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Weird Rolling Resistance & Drag Numbers


#1

I decided to nerd up completely today (quarantine is really hitting me hard) and do some recreational math in the game and create an algorithm for max fuel efficiency. When I got to drag & rolling resistance I noticed things were a bit weird. My math is below if you want to check it, but I’ve checked my results several times (and a few times more while writing this). It says that the rolling resistance coefficient for my tires is about 0.096. Meanwhile, Wikipedia (& Jason from Engineering Explained) claims a conservative estimate for a car tire CRF is 0.015, which is about 1/6 of that. Even if I were using extremely wide, slick tires, it shouldn’t be this high.

  1. I took the top speed given at the proper gearing and the correspondent engine power. For my car, this is 72.111m/s (259.6km/h) @ 129.1kW. This is already considering drivetrain losses. At the crank it produces 140kW (187hp).
  2. I’m considering two main forces: Drag and Rolling Resistance. So P = DV+RV, where V is top speed.
  3. Drag is given by F=RhoV^2Cd*A/2. Rho (Air Density) is given as 1.225kg/m^3 @ sea level and 15ºC, Cd for this vehicle is 0.261, A (effective frontal area) is 0.459m^2, V=72.111m/s.
  4. Rolling Resistance is given by F=Crr*N. The Normal force (N) here being 9.81m/s^2 * 1483.7kg = 14555.10N, and Crr is not given, but we can figure it out.
  5. We also need to multiply those results by the velocity to convert Force (N) into Power (W), and divide by 1000 to get kW.
  6. Since we have everything we need to calculate the drag, we’ll do that first: P=1.225*72.111^(3)0.2610.459/(2) = 27.51kW (this seems really low)
  7. Now that we have drag, we can see that Rolling Resistance is 129.1-27.51 = 101.59kW. This seems weird, at 260km/h, one would expect drag to have a bigger impact than RR.
  8. To solve the equation we had before: 101.59=72.111Crr14555.10/1000 (The 1000 is to keep the units). This works out to Crr=0.096.

Here is my thinking, the Cd seems fine, about the same as a Jaguar XE or a 3 Series. Top speed given the power seems okay, but drag should probably be way higher. So I went online to try to find the effective frontal area of a few cars to compare to. Here are a few results:
Prius is 2.2m^2.
Nissan Leaf is 2.29m^2
Mercedes CLA 250 is 2.16m^2
Chevy Volt is 2.20m^2
For some sportier cars:
Bugatti Chiron is 2.07m^2
Porsche 918 Spyder is 2.04m^2
Clearly, the FA is really, really low on this car. I checked other bodies as well. It seems like the game is calculating frontal area wrong. For the example car, a frontal area that would keep the stats the same but have a more reasonable CRR of the aforementioned 0.015 would be 1.91m^2, which makes sense to me.

One important consideration with this is that while I did not include lift in the calculations, I did test cars with lift that I tried to get as close to 0 as possible, and the results were pretty consistent with the above.

Why is this important? Well, I don’t really know, since the numbers work out in the end for speed and fuel efficiency (I think they do at least, kind of hard to check without more data), but still, I guess it’s the principle of the thing and the fact that Automation has managed to be so good at being realistic with the car stats.

Thank you for reading, this turned out wayyy longer than originally intended.


#2

The A in the drag formula is the actual frontal area, not the effective frontal area. To get the actual frontal area, divide A by Cd. That should get your drag numbers up to where they should be.


#3

Welp, I feel like an idiot, it says right there in the name. That’s what I get for doing math late at night. Thank you so much!