so good. Looks like they are confusing mass and weight. Weight is a force. Mass is not. Maybe they meant it differently than I read it. And then again...

Cornering causes centrifugal force to press the tires downward into the asphalt????

Whaaatttttt?

pgardn

As your equation states, to increase the force of friction you need to increase v, increase g, or decrease r or any combination of these. So go faster in a tighter circle on a more massive planet and you will change the force of friction. And if μ is too small then have a good time skidding off the road.