Fan blade Physics and a Peek inside C2's Black Box

[faach1]

Great read Mathieu, is there a reason why ErgData/the PM cannot give a watts reading for splits below 1:00/500m?

Because they're still using a single byte integer in the PM code and you're going below zero at 1:00/500m (that was done in the past to save RAM in the monitor) so they picked an arbitrary low limit.

Thanks Dougie, seems like a PM6 needs to come out that can accommodate this with heavy hitters such as Chris Scott, Ross Love and Egor Lubskiy etc. all having (to my knowledge) gone below 1:00/500m for at least a few strokes on sliders and/or static C2s

[Nomath]

This is awesome work and VERY well done! It's fun to follow along with your adventure (somewhere between a blind man investigating an elephant and Shackleton's navigation from Elephant Island to South Georgia). Thanks!

Thanks for the praise! The reference to Shackleton is appreciated but much too flattering.

[Nomath]

I have measured the flywheel sensor signal for 5 different drag factor settings : 80 - 100 - 125 - 150 - 200. The graph below shows the coast down results.



What could be expected is indeed observed : the rotation period increases faster with a higher drag factor setting. The different slopes reflect the different drag coefficients C1. The graph below shows the correlation between the ratio C1/MoI and the drag factor setting. The correlation is quite good.



Concept2 doesn't give physical units for the displayed drag factor. Van Holst already observed that it is much too high for identifying it with the coefficient C1. Somewhere I have read that the display drag factor equals C1*10^6. This comes closer too my observation.
Assuming MoI=0.1 kg m², the ratio I found is : DF = 1.2 * C1 * 10^6. The units of C1 are [W.s³] or [N.m.s²].

I recalculated the drag coefficients from the slope of the curves using only the data of the first second in the free run. This is in line with how C2 determines the drag factor: in real-time during the recovery, which lasts about 1 sec.
The results :
- drag factor 80 : drag coefficient C1 = 0.000078 kg m²
- drag factor 100 : drag coefficient C1 = 0.000100
- drag factor 125 : drag coefficient C1 = 0.000124
- drag factor 150 : drag coefficient C1 = 0.000149
- drag factor 200 : drag coefficient C1 = 0.000203
So the agreement is amazingly good. It validates how the calculation is done. For convenience C2 skipped the factor 10^-6.
As for the physical units, the drag coefficient is usually quoted in units [N.m.s²]. As 1 N = 1 kg.m/s², this is the same as [kg m²] , which I prefer because it is the same units as for the moment of inertia of the flywheel.

I did an additional measurement with the flywheel housing removed.
- drag factor 230 ; drag coefficient C1 = 0.000229 kg m². Perfect!

[jcross88]

I was given a link to this topic from a question I asked here: viewtopic.php?f=7&t=199540

This is phenomenal work Nomath! Thank you, very much.

I suppose the natural extension to finish the topic would be to describe the aerodynamic properties of the flywheel housing and fan. I was recently looking at getting a manometer to tune the draft regulator on my oil fired furnace. With a C-Breeze attached to the flywheel housing it may be possible to measure air flow and take drop readings to further reify our understanding of the physics of the fan housing damper itself.

It strikes me how the erg's function contains so many different examples of classical physics in such a seemingly simple little machine. And all these abstract concepts can be experienced directly just by hopping on the thing and pulling! It's quickly become apparent to me that the erg will be a permanent part of my exercise regimen and wellness. Perhaps it's simply in my nature, but when a piece of equipment becomes so pronounced in my life I can't help but want to know every little thing I can about it, even if only for the sake of knowing.

Call me crazy, but it's also stuff like this that's rushing through my head in that last 250m of a 2k. Well, that and the excruciating pain.