Ad Hoc 0-60 mph

My bad. I had originally though there were two people only to subsequently learn there was just one. The earlier drives had the reviewer and clearly a Toyota employee in the right seat. I failed to make that change clear AFTER I got the right weight from Jason.

Bob Wilson

 

This got me thinking of another approach:

You pointed out that anchoring the polynomial at 0,0 would introduce a bias. So I took out the 0,0 point and generated a 6th degree polynominal and could see the Y-axis intercept. But I found the end points of the 6th degree polynomial and switched to a more sable 5th degree polynomial.

Now the true 0,0 is obscured by Jason calling out "GO!" but the rest of the points in the derived polynomial shows the Y-axis error. The answer is to shift the time stamps, left or right, to achieve a near, 0,0 intercept:

• shifting the time scale left, -4.5894691 frames, led to this new polynomial
• 0-60 mph ~9.8 sec

So I recalculated my earlier energy graphs and now have:

My current thinking is the Toyota reported, "blended 121 hp" is the net HP at maximum speed. Also, somewhere around 85 mph, the car begins to ramp up the net power.

Bob Wilson

	time (adj)	speed	F(speed)
1	0.00	0	0.0
2	0.08	2	0.9
3	0.38	4	4.1
4	0.68	7	7.1
5	0.91	9	9.4
6	1.21	11	12.2
7	1.48	14	14.6
8	1.78	17	17.2
9	2.05	19	19.4
10	2.35	22	21.7
11	2.61	24	23.8
12	2.88	26	25.7
13	3.18	28	27.8
14	3.48	30	29.9
15	3.71	32	31.4
16	4.01	34	33.3
17	4.28	35	34.9
18	4.55	37	36.5
19	4.85	38	38.2
20	5.11	40	39.7
21	5.41	41	41.3
22	5.71	43	42.8
23	5.95	44	44.0
24	6.25	45	45.4
25	6.51	47	46.7
26	6.81	48	48.1
27	7.11	49	49.4
28	7.38	50	50.5
29	7.68	52	51.8
30	7.95	53	52.9
31	8.21	54	54.0
32	8.51	55	55.1
33	8.78	56	56.1
34	9.08	57	57.3
35	9.35	58	58.2
36	9.61	59	59.2
37	9.88	60	60.1
38	10.18	61	61.2
39	10.45	62	62.1
40	10.75	63	63.0
41	10.98	64	63.8
42	11.25	65	64.7
43	11.85	67	66.5
44	12.15	68	67.4
45	12.71	69	69.1
46	12.95	70	69.8
47	13.51	72	71.4
48	14.05	73	72.8
49	14.35	74	73.6
50	14.95	75	75.1
51	15.48	76	76.5
52	15.75	77	77.1
53	16.31	78	78.4
54	16.61	79	79.1
55	17.15	80	80.3
56	17.71	81	81.5
57	18.01	82	82.2
58	18.55	83	83.3
59	19.15	84	84.4
60	19.38	85	84.9
61	19.95	86	86.0
62	20.55	87	87.1
63	21.08	88	88.0
64	21.65	89	89.0
65	22.21	90	90.0
66	22.75	91	90.9
67	23.31	92	92.0

 

Not from Jason even though I've e-mailed the question. Jason mentioned being at the end of the runway and the mileage looks like he might have finished his 'road trip'. His trip meter went from 23.9 to 24.3 at 92 mph, ~.4 miles, ~400 meters. Perhaps @Danny might have a clue if there were a single path back to the starting area.

Other videos show the VOR in the back ground for the cone testing which suggests the North end of the North side runway, west. BTW, my speadsheet includes a headwind vector, currently set to 0 mph. If we can get the runway and direction, I can easily add the head wind effect.

Bob Wilson

 

My bad. I started with a 6th degree but even with the highest power coefficient close to zero, I could not get a good match between the formula and data points. So I switch to a 5th degree and very quickly achieved the first graph. I also tried a 4th degree but the divergence was too high. Eventually, I got it close enough using a 5th degree.

For those who may not understand why, the problem is small variations in the raw data means the calculated power has way too much variability. Power calculations amplify any variability. So curve fitting to the raw data points smoothes the variability and tames the power calculations.

I wished Jason had more runway to reach the maximum speed. That would resolve my interest in the '121 hp'.

