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#### Squishy

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Here are three mathematical formulas that I have. The first one deals with tire pressure adjustments once you stray from the stock load rating. The next two were recently stolen from BITOG, dealing with engine efficiency and RPMs, and engine oil change intervals.

This one was picked up from an issue of Toronto Star Wheels. It was mentioned that, for most radial tires, every 3 PSI pressure differential was equal to roughly 88 lbs. of load capacity. For example, my stock XLS 15" tires came with a load rating of 100S SL, which is 1753 lbs at 35 PSI. I usually bump up stock recommendations by 2 PSI to begin with, so I made these calculations with 32 PSI instead of 30 PSI. At 32 PSI, the stock tires would hold (1753 lbs) - (35 PSI - 32 PSI)(88 lbs) / (3 PSI) = 1665 lbs. I averaged out the XLS and XLT stock ratings and came up with 1780.5 lbs. as a target load capacity.

My winter tires came with a load rating of 108Q XL. The XL (extra load) means that load capacity is measured at 41 PSI instead of 35 PSI for standard load (regardless of sidewall max. inflation). That meant a load carrying capacity of 2183 lbs. at 41 PSI. To determine what pressure to put in my new tires, 41 PSI - (2183 lbs - 1780.5 lbs)(3 PSI) / (88 lbs) = 27 PSI.

So in general, to get load capacity at OEM pressures, use:
--> [max load rating] - ([load rating measuring PSI] - [recommended PSI])(88 lbs) / (3 PSI)

Once you have that target load capacity, use the following to calculate a new PSI:
--> [load rating measuring PSI] - ([max load rating] - [target load rating])(3 PSI) / (88 lbs)

Signage matters - for example, if you went down a load rating instead of up, the second half of the above equation would become a negative, meaning your new PSI is higher than before. On the MDX, we went from a load rating of 103T SL for summer to 98S SL for winter. Using the above formula, 35 PSI - (1653 lbs - 1899.67 lbs)(3 PSI) / (88 lbs) = 35 PSI - (-8.41 PSI) = 43.41 PSI. Note the double negative resulting in an addition operation.

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This next equation deals with engine efficiency. It was said that the "sweet spot," or most efficient operation, in most engines is achieved when the piston velocity is between 5 to 6 m/s. For each crankshaft revolution, or 1 RPM, the piston travels twice the length of the stroke. To get piston velocity, the following formula can be derived:

[piston velocity] = (2)[stroke][RPM] / [(60 s/min)(1000 mm/m)]

The last two numbers are for unit conversion - 60 seconds in a minute and 1000 millimetres in a metre.

To rearrange the formula to calculate for RPM instead of piston velocity, we get:

[RPM] = [piston velocity][60 s/min][1000 mm/m] / [(2)[stroke]]

So, for example, the 3.0 L Duratec has a stroke of 79.5 mm. Using an average piston velocity of 5.5 m/s, we plug the following numbers into the formula:
[RPM] = (5.5 m/s)(60 s/min)(1000 mm/m) / [(2)(79.5 mm)] = 2075 RPM

To simplify the formula by combining constants and substituting a 5.5 m/s average piston velocity, we can use:
--> [RPM] = (165000 mm/min) / [stroke]

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The last equation was developed by Ted Kublin of Dixie Synthetics and posted over on BITOG. It calculates oil change intervals using several factors - sump capacity, engine displacement, horsepower, MPG, and oil quality. It is kind of a middle ground between traditional 3000 mile changes and using an oil life monitor. The equation is as follows:

--> [OCI-miles] = (C*)[MPG][sump-qts][CID / HP]

Where C* is a constant based on the quality of basestock and additive packages. Ted notes to replace HP with ft-lbs. of torque for turbo-diesel engines.

Based on Ted's experiences, a standard dino motor oil has a C* of around 50, synthetic around 80, 125 for top tier synthetics like Amsoil, Castrol 0W-30 (the German stuff), or RedLine, and possibly 150 for Amsoil Series 2000/3000 oils, which he found performed best in his fleet. Because of the C* constant, units will not cancel out in this formula.

The 3.0 L engine translates to a CID of 183 cubic inches, with 201 HP. The sump capacity is 5.5 quarts, and my average MPG is 20. I use a fully synthetic oil so I used 80 for my C*. To get my oil change interval...

[OCI-miles] = (80)(20 mi/gal)(5.5 qt)(183 in^3 / 201) = 8012 miles

...which is fairly reasonable for a synthetic oil.

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Feel free to post your own equations. Edited for grammar

#### Dasha

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I'm getting math anxiety just reading that :wacko: .......but thanks for the info! :smile: