Ad Hoc 0-60 mph

Jason Torchinsky wrote The 2016 Toyota Prius Is An Enthusiast's Car and brilliantly thought to record a video of a maximum acceleration. After checking with Jason, he OKed extracting this data from the video:

Version 1.01 - in an earlier chart, the fractional seconds was actually the frame number. In this chart, the frames were converted to fractions of a second. - rjw

Jason also shared via e-mail:

Also, I just looked over your thread, and thought you might like some more data:

• I was alone in the car, and I weigh about 155 lbs or so
• I was on a dry, smooth runway
• Wind was minimal, but that's all I know
• It was about 70°F or so
• The car had been driven about an hour on the highway prior to this

Hope that helps.​

The Jason just floored the accelerator which means part of the launch is to also spin up the engine. A better technique is to force charge the traction battery by holding with the brake and flooring the accelerator. Releasing the brake launches the car and saves 100-200 milliseconds.

FYI, I'll do the engine power metrics later BUT if anyone else wants to do it, I look forward to comparing our results. <GRINS>

Bob Wilson

 

I posted an updated chart. Here is the raw data after converting the frames to fractions of a second:

	time (seconds)	speed (mph)
1	0.00	0
2	0.23	2
3	0.53	4
4	0.83	7
5	1.07	9
6	1.37	11
7	1.63	14
8	1.93	17
9	2.20	19
10	2.50	22
11	2.77	24
12	3.03	26
13	3.33	28
14	3.63	30
15	3.87	32
16	4.17	34
17	4.43	35
18	4.70	37
19	5.00	38
20	5.27	40
21	5.57	41
22	5.87	43
23	6.10	44
24	6.40	45
25	6.67	47
26	6.97	48
27	7.27	49
28	7.53	50
29	7.83	52
30	8.10	53
31	8.37	54
32	8.67	55
33	8.93	56
34	9.23	57
35	9.50	58
36	9.77	59
37	10.03	60
38	10.33	61
39	10.60	62
40	10.90	63
41	11.13	64
42	11.40	65
43	12.00	67
44	12.30	68
45	12.87	69
46	13.10	70
47	13.67	72
48	14.20	73
49	14.50	74
50	15.10	75
51	15.63	76
52	15.90	77
53	16.47	78
54	16.77	79
55	17.30	80
56	17.87	81
57	18.17	82
58	18.70	83
59	19.30	84
60	19.53	85
61	20.10	86
62	20.70	87
63	21.23	88
64	21.80	89
65	22.37	90
66	22.90	91
67	23.47	92

Bob Wilson

 

Ok,

Here is my chart:

• Used Kinetic_Energy = 0.5 * (mass) * (V**2) for each point
• mass = Two_Eco_curb_wt + 200_lb_driver + 8_gal_gas
• time = seconds + (frame_cnt / 30)
  • minimum frame_cnt = 0
  • maximum frame_cnt = 29
  • used 30 frames/second
• speed boundary read when speed indicator was first changing
  • Likely sampling errors as there were single, double, and one triple transition frames.
• Assumed Two Eco, one 200 lb driver, and 8 gallons.

Because of the noise, I will go back and try to use the middle of the transition frames.
Bob Wilson

 

This is about as far as I can go with this data:

• The 0-60 mph time is reasonable
  • The audio indicates the engine was off. By holding the brake with the accelerator max, releasing the brake to launch can save 100-200 milliseconds.
• The cell phone sampling rate fails to meet Nyquist sampling rate compared to speedometer
  • The video sampling rate needs to be 2x the speedometer update rate to make accurate metrics.
  • By tweaking the frame number, +/- 1, we can minimize the sampling anomalies.
  • WARNING: manual data tweaks can lead to a very bad place.
• Initial acceleration is torque limited which also means power limited
  • Too much torque and the tires lose traction and spin (smoking)
• These are kinetic energy based, power numbers, and do not account for other energy losses
  • Unknown vehicle overhead - electrical overhead is typically ~450 W in earlier Prius
  • Unknown vehicle rolling drag - typically a fix force regardless of speed, it is linear with speed
  • Unknown vehicle aerodynamic drag - varies by the square of the speed
• The audio suggests two people who I assigned a weight of 200 lbs each.
• For vehicle mass, I assumed Two Eco and 8 gallons of gas.

Video recording of a speedometer is . . . better than not. It could have been done a little better but we can work with what was available.

A better approach would have been to use an accelerometer APP or a proper accelerometer (as was volunteered.) These have sampling rates many times greater than the speedometer and do not suffer from tire errors. But having any data is much better than comments like "it seemed fast."

As for technique, the best approach if using video or an accelerometer APP would be:

1. Warm-up car - it needs to drive for 15-20 minutes after the first cold-start.
2. Reset trip meter and drive the route - this sets the MPG numbers for fuel consumption base for the run.
3. Force charge (brake+full power) - watch MPG and on 3d time the digit changes, release the brake
4. Accelerate to +65 mph and shift into "N" - this is raw acceleration capture
5. Coast in "N" as long as possible - this is an ad hoc 'roll-down' to get the aero and rolling drag coefficients

If possible, repeat the test in the opposite direction. This will minimize the obvious, high wind and grade effects. The driver did not tell us if he was driving into or with the wind.

Bob Wilson

 

I was thinking about using the 2010 roll-down coefficients with possibly (.24/.25) times the velocity and a similar adjustment to the linear coefficient. Still:

• 121 hp * 745.7 W/hp ~= 90230 W

Close enough! Well done Lee.

Bob Wilson

 

So I added a drag power function using the 2010 Prius values:

• HP = v * (A + B*v + C*(v1*v1)) / 375
• v - velocity in mph
• v1 - v + head wind factor
  
• A = 20.234
• B = 0.01993
• C = 0.01874 * (.24/.25) # Aero adjusted for Cd_2016 / Cd_2010

I also researched weather at El Toro, Marine Air Station November 9th and found the winds were gusty to 21 mph at 1-2 PM. But we don't know the head wind vector. So now my chart looks like:

• adjusted frame numbers - because sampling was below the Nyquist rate and the winds gusty, I adjusted the frame numbers to keep adjacent kinetic energy values somewhat linear. In a perfect world, the test drive would have been done 12 hours later or earlier to avoid the gusty conditions. So I adjusted the data sample times, a hack for gusts and slight dips in runway.
• added 7 mph headwind to aero velocity, the squared velocity factor - this adjusted the drag power so the tail power approximated the peak, a somewhat linear, total power line considering the conditions. I did not add it to the linear factor since that is a drive train and tire factor.

Bob Wilson

ps. They had a runway, a 2015, and a 2016 Two Eco: