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# tire temperatures for racing game

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does anyone know of a good source of how to model good tire temperature readings for a racing simulation? not talking about pressure stagger and camber just yet, just based on weight transfer, convection, conduction, material of tire, and friction. a2k

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I don''t know of any links, I''m not exactly an expert myself. but my dad used to drag race in NHRA. I''d just thought I''d throw out that there are different tires that they use. normal tires for everyday stuff, and slicks for rainy wether.

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newtons law of cooling/heating is some exponential function (which i can''t think of right now). you could probably just use C*e^(-a*x) and pick some values of ''C'' and ''a'' until you got it how you wanted it.

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If friction slows the car from A m/s to B m/s, then

heat energy gained = KE lost = .5 * mass * (A^2 - B^2)
temperature rise = heat energy gained / mass / heat capacity of rubber

temperature rise = .5 * (A^2 - B^2) / heat capacity of rubber

Unfortunately, I have no idea what the heat capacity of rubber is, so some experimentation will be needed.

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still, the temperature won''t rise at a constant rate.

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I have ''Tires, Suspension and Handling'' by John Dixon, which goes into some detail on how the how temperature effects tire properties, though not enough to construct a detailed model.

I think a detailed model would be overkill. Under normal driving (e.g. the tire not flat, not under heavy braking) you can assume the tyre symmetric, and then you are only interested in the temperature at the contact strip which you can treat as uniform. As the stresses are also applied at this strip you can treat it as a simple object in it''s own right.

Better might be something like:

dT/dt = f(stress) - k(T - T0)
or

T'' = T + timestep * (f(stress) - k(T - T0))

where f is a simple (e.g. linear) fn of the stresses on the tire, k is a constant (which takes account of heat dissipation to the rest of the tire) and T0 the ambient/air temperature. Then use a lookup table to translate the temperature to tyre properties such as grip and slip properties, one table for each tyre type/compound/design based on manufacturers data.

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quote:
Original post by Beer Hunter
If friction slows the car from A m/s to B m/s, then

heat energy gained = KE lost = .5 * mass * (A^2 - B^2)
temperature rise = heat energy gained / mass / heat capacity of rubber

temperature rise = .5 * (A^2 - B^2) / heat capacity of rubber

Doesn''t this formula apply to tyres only when they are locked (producing skidmarks and smoke :-)?
When tyres aren''t locked the temperature rise is gained by the braking discs.

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quote:

When tyres aren''t locked the temperature rise is gained by the braking discs.

I don''t think so. The brake''s dissipate thier own heat. They can get very hot and it would do the tires no good if this heat was transferred to the tires. Also the heat generated by the discs varies greatly depending on driving conditions, and it would be difficult to maintain a steady tire temperature having to take into account such variations.

Rather the heat comes from the internal and external frictional effects acting on the tire rubber. You can generate the same effect yourself - take a fork, bend it backwards and forwards repeatedly and it gets warm. That''s why to warm up tires drivers can be seen snaking from side to side to stretch the tire rubber and so warm it up, e.g. in the warm-up lap of a race.

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I would like to know what type of racing game you are making, tires react differently in different types of racing, if i knew what type of racing i could better help you.

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The heat build up in the tire is not only due to the work done on deforming the rubber but also due to the work done by the rubber on the road. The rubber imparts energy to the road and the road reacts imparting energy to the tire (that''s how the car moves!) This is all achieved because there exists a friction between the rubber and the tire. So, there should be a frictional heating term in your differential equation and a deformation heating term. Details of adequate models are above.

Cheers,

Tim

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it''s a game like nascar 4.

i have tire load (including the weight transfer), rate of rotation of the tire, and the slickness of the tire (due to wear and road surface) worked into the equation, but not the friction factor (which i do feel is an important part of it, because tires heat up when you brake and skid the tires against the road).

so far, johnb''s function works best because it takes into acct heating, cooling, and not exceeding the lower limit of the atmospheric temperature.

a2k

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You''ll have to know the coefficient of the friction for both the tire and the surface upon which the tire is exerting force. I guess if you want to get really technical, you will have to keep up with the changing properties of the tire as it heats (frictional and otherwise).

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The next time I run into one of my buddies I''ll ask them (most of them are automotive engineers, and one if them works with tires).

If I remember correctly, an average automobile''s tires heat up to about 150F on the freeway (or was it 250F...).

Anyway, the first thing they teach you in automotive engineering is to take any theory you have and toss it, ''cause it''s oh-so-rarely accurate. You need empirical data, and models based on that data.

The problem of dynamicly determining tire temperature is far more complicated than just plugging in the coef. of friction and speed. There''s force convection involved, which means the friggin'' temperature and humidty of the air matters. Alot.

Braking will affect the tire temperature, eventually. How much and how fast are the hard questions to answer. If a vechicle brakes too much for too long you can boil your brake fluid... or glass-over your brake bads (the material the brakes are made out of lose effectiveness (frictional forces) as the temperature increases, critical so at a high enough temp. which of course depends on the brake).

In short, if you want to know how a tire behaves; you have to test it and collect data on _that type of tire. If the manufactoring processes are consistent, all tires of that type will perform likewise. If you want to know how tires in general behave, you have to collect and analyze data on a pile of different tires.

General newtonian physics just doesn''t correlate the the real world very well. There''s too many assumptions made to make the math easier, that don''t hold true.

PS I write software to test brakes for a living.

Magmai Kai Holmlor
- The disgruntled & disillusioned

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yes, i''ve also worked in convection, but a fake one based on the rate of rotation of the tire. it works okay for now. my "data collection and analysis" has only consisted of studying nascar racing 4 tire temps, and that''s about as far as i''ll go with analysis, other than other formulas that other people may have. thanks for the help guys, keep the ideas coming...

a2k

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