Tawpie Posted February 23, 2022 Share Posted February 23, 2022 (edited) With all the new wheels coming out and having one on pre-order, I'm of course curious what sort of range I might expect to get. As an avid EUCWorld user, I log basically all of my tours and thought: I wonder if a polynomial fit (equation) of my typical energy consumption would be able to give me insight as to what I might expect from my new wheel and how does that change based on my speed? So I pulled up a selection of my tours and manually (@Seba?) copied down my average energy use and average riding speed from each tour and entered them into this website https://arachnoid.com/polysolve/ and was rather surprised at what it showed. That made me curious about what other riders observe from the data provided by EUCWorld—I think it would be fun if others would do the same and share! In my chart, two things really stood out: my energy consumption relative to speed is shockingly linear, I was expecting to see more drag effect. Obviously I'm not going fast enough for drag to be a significant factor because physics isn't supposed to lie, right? I'm going to get near marketing numbers for range from my new wheel. Neener neener! (until I start going faster, which I fully expect will happen even though I don't especially strive for speed) As a baseline, here's some facts about my test conditions: riding weight: 61kg (basically the same as the rider used by KS to quote 200km for the S20) gear: 11kg of moto gear so I'm a bit of a marshmallow… hiking boots, armored textile pants and jacket, HJC i90 helmet height: 170 cm (not counting the Jack-in-the-box helmet) ride style: conservative… I don't ride like I have the zoomies and in general I go desperately slowly, pretty much Marty except I don't know how fast he really rides ambient temperature: 5-9C altitude: sea level to 100m riding path: mostly paved multi-use path free of cars but some urban riding included (downtown Seattle) minimum ride distance: 9.78 km My data (with added 0, 0 data point) fits a fourth order polynomial with these coefficients: -1.0876612882487601e-002 1.0764557707167037e+000 -9.1082228460135362e-003 -1.9690444537539403e-003 6.0877300160098145e-005 Wh/km = -0.01 + 1.07v - 0.009v^2 - .002v^3 + .00006v^4 where v is my average riding speed in km/h. In very loose terms for head computation, every km/h cost me 1 Wh/km. Here is a chart of tours at a range of average riding speed in very similar routes. The bulk of the tours were basically dead flat but mixed in there are some runs up and down the 100m tall hill that overlooks my route. 22 of the tours were on my H666 shod KS16XS that has two batteries, 5 tours were on an S18 running a TR1 knobby. The low speed tours were from last year when I had only been riding for about 3 months... I had to go back a ways. I added a data point at 0 Wh/km and 0 kph average riding speed to anchor the chart. The y axis is Wh/km for the tour, the x axis is average riding speed. You can see the curve is starting to experience the expected cubic relationship to velocity, but I'm not quite into the true drag penalty yet. Rolling resistance and mass still dominate. The raw data: Wheel Date Highest Battery Distance Riding Speed Wh/km 16X 2/4/21 84.5 16.2 15.4 11.9 Alki AK Junction 16X 1/9/22 82.9 11.4 17.9 8.9 Alki Lincoln Park 16X 1/8/22 77.3 16.5 19.6 12.9 Alki Lincoln Park 16X 2/6/21 82.6 39.9 14.8 10.3 Alki Lincoln Park 16X 2/9/22 84.5 15.4 20.7 10.6 Alki 16X 2/5/22 81.1 18.6 19.2 10.7 Alki 16X 2/3/22 83.1 13.5 24.7 12.4 Alki 16X 1/31/22 82.3 15.7 22.6 11.4 Alki 16X 1/10/22 81.6 12.1 20.3 10.5 Alki 16X 1/7/22 76.5 15.5 20.7 13 Alki 16X 12/15/22 78.4 15.6 24.9 15.6 Alki 16X 12/8/22 81.3 15.3 22.6 14 Alki 16X 12/5/22 83.8 15.3 23.6 14.4 Alki 16X 12/2/22 78.2 15.2 23.6 13.8 Alki 16X 12/1/22 80.9 15.1 19.9 12.9 Alki 16X 1/23/21 79.3 9.98 14.1 9.8 Alki 16X 1/28/21 80.9 10.5 12.2 8.3 Alki 16X 2/3/21 84.2 9.78 17 10.9 Alki 16X 1/30/21 83.1 22 13.3 10.6 Burien 16X 2/12/22 84 45 21.3 12.2 SNR 16X 2/6/22 82.9 70.9 24.3 12.3 South Lk WA Loop 16X 1/26/21 83.5 10.6 14.2 10.3 WS Hill S18 2/14/22 78.9 14.3 19.2 12.6 Alki AK Junction S18 2/8/22 82.9 15.2 19.8 10.2 Alki S18 1/3/22 80.6 14.3 20.1 13.9 Alki S18 12/16/22 79.7 21.4 22.8 13.8 Alki S18 12/18/22 83.5 19.1 13.9 11.5 Lincoln Park AK Junction Edited February 23, 2022 by Tawpie typo 1 1 Quote Link to comment Share on other sites More sharing options...
