Awesome, thanks!! I did 4 laps in a high school parking lot that has about 6ft'. Thanks again!

I wrote some simple code to implement the VE method. And tested whether it revealed the difference with a visor (and without). I rode a lumpy 1km "half-pipe" loop about 30-odd times, varying the speeds a bit. I do have a braking zone at one end as I turn around. So I hit the Lap button each time on my Garmin. My code inspects the .tcx file and throws out brake zone laps and keeps the "loop".

My code can flatten the graph automatically etc. Seems very straightforward to code up and I get a family of solutions (Crr, cdA).
I also find a difference without/with visor. (Not a tri-bike or regular bike but still method applies.) So far, so good.

Then, because I have varying speed runs, see histogram, I graph all the (Crr, cdA) pair solutions over a range of Crr.
I pick the pair that has the least overall deviation for the top3 fastest and slowest runs.
Problem is, the best Crr I get is perhaps unrealistically low, around 0.0035, 0,004.
(Continental GP 5000 S TR 32-622 tubeless with Vittoria Airliner on the back and Contact Urban 32-406 with super thin butyl in front. Not a regular bike.)

Hmm, I have good rho data from our university's dept of Hydrology and Atmospheric Sciences weather station.
(I live at elevation and rho < 1 usually, so it's a good sign it's station pressure.)
I use a wireless Garmin Speed Sensor 2, and don't rely on GPS speed.
The data is recorded one per second by my Garmin computer.
I do not correct for the initial data point, as it requires the data point 1 sec before my start, but I rely on hitting Lap.
I do use the velocity correction for the lag detailed in the slides.
I have the Assioma powermeter pedals. I modify the watts reported, multiplying by a factor bit less than one to account for drivetrain inefficiency.
I didn't detect significant wind during my run, but perhaps I'm mistaken and there was some wind.
(So last week, I bought the Bluetooth windmeter mentioned in the other thread and threw together 5 min code to extract the wind speed. Next time, I can mount the windmeter in front and get V_air.)

Anyway, I have a simple question about the slope equation formula. I notice the Crr part doesn't take slope into account for simplicity.

Given an incline, Crr is conventionally defined with respect to force normal to the incline, so shouldn't we multiply by the cosine of the slope?
If I do that, the VE curves look significantly different. So I must be missing something.

See handwritten picture with f(s) = 0 and f'(s) for the revised formula. I solve numerically for s (slope).
Plotted, the deviations are initially small, but as you can see in the last picture, they add up and the VE graph looks different, formula vs. formula2.
Garmin GPS profile is also shown here, but of course, I don't use it in my calculations.

Sorry, I forgot to append the slope formula and modified with cosine slope formula to the previous post.
Here's the code in Python, I can write it in any programming language, but Python is accessible to anyone and easy to read.
Just in case I made a silly error.

CdA values are not in the expected range for a cyclist, what unities do you use?

Not that it's relevant, but I'm using something a bit more aerodynamic than my road bikes.
It's the same principle at work.
I'm testing the effectiveness of the visor in this picture.

can you post the .fit file?

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What's your CdA?

I have the .tcx file. That's what I download from my Garmin Connect. Will that do?

What is the vehicle ? Where/how is power measured ?

Ok, such fully faired recumbents can have really low cdA (for example see attached paper, unfortunatelly in German).

Crr of 0.0035 - 0.0040 is possible.

Dear Maracag, I believe I posted a picture of the vehicle above after my initial message. It's in an attachment. If you can't see it, I can email it. And I mentioned I'm using Assioma pedals. And front wheel alignment is accurate to the mm level. Thanks.

Nice find! thank you.

How about my question about a modification to the formula for Crr? :-)

Even at 10% slope the Crr is still 99.5% of Crr on flat ground.

I would do separate testing of Crr and CdA improvements since neither is very likely to be constant across speed anyway.

And at 10% the contribution of rolling resistance is probably very low.

I computed the cosine factor here. So 0.999 etc., so it looks right. Thank you so much for confirming.

