Bigger tires and their effect on handling.

Over the holidays a rider bud and I got into a heated argument about motorcycle tires and their effects on handling, especially in a corner. Well here's how I (a science grad) sees it.

Friction does not depend on the area of the tire contact patch (when there isn't any water between the tire and tarmac); but a wider tire would help in maintaining contact over a far wider (pitch)angle. The width of the tires are dictated by the maneuverability that is expected of the bike,the turning radius and of course fuel efficiency.

Width of the tire would definitely help your cornering ability, however beyond a point it does not help. That point can be determined by the farthest contact point at the highest steering and roll angles.
As shown in the picture below with increase in the steering and roll angles(while cornering) the contact point on the tire will shift towards the left(away from the road surface). Therefore to maintain contact while turning sharper turns at a higher roll angle (higher speeds) you need wider tires.

A motorcycle is said to be in equilibrium(in balance) as it takes a turn when the centrifugal forces generated by taking the turn are negated by the lateral forces generated at the tires due to the camber of the tire. It is partly due to this reason it is generalized as an inverted pendulum.

The required lateral forces are taken care of during the design of the frame when the trail etc are determined.Since this doesn't concern our question I am going to skip the part.
The wheel's design is made considering that during cornering, the tire must maintain a contact patch with the road surface at all times.

where;
xPf = x-coordinate of the contact point of front wheel
yPf = y-coordinate of the contact point of front wheel

(a derivation of this maybe found in Motorcycle dynamics by Vittore Cossalter,I am not including it here as it would be a long thing)

If you can measure some of these parameters and substitute for the  maximum steering angle we could arrive at the contact point while the  motorcycle is executing its tightest turn. My wild hunch is the Duke's  tires aren't too wide but the motorcycle in the picture below would  probably be an overkill,but then its wheelbase is significantly larger:

To generalize, a motorcycle with a higher wheelbase and tires with bigger radius will need wider tires,this will also increase its turning radius and reduce maneuverability.

Where:
p = wheel base of the vehicle
ε = caster angle*
δ = steering angle
Φ= roll angle
Rc = turning radius
As you might have seen scooters can easily zip through traffic while motorcycles with higher wheelbase (eg: an Enfield) have a much bigger turning circle,in turn these are more stable due to the lateral force generated by their higher trails, but that is another story.

Picture courtesy:
Motorcycle Dynamics by Vittorio Cossalter,English edition
http://www.hdforums.com/forum/dy...