Not Everyone Knows That…
It is universal belief among us motorcyclists that motorcycle cornering speed is strictly related to weight, i.e. that light bikes are faster in cornering than heavy ones. It is an axiom, and as such it is an indisputable fact: it is what it is, plain and simple, no chance to reply. Supporting something different would lead to boos in the company, followed by dozens of examples that demonstrate unequivocally that light bikes turn lightening-fast and humiliate the heavy ones in all the curves and especially in the tightest ones.
But are we really sure that all this is true?
Let’s take two bikes different in weight but identical in all other features: wheelbase, ground clearance, center of gravity, suspension geometry, wheels and tires etc., and let’s ask ourselves how this weight difference affects their cornering.
The first question to ask is whether this difference implies, for the same speed and turning radius, a difference in leaning angle. If it were any, there would be a clear advantage for the bike that leans less, because at its maximum leaning angle, when the pegs scratch the pavement, it would travel faster.
Now, for any motorcycle, a given travelling speed along a curve of given radius corresponds to a precise leaning angle of the motorcycle+pilot system, according to the following formula:
α = arctan (v² / (r ∙ g))
where α is the angle sought with respect to the vertical, v is the speed, r the radius of the curved trajectory and g the gravitational acceleration.
As can be seen, weight is absent from the formula; consequently, a light motorcycle and a heavy one, all other characteristics being equal, lean exactly at the same angle while travelling along the same curved trajectory at the same speed, therefore under this point of view there is no advantage in riding a lighter motorcycle.
So let’s ask ourselves if the weight can influence road holding. In other words, we try to understand whether a greater weight reduces the ability of the tires to remain stuck to the ground without skidding during a curve.
First, it is intuitively obvious that a heavier bike resists more to change trajectory and then develops a greater centrifugal force.
The formula of centrifugal force is as follows:
Cf = (m ∙ v²) / r
where m is the mass of the motorcycle+pilot system, v is the speed and r the radius of the curved trajectory.
As shown, the centrifugal force increases linearly when the mass increases; the tires must therefore counteract a greater force when the bike + rider system is heavier.
We must therefore ask ourselves whether and how the grip of the tires varies when the mass of the motorcycle increases.
The adherence, i.e. the friction force that a tire can offer, depends on (1) the coefficient of friction, that is, from the tread’s ability to adhere to the pavement in the presence of forces applied tangentially with respect to it, and (2) the load placed on the wheel, according the following formula:
F = Fc ∙ l
where F is the friction, Fc is the friction coefficient of the given tire on a given surface and l is the load placed on it.
As can be seen from the formula, the adherence depends linearly on the load on the tire, which in turn is a linear function of the weight. It follows from this that the adherence increases linearly as the weight increases.
In summary, all other characteristics being equal, when the weight increases:
the leaning angle of a bike along a curve of given radius does not change
the centrifugal force increases linearly with the weight
the adherence increases linearly with the weight.
Therefore, as the relationship between centrifugal force and adherence remains constant as the weight varies, it happens that the maximum speed with which a given bike can go along a given trajectory curve does not depend on its weight.
In other words, a light motorcycle and a heavy one, all other characteristics being equal, can travel along curved trajectory of equal radius at the same speed.
Surprising, uh? But it’s the way it is.
But… lighter bikes are indeed faster than heavy ones on winding roads!
Yes, it is true, but it depends on a number of factors besides weight, which we will see in a future article.