Calculating Tire Pressures for Different Load Indices

[Crickett]

** WARNING: MATHS CONTENT! **

So I got to thinking – trouble I know – about what to do with tires of different size than our OE 225s & 255s. Daydreaming about running square 245s, I realized I didn't know what pressures I'd use, so I looked up what goes into the manufacturer's recommended pressures & started learning about a tire's service description & load index.

Logically, it turns out a given tire is rated to support a given weight for a given pressure, & those numbers are found stamped on said tire's sidewall as its load index & maximum pressure. So, I further deduced that if I had a manufacturer-recommended pressure for a given load index & vehicle weight, I should be able to calculate a new "recommended" pressure for a new tire (i.e. a new load index).

I then hit the Google to see if I could find such a formula & came across a post on a Dodge forum by a Dutchman claiming to have combed the European Tire & Rim Technical Organisation 2007 standards manual & found the following formula for calculating a given tire's "correct" pressure ("P") for a given load ("L") knowing its maximum pressure ("Pmax") & load index ("Lmax"):

P = Pmax x (L / Lmax) ^ 1.25

And its algebraic equivalent solved for a load at a given pressure:

L = Lmax x (P / Pmax) ^ 0.8

Using that last formula, I plugged in the ZHP's OE tire specs (Lmax = 1235 lbs front, 1323 lbs rear; Pmax = 51 psi for both) & discovered that, apparently, BMW's recommended pressures for our OE tires (with a 10% buffer) are calculated for a vehicle weighing 3,485 lbs (about right) with 44.9% of that weight on the front axle. What happened to 50/50?

In any case, using that calculated weight & F/R ratio, I plugged in my current Continental DWSs' specs (Lmax = 1389 front, 1477 rear; Pmax = 51) & crunched out a recommended pressure of 27 front, 33 rear. These numbers seem to make sense, as the tires are rated to support more weight at a given pressure (from their higher load index), so to support the same weight as OE tires they would require less pressure. Right?

So this whole escapade still leaves me with a couple questions:

1. Why does a car with a supposedly 50/50 balance require different pressures front-to-rear? I would initially suspect the staggered setup, but somewhat counterintuitively, the rear's higher load index should require less pressure to support the same weight as compared to the fronts, no? (I plan to get my car on a two-axle scale to get a real-world curb weight & F/R ratio to revisit this.)

2. Am I completely overthinking this??

[danewilson77]

There's a lot more to think about than just load. I'm thinking that the oe specs are dtermined not only on what you talk about above, but also many different dynamic features of the car. Most likely things we're not even thinking of. Your calculatiosn, right now, are from a purely static standpoint.