So how does the vertical position of the CG affect turning

performance?...

Well, to achieve a 1g lateral acceleration in a turn, one would

expect to have to lean the bike over to 45 deg from

the vertical. But to counter the gyroscopic forces one has to lean it

over even more. Below is a table showing the

lean angle required to achieve a 1g turn as a function of the bike's

vertical CG position, for a particular case, namely

my bike at 100kph.

% -------Results-------

% ZCG (m) Bank (deg)

% 0.0000 90.0000

% 0.1000 82.4798 ZCG - height above ground of CG

% 0.2000 65.2291 Bank - angle of lean of bike

% 0.3000 59.0005

% 0.4000 55.7331

% 0.5000 53.7108 Note : Ignoring Gyroscopic forces

% 0.6000 52.3332 gives a bank angle of 45 deg.

% 0.7000 51.3334

% 0.8000 50.5742 Radius of turn Tr = 78.65m

% 0.9000 49.9780 Time to 360 deg 1/O*2*pi = 17.79sec

% 1.0000 49.4973

Note: The only variables that affect this angle are the speed of the

bike (100kph/62mph) and the ratio of the mass of

the wheels to the bike (11% per wheel).

So one can see from this that lowering the bike's CG increases the

required lean angle for a particular turn, thus

reducing the bikes turning performance. Answering the initial

question.

But as we all know, it is not practical to steer a bike by shifting

one's weight, one has to counter-steer. The reason

why this works is again because of the gyroscopic forces, and one

neat trick called precession. What precession

means is that if you apply a moment to a gyroscope (counter steer on

your front wheel) your force applied will be

rotated through 90 deg in the direction of rotation. This means that

any turning force applied to your handle bars is

then applied to your bike, tipping it over in the opposite direction.

Note that the steering does not turn but the bike is

pushed over. This is then opposed by the gyroscopic force due to the

turning of the bike through the turn. You can

either stop applying the counter-steer at this point and use the

bike's mass to hold you in the turn, or hold the turn

with continual counter-steer thus reducing the bike's required lean

angle (interesting idea! don't try this at home

kids). So back to the initial question, a bike with a low CG will

require a larger force on the handle bars to turn it.

Now back to the inertia debate, a quick calculation of the force on

the handle bars to a achieve a rapid lean of the

bike (45 deg/s in one second - more than the average) taking into

account the inertia (guess) of the bike, gives a

force of about 41Nm (8kg - for a 0.5m handlebar). Probably a more

realistic value would be half of this.

Interestingly the righting force (gyroscopic) for the above 1g case

is 288Nm (58kg at the bars - obviously further

leaning is necessary).