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Old 06-16-2013, 12:29 AM   #1 (permalink)
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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):


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:
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

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Old 06-16-2013, 02:55 AM   #2 (permalink)
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The formula for power should have a component of velocity cubed.
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Old 06-16-2013, 10:29 AM   #3 (permalink)
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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.
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Old 06-16-2013, 11:25 AM   #4 (permalink)
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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.
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Old 06-16-2013, 11:36 AM   #5 (permalink)
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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.
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Old 06-16-2013, 12:48 PM   #6 (permalink)
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Quote:
Originally Posted by bwilson4web View Post
drag HP = (A + B*v + C*(v*v)) / 7.5
Bob Wilson
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

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Old 06-16-2013, 04:26 PM   #7 (permalink)
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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

Last edited by gone-ot; 06-17-2013 at 06:59 PM..
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Old 06-17-2013, 03:01 PM   #8 (permalink)
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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
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Old 06-17-2013, 06:33 PM   #9 (permalink)
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Quote:
Originally Posted by PressEnter[] View Post
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.
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.
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Old 06-17-2013, 06:35 PM   #10 (permalink)
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Quote:
Originally Posted by HypermilerAX View Post
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
Of course, figuring out Cr, Cd, and A are not simple feats...

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