# dynamic theory

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hi to everybody

sorry for my language,

i'm italian.

i have a question....

i have readden many books,done some track school and track days here in italy,

put easily knee down,

but there is a question that i'm not able to answer...

before some considerations...

if the turning of bike is determined by leaning and steering of handlebar ...

and....if body hanging determines less bike lean angle(at same speed and radius of turn)....

when we do a turn, hangin off , bike lean less, what make it turn the same as it was leaned more (without hangin off)?

what i mean is:

in same turn , same speed,

if we hang off, the bike make same turn, but less lean, what makes it possible?

more handlebar turn?

in a car what makes it tur is only steer,

in a bike it is turn and lean at various degree

i'm courious what makes it do same turn with less lean....

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Great question!

To negotiate a bend (corner) we want to turn the bike. That’s our goal, objective or purpose.

To accomplish this, one of the things we do as a prerequisite (thing we do beforehand) is we lean the bike. The countersteer and relax of input at the handlebars establishes the lean angle.

To make the bike turn, the wheel turns slightly into the direction of the corner. Depending upon many things (speed, road surface and type, tire size differential, throttle application, etc) the amount the front wheel turns gives us the turn radius that gets us through the corner. The art and skill of the rider in applying known inputs a predictable amount will determine if we get through the corner effectively or not as effectively.

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you have done the perfect abstract of what i learned in last times.

but the perplessity is on what makes the bike turn the same but with less lean.

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A motorcycle is a series of gyroscopes. Gyroscopes resist changes in planes of motion and exert forces at 90degrees the plane of rotation. These gyroscopes are what keeps the bike in balance and it is the interaction of the forces along with the subtleties abovementioned that make what you observe. It’s why a rider cannot “muscle” a bike to do his/her bidding; it must be asked according to laws of kinematics.

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Your language is good enough for us to communicate about dynamic of motorcycles, my English is not much better.

According to Newton, everything that has some speed wants to move on a straight line by itself and must be forced to turn.

The forces of steering (wheels pointing in different directions) and friction between tires and pavement are the only things that force a car, truck or a motorcycle to turn, not the lean of the bike.

A motorcycle can be leaned and still move on a straight trajectory if both tires are kept perfectly aligned forward.

We only lean the bike to create a balance of forces between gravity and centrifugal effect and that balance is kept during the turn regardless of how much the rider hangs off.

The more you lean a bike, the less misalignment both tires must have to keep the same circular trajectory and the front contact patch moves away from the rear one, which means less steering is needed (although the difference may not be noticeable).

One of the reasons is that the distance at which the axis lines of both tires intersect each other must increase as the bike is leaned in order to keep the same horizontal radius of the curve.

Please, take a look at these schematics and text in Italian:

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11 hours ago, Lnewqban said:

Your language is good enough for us to communicate about dynamic of motorcycles, my English is not much better.

According to Newton, everything that has some speed wants to move on a straight line by itself and must be forced to turn.

The forces of steering (wheels pointing in different directions) and friction between tires and pavement are the only things that force a car, truck or a motorcycle to turn, not the lean of the bike.

A motorcycle can be leaned and still move on a straight trajectory if both tires are kept perfectly aligned forward.

We only lean the bike to create a balance of forces between gravity and centrifugal effect and that balance is kept during the turn regardless of how much the rider hangs off.

The more you lean a bike, the less misalignment both tires must have to keep the same circular trajectory and the front contact patch moves away from the rear one, which means less steering is needed (although the difference may not be noticeable).

One of the reasons is that the distance at which the axis lines of both tires intersect each other must increase as the bike is leaned in order to keep the same horizontal radius of the curve.