Bob Wilson

 

That sensitivity of the 6 deg polynomial is what drove me away from it. I couldn't get a good match for the data points. But then I only use the polynomial derived data points for speed and settled for 'close enough.' But I accept your observations that higher degree functions lead us into the 'weeds.' FYI, there is some old data from years ago:

The NHW20, 2004-09, had a curious 'knee in the curve' between 85-90 mph. They had reported a fuel consumption dip that was never fully explained. Seeing a similar inflection point in Jason's data doesn't surprise me. Sill, I'm open to cautions and alternate interpretations.

Bob Wilson

 

The next step is to figure the wheel torque using 856 Revs per mile (source: @john1701a User Manual for NHW20, 15 inch tires.)

• Initial results indicate a maximum, drive wheel torque of ~600-700 lb-ft

I have to do a parallel analysis to verify this explains the data I'm seeing.

With the wheel torque, we can begin playing 'what if' games to see what might change the acceleration profile:

• Lower diameter front tires - assuming the phase angle between front and rear tires, the traction control, limits power. The smaller diameter provides more motive force for the same input torque. The problem is a smart, traction control system will notice the different revs/mile and adjust their torque limiter parameter. If using a 'donut' spare on a front wheel, this would be critical to avoid some hazardous driving. Unlikely to have the desired result.
• Spoofing drive tire encoder, rear to front - wire the rear tires to drive the front tire encoders. Unfortunately this would mean no torque sensing of the drive wheels. A smart traction control would detect the condition and revert to 'table lookup' and possibly throw a code. But this needs experimental verification. The table might also be a hard-coded, drive wheel torque limiter.
• Spoofing drive tire encoder, Arduino - pre-process the tire encoders to reduce the relative phase angle of drive and rear tires during acceleration. If 'table lookup' doesn't limit the front torque, this would be a sweet solution for tricking the Prius into faster acceleration.
• Smaller diameter tires all around - oblivious to the actual tire diameters, the traction control would see the same wheel dynamics but not realize the smaller diameter is putting more motive force on the road. In theory, four, undersized tires would give the Prius more acceleration.
• Get e-AWD - although 7.5 hp may seem small, the real effect is to stress the rear wheels at low speed so the front wheels can drive harder.

Now if we can just find someone with an older Prius and the skills to test some of these approaches . . .

Bob Wilson

 

So what happens when you combine:

• 2016 maximum acceleration
• 2010 maximum acceleration - both directions
  • Applied a 6% adjustment for OBD km/h to match GPS and tire calibration
  • Removed two outliers in OBD data due to HEM recorder SD card write

• Around 85 mph, the 2010 seems to get a boost in HP that is evident in the split of the two runs. Below this speed, the 2010 appears to run the same HP at a given speed.

• In the 0-60 mph range, they are dead on. It is entirely possible to have control laws that enforce a desired speed distribution by moderating the power. In effect, consistent acceleration performance.

• Within limits, it looks like all three achieved 60 mph in about 9.9-10.0 seconds.
• These are ad hoc tests:
  • different days: temperatures, humidity, wind
  • different routes: runway in California versus a divided highway in Alabama
  • different fuels: we did not use the same gas

Bob Wilson

ps. I found the 2010 Prius requires a speed of 78 mph before the engine rpm will reach maximum 5,200 rpm. Also the peak SAE J2908 measured at 116-120 hp.

 

Offered just to compare the SAE J2908 of the 2010 Prius to the 121 HP of the 2016:

• Maximum 5,200 rpm reached only after ~76 mph regardless of load.

The gear ratios between the engine power shaft, MG1, and MG2 are fixed. MG2 rpm is a function of vehicle speed. Engine rpm is limited by the engine controller in response to the hybrid vehicle ECU that also controls MG1. It is computer management of MG1 that provides the counter torque needed to get engine power to the wheel gears. But now we have data showing why power seems to ramp up as seen a few seconds later at 85 mph in the 2010.

As for the 2016, we see the ramp up appears to happen around 90 mph during Jason's maximum acceleration. This suggests it is harder to reach maximum rpm. To achieve more power, an engine would need to provide more torque at lower rpm. Improving the intake manifold air flow, a documented enhancement would do it.

Bob Wilson

 

I am always happy to share what I know and realize that sometimes I'm speaking 'jargon'. Feel free to ask questions as it helps me understand how to explain what is going on.

