Oppo: Maths Question

"Maxima Speed" (maximaspeed) 10/12/2018 at 23:16 • Filed to: None

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Ok so here’s what I’ve got. I am trying to calculate the temperature increase of tire from stationary non running ambient temperature up to its plateau during the trip. The work truck has digital tire monitors which give me live pressure readings. Here are the stats I have, is it possible to calculate the temperature increase with some proximation of accuracy? If so how do I do that, thanks.

Initial tire pressure: 68 lbs

Initial ambient temperature: ~ 51 degrees Fahrenheit

Initial humidity: ~ 81%

Initial Altitude: ~614 ft

Peak Tire Pressure: 74 lbs

Ambient temperature at peak pressure : ~ 51 degrees Fahrenheit

Humidity at peak pressure: ~ 81%

Altitude at peak pressure: ~614 ft

farscythe - makin da cawfee! > Maxima Speed 10/12/2018 at 23:28

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the answer is 42

Aremmes > Maxima Speed 10/12/2018 at 23:32

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This could be solved with a modicum of accuracy assuming some variables (constant volume, ideal gas, no heat loss, etc). However, you’re missing the volume, i.e. the tire's interior volume, since that determines the mass of air in the tire that results in the temperature-induced pressure increase. In other words, what tire size does your work truck use?

The Dummy Gummy > farscythe - makin da cawfee! 10/12/2018 at 23:32

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this guy lives in the universe .

gmporschenut also a fan of hondas > Maxima Speed 10/12/2018 at 23:34

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goodyear estimates 1-2psi for every 10deg F ambiant temp . Driving will warm up the tire, warming the air inside. After a while (going by 6psi increase, I would guess. 30-60F warmer than ambiant temps. Now was this peak pressure while moving?

The Dummy Gummy > Maxima Speed 10/12/2018 at 23:35

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T ire pressure will go up approx   1psi  for every 10 degrees F. So you’re looking at an increase of 60degrees.

Maxima Speed > gmporschenut also a fan of hondas 10/12/2018 at 23:36

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Yes

Maxima Speed > Aremmes 10/12/2018 at 23:37

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Aha, I thought about that and should have grabbed the specs but I didn’t. Will have to do that next time.

gmporschenut also a fan of hondas > Maxima Speed 10/12/2018 at 23:40

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using ideal gas law pv=nrt. N, R, shouldn’t change. Assuming V is the same (moving, flexing tire would be weird). P1/T1=p2/t 2. coverting psi to kpa, 468kpa/283 kelvin= 510 kpa/t2, so 308kelvin or 95F

Maxima Speed > gmporschenut also a fan of hondas 10/12/2018 at 23:46

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Wow, hard core maths. My brain might be sizzling  Thanks.

gmporschenut also a fan of hondas > Maxima Speed 10/13/2018 at 00:15

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part that gets a bit weird is how tire flex affects volume. 

ttyymmnn > farscythe - makin da cawfee! 10/13/2018 at 00:18

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Yes, but do you have your towel?

farscythe - makin da cawfee! > ttyymmnn 10/13/2018 at 00:25

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always

You can tell a Finn but you can't tell him much > gmporschenut also a fan of hondas 10/13/2018 at 01:07

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That shouldn’t matter since the volume of the tire remains the same whether it’s hot or cold. Your reply saying to use the ideal gas law will give a decent approximation for the temperature rise. There will be some error due to all the assumptions in the ideal gas law, but the answer should be in the ballpark. 

I like cars: Jim Spanfeller is one ugly motherfucker > Maxima Speed 10/13/2018 at 10:35

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PV=nRT. N, V, and R are constant, so rearrange so they’re on the same side, you get P/T = nR/V. You have your initial and final P and initial T, so solve for final T with Pi /Ti = Po/To. Rearranging, you get To = Ti* Po /Pi . Using T in Kelvin, you get To = 96 F. 

Maxima Speed > I like cars: Jim Spanfeller is one ugly motherfucker 10/13/2018 at 10:47

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Thanks, gmporschenut came up with 95F. Id say between  95F -96F is plenty close enough for some idle musing :)