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Old 05-13-2013, 11:13 PM   #1 (permalink)
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Something doesn’t add up: aero drag coefficient

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 = ˝ * ρ * v˛ * 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 m˛
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?

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Old 05-13-2013, 11:49 PM   #2 (permalink)
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Old 05-14-2013, 06:10 PM   #3 (permalink)
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results

Coastdown measurements are the only other option for ascertaining drag coefficient short of wind tunnel testing.
The technical requirements for SAE-approved (scientific) coastdown tests are virtually beyond the scope of do-it-yourself.
If you seriously want to pursue coastdowns,get a hold of the SAE Handbook (4-volumes plus Index) and you'll find their testing protocol .It's 3-pages of differential equations solving simultaneously for a handful of unknowns unless you can absolutely control your testing environment.
I'll let you do the research and make your own decision.I can tell you that what you're doing will never produce useful quanta.
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Old 05-14-2013, 07:19 PM   #4 (permalink)
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Yes, SAE-approved is well beyond DIY. The values I produced from the measurements are good enough to see that Cd of 0.287 is wrong by a factor of 1.9 ± 15%. Any measurement have a margin of error, and you can tell how much approximately it is.

Also, the maximum speed achieved by the car tells that my values are quite correct. So does acceleration rate.

What comes to Prius, the Cd of 0.25 is not right either, not even close. It's pretty much impossible to have that low Cd when we know the range in electric mode that has been verified.
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Old 05-16-2013, 06:22 PM   #5 (permalink)
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quite correct

Quote:
Originally Posted by MikkiHuuru View Post
Yes, SAE-approved is well beyond DIY. The values I produced from the measurements are good enough to see that Cd of 0.287 is wrong by a factor of 1.9 ± 15%. Any measurement have a margin of error, and you can tell how much approximately it is.

Also, the maximum speed achieved by the car tells that my values are quite correct. So does acceleration rate.

What comes to Prius, the Cd of 0.25 is not right either, not even close. It's pretty much impossible to have that low Cd when we know the range in electric mode that has been verified.
Here are a few things to consider:
*The test car must be at its official EPA test weight (300-lbs over curb weight ).
*The test car must be driven for a half hour at 50 mph immediately before testing begins to stabilize all fluids and lubricants as well as tires and bearings at ambient equilibrium conditions.
*Tires must be inflated 'cold' to Mfgr's specifications.
*Test area must be absolutely level.
*Test area must be absolutely straight.
*Test area must be dry.
*There should be zero wind.If wind is present,its magnitude and direction must be monitored and recorded for each run for the entire test period.
*Accurate temperatures must be monitored and recorded for each run for the duration of testing.
*Station Pressure must be monitored and recorded for each run for the duration of testing.
*Actual air density must be paired to associated runs.
*Road surface must be evaluated for the test area.
*Velocities must be measured to 1/10-mph accuracy.
*Velocities must be recorded at 10-samples per second resolution with calibrated distance-measuring equipment.
*Test runs must begin above and coasting to 70 mph,then down to include 20 mph.
*A minimum of 10-runs must be made,back-to-back in alternating directions.
*Technically,the fuel tank must be topped up between every run to preserve a constant inertia.
*Polar moments of inertia should be measured for all rotating components of the car.They can be estimated,short of actual measurements.
*No 2-run 'pairs' may vary by more than a couple percent of each other.If they do they must be thrown out.
--------------------------------------------------------------------------
Only after the successful coastdown test and data reduction will you actually know what the Rolling-Resistance portion of the Road Load Power is,from which to deduce the Aerodynamic portion,from which you may extract the Cd.
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Old 05-16-2013, 07:17 PM   #6 (permalink)
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Why does Prius PHEV go around 20 km when it should go at least twice as much if its Cd is 0.25? What is Prius' real Cd?
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Old 05-16-2013, 07:39 PM   #7 (permalink)
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20km--------------

