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Here are speed data from two coastdowns I did yesterday afternoon. The speeds are in km/h at one second intervals. As I said, these were coast downs so power, of course, was zero. I forgot to weigh myself and the bike when I got home so I'm guessing the all-everything mass to be around 86 kg. I didn't measure air density but I'm thinking it must be around 1.17 kg/m^3. And the total drop from entry to exit of the test section was about 5 meters. Besides not measuring my mass or the air density, there was a tiny amount of wind in my face during the test runs -- but let's ignore all those problems and simply assume wind was zero and everything was exactly as noted above.

Here's the challenge: based on these data, can you estimate my CdA and Crr? Show your work. This was on my commuter bike and I was wearing street clothes so don't give me crap about my drag numbers.

Run 1:
15.2 15.8 16.3 16.9 16.9 17.4 17.7 18.1 18.5 18.9 18.6 17.9 17.9 18.6 19.7 20.0 20.9 21.6 22.5 22.5 23.4 23.7 23.5 24.3 25.1 25.7 26.0 25.6 25.3 24.6 24.2 23.9 23.5 23.1 22.9 22.6 22.3 22.3 22.0 21.9 21.7 21.8 21.4 20.7 20.9

Run 2:
26.6 26.6 26.6 26.5 26.6 26.8 26.1 25.4 25.6 26.3 26.8 27.3 27.9 28.4 29.1 28.7 29.6 29.8 30.6 30.3 29.7 29.2 28.7 28.3 27.4 27.2 26.7 26.1 25.8 25.5 25.3 25.0 24.5 24.2 23.9
RChung wrote:
Feels like high school all over again :)

Classifieds FS | WTB
I'll bite. I could be way off base here though.

F = ma = (1/2)(rho)(CdA)(v^2)

Acceleration can be found by the slopes between each data point. A plot will estimate CdA (the only unknown) with a line of best fit. I'll crunch these in Excel when I get home.

Classifieds FS | WTB
Close. How will you find Crr?
'Integrate' using the trapezoids to obtain total displacement.

Use the stated 5m drop with displacement & we have a slope (theta).

F = ma = Crr*N, where N = mg*cos(theta)

A plot with line of best fit will estimate Crr. Am I close?

Classifieds FS | WTB
Very good. Now make the estimates.
Ok Final Solution. I think I had it wrong before. I'll run these in excel in a few hours & put up the results.

F(rr) + F(CdA) = ma

Crr*N + (1/2)*(rho)*(CdA)*(v^2) = ma -------------------------------------------------- (1)

Acceleration a is found using the slope b/n velocity data points. The v used in (1) is the average velocity between points n & n+1.

Find the area underneath the velocity points (trapezoids) for total displacement. Using drop h = 5m, we find average slope theta

N = mg*cos(theta)

In equation (1), the only unknowns are Crr & CdA. Dividing throughout by N, it takes the form "y = mx + b", & we can estimate Crr (intercept) & CdA (slope) from the line of best fit.

Classifieds FS | WTB
Let me try: CdA=0.37 and Crr=0.0066

Ale Martinez
www.amtriathlon.com
Ale Martinez wrote:
Let me try: CdA=0.37 and Crr=0.0066
That's what I got.

Anyway, now that so many people have bike computers that can record speed (like the Garmin units) I thought it would be good to point out that it's possible to estimate drag using one even if you don't have a power meter.
What was the difference between Run1 and 2? The ave speed was higher for 2

Styrrell
styrrell wrote:
What was the difference between Run1 and 2? The ave speed was higher for 2
I purposefully started the second coast down run at a higher initial speed.
I got that Crr but my CdA is off .....

Classifieds FS | WTB
Jamaican wrote:
I got that Crr but my CdA is off .....

May be because your force balance equation (1) above lacks the gravitational term

Ale Martinez
www.amtriathlon.com
RChung wrote:
Ale Martinez wrote:
Let me try: CdA=0.37 and Crr=0.0066

That's what I got.

Anyway, now that so many people have bike computers that can record speed (like the Garmin units) I thought it would be good to point out that it's possible to estimate drag using one even if you don't have a power meter.

Yes, is quite interesting if you have the rigth venue!

BTW, did you use VE for the solution ? I have used an energy conservation approach.

Ale Martinez
www.amtriathlon.com
Ale Martinez wrote:
Quote:
now that so many people have bike computers that can record speed (like the Garmin units) I thought it would be good to point out that it's possible to estimate drag using one even if you don't have a power meter.
Yes, is quite interesting if you have the rigth venue!
This was just a normal street between my house and office where there's not much traffic. In fact, I noticed at lunch time that it appeared to be almost calm so I did a couple of coastdowns then went back to the office (as I said, on my commute bike and wearing street clothes). When I ran the numbers I was shocked that I was so far off from what I expected. Either the Crr or CdA was way off. So I checked my tires and realized that both my front and rear tires were way under-inflated. I pumped up the tires and tried again on the way home. These were the data from the afterwork runs, though by then there was a tiny bit of wind. I was using my frame pump so I don't know what the tire pressure was before or after.

Quote:
BTW, did you use VE for the solution ? I have used an energy conservation approach.
I do both. I used the closed-form approach to solve it but I used VE to check the answer.
RChung wrote:
styrrell wrote:
What was the difference between Run1 and 2? The ave speed was higher for 2

I purposefully started the second coast down run at a higher initial speed.
I should perhaps add that starting the second coast down at a different speed than the first is what makes both CdA and Crr estimable.

That's one of the reasons why I recommend that when you're doing "regular" VE runs that you do them at different speeds.
Can you post a spreadsheet that calculates this?
CptanPanic wrote:
Can you post a spreadsheet that calculates this?
Ugh. I'm horrendous at doing spreadsheets.

I'll try to pull together something understandable later this afternoon.
Since your speed dropped after you got down the hill did you just use the data from going down the hill to figure out the acceleration or did you do it all by parts?
jaretj wrote:
Since your speed dropped after you got down the hill did you just use the data from going down the hill to figure out the acceleration or did you do it all by parts?
Actually, the entire test section was downhill -- however, the slope wasn't constant. The end of the course was pretty shallow. The slope varied so the speeds and accelerations varied. In addition, I started the coast down runs at different speeds. Those speeds and accelerations (and decelerations) help in nailing down the CdA and Crr.
CptanPanic wrote:
Can you post a spreadsheet that calculates this?

I've wrote this little one, you can load up to 10 coast down tests (in Run1, Run2, ... columns and n=number of tests), Mass (M), Air density (rho) and descent (h in m) and it gives you estimates of CdA and Crr via linear regression and a graph with virtual elevation for each run:

Ale Martinez
www.amtriathlon.com
So how did you collect all the data points? Memorization?

"A useless man is a waste, two is a law firm, and three or more is a Congress." -John Adams
Ale Martinez wrote:
CptanPanic wrote:
Can you post a spreadsheet that calculates this?

I've wrote this little one, you can load up to 10 coast down tests (in Run1, Run2, ... columns and n=number of tests), Mass (M), Air density (rho) and descent (h in m) and it gives you estimates of CdA and Crr via linear regression and a graph with virtual elevation for each run:
You used regression? What was the model you were estimating.

CptanPanic: Sorry, I told you I'm terrible at spreadsheets. I worked on it a little but then got distracted by something else and didn't get back to it. Ale's is nicer anyway.

osugasman: I recorded the speed data with my power meter but if you have anything like a Garmin (which many people do) you can use that to record the data.
I love you guys!

I can't wait to try this!