Counter-steering -- how it works: Part 2 -- force causing acceleration

August 23, 5:16 PMDC Motorcycle Travel ExaminerMark Poesch

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While it’s true that there is no “lean angle” control on the motorcycle, at speeds above 10-15 mph, the rider has indirect control of lean angle.  We call it: counter-steering.

Italy's Valentino Rossi on his Yamaha is seen on his way to win the MotoGP race of the Czech Republic Motorcycle Grand Prix at the Brno circuit in Brno, Czech Republic, Sunday, Aug. 16, 2009. (AP Photo/Eckehard Schulz)

• Counter-steering revisited: Redux -- how it works
• Counter-steering -- how it works: Part 2 -- force causing acceleration
• Counter-steering -- how it works: Part 3 -- balancing torques
• Counter-steering -- how it works: Part 4 -- lessons learned
• Counter-steering -- how it works: Part 5 -- lean-angle force dynamics

Counter-steering works by causing the front tire to drive away from the inside of the turn:  When you “push the left grip forward to go left” you really are steering out of the turn.  The result is that the bike “falls” to the left.  But, we call it leaning because, at speed, something immediately balances that fall.

Instead of falling, the bike arcs into the turn at a particular radius that is directly proportional to the speed and that lean angle.  As described in Motorcycling 101: Counter-steering essentials, the function that describes this radius is:

Radius = Speed^2 / ( Gravity * tan( CG Lean Angle ) )

But why is it that the speed and lean of the motorcycle determine the radius, and not the other way around.  How can we be sure that the lean angle isn’t a result of the speed and the radius of the turn?

While the full mathematics involved in all the forces affecting a motorcycle in a turn is beyond the scope of this article, we are fortunate that the equation shown above derives from a single force that is typically the dominant force.   What is this magic force?

We have all heard of centrifugal force.  Whether it’s a ball on a string, a child holding onto a merry-go-round, or a rider and motorcycle in a turn, it’s all the same, and it’s not a force!  The force exerted by the string, or by the child’s hands and friction on the merry-go-round, or by the motorcycle’s tires lateral friction with the ground is called centripetal force.  It is the force that drives the object in question into the arc; that is, centripetal force is the force that is accelerating the object toward the center of the turn, thereby overcoming Newton’s First Law of Motion, which says that an object in motion stays in motion unless it is acted upon by an external force.  Centripetal force is the external force in this case.

So, while we know that the centrifugal force affecting all these spinning, turning, circling objects is described as:

Centrifugal “force” = Mass * ( Speed^2 / Radius )

Now, we also know that this isn’t a real force, and it doesn’t cause the turn.  In fact, it is the result of the turn!  Or perhaps, more clearly, this is the amount of force required to generate the turn.

The dominate force that is driving the motorcycle into the turn can be described simply as:

Reactive Force = Mass * Gravity * tan( CG Lean Angle )

Does this come from some particular geometry of the tires and bike, by the shape of the tires, or the weight ratio between the tires?  Again, luckily for our simple analysis, no!  But, why call this a reactive force?  What is being reacted?

As the bike tire turns away from the center of the turn, the bike begins to fall into the turn, and is counter-balanced by a force.  Something is pushing on the tire; the further the bike leans into the turn, the harder this “something” pushes.  If the tire is initially turned out of the turn, it’s not likely to be rolling contact patch that provides this force.  So, what is it?

The equation for the total magnitude force at the contact patches is Mass * Gravity.  That’s it.  The weight of the bike and rider!

The vector of this force is a function of the force magnitude (Mass * Gravity) and the lean angle of the CG of the bike and the rider.   For our analysis, the vector has two components, a vertical component that is the weight of the bike pushing against the ground, and a horizontal component that is reacted at the contact patch.  In short: the force due to the bike/rider's mass accelerated by gravity provides the centripetal force that drives the bike into the turn as it leans.  As the bike leans further, the force increases.  As shown above, the lateral component of this force, the force driving the bike into the turn is simply:

Reactive Force = Mass * Gravity * tan( CG Lean Angle )

While there are many other variables at play, including weight ratio between front and rear, tire profile, rake and trail, chassis design, and much more, this dominant force says: "The force driving the motorcycle into the turn is directly proportional to the tangent of the lean angle of the center of gravity of the bike and rider.  Or simply, the bike turns due to its lean angle."

Understand this, and you’ll understand the full importance of using counter-steering properly.

But, what about the question of balance.  How does the bike balance in the turn?  Is it the same forces resulting from momentum that keep the bike upright at speed?

Next: Counter-steering – how it works: Part 3 – balancing torques