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.

[yarrr]

Originally Posted by sbergman27

the power required to overcome wind resistance increases as the *cube* of the speed.(!)

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

50^3/50^3 = 1
55^3/50^3 = 1.331
60^3/50^3 = 1.728
65^3/50^3 = 2.197
70^3/50^3 = 2.744
75^3/50^3 = 3.375

[sbergman27]

Originally Posted by yarrr

50^3/50^3 = 1
55^3/50^3 = 1.331
60^3/50^3 = 1.728
65^3/50^3 = 2.197
70^3/50^3 = 2.744
75^3/50^3 = 3.375

That's what the wind resistance looks like. But the total resistance is the wind resistance + the mechanical friction.

We're assuming, for the sake of this discussion, that at 50 mph they are equal. For simplicity, let's call each value "1".

So the total resistance at 50 mph is 1 + 1 = 2

Looking at it that way, at 75 mph, the power going to overcome wind resistance goes to 3.375, as you say. The power going to mechanical friction goes to 75/50 = 1.5

3.375 + 1.5 = 4.875 is then the total resistance. At 50 it is 2.

4.875 / 2 ~= 2.44

So the total resistance at 75 mph is 2.44 times the resistance at 50 mph.

Sorry I didn't go into more detail in the original post. I got lazy. ;-)

-Steve

[yarrr]

^^ ok you're right then, I took the post to mean just to overcome wind.

[nemelek]

Highway speed where I live is 75 mph. When doing 80 mph I'll get 35-36 mpg. When going 60 mph I'll get over 40 mpg. I have to decide if my time or money is worth more.

[yarrr]

Originally Posted by nemelek

Highway speed where I live is 75 mph. When doing 80 mph I'll get 35-36 mpg. When going 60 mph I'll get over 40 mpg. I have to decide if my time or money is worth more.

Tires wear faster with speed. Throw in a ticket every now and then and the equation gets lopsided real quick

[YarisOwnersDad]

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.

Steve, I have to ask you a question...



































Did you stay at a Holiday Inn Express last night?

[Kal-El]

Interesting post.

Of course there's many variables that create endless mpg possibilities.

What kind of wind resistance is this considering? A calm non-windy day?

How about the direction of the wind? Is it a heavy noise wind? Tail wind?

Then it all depends on the gradation of the road.

There's a million variables to fuel efficiency.



And then people go and complain about not getting EPA estimates, LOL.

[sbergman27]

Originally Posted by Kal-El

Interesting post. Of course there's many variables that create endless mpg possibilities. What kind of wind resistance is this considering?

I can tell you what I've been dealing with the last couple of days. Cross-winds. Strong cross-wind from the north as I traveled due-west on I-40 on Friday... and strong cross-wind from the south as I traveled due east on i-40 on Saturday. Except that I think it was a direct head-wind for a while on the way back. It's hard to tell in the Yaris.

But yes, wind is a very complex topic, which makes a huge difference even when one doesn't notice it.

What's the Yaris' "Side CdA", I wonder? Or 45 degree CdA? Yes. It gets very complex very quickly.

In my post, I implicitly assumed the simple case of still air and a moving car.

-Steve

[sbergman27]

Originally Posted by YarisOwnersDad

Did you stay at a Holiday Inn Express last night?

No. I'm a Motel 6 kinda guy. :-)

-Steve