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do the PSI change if I change the tire brand or model?
Short answer is NO. Always set pressures according to the owners manual, which for the R3 is 29PSI (200kPa) front and 36PSI (250kPa) rear. Pressures are the same for all load conditions, right up to the maximum load of 353 lbs. (160kg).

NOTE: the above does not apply to racing the R3. For racing most people recommend 28psi to 30psi on the front tire and 30-32psi at the rear.

The reasoning for this is: the lower the pressure, the more the tire will deform at speed – deformation creates more friction between the tire and the track which in turns generates heat. And the more heat (up to a point) the more grip you’ll have. Lowering tire pressures also creates a larger contact patch, which means more rubber in contact with the track and hence again more grip.
 

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The above answer also does not apply if you change tire sizes.
 

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The above answer also does not apply if you change tire sizes.
That's true when you are making significant changes to tire sizes.

The R3 has very limited room to change tire sizes, probably just one size up or down on both the front and the rear. There is no need to change tire pressures from the manufacturer recommended ones with this minor of a size change. And going up two sizes on the rear will negatively affect handling anyway because the rim width is too narrow for such a wide tire.

Everyone seems to have their own opinion about tires (sizes, pressures, brands, etc.) but I have never read anything by knowledgeable tire experts that contradicts the above information.
 
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