# Motorcycle model and tire force

• I
• LucaCaiaffa
In summary, the problem is that the wheel hub does not rotate with the tire, so the rear radius is not included in the equation for the generalized force.This results in same vehicle acceleration but different applied torques, but i don't know how to handle this issue.

#### LucaCaiaffa

I'm having issues in the application of tire forces while deriving a multi-body model of a motorcycle via Lagrange.

In particular, I considered several bodies that are: swingarm, main frame,
front upper fork, front lower fork and wheels.

I suppose the wheels to have zero slippage, then knowing the wheel rear torque
as ##T## and the rear radius as ##R_r## we have that ##F_x=T/R_r##

The kinematic model is correct and also forces from suspensions (the model
have been validated).

The problem arises from the application point of ##F_x##.
While calculating the generalized force from ##F_x## the rear radius disappear,
meaning that the applied force acts like if it is applied in the center of the rear wheel instead of the contact point of the tire.

This results in same vehicle acceleration but different applied torques, but i don't know how to handle this issue.

I saw that many models found the same problem, but i don't get the point why this appears.

The represented force points in the wrong direction.
The pavement-tire contact patch is the fulcrum of a lever.
The chain applied force is at top of the rear sprocket, the reaction force is applied to the axis of the tire, which moves forward, pushing the chassis via swingarm.

Last edited:
LucaCaiaffa said:
While calculating the generalized force from ##F_x## the rear radius disappear
What do you mean by "it disappears"?

Lnewqban said:
The represented force points in the wrong direction.
No, it's not if it is the reaction force from the ground acting on the motorcycle.

jack action said:
What do you mean by "it disappears"?
I mean that there is no difference in applying the longitudinal tire force in the contact point or in the wheel hub.

This happens because no generalized coordinates relates the wheel hub and the tire contact point, and their jacobians for computing the generalized forces result the same.

For this reason I think I am "losing" a torque contribution in doing this.

Simplifying the problem, if i consider the motorcycle as a unique rigid body, I should have a torque contribution from the longitudinal force as ##T=F_xh## where ##h## is the height of the center of mass.

My model instead seems to lose the radius from the height of center of mass.

LucaCaiaffa said:
This happens because no generalized coordinates relates the wheel hub and the tire contact point,
I don't have real experience with the Lagrange equation, but can't you include the rotational wheel mass and angular velocity? The wheel angular displacement ##\theta## does relate to the motorcycle displacement ##x## with ##x= \theta R_r##.

Lnewqban

## 1. What is the importance of tire force in motorcycle models?

Tire force is crucial in motorcycle models as it directly affects the stability and handling of the motorcycle. The force exerted by the tires on the road is what allows the rider to accelerate, brake, and navigate turns safely and efficiently.

## 2. How is tire force calculated in motorcycle models?

Tire force is calculated using a complex mathematical model that takes into account factors such as tire size, pressure, tread pattern, and road surface. These calculations are typically done using computer simulations and can vary depending on the specific motorcycle model and tire type.

## 3. How do different tire types affect the force in motorcycle models?

The type of tire used in a motorcycle model can significantly impact the force exerted on the road. For example, a slick racing tire will have more grip and therefore generate more force compared to a touring tire with a tread pattern designed for longevity. The type of tire also affects factors such as cornering ability and braking distance.

## 4. Can tire force be adjusted or customized in motorcycle models?

Yes, tire force can be adjusted to some extent in motorcycle models. Riders can change tire pressure, tread pattern, and even tire size to alter the force exerted on the road. However, these adjustments should always be made with caution as they can greatly impact the handling and safety of the motorcycle.

## 5. How does tire wear affect the force in motorcycle models?

Tire wear is a crucial factor that affects the force in motorcycle models. As the tire tread wears down, it loses its ability to grip the road, resulting in decreased force and potentially dangerous handling. It is essential for riders to regularly check their tire tread and replace worn tires to maintain optimal force and safety on the road.