EPA roll-down coef vs HP at 100 mph
 

Hi

Recently we were discussing the HP-to-road power in a thread over at PriusChat. So I posted a recent chart showing the power required for a Volt vs Prius Plug-In (PiP):
http://hiwaay.net/~bzwilson/prius/Volt_PiP_010.jpg

One of the posters correctly pointed out that my chart projects ~27 hp at 100 mph. Obviously something is wrong as this is off by a factor of four. Perhaps you' all can spot my error?

I'm using the following:

• Test Car List Data Files | Cars and Light Trucks | US EPA - source of roll down coefficients
• drag HP = (A + B*v + C*(v*v)) / 7.5 :: "v-velocity mph", A, B, C from tables

Now in the past, I've used an OBD scanner to record ICE rpm and MG1 torque to calculate shaft HP. This has been in fine agreement with the specs for our NHW11 (2003 Prius.) So I need to repeat this analysis using the EPA roll down coefficients and compare. But I'm really scratching my head on this one.

Any thoughts?

The reason this is important is the title of the thread,"64% of Prius Power gets to wheels during max acceleration?" The original poster is using some raw acceleration numbers and the vehicle weight to calculate the HP-to-road metric and found only 64% is getting there. This suggests an exceptional transmission efficiency loss.

Understand, I'm OK with this as it may provide more insights about Prius transmission efficiency . . . if we can find independent confirmation. Unfortunately, I did a bad thing . . . loaned out my 2010 Prius OBD scanner. This one can read out ICE rpm and MG1 torque providing the raw HP data at the input to the transmission.

Thanks,
Bob Wilson

The formula for power should have a component of velocity cubed.

I don't know if you are wrong on the 27HP for 100 mph, a Ninja 250 has 25-26hp and tops out right around 100 mph, and it's far less aero efficient than most cars.

fyi torque for android will give you lots of nice numbers and they have special pids for the prius http://ecomodder.com/forum/showthrea...4-a-25216.html
And it is insanely cheap if you have an android already, I spent $17 on software and adapter. It has torque/rpm for mg1,mg2,ice and all sorts of things (check out the spreadsheet of custom prius pids), I even use it to tell me the brake friction pad horsepower so I get a feel for how much I can brake on regen alone.

But yes, under acceleration/high current it certainly feels "lossy". And all that mechanical to high current electrical, to a buck/boost/inverter to mechanical, it would not suprise me. It is basically a glorified torque converter, and mg1 always needs or generates power to oppose engine torque to get any useful work out of the planetary gear carrier.

I have not gone 100mph, let alone looked at the power demands, but will let you know if I do :) But do check out the custom prius pids on a link in that link, good stuff.

So what numbers would you expect for the PiP. I am not willing to take my Jetta to 100 mph, but it takes 12 horsepower to hold at a steady 60 mph, and 16 at 80 mph...which is pretty close to the PiP's curve in your chart.

Hi Bob Wilson,
Do you have a source for this formula? In context of EPA dyno testing, it looks like the estimated road power at 50 mph. The proper conversion coefficient, considering units of lb and mph, should be 375 and there should be another mph term:
drag HP = v * (A + B*v + C*(v*v)) / 375
using 26.050,-0.01200,0.018200 as A, B, C for the Volt I get
9 at 50 mph
55 at 100 mph

-mort

That is the EPA standardized formula and it's what each manufacturer uses to establish the dynamometer Test Load HP coefficient they derive FROM their "road load" coastdown tests.

However, that EPA equation is (to my knowledge) ONLY valid for 50 MPH since it is actually published as (EPA test speed is 50 mph):

TLHP = (a + 50·b + 2500·c)/7.5

Fr = Cr*m*g
Fa = 0,5*rho*CdA*v²
Fg = m*9,81*sin(atan(slope/100)) (slope in %)

P = (Fr+Fa+Fg)*v

Power required to overcome aerodynamic drag is proportional to velocity cubed. If you know how much power is needed at a specific speed to overcome aero drag, you can figure it out at other speeds.

If it takes 12hp to keep your car going at 60mph on level ground (assume 10hp for aero, 2hp for rolling resistance) you'll need 24hp at 80mph and 46hp at 100 just to overcome aero drag.

Rolling resistance is directly proportional to velocity, so it would be about 26hp and 50hp total, respectively.

Of course, figuring out Cr, Cd, and A are not simple feats...

I was giving actual numbers reported by my SGII...12 and 16 horsepower at 60 and 80 mph respectively, which fit a similar curve to the Prius on the chart.

