# Is the Hertzian Contact Model Suitable for Simulating Car Braking on Wet Roads?

• ROOT0X57B
In summary, the physics teacher recommended a "solid, undeformable" tire model for this homework, but after investigating further, the student found that this is not realistic and is instead an optimization problem. After looking for published papers on the topic, the student found two places to start.
ROOT0X57B
Homework Statement
How does the presence of water on the road influence the emergency braking distance of a car?
Relevant Equations
-
Hi there!
First of all, I do not have a clear homework statement or relevant equations to give but I still put this thread in here because it's related to school work and I've previously got a warning for not doing so.

I'm a french student who is going to start his second year after high school in september.
At the end of the year, I will have competitive exams to get into an engineering school.
For this exam, I have some research to present. I work on "How does the presence of water on the road influence the emergency braking distance of a car?".
I would like to have a preferably simple but rather realistic physical model of a tire to simulate a car braking with and without water on the road surface.

My physics teacher told me that with a "solid, undeformable" tire model like I use to do in this thread, I will be way too far from reality and told me to try the Hertzian model, which he told me was quite simple.
Problem is, that the very first hypothesis of the model is that there is only a normal force, thus no friction. This makes me quite skeptical about the relevance of this model. Moreover, after two weeks of research, I haven't seen anyone using it in the context of a moving vehicle.

So do you think this model may fit my needs? Or what other model could I take a look at?
I'm thinking about the JKR model, which seems to be very close to the one of Hertz, but admits friction.

ROOT0X57B said:
Homework Statement:: How does the presence of water on the road influence the emergency braking distance of a car?
Relevant Equations:: -

Hi there!
First of all, I do not have a clear homework statement or relevant equations to give but I still put this thread in here because it's related to school work and I've previously got a warning for not doing so.

I'm a french student who is going to start his second year after high school in september.
At the end of the year, I will have competitive exams to get into an engineering school.
For this exam, I have some research to present. I work on "How does the presence of water on the road influence the emergency braking distance of a car?".
I would like to have a preferably simple but rather realistic physical model of a tire to simulate a car braking with and without water on the road surface.

My physics teacher told me that with a "solid, undeformable" tire model like I use to do in this thread, I will be way too far from reality and told me to try the Hertzian model, which he told me was quite simple.
Problem is, that the very first hypothesis of the model is that there is only a normal force, thus no friction. This makes me quite skeptical about the relevance of this model. Moreover, after two weeks of research, I haven't seen anyone using it in the context of a moving vehicle.

So do you think this model may fit my needs? Or what other model could I take a look at?
I'm thinking about the JKR model, which seems to be very close to the one of Hertz, but admits friction.
The first thing to do is take what you have learned so far to the teacher and ask if he would change his recommendation based on your information.

Sure, but it's vacation time and I don't have any way to join him, that's why I'm asking here actually.

Note : we haven't seen anything about the physics of deformable materials and surfaces.

ROOT0X57B said:
Sure, but it's vacation time and I don't have any way to join him, that's why I'm asking here actually.

Note : we haven't seen anything about the physics of deformable materials and surfaces.
I suggest researching the problem looking for published papers dealing with the topic and then apply the appropriate level of detail for your project.

Here are a couple of places to start; https://www.researchgate.net/publication/242572582_DETERMINATION_OF_BRAKING_DISTANCE_AND_DRIVER_BEHAVIOUR_BASED_ON_BRAKING_TRIALS

https://www.trafitec.dk/sites/default/files/publications/braking distance - friction and driver behaviour.pdf

What does the term "Hertzian contact" mean?

## 1. What is Hertzian contact with friction?

Hertzian contact with friction is a phenomenon that occurs when two surfaces come into contact and experience frictional forces. It is named after the scientist Heinrich Hertz who first studied the mechanics of contact between two solid bodies.

## 2. How does Hertzian contact with friction affect the surfaces in contact?

Hertzian contact with friction can cause wear and damage to the surfaces in contact. This is because the frictional forces between the surfaces can generate heat and cause material to be removed from the surfaces.

## 3. What factors influence Hertzian contact with friction?

The factors that influence Hertzian contact with friction include the materials of the surfaces in contact, the surface roughness, the amount of force applied, and the speed of the contact.

## 4. How is Hertzian contact with friction measured?

Hertzian contact with friction can be measured using various techniques such as tribometers, which measure the frictional forces between two surfaces, or profilometers, which measure the surface roughness of the contact area.

## 5. What are the practical applications of understanding Hertzian contact with friction?

Understanding Hertzian contact with friction is important in various industries such as manufacturing and engineering, where the contact between two surfaces is crucial for the functioning of machines and equipment. It also helps in developing better lubricants and materials to reduce wear and damage caused by friction.

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