Please, take a look at these schematics and text in Italian:

no no!

not so simple....

in that link is explained the correlation of sticking forces of tyre on tamrac, and tyre lean, and "deriva"

but don't concerns my question

and many assumption you made are wrong

read the book of tony foale on chassis deigns....

you'll be amazed of many info!!

if what you says was true, the rider that do japanese gimkana, due to high leaning of bike, shoud have handlebar no steered,

instead they combine both steer full stop lock and hig lean angle

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quote from tony foale book:

2-20 Tyres
Camber force (thrust)
The previous section explains how steering a wheel generates the force necessary to force a vehicle to turn around a bend. However, bicycles and motorcycles must lean when taking a corner and this leaning also creates a lateral cornering force. In fact at all but the slowest of speeds and cornering accelerations this force will likely be the major contributor to the total cornering force, and the steering effects will just make up for the difference between the required cornering force and that provided by the lean. Hence, the degree of steering necessary on a motorcycle is much less than that required by a car. The lateral tyre force due to the tyre camber angle is known as camber thrust or camber force. Let’s look at Fig. 2.18 to see how this force is created.
Fig. 2.18 The top left sketch shows how the contact patch of the tyre flattens at an angle and effectively becomes a slice of a cone which tends to turn around the geometric apex of the cone. The other two diagrams show how this cone tries to turn a tighter circle than the actual bend radius.
As the inside edge of the tyre is forced to adopt a smaller radius than the outer edge, then for a given wheel rotational speed, the inner edge would prefer to travel at a slower road speed, this happens if the wheel is allowed to turn about a vertical axis through the apex of the cone. Just as a solid cone on a table would, if given a push. If the bike was leaning over at 45° then for a normal size tyre the horizontal radius to the cone axis would be approximately 450 mm, an impossibly tight turn. However, we’ve seen before that Conservation of Momentum will want to make the bike go straight which tends to work against this desire to turn about the effective cone centre, these conflicting effects will form a balance where the actual corner radius described is considerably greater than the cone radius.

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in other word the bike steer also because the bike wheel can be seen as a cone

and a rotation of a cone decribe a radius rotating

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Same radius and speed, but less lean angle would be more turn of the handlebar into the turn.

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It's a combination of camber thrust and steering angle.

At a 45 degree lean angle, the profile of the tire generates alot of camber thrust, like when you roll a cone on the ground, it rolls in circles.

Camber thrust at 45 degrees makes the bike want to turn at a radius of about 5 - 10 feet depending on your specific tire profile. This radius is much less of a radius we negotiate at the track. This is why we can have situations where the front wheel is actually pointing towards the outside of the turn during cornering rather than the inside. That is because camber thrust is TOO large.

without a rider on a bike, if it leans to 45 degrees at 100 meter radius is 112km/h

If you add a rider and rider is sitting on bike in the center same condition. 45 deg, 100m 112km/h

If rider is hanging off, 2 things can happen:

1) bike is leaning 43 degrees 100 meter radius 112km/h (contact patch to center of gravity angle is now 45 deg)

2) bike is still leaning 45 deg 100 meter radius ~120km/h (contact patch to center of gravity angle is now 47 deg)

Hanging off the bike reduces bike lean angle, so suspension works more efficiently and you gain more mechanical grip regardless of the coefficient of friction of your tire.

If you hang off the bike alot, you reduce the effect of camber thrust, and your front tire will have to turn more into the corner.

If you are a beginner rider, you do not need to hang off the bike because you don't need the extra 1% suspension effectiveness.

A bike doesn't fall because the steering rack can turn. It's not the rotating mass of the wheels.

If you weld your steering column so the front wheel cannot turn, your bike will fall.

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On 3/27/2019 at 9:46 AM, gianco said:

no no!

not so simple....

in that link is explained the correlation of sticking forces of tyre on tamrac, and tyre lean, and "deriva"

but don't concerns my question

and many assumption you made are wrong

read the book of tony foale on chassis deigns....

you'll be amazed of many info!!

if what you says was true, the rider that do japanese gimkana, due to high leaning of bike, shoud have handlebar no steered,

instead they combine both steer full stop lock and hig lean angle

The﻿ book that you have mentioned has the answer to your original question: "What makes the bike turn the same as it was leaned more without hanging off?

It is exp﻿lained in Chapter 3: Less lean angle requires more effective steering angle in order to keep the same radius of turn (please, see figure 3.18 of page 3-13): "Increasing lean angle tends to increase the effective steering angle."

It is a simple geometrical problem, there is no need to complicate it with camber thrust, slip angles, etc., because the magnitudes of the forces of cornering and the dynamic lean angle remain the same, either or not you hang-off.

The chassis reduces its le﻿an angle when the rider hangs-off while cornering, which changes the relative geometry among the three planes: the ones containing the rear tire, the steered front tire and the curve (track surface).

﻿

You may want to do the following experiment:

Fill up a wide recipient with water (the surface of the water will work like the plane of the curve).

Make a central 10-degree bend in a small rectangular piece of cardboard (one side will work like the plane containing the rear tire and the other side like the plane of the front ti﻿re).

Keeping the bent edge and both sides vertical, deep the piece of cardboard into the water.

Looking from above, turn the cardboard just like a bike would lean over ﻿to﻿﻿ turn and note how the angle formed between both lines that intersect the surface of the water and each side of the cardboard g﻿ets bigger a﻿s the lean angle increases.

That angle is the effective (or kinetic) steering angle, which would force the bike to turn tighter (﻿reduc﻿﻿e﻿﻿d﻿ radius of turn) if the rider would not compensate for this phenomena by steering a little less.﻿

If that experiment still does not convince you, we could use the following well stablished formula:

Radius of turn = [Wheelbase x Cosine of chassis lean angle] / [Steer angle x Cosine of caster angle]

As wheelbase gets a little bit smaller and caster angle remains constant, when the rider hangs off while cornering, the cosine of the chassis lean angle increases (example: cos 45=0.707 and cos 40=0.766).﻿

That change would increase the radius of turn some, making the bike run wide respect to the desired trajectory.

In order to avoid that from happening, the rider must compensate by increasing the steer angle a little.

Another﻿ geometrical way to analize that: Imagine a perfectly vertical line running underground by the center of the circular trajectory of the motorcycle.

Disregarding slip and camber thrust, the extended axis of both wheels must intersect with that vertical line.

As those wheels are leaned more, the point of intersection moves deeper into the ground, which reduces the angle formed between the e﻿xtended axis of both wheels.

Hence, the steering angle must be reduced some in order for the bike to keep tracing the same circular trajectory. ﻿﻿

A leaned motorcycle will always have an effective steering angle that is smaller than the one for a 4-wheel vehicle describing the same curve.

﻿

The exercise of Motorcycle Gymkhana is a different solution to a problem that is different: make the tightest quick turn around a cone.

The maximum speed at maximum lean angle will make you slower in this particular case, try that experiment as well.

Since speed must be much smaller than during normal Superbike track cornering, the smallest radius of turn of the rear tire is the key to turn the bike 180 degrees as quickly as possible.

For the same reason explained above, the Gymkhana rider wants the chassis to be as leaned as possible during the slowest section of the tight turn.﻿

At full stop lock of the steering, the radius of turn (and the circular trajectory of both tires) will be smaller as the chassis lean angle increases: there is a greater effective steering angle.﻿

Lock the steering of a bicycle at a pronounced angle and push it while at different sustained lean angles for each completed circle and you will see that the smallest circle corresponds with the biggest lean angle.

For the above formula and description of angles, please see "Steering angle" here:﻿﻿﻿﻿﻿﻿﻿﻿﻿

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mmhhhh very interesting!!!

undestood some principles that were "growing " in my head , but that i was not able to reach

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the difference in ginkana technique is that the max lean is obtained at low speed ?

i'm right?

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22 hours ago, gianco said:

the difference in ginkana technique is that the max lean is obtained at low speed ?

i'm right?

You are correct, Gianco.

It is about covering the course as quickly as possible, using street tires only.  The riders need to go fast between cones (or pylons), braking-in and accelerating-out very hard as well; that is why they install bigger than normal rear sprockets.  Around the cones the situation gets reversed and they need to go slow to rotate (change directions) as quickly as possible. They don't discuss cornering mph, but degrees of rotation per second.

Because centrifugal effect depends on the square of velocity and on inverse of radius, at very low velocities the radius becomes much more important in that equation.  If the rider reduces the radius to a minimum without quickly slowing down (as much as needed), the centrifugal effect will flip the bike out of the turn (bassically an out of control counter-steering).

At full lock (no chance to steer), the balance is achieved by braking (more lean angle and tighter circle) or accelerating (less lean angle and wider circle).  Of course, moving the upperbody in or out also changes lean angle and radius of turn (low speed = small gyroscopic effect), but main balance is carefully achieved by controlling a very accurate slow speed during a critical section of the circular trajectory.  Either or not parts of the chassis drag over the pavement is a consequence of all the above: proficient Gymkhana riders don't need or purposely look for maximum lean angle.

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