Newton is bad (ED: good) at math (equations of motion)

Newton is bad (ED: good) at math (equations of motion)

Postby brookside » Tue Aug 01, 2017 5:24 pm

Having done two days of riding in hillier country than I usually ride I was taken back by the power numbers the Newton was reporting in real time, and which I saw in Isaac afterwards (and after an Analyze Route, which is obligatory to get the start and end elevations correct and to remove the headwind bias from almost every ride, even though I do a Wind Cal before each). When back home the next day I did a ride with a Ptap wheel and I marked, with laps, a number of sections to analyze later (after the Analyze Route). I used the power and speed calculator at https://www.gribble.org/cycling/power_v_speed.html and input the same CDA, Crr. weight, and CM as in the Newton then input the speed, slope and wind from the Newton for each of the 4 sections. The four sections were: two flat, one aiming to hold 200 watts (2.5 minutes), the other 300 watts (3.5m); one uphill at 7% grade (1m) and one slightly downhill at -.9% grade (5m).

I compared the Newton and Ptap average power over those sections to what the equations of motion said the average power should be, using both speed vs ground and speed vs wind as reported by the Newton. I should say that my bike speed is correctly dialed in, I've done 100+ mile rides with this setup and the Newton odometer has been off by only a few 10ths of a mile from the ridewithgps mileage. The results were (using speed vs wind):
_____________Newton____Ptap___Eq of Mot.
200W section:....243.........206......205
300W sect:........307.........299......292
Uphill 7.1%:.......288.........233......233
Downhill .91%:....160........132.......140

Over the total of 12 minutes, by time weighting the 4 sections, the Newton was on average 25 watts high vs the calculated value, and the Ptap was 1 watt low.

I had thought the ongoing problem of the Newton consistently reporting watts that were too high was a problem with its wind or slope sensing, but it looks now like those are accurate (confirmed by the Ptap), and the endemic problem is that it can't do the equations correctly. What do you think?

Ride file attached, the laps in question are 2, 4, 8, and 10 in the lap list.
Attachments
iBike_2017_07_31_1114_30_Miles.ibr
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Re: Newton is good at math (equations of motion)

Postby Velocomp » Tue Aug 01, 2017 7:13 pm

You have to be extremely careful when using bike calculators. All calculators assume CONSTANT conditions.

In every interval you selected, there are significant changes in slope and bike speed. Bike calculators won't provide good analysis when ride conditions are changing.

To use the calculator properly, what I did is select smaller sections your intervals, where the bike calculator assumptions are satisfied. I was careful to find places of reasonably constant slope and bike speed. I also accounted for relative wind (headwinds/tailwinds). I did not "cherry pick" any of the sections used. I just found places where the assumptions of calculator apps are reasonably satisfied.

I have not tried gribble, but I am familiar with bikecalculator.com. I like this one because it allows for differences in CdA.

For my comparisons I used the "drops" position in the calculator, because your CdA is somewhat low (0.31)



So, here are my results (in general, the PT is low)

Uphill (lap 8)

There are actually TWO grades, not one (you can see this in the Newton slope data).

Screen Shot 2017-08-01 at 6.12.40 PM.png
Screen Shot 2017-08-01 at 6.12.40 PM.png (346.47 KiB) Viewed 84 times


So, I broke up the interval into two parts. In each section the slope is about the same

In the latter section of the hill the two PMs are essentially identical, and very close to the theoretical prediction (theory 279W, Newton 270W, PT 266W)

Screen Shot 2017-08-01 at 5.51.00 PM.png
Uphill theory
Screen Shot 2017-08-01 at 5.51.00 PM.png (355.98 KiB) Viewed 84 times


Screen Shot 2017-08-01 at 5.51.42 PM.png
PT Uphill, second climb
Screen Shot 2017-08-01 at 5.51.42 PM.png (300.86 KiB) Viewed 84 times


Screen Shot 2017-08-01 at 5.51.51 PM.png
Newton, second climb
Screen Shot 2017-08-01 at 5.51.51 PM.png (298.02 KiB) Viewed 84 times


The first part of the climb is where there is a significant difference. Which PM is correct?

Theory, first climb (360W)

Screen Shot 2017-08-01 at 5.53.24 PM.png
First Climb, theory
Screen Shot 2017-08-01 at 5.53.24 PM.png (356.09 KiB) Viewed 84 times


Newton, first climb (325W)

Screen Shot 2017-08-01 at 5.53.01 PM.png
Newton, first climb
Screen Shot 2017-08-01 at 5.53.01 PM.png (282.41 KiB) Viewed 84 times


PT, first climb (206W). The PT is extremely low, and if you look at the PT data, you'll see that the PT seemed to flatline during part of the climb:

Screen Shot 2017-08-01 at 5.53.11 PM.png
PT, first climb
Screen Shot 2017-08-01 at 5.53.11 PM.png (291.64 KiB) Viewed 84 times


I went through all the remaining laps in the same manner.

Lap 10 (downhill)

I selected a portion of this lap where speed, wind and slope were approximately uniform (the original lap 10 has too much variation)

Theory: 160W; Newton 162W, PT 135W

The PT is low

Screen Shot 2017-08-01 at 6.01.43 PM.png
Lap 10, theory and Newton
Screen Shot 2017-08-01 at 6.01.43 PM.png (1.15 MiB) Viewed 84 times


Screen Shot 2017-08-01 at 7.10.30 PM.png
Lap 10, PT
Screen Shot 2017-08-01 at 7.10.30 PM.png (319.21 KiB) Viewed 84 times


Lap 2

I selected a place where speed was unchanging.

Theory: 251W; Newton, 275W; PT, 217W

PT is low

Screen Shot 2017-08-01 at 6.06.18 PM.png
Lap 2, Theory and Newton
Screen Shot 2017-08-01 at 6.06.18 PM.png (1.1 MiB) Viewed 84 times


Screen Shot 2017-08-01 at 6.06.10 PM.png
Lap 2, PT
Screen Shot 2017-08-01 at 6.06.10 PM.png (1.06 MiB) Viewed 84 times


Lap 4

The differences between Newton and PT are less than 5%

Screen Shot 2017-08-01 at 6.07.31 PM.png
Lap 4, Theory and Newton
Screen Shot 2017-08-01 at 6.07.31 PM.png (1.11 MiB) Viewed 84 times


Lap 4 PT

Screen Shot 2017-08-01 at 6.07.40 PM.png
Lap 4 PT
Screen Shot 2017-08-01 at 6.07.40 PM.png (1.09 MiB) Viewed 84 times


I think the Newton is good at math, and it just might be that your PT is ready for some factory service. :-)
John Hamann
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