# Forces on a tire and correct Angular Velocity of a wheel in vehicle simulation !?

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Hi to all, this is my first post and i just signed up to this forum to eventually get some help on this topic... I am also learning math/physics related to vehicle physics... and i already did some implementation on vehicle based on some papers and other programs available for Unity Engine. I wrote a tire simulation based on Pacejka ( from Brian Beckman's paper ) and i had the vehicle traveling well enough for a time until i started to add more of the torques applied naturally to the tire.

This might sound a little noobish but i try learn

So i am having problem to understand how you would integrate all the torques/forces applied to the tire and then calculate the angular velocity from all of these torques/forces.

1. What are considered all of the basic torques/forces applied to the tire in order to get it work correctly ?

What i am doing now is:

• adding free rolling based on wheel velocity ( a little confusing while there may be some driving torque also applied, and also saw another implementation that there is no free rolling calculation but it is somehow coming into the simulation )
• adding drive torque from engine
• adding friction torques ( brakes / handbrakes)

My problem is that if i change the order of these forces, i get some weird problems like torque from engine is no more applied.

2. So is there a correct order of adding all of the needed forces or they can be added in any way ( for example first engine torque and then brake torques or vice versa etc... ) ?

3. Do you need to zero out the angular velocity in the beginning of the frame or it is continuously integrated over time ?

If someone could try explain the idea behind correct way of applying forces and calculate angular velocity would be so great !

Thank You !

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Posted (edited)

Well, if the angular velocity is the rate of change of the rotation angle of the wheel, it depends on the distance (distance / 2 * p i * r) and the time needed to travel that distance (from the travelling speed). In this case the speed and the distance would have to be calculated before the angular movement of the wheel. But if you come the other way, from the engine's torque, force at the wheel and deduction of all types of friction etc., then the wheel spinning speed would have to be computed first and the travelled distance and angular velocity would be outcomes of the integration.

Could this be of help for the force calculation ?

Or are you looking for something more sophisticated ?

Edited by Green_Baron

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Posted (edited)
42 minutes ago, Green_Baron said:

Well, if the angular velocity is the rate of change of the rotation angle of the wheel, it depends on the distance (distance / 2 * p i * r) and the time needed to travel that distance (from the travelling speed). In this case the speed and the distance would have to be calculated before the angular movement of the wheel. But if you come the other way, from the engine's torque, force at the wheel and deduction of all types of friction etc., then the wheel spinning speed would have to be computed first and the travelled distance and angular velocity would be outcomes of the integration.

Could this be of help for the force calculation ?

Or are you looking for something more sophisticated ?

Hi, thanks for the feedback. I went many times through this website and many others.

As you mention i am calculating free rolling by using the distance traveled and the 2 * pi * wheel radius which by itself it's working perfectly !

Also, if i get torque from engine only, without calculate braking and free rolling etc. and transfer the torque to wheels, i get the correct wheel spin and forces applied to wheels ( at least it looks correct, as when angular velocity gets small after releasing throttle, the wheel stops rotate and with small friction the car is moving but wheels are not free rolling - this was for the sake of the test which seems ok ) !

The point is that i struggle combining all the forces because i am not really sure if i do all of them and in correct way.

What i am trying to do now is:

1. calculate free rolling first and integrate the angular velocity

2. then calculate drive torque ( the engine torque ) and Integrate angular velocity again.

3. then, based on wheel movement ( velocity ) and current angular velocity i calculate the SlipRatio and SlipAngle and based on them calculate road friction force and integrate angular velocity again.

4. then calculate braking forces, and integrate changes into angular velocity.

This is all i am doing and it does not work, like the car is not moving and brakes are not working.

I am not sure if this is correct in terms of order and math. I think i got all formulae correct as i checked them many times.

So, it's like is there any difference if you should calculate all of these forces in specific order and if you should calculate angular velocity after you have added all the forces to the tire and get the correct values to integrate the angular velocity step ?

I just need some basic explanation on how one suppose to integrate all of the torques and forces and in what order just to be sure i am doing all correct or all wrong  .

Edited by ventsi

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Posted (edited)

I think what you're looking for is numerical integration. Calculate the different forces/time independently and after all have been determined, integrate them, for example by calculating some sort of midpoint between them all. That should work, and then the sequence would not matter.

