Accurate slope range

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Zoltan
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Accurate slope range

Post by Zoltan »

I am just testing my unit, did tilt calibrations etc. It seems that within -20% and +20% the slope displayed is accurate. Just for fun I was holding iBike at 45 degree and the screen did not show 100% what it should have been, but around 70%. When I held in vertical position I did not get a supra high number, simply just 100%.

So my question is that what is the range within slope is displayed accurate. +/-20%? Or +/-25%? Maybe more? Or with other words the accuracy of 0.1% at steady state (at rest or at constant speed) is true for which range?

Thanks,
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lorduintah
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Re: Accurate slope range

Post by lorduintah »

So when do you plan on riding up the face of the Empire State Building - or any skyscraper :roll: ?

Tom
Zoltan
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Re: Accurate slope range

Post by Zoltan »

lorduintah wrote:So when do you plan on riding up the face of the Empire State Building - or any skyscraper :roll: ?

Tom
I did ride up 27% several times. And once something around 30%. They were not long stretches, just like 100-150m. BTW the Thursday stage of Vuelta had an ascent where max. slope was 29%.

My point is that it can happen that people would like to measure the slope of a hill, where they are just shove up their bike.
Zoltan
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Re: Accurate slope range

Post by Zoltan »

I did an outdoor test with the unit on steep ascent. It is measured as max. 27% by the road maintenance company as the warning traffic sign shows it.

Stomping the pedals on the ascent I got 24.5% and 24.2% as max slope ( I made two test, my legs did not allow more :-) ) I was on the saddle not to make any bias due to moving my body frontward.

Rolling down on the descent I got 26.5% and 27.6% as max. slope in absolute terms. I could not avoid my body going frontward. Consider that I was braking and sometimes I let the brake level go, IOW there were sudden bike accelerations. Due to lack of 4 speed spoke magnets :-) (see http://www.ibikeforum.com/viewtopic.php?f=6&t=1563) I guess it added short term total acceleration fluctuations which cannot be measured due to low speed.

So the final test was getting off the bike and placeed it on the different part of that stretch where I got the max numbers. I measured 23.2% as max slope.

I guess that my tilt calibration was done in a perfect way, even if I am a beginner with iBike, moreover I got -0.3% and -0.4% as tilts on my first calibration rides, which is in line with the example of the sw manual.

So my original question still persists. It really seems for me that Gen3 is very accurate with grades at low level grades, but it seems that its accuracy is gradually decreasing, so there must be some function between its accuracy and the grade level being inherent from the working mechanism of the tilt sensor.

Can we say eg that the accuracy at steady state is
+/-0.1% between -5% and +5%,
+/-0.3% between +5% and +10% & -5% and -10% ,
+/-0.6% between +10% and +15% & -10% and -15%,
+/-1.0% between +15% and +20% & -15% and -20%,
+/-1.5% between +20% and +25% & -20% and -25% etc???

Otherwise it would not display 68-70% as tilt at 45%.
Zoltan
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Re: Accurate slope range

Post by Zoltan »

Guys, we have a Hungarian proverb maybe existing in English too: "Thyself, My Lord, if thou hast no servant".

And we have another saying, too: "Don't be so stupid any longer". :lol:

I just simply forgot or just did not come to my mind what I knew pretty clearly earlier, namely that there are two definitions for rise/run (or slope or tilt or grade or etc). When playing with iBike so far, I was thinking in GPS logic, sorry about that, because GPSs use the tangent approach due to their measurement capabilities. Run is just the horizontal projection of the run, but there is the other the sine approach, where run is the real run eg on a bike. (we can call it diagonal or more precisely hypotenuse) For the two definitions http://en.wikipedia.org/wiki/Grade_%28slope%29

iBike definitely displays the sine, so this is why my fast test at 45 degrees showed 68-70%, because it has to be 1/2^0.5=0.707=70.7%

Although at 90 degree iBike should not display 100% if we stick to real life approach, but definitely it should display 100% if we rely on the sine approach, because sine(90°)=1

Conclusion since road companies use tangent approach as a standard, the traffic sign of 27% is around 26% by iBike. So 1 percentage point difference between the sign and the reading on the field is explained. All the other can be explained by other factors, so I decided just to make a last check on a cube cut by two to get 45 degree. If the result will be 70.7%, i will be a happy camper.