But although it tracks the same initially, it does cause a discrepancy eventually in my VE (See profiles in the graph below - formula = standard, formula2 = formula with cosine factor.)
Scratch my head... maybe there is an error in my code I didn't see.

>>> profile(runs[1])
discrepancy: cos(-0.0372) = 0.9993 (-0.0386)
discrepancy: cos(-0.0609) = 0.9981 (-0.0632)
discrepancy: cos(-0.0557) = 0.9984 (-0.0588)
discrepancy: cos(-0.0648) = 0.9979 (-0.0689)
discrepancy: cos(-0.1003) = 0.9950 (-0.1062)
discrepancy: cos(-0.0937) = 0.9956 (-0.1013)
discrepancy: cos(-0.0762) = 0.9971 (-0.0855)
discrepancy: cos(-0.0587) = 0.9983 (-0.0696)
discrepancy: cos(-0.0583) = 0.9983 (-0.0706)
discrepancy: cos(-0.0533) = 0.9986 (-0.0670)
discrepancy: cos(-0.0163) = 0.9999 (-0.0305)
discrepancy: cos(0.0073) = 1.0000 (-0.0066)
discrepancy: cos(0.0193) = 0.9998 (0.0059)
discrepancy: cos(0.0167) = 0.9999 (0.0038)
discrepancy: cos(0.0356) = 0.9994 (0.0235)
discrepancy: cos(0.0502) = 0.9987 (0.0392)
discrepancy: cos(0.0577) = 0.9983 (0.0478)
discrepancy: cos(0.0270) = 0.9996 (0.0176)

I found today that Charles Henry conducted tests back in 2015 on a tarmac velodrome in Switzerland. His graph confirms the Crr1 and Crr2 where Cr1 is a constant and Cr2 a tiny speed dependent factor for bicycle tires.

I too think that independence of Crr from speed and load is an approximation, however it may often be justified.

Tests on my "big" drum test rig usually show increasing Crr with increasing speed and / or load or normal Force respectively.

Thanks for sharing! What tire is that? Is there an appropriate conversion factor from the Crr on your drum to smooth tarmac? Maybe just wishful thinking.

I have to check, but I think it was a Conti Supersonic 622-23 with latex tube at 8 bar on a Citec 8008 ultra.

An appropriate conversion factor? I don‘t know how smooth a smooth tarmac is in the US. I think here a good rolling smooth tarmac is not that much worse than my drum. I guess the conversion factor is definitely smaller than 1.5.

I added the windmeter for testing. It is mounted rigidly but a distance above the vehicle, just like with Solar car testing.

Here is the Speed vs. AirSpeed on an almost calm night. Looks quite good to me.
I wrote code to Merge the recorded windspeed data on my iPhone with the Garmin .tcx file.

Is that on an "out and back" or loop ?

Out and back on the same road with a cul-de-sac for a non-braking turnaround.
After midnight, no traffic.
I use the lap button to start and stop the recording at the same location.
There is braking required to go around a rotary at the end before returning to the start, but that section is excluded by software.

So it looks like the air speed needs a small factor applied to it (maybe an offset, but probably a multiplier)
The difference between airSpeed and speed is basically wind
In theory the wind on the out = -1 * wind on the back
So if the yellow line comes up a bit, you will have a tailwind on the out and a headwind on the back

If I am reading your chart properly

So how to determine a value for the multiplier? Perhaps when the end points match up (same elevation)? Would that be reasonable?

Thanks!

Different aero sensors/apps have a protocol to determine this. The level of "sophistication" from app to app varies.

I noticed you are posting in the Cda/Crr app so if using that I am pretty sure they have one.

The windmeter manufacturer uses a linear ax+b formula to convert from impeller rpm to m/s wind speed. So I read impeller rpm and just use the values of the constants a and b that they provide.

Doing k(ax+b) where k is a fudge/calibration factor doesn’t seem so easy to do. There is always a bit of wind outside. Seems it’d have to be done indoors (no wind), ride at a selection of fixed speeds down some long corridor. Then one might as forget k and just use the new empirically determined a’ and b’ values.