But maybe a more experienced person shows up and elaborates further 🙂

Edited by Green_Baron

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As @Green_Baron mentioned, separating the force/torque calculation and integration is a good idea. In theory the order should not matter. But, since the brakes could lock up the wheels that could introduce some extra "fun"

On 5/17/2019 at 3:36 PM, ventsi said:

1. calculate free rolling first and integrate the angular velocity

In normal circumstances you would not need to care about this at all. The free-rolling angular velocity is a derived value and has nothing to do with the simulation. Your others steps seem right to me.

You only need the torques that change the speed of the wheel and don't have to zero the angular velocity! The torques only give you the angular acceleration that change the velocity in every frame.

On 5/17/2019 at 3:36 PM, ventsi said:

Also, if i get torque from engine only, without calculate braking and free rolling etc. and transfer the torque to wheels, i get the correct wheel spin and forces applied to wheels ( at least it looks correct, as when angular velocity gets small after releasing throttle, the wheel stops rotate and with small friction the car is moving but wheels are not free rolling - this was for the sake of the test which seems ok ) !

This might not be related, but at low speed you can expect some problems. The tire formula is designed to work at speed. Below around 5m/s it becomes "unstable". That shouldn't affect the overall movement of the car, but the angular velocity calculation gets problematic.

Search for Tire relaxation length method or SAE950311, also there is a simpler way of doing it but I don't remember its name

For me it looks like this:
if (ground_seed < 1)
slip_ratio = 2 * (wheel_speed - ground_speed) / (1 + ground_speed^2)
else ... use normal slip ratio calculation...

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Posted (edited)

Hi @bmarci, thanks for the input.

I am still learning and as i read more and more in internet, there seems to be quite some tricks involved in the whole tire simulation.

16 hours ago, bmarci said:

In normal circumstances you would not need to care about this at all. The free-rolling angular velocity is a derived value and has nothing to do with the simulation. Your others steps seem right to me.

1. If i understand correctly, this suppose to get calculated when subtracting the angular velocity based on road friction force which should still be some value with small slipRatios from where the free rolling effect is coming !?

16 hours ago, bmarci said:

This might not be related, but at low speed you can expect some problems. The tire formula is designed to work at speed. Below around 5m/s it becomes "unstable". That shouldn't affect the overall movement of the car, but the angular velocity calculation gets problematic.﻿

Search for Tire relaxation length method or SAE950311, also there is a simpler way of doing it but I don't remember its name

For me it looks like this:
if (ground_seed < 1)
slip_ratio = 2 * (wheel_speed - ground_speed) / (1 + ground_speed^2)
else ... use normal slip ratio calculation...

2. I get the car shaking when it's stationary only  but slowly moves to the left. I also get a strange behavior when using the Brian Beckman's combined force method. If i put car in scene origin and start drive forward as soon as i start turn left or right the car accelerate a lot. This might be related on slip ratio values, but i am not really sure. Is it normal to actually get such behaviour ?

I did implement a slip ratio method based on this web site (http://web.archive.org/web/20050308061534/home.planet.nl/~monstrous/tutstab.html),  which seems to be based on SAE950311 with removing of the oscillation, but the wheels start to change their rotation direction when drive for a little and slipRatio can go high as 7-80 . Looks so strange but i am not sure why is that happening

I may be having some bugs or there is still some work to be done just to get the wheel turn correctly !

3. This paper shows a Non-singular slip ratio method, but it's paid. Still if some one is interested and not aware of it !

Edited by ventsi

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1 hour ago, ventsi said:

That telemetry data is suspiciously similar to the Telemetry of Vehicle Physics Pro

Even I recall old versions (~3 years ago) using the label "Angular velocity Y" instead of the current "Yaw rate", and the engine data showing "load/torque" only instead of the current "load/torque/power".

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Hi Edy

yes, in a matter of fact you are my main inspiration and i tried your demos many many times and started read papers in the will to create a custom vehicle physics myself based on Brian Beckman physics and Unity's AVP for this Drift Challenge Game i want to build for so long time. This telemetry is based on yours but i haven't implement all the things and there is stuff just sitting there !

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Great, keep the good work!

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