“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Saturday, June 02, 2007

First principles

This post is a continuation of the previous one in which I tried to reason the cause of my inability to coax better mileage out of the LR3. I was able to show through an analysis of manifold pressure, engine frequency (r.p.m.) and the chemical mixture requirements for combustion that the vehicle was burning fuel at a rate that equated to 13.3 m.p.g. at 55 m.p.h. on level ground. While this is in the ballpark, it's certainly not close to the base, so I tried reasoning from first principles, as the mathematicians say.

I started with the assumption that the fuel/air mixture in the manifold (and the cylinder during the intake stroke) is an ideal gas. I carried through an analysis on that basis (from the details of which I'll spare my patient readers) utilizing the absolute pressure and the manifold air temperature as reported by the Scan Gauge II I have attached to my engine.

I ran my analysis using the approximation that gasoline is normal heptane and that air is 22% O2 and 78% N2. From there, I proceeded to calculate from the ideal gas law. As Scotty used to say on Star Trek, "you canna change the laws of physics." I didn't expect to determine a fuel consumption number that matched the indicated m.p.g. from the Scan Gauge II to the nearest 0.1 m.p.g., but I did hope for something within, say, 10%.

Nope. The calculated result was worse than my previous calculation, coming in at 11.06 m.p.g. So what gives?? I have begun reading a treatise entitled "The Internal-Combustion Engine, Theory and Practice" by Taylor, since it's obvious that my level of understanding of the physics of internal combustion engines is inadequate to the problem at hand. It's a two volume tome, and exhaustive in scope and detail. When I learn enough to see where I've gone astray with my analyses, hopefully I'll also understand the mysteries of the LR3 vs. Grand Cherokee Limited engine comparison.

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