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I have been some discussion about this topic but everytime people ends talking about counter steering and leaning in order to compensate for the centripetal force and don't fall, but those are not my questions here.

I know that to start leaning you have to counter steer (my question is not about how to lean) and I know that if you turn your front wheel without leaning you will fall to the opposite side because of centripetal force (my question is not why you have to lean to turn at speed).

My question here is why a motorcycle that is already leaning, and with the wheels straight turns around instead of just going straight?

I have seen two possible answers, one says that the bike wants to fall to the inside but as you are going at speed it just keep going in circles (like a coin rolling on its corner) and the centripetal force helps you to not fall to the inside. But, can a bike go straight if it is leaning but the CoG is completely centered as if it was straight?

The other answer was about the difference in diameter between the center and the sides of the motorcycle wheels, but a coin has de same diameter on the sides that on the center and it still turns when is leaning.

What is the correct one? Why an already leaning bike with both wheels straight turns instead of going straight? Why the bike below turns to the right if the front wheel is pointing straight forward?

Example image of a bike turning with both wheels straight

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    $\begingroup$ It looks like the wheel is straight at this moment. Perhaps it is because the driver must continually adjust, and sometimes it is straight. Perhaps it is slightly turned. On the average, the wheel must be turned for the bike to turn. veritasium.com/videos/2021/11/30/… $\endgroup$
    – mmesser314
    Commented Feb 25, 2022 at 15:31
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    $\begingroup$ Re, "if you turn...without leaning you will fall." Also, if you lean without turning you will fall. In aviation, the condition of having the appropriate "lean" for the radius and rate of turn is called a coordinated turn. I don't know if motorcycle riders have a special name for it though: In aviation, an un coordinated turn is a maneuver that you can do without harm. On a motorcycle, not so much. $\endgroup$ Commented Feb 25, 2022 at 18:46

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Considering the construction of front wheels, the point of a tyre touching ground is few centimeters behind the intersection of ground plane and extrapolation of rotation axis.

The primary idea of this design, shared with bicycles (I am an active bicycle rider), is direction stability of a motorbike/bicycle. With decreasing distance of these two points, a vehicle becomes directionally unstable (like when you release the hand grip) and have tendency to sudden direction change. With switching of the position of these two points, a vehicle would become a suitable device for circus artists.

As the secondary side effect, when the vehicle leans, even if set to go straight-ahead, the distance of these two poins forms alloes forming a torque trying to turn the wheel in agreement with leaning direction.

A torque is for rotation moving as a force is for translation moving. A nonzero net force starts linear acceleration of an object. Similarly, a nonzero torque starts angular acceleration of an objects. The torque $\vec M=\vec r \times \vec F=\vec r \times amg \cdot \sin{(\alpha)}\vec n$, where

  • $\vec r$ is the distance between "trail" and "tyre patch" from the picture below (more exactly, its projection perpendicular to the rotation axis).
  • $\alpha$ is the leaning angle
  • $m$ is total bike mass
  • $g$ is gravitational acceleration
  • $a$ is coefficient of distribution of weight between the wheels
  • $\vec n$ is a unit vector perpendicular to bike direction, parallel to surface.

See e.g. the article calfeedesign.com - geometry-of-bike-handling and referred picture:

geometry-of-bike-handling

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  • $\begingroup$ I think you answer is about why leaning makes the front wheel turn. But after any action that makes a bike turn, a motorcycle leaning with both wheels parallel or straight is still turning, that is what I don't understand, the front wheel is not making it turn (it is parallel to the rear wheel), still it does, why? :/ $\endgroup$
    – BraisC
    Commented Feb 25, 2022 at 14:00
  • $\begingroup$ @BraisC Yes, my answer is about that, according to how I have understood the question. I am sorry if I have misinterpreted it. I have addressed this: My question here is why a motorcycle that is already leaning, and with the wheels straight turns around instead of just going straight? In other words, why leaning makes you turn? and ending: Why a leaning bik with both wheels straight turns instead of going straight? Leaning causes torque, torque causes wheel turn, turned wheel cause turning. $\endgroup$
    – Poutnik
    Commented Feb 25, 2022 at 14:07
  • $\begingroup$ okay maybe I wasn't completely clear as english is not my mother language. Lets imagine that we just take a bike and put it magically on the road already leaning to the right (just ignore everything that happens between straight to leaning), with both wheels pointing to the same point, just exactly as if it was going straight but leaning to the right, then we give it some speed, it will turn even when both wheels are going straight, what makes it go right? It is not the front wheel as it is pointing straight. I edited a little bit my question, I hope it is clearer now. $\endgroup$
    – BraisC
    Commented Feb 25, 2022 at 14:17
  • $\begingroup$ The front wheel will not stay straight for long, due the torque. see the answer update. ( I m not native either. :-) ). $\endgroup$
    – Poutnik
    Commented Feb 25, 2022 at 14:31
  • $\begingroup$ So a leaning motorcycle, even if it looks like the front wheel is straight (I suppose it can be turning slightly and looking like straight) , turns because the front wheel is turning? $\endgroup$
    – BraisC
    Commented Feb 25, 2022 at 14:34
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A bit late to the response but here goes:

There are multiple factors that come into play - the physics of it is pretty involved, but the most important thing is Camber Thrust

When a cone is placed on the ground , it wants to roll in a circle. If it is forced to go straight, the inner side of it will have slippage against the ground. In motorcycles the cone angle is defined by lean angle, but the cone turning radius is way lower than what any bike ever can corner at. This means there is a scrubbing force trying to make the bike go in a tighter turn - this is termed "Camber thrust".

This mismatch between the cone radius and the actual turn radius at the given lean angle and speed is what makes the sides of the tires get shredded when cornering.

There is only one speed and lean angle (probably a very low one) and one radius where the cone turn radius matches the bikes turn radius.

In all other cases, there is either an excess or dearth of camber thrust.

In order to manage this, the rider turns the front handlebar to introduce slip angle. When camber thrust is not enough, steering into the curve increases the front slip angle, compensating for the lack of camber thrust

When camber thrust is too high, turning away from the inside of the curve does the inverse, reducing the effect of camber thrust.

You can notice the latter phenomenon with flat track dirt racing where everyone's front wheel is actually pointed away from the inside of the curve.

There is also one more aspect - In a straight line, the momentum of the bike acts on the contact patch to keep the front wheel in line with the back - the same applies when there is a steering angle - there is a force that acts to return the front wheel in line with the back.

The geometry of the bike determines how much this force is - sport bikes have less of it due to reduced rake and trail while larger road going bikes have more of it. This is what determines steering effort, since the rider has to fight this force to keep the steering angle fixed.

Tony Foale is a fantastic resource for this stuff - https://motochassis.com/Articles/Tyres/TYRES.htm

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