Hello,

I’ve been trying to figure out different cars’ aerodynamic drag. I’ve calculated air drag and power requirements of some vehicles.

Long story short, drag coefficients that you can find in many places and nowadays often told by car producers do not give you the correct air drag force acted upon the vehicle if you use that formula that is used in Aerodynamic & rolling resistance, power & MPG calculator. The formula is of course F = ½ * ρ * v² * Cd * A.

In order to determine a Toyota Yaris’ air drag coefficient, force to move and power required I’ve run several tests. In the tests I accelerated to about 160 (100 miles/h) km/h and took speed values from a GPS navigator.

According to the measurements the air drag coefficient of the car is 0.55 if we use the aforementioned formula.

Car: Toyota Yaris 2011, 1.3 liter 6-speed manual

Weight during the test, approximation: 1289 kg

Rolling resistance, measured with scale: 0.0074

Frontal area: 1.96 m²

Cd according to Toyota: 0.287

Here are some of the values of force and power I’ve derived from the data.

Code:

Speed (km/h): Speed (miles/h): Force Aero: Force total: Power:
162 101 1,310 N 1,403 N 63kW
150 93 1,129 N 1,222 N 51kW
122 76 768 N 858 N 29kW

The measurements are not very precise. The navigator gives the speed in km/h, no decimals, updates once per second, the road is not entirely flat etc. However, I‘ve made enough runs and was going fast enough for air drag to be large enough. The road also was quite flat, and of course I drove both directions several times.

If you enter the values of the car I used for testing into the calculator, the air drag forces for those speeds are approximately these:

162 km/h (101 miles/h) 697 N

150 km/h (93 miles/h) 600 N

122 km/h (76 miles/h) 397 N

The measured force is 1.88-1.92 times as much as in the table. That would give a Cd of 0.55.

The second way I checked the formula and Cd on is by the given specification numbers on Toyota Prius PHEV.

According to the calculator at 80 km/h (50 miles/h) total force is 275 N, and air drag is 166 N. If we calculate the energy output from the battery and divide it by distance (20 km on electricity) we get 178 Wh/km.

4400 Wh * 0.85 (discharge proportion) * 0.95 (efficiency) = 3553Wh. At 109 N for rolling resistance it consumes 30 Wh/km. 178 Wh/km – 30 Wh/km = 148 Wh/km for air drag. 148 Wh/km for air resistance equals 531 N. Whopping 3 times as much as the calculator suggests.

If it really was 275 N for total force, then Prius PHEV could go 47 km (29 miles) on battery.

What is wrong with the calculations? Is ecomodder’s calculator wrong? What is the real Cd for Yaris? For Prius?