“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, February 07, 2009

More on wind

In my post on headwinds I bemoaned the destruction of fuel economy I suffered in driving head-on into our Southern California Santa Ana Winds. I drove home in the rain last night, and began thinking about the effect of rain soaked roads on fuel economy so, naturally, I Googled it. As commonly occurs when Googling fuel economy related issues, a highly placed hit took me to an ecomodder post. That led me, in turn to a site where a Prius fanatic (zealot?) writes about a "Prius Palm Mileage Simulator." I don't have a Prius, nor do I have a Palm but this software appears to be truly amazing. I can't begin to do it justice in this post, but I'd strongly recommend that anyone reading this take a look.

In any event, the author of that site writes about the effect of wind on mileage. As is common in my reading, he brings up many points I had not considered. The kernel of the information is that wind is much worse than I had considered. For example, to a first order approximation, wind from 70% of the compass will hurt mileage. Even wind with a significant tailwind component hurts, and a direct crosswind of a given magnitude hurts worse than a similar direct headwind. I have to take his word (and that of his software) for this at this time because the analysis would be complex. I assume the reason crosswinds and quartering tailwinds are detrimental is that, in order to maintain a desired track, one must steer into them. This, it seems to me, would have two negative effects: necessitating the force vector applied by the road to the vehicle to be misaligned with the direction of travel; and increasing loss of energy to the tires as they are traveling in a direction outside of their plane. This must increase their rolling resistance.

The tire situation would be, I suspect, quite complex but I can quickly run some numbers and find out, to at least a first approximation, the effect of the force. I'll assume (I always must make assumptions) that I want to move down the road at 55 m.p.h. and that a direct crosswind (i.e., at precisely 90 degrees to my direction of travel) of 15 m.p.h. is blowing. What effect is this likely to have?

I'll need to determine the force on my LR3 from the crosswind. From this Motortrend location I found the dimensions of my vehicle and determined that the area presented to a direct crosswind to be 9.18 m^2. I don't know the coefficient of drag for the LR3 in that direction and at that wind speed, so I'll assume it's worse than the 0.41 for wind on the nose, let's say 1.0, or pretty darn bad. That would mean that the wind is pushing my vehicle to the side with a force of about 248 N (Newtons, or about 56 pounds).

I calculated in this post that it takes a force of about 743 N to propel the LR3 at 55 m.p.h. Working the vector equation (or finding the hypotenuse of the right triangle), it will take about 783 N to produce a resultant force of 743 N in the direction of travel. Since, at a fixed speed, fuel consumption is directly proportional to force to be overcome, this increase of about 5.4% in force would result in a 5.4% increase in fuel used per mile, or just slightly over a 5.1% reduction in m.p.g.

If this is true, and if the Prius fan's program is correct, much of the deterioration in gas mileage caused by a crosswind must come from an increase in tire rolling resistance as the steering wheel is held into the wind since a 15 m.p.h. headwind will certainly result in more than a 5% decrease in gas mileage. I'm not sure how to calculate this effect, maybe I can get the owner of that site to enlighten me.