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## [Car physics] Wheels / Tire Traction torque

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### #1jujunosuke  Members

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Posted 30 June 2013 - 08:02 PM

Hi everyone,

I am not sure how i should calculate the traction torque that act as a brake/resistance on the engine.

For example, the real wheels of my car spins, and lets say that each wheels return 3000 Nm of Force.

I am pretty sure that to transform that force in torque i need to multiply the returned force by the wheel radius right ?

So, for a rear wheel drive car for example, the Traction Torque that act as a Brake on the engine would be

3000 Nm * wheel radius + 3000 Nm * wheel radius = traction torque of both rear wheels ?

Right now, i am doing 6000 Nm * wheel radius.

I am a little bit confuse.

At the moment, my car traction torque is very huge and my car acceleration feel quite slow.

The car doesn't rev very well.

Any feedback would be greatly appreciated.

Best regards.

### #2kunos  Members

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Posted 30 June 2013 - 11:06 PM

You forgot to insert the transmission ratio in your calculations. Engine torque is multiplied by the gear ratio, wheel torque is divided by the gear ratio.

### #3jujunosuke  Members

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Posted 30 June 2013 - 11:43 PM

Hi kunos, long time no see!

Thank you for your very quick answer!

Oh, i see! Now that you told me that it looks very obvious!

That is why my brake torque traction was so strong! (And very wrong because the brake force was the same for all gears...)

kunos, i just can't count how many times you saved me from the mess..

I will test and report (as i always do) but i am pretty sure that it will work on my problem is solved.

Best Regards.

### #4jujunosuke  Members

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Posted 01 July 2013 - 07:22 AM

Hum, i divided the traction torque by the gear ratio and now i got catastrophic results...

So traction torque seems completely out.

In the first 3 gears, the needle keep bouncing on the rev limiter like i had 3000 hp. (Now my car is arround 280 hp RWD).

I might be doing something wrong somewhere.

Just to recap,

Rev engine ---> getForce ---> multiply by GearRatios ---> getTheWheelsSlip on the ground ---> slipRatio Calculations ---> GetTractionForce that make move the car forward.

Then the TractionForce is multiplied by the Rear Wheels radius and divided by the gearRatios to get the traction Torque that will slow down my engine.

So, if i get 3000 Nm of force for a 1 wheel that mean 6000 Nm of force that make the car move forward.

Then

TractionTorque = 6000 * wheelRadius / gearRatios;

So

6000 * 0.34 / (3.82 * 3.26)     (first gear + final drive ratio)

= 2040 / (12.45)

= 164 (its ridiculously low!!)

At first i though i made a mistake and tried to multiply by the gearRatio instead of dividing it, but it just reversed the problem.

If the above pseudo code is correct, that mean that my problem is somewhere else then..

### #5kunos  Members

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Posted 01 July 2013 - 07:32 AM

164 nm is not low at all, same ballpark you should get from your engine

### #6jujunosuke  Members

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Posted 01 July 2013 - 08:20 AM

So, if 164 nm is not low at all, that mean that my above code is correct ?

Strange, i might have a problem or something i forgot somewhere..

My engine produce around 450 Nm at 3600 rpm.

I then divide the 450 Nm by the inertia of a cylinder and multiply it by the gearRatios

So @3600 rpm i get angularAcceleration = (450 / cylinderInertia) * gearRatios;

And that is how i got my angularAcceleration on the rearWheels.

Then

angularVelocity += angularAcceleration * Time.deltaTime;

### #7kunos  Members

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Posted 01 July 2013 - 12:56 PM

woah.. 450Nm @ 3600 ? Is that a truck ?

Anyway.. the calculation look correct to me.. perhaps the feedback torque from the tyres looks a bit low.. with a 1000kg car taking into account weight transfer and high performance tyres you're looking more into the 10000 Nm going back to the engine.. of course, in first gear, that's still not enough to stop wheel spin.. so when you see your RPM going to the roof that's right, you're spinning.

Another very important factor to consider is rotational inertia of the transmission. I am not sure if we have already covered the topic here, but, briefly, the angular inertia of the entire drivetrain (engine, clutch, gear, final, diff, wheels) "seen" by the engine is different from the intertia "seen" by the wheels.. the calculation is tricky and  a good starting point to figure out the math (it worked for me) is this: http://www.racer.nl/tech/effinertia.htm

### #8jujunosuke  Members

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Posted 01 July 2013 - 07:26 PM

I made a mistake its 350 Nm @ 3200 (BMW M3 E36)

Still very powerful

The fact is i was used to play with wrong torque feedback (forget to multiply by gear ratio), so my torque feedback was insanely strong.

And i made all the other car settings based on that setting.

So yesterday i tried to play a little bit with the "new" settings and by increasing the grip on the wheels, and tweaking the cylinder inertia formula, i get much more decent results now.

Also my Tachometer RPM needle feel really smooth hehe.

Thank you for the link, i have some reading now.

I am a little bit scared every time i have to add one more thing to my transmission model (which is quite complex already).

Its just another chance to forget something and make a single mistake that will screw up all the calculation

But i consider this topic as answered!

Thank you very much for your time dear kunos!

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