Quote:
Originally Posted by MikkiHuuru View Post
Why does Prius PHEV go around 20 km when it should go at least twice as much if its Cd is 0.25? What is Prius' real Cd?
Is the 20 km range an actual real world measurement or was it published? The reason I ask,is that Toyota may be down-playing performance figures such that under the worst circumstance,that the car will never under-perform.
Many gasoline cars are far exceeding their EPA HWY mileage ratings and it looks like these numbers are very conservative.
As to the Prius' actual Cd,other wind tunnels have discounted what Toyota claims,but they're still in the 'neighborhood.'
All tunnels employ a universal/global NACA airfoil calibration model and all their results are within a few percent of one another.
I don't think Cd 0.25 is really off the mark.
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Old 05-16-2013, 11:15 PM   #8 (permalink)
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20 km is 12 miles. Wikipedia says this:
"Toyota estimates that the all-electric range varies between 10 to 15 miles (16 to 24 km) on a full charge depending on quick acceleration and braking, road and vehicle conditions, or climate control use."

This is what I copy-pasted from some forum:
"Consumer Reports field tested the Prius PHV for two weeks and reported an all-electric range between 14 to 17 miles (23 to 27 km) "

I just took the average from the first source, but it seems you can go 23-27 km in real world. Another assumption I made is 95% efficiency of electric motor and drivetrain. I don't how much it is, but if it as low as 80%, the Prius should go 25 miles. That's almost 150% of what it actually does. Cd can't be 0.25.
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Old 05-18-2013, 02:00 PM   #9 (permalink)
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estimates

Quote:
Originally Posted by MikkiHuuru View Post
20 km is 12 miles. Wikipedia says this:
"Toyota estimates that the all-electric range varies between 10 to 15 miles (16 to 24 km) on a full charge depending on quick acceleration and braking, road and vehicle conditions, or climate control use."

This is what I copy-pasted from some forum:
"Consumer Reports field tested the Prius PHV for two weeks and reported an all-electric range between 14 to 17 miles (23 to 27 km) "

I just took the average from the first source, but it seems you can go 23-27 km in real world. Another assumption I made is 95% efficiency of electric motor and drivetrain. I don't how much it is, but if it as low as 80%, the Prius should go 25 miles. That's almost 150% of what it actually does. Cd can't be 0.25.
Toyota may be reporting EPA "Combined" range based on 55% Urban/45% Highway ratings and a performance discount which includes use of the air conditioning.
-------------------------------------------------------------------------
During EPA CAFE certification testing,the car is driven on a twin-roll chassis-dynomometer,with only the front wheels rotating and an electric fan blowing air into the grille.No accessories are operated(no AC).
The dyno is adjusted for aero and R-R loads provided to the EPA by Toyota.
Only a fraction of testing is actually done by the EPA,with the majority of tests conducted by the carmakers themselves.
The 'original' EPA Highway portion includes stops and starts,has a maximum of only 60 mph,and averages only 49.6 mph over the speed trace.There is a higher speed test done in conjunction with accelerations up to,I think,75-mph.
With all the transient loads of this kind of testing protocols it's tough to single out pure R-R or aero contributions.
If the Prius were fully-charged,then started and accelerated up to a highway velocity and held there at constant velocity,we'd have a better chance to predict a performance under such limited conditions.
I suspect that the limited range of the Prius is a result of the inertial losses of acceleration/deceleration,stops,starts,and the air conditioner cannibalizing the battery as it moves along.
It would be very difficult to sort it all out.
And this is exactly why they'll use the wind tunnel to ascertain a cars Cd,as it is so difficult to learn from 'driving'.
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Last edited by aerohead; 05-18-2013 at 02:01 PM.. Reason: spelling
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Old 05-18-2013, 03:21 PM   #10 (permalink)
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Yes, I'll try to find more on the actual range with steady spead and as little parasitic as possible. And I haven't put much details on my calculations, so I'll put them here later.

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