Inside the transaxle, there are two motor generators, MG1 and MG2, that combine with the engine and power-split device to provide:

• electronic controlled, continuously variable gearing between the engine and wheels
• load the engine so it will pass power through the power-split device

MG1 and MG2 have some other functions such as starting the engine, charging the traction battery, regenerative braking, and reverse. Under computer control, there is a 'mad dance' of which half, the torques, are invisible. So this turns out to be an exceptionally difficult transaxle to understand. It took me nearly three years to reach: Introduction to Prius Power Flow | PriusChat





In the past, people would add the engine and MG2 power and say,'This is the power.' But in reality, there are limits based upon electrical, mechanical, and thermodynamics about what combinations are allowed. This is why they have to be measured on the running car and not the misleading sum of the parts. Consider Taekwondo that allows use of arms and legs. One can apply 100% of the arm strength or 100% of the leg strength but together, you don't get 100% + 100% but some smaller portion because thrusting with one's leg limits the anchor needed for application of one's arm at the same time.

Bob Wilson

 

Happy day, the EPA has released the 2016 test vehicle data that includes the 2016 Prius, roll-down coefficients:

	Vehicle	Test	A (lbf)	B (lbf/mph)	C (lbf/mph**2)
1	16-ZV2H ECO	FTP	17.13	0.28731	0.013857
2	16-ZV1H	FTP	18.272	0.29545	0.013793
3	10-ZW1H	FTP	18.501	0.02235	0.01811
4
5	16-ZV2H ECO	FTP	19.034	0.31923	0.015397
6	16-ZV1H	FTP (cold)	20.302	0.32827	0.015326
7	10-ZW1H	FTP (cold)	20.234	0.01993	0.01874

I appreciate the improved aerodynamic coefficient, C, but am bothered by the linear drag coefficient, B, that has gone up so much for the 2016. The static coefficient, A, should correspond to rolling drag and the slight decrease is the right direction. For those who 'see math' the B and C coefficient values raise questions.

Here I've plotted the 'drag horsepower' in both a low-speed and high-speed graph. The drag HP is how much power is needed to keep the car at that speed on a level road, standard weather day, and no wind:

• It looks like the 2010 has lower drag energy requirements than the 2016. This maps directly to the B coefficient.
  • Tires - minimize rolling resistance, high-pressure and low rolling resistance
  • Transaxle lubricant - needs to be optimized, early change
  • Weight - directly effects rolling resistance but at +3,000 lbs, it is hard to reduce
• As speed increases toward 55 mph, the lower aerodynamic drag of the 2016 becomes apparent.

At higher speeds:

• Relative to the 2010, the 2016 should excel at Interstate speeds.
• Cold drag is unusually high which makes me wonder if something is wrong. The difference in the 2010 is significantly lower so one wonders if the cold roll-down coefficients might have had a problem (i.e., did the bumper inlet vanes not close?)

FOLLOW UP

1. We need low speed, mph vs MPG in the 25-55 mph range, especially in the 35-45 mph range for both the 2016 and 2010. This is the speed range with the maximum drag difference.
2. Need to investigate the "B" coefficient in the 2016 as both the cold and normal values are way too high. Compared to the 2010, these are too high.
3. We need 50-55 mph, dry, cold weather, benchmark at or below freezing, of the 2016 and repeat the test on a standard day, ~65-75 F, dry. This is the speed range of the maximum drag power difference in the 2016.
   1. If there was something wrong with the cold weather roll-down, it would explain the problem.
4. Improved 2010, bumper air inlet blocking should make a significant performance improvement. Dynamic would be best to handle hight temperature, steep hill climbs. Something to investigate.
5. Weight reduction, possibly removal of rear seat backs, needs to be investigated. This is the only significant, removable weight.

Questions?

Bob Wilson

 

The problem is the test vehicles are identified but we don't have a mapping to specific models. You are right, the 17" wheels could explain the B coefficient.

What also confused me is there are three test vehicle models but the same roll-down coefficients were used for all three. We may be seeing Toyota 'sandbag' using just the worst-case coefficients. In which case, 2016 Prius owners may see exceptionally higher MPG numbers . . . a nicer form of what the cheat-diesel owners thought they were seeing.

Here is the source: Test Car List Data Files | Cars and Light Trucks | US EPA

Bob Wilson