About wind resistance...

[sbergman27]

Interstate road warrior that I am... wind resistance is a topic near and dear to my heart. So I should probably talk a bit about it.

We Yaris owners are doing pretty well. The sedan has a drag coefficient (Cd) of 0.29. The 3 and 5 door HB models have drag coefficients of 0.30 and 0.32... though I confess that I can't remember which is which.

By comparison, the 2nd generation Prius is heralded for its 0.26, and the 3rd for its 0.25. The Smart Fortwo is a relative aerodynamic brick, at 0.38.

But what does that mean, exactly? Well... not as much as the harder to find CdA number. The CdA is the drag coefficient multiplied by the frontal area of the car. While the drag coefficient is nice for marketing, the CdA really gives you the relative drag between cars at a given speed. The Yaris has a lower frontal area than the Prius, so we do even better against the Prius on that number. Yaris Sedan: 6.13, Prius: 5.89. Prius still wins. But only by 4%.

Here is a table of Cd and CdA values for various cars. I have a sortable spreadsheet which I might make available later:

http://tinyurl.com/yzdxfrh

So... what is the significance of wind resistance? It all very much depends. Because, you see, wind resistance is very different from friction. Whereas the force from friction remains constant with speed, wind resistance increases. To make things even more interesting... it does not increase linearly with speed, as one might naively assume. The force of wind resistance increases as the *square* of the speed. Since power is work/time and work = force x distance, and distance per second increases with speed, the power required to overcome wind resistance increases as the *cube* of the speed.(!) The power required to overcome mechanical friction, like tire rolling resistance, increases directly as the speed.

I remember a GM engineer commenting that on their early 1980s 'A' body cars (Buick Century, et. al.) wind resistance was approximately equal to mechanical friction at about 50 mph. (The 'A' body cars were known for their good aerodynamics at the time. We'd finally figured out that it mattered.) Using that as a basis, let's make a table.

Total power to maintain a particular speed. (50 mph = '1'):

50 mph : 1.00
55 mph: 1.22
60 mph : 1.46
65 mph: 1.75
70 mph: 2.07
75 mph: 2.44

This means that, for example, it takes 2.44 times more engine power to maintain 75 mph than 50 mph. (Would you have expected that?)

Since you cover 50% more miles per hour at 75 mph than at 50 mph, the decrease in fuel economy is mitigated a bit. Taking that into account, let's make a table of expected *decrease* in mpg, compared to the MPG at 50 mph, at various speeds:

50 mph: -0%
55 mph: -9.8%
60 mph: -18%
65 mph: -26%
70 mph: -32%
75 mph: -39%

So if you are getting 60 mpg at 50 mph, according to this model you could expect to get about 44 mpg at 65 mph, and 31 mpg at 75 mph.

If aerodynamic drag represents 50% at 50 mph, it represents 70% at 75 mph. Meaning that at 75 mph, CdA is nearly 2.5x as important as mechanical friction.

My impression is that the Yaris' excellent CdA makes the drop off somewhat less steep than this. More like 44 mpg at 65 mph and 38 at 75 mph.

But the faster you go, the less, e.g., the pressure in the tires actually matters. Because wind dominates more and more.

-Steve

P.S. I'm sure that this post is going to need some cleaning up. But I'm clicking "submit" now anyway.