Maybe I'm missing something, but I think most of the horsepower used at 60 mph is just keeping the engine up to speed, with only a few additional needed to overcome rolling resistance and aerodynamic drag at that point, so you're starting with maybe 3 or 4 horsepower in the equation, not 12.

Recently I tried to measure the roll-down coefficients and found they are impractical for my studies. But I did find a 'good enough' approach using three benchmark points and better still, four points.

EPA ROLL DOWN PROTOCOL (SAE J1263)

The EPA publishes the roll-down coefficients for:

• A (lbs/velocity**2) - corresponds to aerodynamic force
• B (lbs/velocity) - corresponds to rolling drag
• C (lbs) - corresponds to vehicle overhead

So following the protocol of SAE J1263, I tried to locally replicate but was disappointed. The full protocol requires 16 bi-directional passes on a sufficiently flat track. Using the closest road to the airport:
http://hiwaay.net/~bzwilson/TSLA/GPS_track_100.jpg

For my first tests, I used "Scan My Tesla" and "Speedometer" GPS records:
http://hiwaay.net/~bzwilson/TSLA/GPS_graph_100.jpg

• There were problems getting the same section of the test track. I'll have to re-run to identify the specific start and stop spots after doing a dash cam plot.
• GPS data is notorious for having altitude challenges.

http://hiwaay.net/~bzwilson/TSLA/SMT_graph_100.jpg

• The South bound runs were consistent because I'd mapped the starting position accurately.
• The North bound runs were less consistent so their runs, especially below 40 mph, had significant variance.
• There is no altitude metric in "Scan My Tesla".

I'll have to survey the test track and get a better start positions identified on both the North and South bound routes. I also have a high-resolution, 6-axis accelerometer that can provide altitude changes as well as acceleration and derived velocity. Combining the data is doable but not trivial. Still, I should be able to get credible A, B, and C coefficients.

BENCHMARK SOLVING QUADRATIC

My faster, alternate is three point, benchmarks:
http://hiwaay.net/~bzwilson/TSLA/mi_Wh_020.jpg

• Perform at least three different speed, benchmark:
  • < 15 mph - Prius benchmarks show the maximum is in the 15-20 mph range. The low value sets the maximum range part of the parabolic curve to real world values.
  • > 20 mph - Set the range of the minimum power, curve, which in the Prius is 15-20 mph. We need the minimum power value to evaluate the effect at ordinary speeds.
  • 40-45 mph - A middle range speed used for urban travel. Not necessary BUT in this case, accidentally having the heaters on result in a significant increase in Wh/mi.
  • 65-75 mph - The high-speed benchmark gives a way to evaluate aerodynamic changes.
• Use a "Three Point Parabola Calculator" or "Three Point Quadratic Calculator"
  • Use at least three benchmark points, more helps identify problem (see bad data point)

Unlike roll-down benchmarks, these can be performed in 1-2 hours. Also, the sensitivity of roll-down appears to be poor at slow speeds. Regardless, make sure to use a checklist to avoid problems like my unplanned heater test. Hold as many environmental parameters constant.

Bob Wilson

roll down
 

I've never heard of a 'roll down' coefficient.Can you expand on that?

It is a sophisticated (i.e., technically challenging) EPA technique that takes a car to at least 70 mph and measures how long it takes to reach 15 mph, SAE J1263:

• Standard day temperature, ~60 F.
• Very level, +/- a few feet, straight at least a mile track.
• Wind and other climate limits.
• 16 bi-directional runs.

From the roll-down metrics, you can develop three drag coefficients:

1. A - lbs per mph squared
2. B - lbs per mph
3. C - lbs

With these three coefficients, you can plot the drag force as a function of speed or more useful, the drag power needed as a function of speed. Combine that with the drivetrain efficiency, you can make a curve showing the MPG or kWh per mile as a function of speed.

My technique is to use at least three benchmarks to derive the quadratic equation. Two have to be on either side of the local minimum or maximum, and the third out into the high-speed region. Then use a quadratic solver to derive the A, B, and C coefficients. This is much easier and less complicated than the SAE J1263 procedure.

Using this procedure, we can test changes to improve a car's performance, either acceleration and/or range.

Bob Wilson

roll down
 

It doesn't sound rigorous enough.The SAE Handbook lists the procedure for coastdown testing.The technical and instrumentation requirements are so rigorous as to be,in my opinion,beyond the reach of individuals like us.
Without the polar moment of inertia for every rotating mass on and in the car,it's impossible to accomplish the data reduction necessary to reveal the coefficients.I've tried it and gave up,ending up paying a qualified 3rd party to test it for a fee at a test facility.$500 in 1991 dollars.