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 = 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.
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?

wow....
good news is your smart enough to play with the best of us (however, not me!!)

But Welcome!
Believe me you'll get some responses.....

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.

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.

quite correct
 

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.
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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.

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?

20km--------------
 

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.

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.

estimates
 

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.
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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'.

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.

What gear did you use for your power calculations? The sixth gear is long, at 162 km/h you will rev the engine way below the revs for max power. So you'd use less than 63 kW, and your calculations are off by less.
Your estimate for rolling resistance seems low to me, but I really have no data, just gut feeling.
Wind, in fact any wind but straight tail wind, will raise air resistance too. Side wind even more so than head on. They really should publish a car's air resistance when the air comes in at a 10 degree angle, you'd he amazed how much impact that has.

Some EV numbers
 

I went through the limited info I have on EVs and am posting,so as to help us think about these:
*Texas CO-OP Power(Magazine) was given access to a Toyota Prius PHEV.
They reported a range for the car of 13-miles (21.3 km) at 60 mph (98 km/h) which works out at 2.95 miles/kWh (4.84 km/kWh).
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Google.org's Toyota Prius PHEV-30,Hymotion Inc.'s 5kWh Lithium-polymer kit promised 30-miles city range.
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Toyota's pre-production Prius PHEV was rated at a max.62 mph before enngine would kick in,at 8-miles range (13 km)
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The Chevy VOLT returns about 35-miles with 16-kWh pack,for 2.187 mi/kWh (3.586 km/kWh)
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The 2011 SMART ED got 3.818 miles/kWh (6.25 km/kWh)
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The NISSAN LEAF got 4.08-4.7 miles/kWh (6.68-7.7 km/kWh
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The 1992 NISSAN FEV got 4.5 miles/kWh (7.37 km/kWh)
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The 1992 Toyota Paseo 'AESOP' got 1.82 miles/kWh under slow city driving (2.98 km/kWh)
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The 1991 GM IMPACT got 8.9 miles/kWh
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A generic EV (ROAD & TRACK) 1992, absorbed 3kW at a constant 30 mph (49 km/h)
With air conditioning on the same car absorbed 4.2 kW at same speed.
'The most efficient A/C will cut range by 20%.'(CAR and DRIVER,May,'92)
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The 1996 GM EV 1 was rated at 79-miles 'combined.'
with 30 kWh/100 miles CITY
with 25 kWh/100 miles HWY
4.846 miles/kWh combined (7.944 km/kWh)
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The Mitsubishi i-MiEV returned 3.125-5.0 miles/kWh (5.122-8.196 km/kWh)
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William H.Kemp's 'ZERO-CARBON CAR',Maxda MIATA EV got 2.583 miles/kWh (4.236 km/kWh)
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The 1992 BMW E1 returned 5.98-8.07-miles/kWh (9.8-13.2 km/kWh)