“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)

Tuesday, June 05, 2007

Another comparison

I'm still trying to understand the differences between the Jeep Grand Cherokee Limited I had until late November of 2006 and that was the topic of many of my posts, and the Land Rover LR3 HSE I have now. Right now, I'm thinking about the 31 m.p.g. the Jeep exhibits at 55 m.p.h. versus the 21.5 shown by the Land Rover. My last post dealt with the LR3 from the point of view of a big fuel burning air pump. I decided to compare what the two vehicles "should" require.

I gave some figures that should help out in this effort a few posts back. Let's run a few numbers. The LR3 has a frontal area of 3.15 m^2 and a coefficient of drag of 0.41. We have a dynamic pressure at 24.6 m/sec (approx. 55 mph) and air density of 1.16 kg.m^3 of 351 newtons/m^2. Thus, for this condition and drag coefficient, my aerodynamic drag is approximately 453 newtons (dynamic pressure times frontal area times drag coefficient).

Tire rolling resistance (as best I've been able to find) is about .015 times vehicle weight, or about 392 newtons. Total external forces to be overcome by the engine at 55 mph are therefore about 743 newtons or 167 pounds force. Now, force times speed is power, so the engine must provide 743 newtons at 24.6 m/s or about 18,280 watts. This equates to about 24.5 horsepower.

Obviously, much of the energy in the gasoline is lost to heat, engine and driveline friction, and pumping various fluids (refrigerant if the a.c. is on, water in the cooling system, air through the fan, oil, etc.). So enough gas must be burned per second to overcome all of these "dissipative" forces and still provide 24.5 horsepower.

For the Grand Cherokee, frontal area is 2.48 m^2, coefficient of drag is 0.44. Running through the same calculations, I get the external forces to be overcome by the Jeep at 55 mph are 383 newtons of aerodynamic drag and 289 newtons of rolling resistance for a total of 672 newtons or 151 pounds force. Enough energy must come from the fuel per second to overcome the dissipative forces and provide about 22.1 horsepower to maintain 55 mph against the external forces. So, if all else were equal, the LR3 should burn about 10.9% more fuel per mile at 55 mph. In fact, it burns about 44% more fuel. Or so the gauges say. So obviously, all else isn't equal.

These are the types of things I'm trying to understand.