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And if you live at 7000 ft like me?....the inside the tire sensor can’t compensate for the reduced air pressure surrounding the tire. My tires at a sensor reading of 32psi are firmer than if I was in Houston at the same sensor reading.
 

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Mark – 2015 R1200R-LC Exclusive
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I believe ‘cold’ means before riding, as the tyre temperature rises substantially above ambient when in use. As you say, @Dougl, ambient temperature is not of great significance.
 

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And if you live at 7000 ft like me?....the inside the tire sensor can’t compensate for the reduced air pressure surrounding the tire. My tires at a sensor reading of 32psi are firmer than if I was in Houston at the same sensor reading.
The tire is presumably rigid so it shouldn’t expand like a weather balloon with increasing altitude and the pressure inside won’t change. However your tire gauge has a diaphragm or transducer which works against ambient pressure. It reads higher at higher altitude. However, the TPMS should read absolute pressure. As I live at 5000 ft, this would explain why the TPMS reads 2-3 lbs lower than the gauge when the tires are “cold” and the ambient temperature is about 20C.
 

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@Dougi
Damn it's been a long time but what you reference, sorta, is the Ideal gas law. What this law states is that a given volume of gas (the air in your tires) will increase as temperature goes up. The volume does not stay the same. It increases slightly, but since the tire is a confined space with limited expansion, as the temp increases so does the pressure. The number of molecules in the tire remains constant, but they spread out more, and bounce around more exerting a higher pressure.

@r0ckrat
I don't disagree with you, but I think this is a fuzzy area as you may not reach optimal temp on your ride. I know tires get "hotter," but how much? (IN the Patent you sent there is a temp sensor, but does that exist in ours?). I am just throwing this out there because this topic has come up ever since TPMs on BMW existed...like over 10 years? and often what the conventional wisdom is, is to say screw the tpm, I am just going to use my XYZ digital gauge that Joe at XYZ mechanic told me was the best...or something like that. Admittedly TOTALLY unscientific and probably approaching Luddite. TBC, that is NOT me. Like y'all, I think about this also (not a lot because I have a life, but ... :))
What I do is I check the temperature of the garage. If it is nearly 68F I use my "trusty pencil gauge" and fill to 36/42 and my OBD will show close to 36/42 and sometimes right on the mark.
If it is warmer, the usual circumstance (New Orleans) I will inflate to read a bit higher, say 38ish/43ish and my OBD usually shows pretty close to 36/42. The garage rarely gets colder than 64 and at that I'll go with ~~~35/40+. Works for me, but that's a result of a lot of trial and error. I always check the OBD TPM when I am just starting out to note how close my gauge is to the OBD. And yes, when cold I don't do any acrobatics until the engine temp is normal

@Panzermann
I notice some minor changes in the readings as I am underway, but never really paid attention to the changes, they are slight, but to the actual number. If it's close to fine, I switch back to RANGE.
I think PSI may be more accurate than bar in that there are nearly 15 psi_s in 1 bar. The bar readout is in tenths so it is a grosser number, so between 2.0 and 3.0 bar there are 15 psi. IOW it is possible for small changes in PSI to go un-reflected in your bar readout. The differences would be slight

BTW, this is the BEST discussion of this topic I have encountered on any BMW forum and it comes up at least once a year.
And I guess the advice to the most anal of us is to inflate the tires to 36/42 as displayed on the OBD.
 
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