“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, May 19, 2007

### Comparison

As mentioned in my previous post, I am now driving a 2006 Land Rover LR3 HSE. I have been trying to achieve fuel economies that exceed the EPA rating for the vehicle as I was easily able to do in my 2001 Jeep Grand Cherokee Limited. I have failed utterly.

I'm now trying to analyze the reason for my failure, as well as the reasons for the much lower fuel economy of the LR3 in contrast with the Grand Cherokee. Further, my driving methods seem to make much less difference in the LR3 than they did in the Jeep. I'd sure like to find the reason for that, as it could influence many of my earlier conclusions about the extent to which fuel consumption in the U.S. could be reduced by the large scale adoption of fuel conserving driving techniques.

For reference, the following represents some comparative information on the two vehicles, as best I have been able to determine it. Should anyone have more accurate data or an authoritative source, I'd like to know of it.

 Jeep Land Rover Average Weight (pounds)* 4338 5893 Coefficient of Drag 0.44 0.41 Frontal Area (square feet) 26.69 33.9 Engine Size (L) 4.7 4.4 Rated Power (HP) 235 300 *Normal cargo, single occupant, half full fuel tank

So the key suspects seem to be the weight and the frontal area. I am going to hypothesize that the engine friction is directly proportional to r.p.m. and hence, in a given gear, to speed. I will speculate that the force required to pump fluids is proportional to the square of r.p.m., and thus, in a given gear, to speed. I will assume that tire rolling resistance is a constant for a given vehicle weight. Finally, I will declare that aerodynamic drag is proportional to the square of velocity. Thus, the force to be overcome as a function of speed and thus the force to be supplied by the engine to maintain a fixed speed is of the form f(v) = a + b * v + c * v^2. If I know the force required to maintain a given speed, I can calculate power required, since force times speed is power. Then I can compare the power required by the Grand Cherokee versus power required by the LR3 at various speeds.

I am also suspicious of the rated power of the engine - the LR3 is rated at 300hp at 4.4L displacement versus the Grand Cherokee's 235hp at 4.7L displacement. The compression ratios are 10.5:1 in the LR3 versus 9.3:1 in the Jeep. But really, a higher rated power is the same as saying that an engine can burn more fuel per second. After all, power is the rate of doing work and that work is done by the energy released by the burning fuel. Nevertheless, I am not enough of an expert on the physics of internal combustion engines to know how much additional power can be had from an engine by increasing the compression ratio.

This analysis will be continued over the next couple of posts.