Eucner Posted February 23, 2022 Share Posted February 23, 2022 Impressive. Did you try to fit the point to 3rd order polynomial before you went to 4th order? 1 Quote Link to comment Share on other sites More sharing options...
Tawpie Posted February 23, 2022 Author Share Posted February 23, 2022 (edited) 19 minutes ago, Eucner said: Did you try to fit the point to 3rd order polynomial before you went to 4th order? I did. That website has a button to increase/decrease the polynomial order. 2nd order third order deets on the third order Mode: normal x,y analysis Polynomial degree 3, 28 x,y data pairs. Correlation coefficient = 0.8174037021139763 Standard error = 1.23574852201512 Output form: simple list (ordered x^0 to x^n): -1.7563746529069335e-002 1.4807379667252345e+000 -7.5312756298021810e-002 1.5493725588177161e-003 Copyright (c) 2019, P. Lutus -- http://arachnoid.com. All Rights Reserved. Edited February 23, 2022 by Tawpie 1 Quote Link to comment Share on other sites More sharing options...
Eucner Posted February 23, 2022 Share Posted February 23, 2022 19 minutes ago, Tawpie said: I did. That website has a button to increase/decrease the polynomial order. Nice, why did you choose 4th order? They look pretty same. Physics theory is only up to 3rd order. Now you need to ride more at the low speed to fill all those empty data points . 1 Quote Link to comment Share on other sites More sharing options...
Tawpie Posted February 23, 2022 Author Share Posted February 23, 2022 (edited) 56 minutes ago, Eucner said: why did you choose 4th order? because the button let me! And it provides a slightly more pronounced visual effect of the 3rd order term. But you're correct, 4th order or higher is meaningless. The correlation is starting to break down at 4th order and only gets nutz at higher order. 56 minutes ago, Eucner said: Now you need to ride more at the low speed to fill all those empty data points . uh... I did my part with the mid-speed numbers. Low speed and fastfastfast is for "others" to contribute! (I do have numbers for low speed off road—they don't really belong with the pavement numbers though). Maybe somebody that likes to ride distances backwards can give us the low speed numbers? Edited February 23, 2022 by Tawpie 1 Quote Link to comment Share on other sites More sharing options...
RagingGrandpa Posted February 28, 2022 Share Posted February 28, 2022 EUC World calculates Wh/mi as Power / Speed. If the speed is very low, changes in riding style have a huge impact on the result. Below is real data- see if you can puzzle through how such an inefficient number might occur At least 5 what-if's are answered by the various parameters logged... GPS-based altitude is rather noisy in the forest (hint); this ride had no elevation change. Quote Link to comment Share on other sites More sharing options...
Tawpie Posted February 28, 2022 Author Share Posted February 28, 2022 (edited) Doesn't Begode/Gotway report something like phase current so the 'power' numbers are ~3x what's actually taken from the battery? At the rate you were going though, your day was going to end at 20 miles I chalk up poor Wh/mi at low speeds to the fact that torque takes loads of power but might not result in much distance travelled. So yeah, there's some lower bound where Wh/km isn't terribly useful. Edited February 28, 2022 by Tawpie Quote Link to comment Share on other sites More sharing options...
supercurio Posted February 28, 2022 Share Posted February 28, 2022 (edited) A few months back, with EUC World 2.6, @Seba replaced the "current" view from phase current to battery estimated current, as described here @Tawpiehttps://euc.world/blog/battery-current-vs-motor-phase-current/ Edited March 1, 2022 by supercurio 3 Quote Link to comment Share on other sites More sharing options...
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