Finally although the tangent approach would be more in line with standards, I understand why Velocomp opted for the sine, because the sine rise/run gradient is what needed to calculate the Fgrav, so practically the gravity component of the total power. I fully understand because I did the same with my Excel sheet power calculator two years ago, I just forgot it for two days. :oops:
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racerfern
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Re: Accurate slope range

Post by racerfern »

Is the bottom line of this post, "Oops I was wrong"? The iBike is accurate at all grades, even if I can't ride up it. You're a good man for recognizing the problem with your logic.
Fernando
KenS
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Re: Accurate slope range

Post by KenS »

Not really wrong technically; but for practical purposes the simplification of using sin rather than tan is a sensible one to reduce the calculation time and eliminates possible divide by zero errors

For angles less than about 15 degrees (or 26%), the difference between sin and tan is not very significant
But next time I'm riding up a vertical cliff I'll know why it feels harder than the iBike tells me :)
-- Ken
Zoltan
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Re: Accurate slope range

Post by Zoltan »

racerfern wrote:Is the bottom line of this post, "Oops I was wrong"? The iBike is accurate at all grades, even if I can't ride up it. You're a good man for recognizing the problem with your logic.
Yes, that is the bottom line.
Zoltan
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Re: Accurate slope range

Post by Zoltan »

KenS wrote:Not really wrong technically; but for practical purposes the simplification of using sin rather than tan is a sensible one to reduce the calculation time and eliminates possible divide by zero errors
The second part of your comment is interesting. We agree about the benefit of less calc time, but in which cases there could be divide by zero errors using tan? Of course, at real vertical climbing or perfectly vertical freefalling from a cliff the slope would be undefined. :-)
KenS
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Re: Accurate slope range

Post by KenS »

I was also thinking numeric overflow but the issue could arise if you take your iBike off the mount and hold it upright (for instance while connecting it to your computer) causing it to crash with a divide by zero error. So extra code is needed to avoid that.
-- Ken
Zoltan
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Re: Accurate slope range

Post by Zoltan »

Zoltan wrote:
racerfern wrote:Is the bottom line of this post, "Oops I was wrong"? The iBike is accurate at all grades, even if I can't ride up it. You're a good man for recognizing the problem with your logic.
Yes, that is the bottom line.
The good (?) man is back.

Finally I figured out how to set the tire circumference to 419 mm that is 2095/5, so I mounted 5 spoke magnets evenly spaced on my first wheel . Note: the front wheel has 20 spokes on a paired rim. I could have borrowed more spoke magnets to mount 10, but 5 was enough for testing. And it was ugly enough :lol:

I made several short rides, and my findings are the following.

1) With 5 magnets the fluctuation of the slope when accelerating is visibly less as I expected, although Gen3 still needs some time to "zoom" on the true slope in case of a sudden burst when standing out the saddle. I bet adding more magnets would not result in really better accuracy, because the problem is not the acceleration itself, but the moving handlebar and the moving body (Note: my unit on the handlebar, maybe on a stem the effect would be a bit smaller).

2) During my short rides I experienced that the slope is STILL not exactly symmetric when ascending or descending on the same route. It is true with 5 mounted magnets, but also when a single magnet is on.

i) First I thought it was my fault to make not perfect tilt calibration, so I made some more between each phase of the test. But after the calibrations I always tested it on a pretty smooth pavement with putting the bike in one direction and turning the bike with 180 degree. The displayed slopes were either perfectly symmetric to zero or with an error of +/-0.1%. So I am sure that the tilt calibration how I do it is perfect.

ii) The calibration rides I made last week always ended up with a ride tilt of 0.3% and rarely 0.4%. I assume from the beginning that the ride tilt comes from the extra weight of the biker, so it is the extra tilt to be considered after a proper biker-free tilt calibration. But let me ask whether I am correct?

iii) So if my logics are correct and I did the tilt calibration properly and my ride tilt is also OK, there must be something else to explain the differences.

3) Some data.
i) Coasting down on a relatively longer stretch of slight gradient without acceleration gave -2.2 -- -2.3%, while steadily climbing it gave +2.9 --+3.1%
ii) Coasting down on a shorter stretch of substantial gradient with some acceleration (5 magnets on) gave a max of -9.7%, while steadily climbing it gave a max of +10.3%
iii) Going down on a shorter stretch of very steep gradient without substantial acceleration (I used the brakes to try to minimize the acceleration, 5 magnets on) gave a max of -26.7%, while climbing it gave a max of +25.1%

4) Conclusions

i) Even some small acceleration can influence the accuracy of the slope measurement, and in line with the manual the accuracy may be within +/-1%. 5 magnets maybe came it below +/-0.5%, but it is just a speculation from me.
ii) But apart from the acceleration issue there is some asymmetry when ascending or descending. I was very careful with my posture in the test of 3/i) ,so I suppose it did not influence the readings. The difference is more than +/-0.1%. Why? Maybe due to auto tilt, but I have no better guess.

5) As a sidenote I have found that measured wind data is far from symmetric, which is normal, nature is nature, but the extent of asymmetry of wind speed is too much. I also made wind calibrations every time, but my guts feel that something must be with the speed measurement. Again it is a speculation, but the wind profile was so strange on a straight, traffic-free road of 1 km or so. The measured wind was fluctuating between an absolute headwind of 9 km/h and an absolute tailwind of 10 km/h.

6) Other sidenotes

i) the processor of Gen3 seems to be pretty fast and/or the programming logics of the firmware is quite well done. iAero receives and displays the ANT+ information much faster than the other tools of mine
ii) It is time to give up chasing a better slope accuracy than +/-0.5% on ascents and +/-1.0% on descents
iii) it was proved that the slope measurement of Gen3 is not sensitive to changing ambient air pressure coming from wind burst, so it is the most reliable inclinometer that I have ever had
iv) I will keep the 5 magnets on
KenS
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Re: Accurate slope range

Post by KenS »

Don't forget that tilt is affected by more than just your posture on the bike and acceleration from gravity. If you are pedalling the torque at the rear wheel causes the front of the bike to lift up. If you are braking the front of the bike will pitch downwards.
-- Ken
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Russ
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Re: Accurate slope range

Post by Russ »

Zoltan,

ii) is basically correct, but actually it is the sum of everything including KenS point of crank torque lifting the front a bit, assuming during your cal ride you are cranking at a steady and equal power both ways (ha! ), etc. Mostly your weight which is more on the rear tire.

Now I visualize on a hill climb my center of gravity shifted back further and more forward on a descent. So there are numerous uncontrollable and unaccountable variables going on and the iBike does amazingly well.

You have me thinking about adding at least one more magnet again :-)

Oh and yes the stem mount removes the handlebar flex contribution quite well.

Nice analysis,
Russ
Zoltan
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Re: Accurate slope range

Post by Zoltan »

Thank you guys for the feedback.

I forgot to mention that I made a very very short test with 5 magnets on but with the original tire circumference of 2096 mm set. First it gave me false slopes due to the artificially inflated bike acceleration, and of course I could speed at more than 200 km/h. :-) My observation is that speed may be limited at 150km/h or so and there is some overflow or some similar beyond.

Another experience that the max power displayed is 999watt, so my real peak power of 5sec was cut.

Going back to the example in 3/i. The grade was small, the torque on the ascent was low also, the posture was the same that I tend to think the difference comes from the imperfect measurement of ride tilt.
Maybe it is a bad idea but I try to find not a flat but a long slight ascent for a new cal ride and see what ride tilt I get.
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