You know, it's possible to estimate CdA and Crr without a power meter
#1
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
You know, it's possible to estimate CdA and Crr without a power meter
Y'all probably know that it's possible to estimate CdA and Crr with field tests using a power meter. It's also possible to do it without a power meter -- it's more hassle but it's still possible.
There are several ways to do this but if you happen to have a way to record speed accurately and precisely then it's a bit less of a hassle than it used to be. And, many riders now have GPS units on their handlebars that can record speed. That's the point of this post: even if you don't have a power meter but have a way to record speed you can do this.
You'll still need a place to test that's protected from the wind and traffic. And, you'll get better results if you have one of those dedicated wheel sensors for speed rather than relying on the GPS signal -- that's especially true if your test venue relies on tall trees to help protect it from the wind. Don't use "smart" recording -- set your GPS to record second-by-second.
Here are speed data from two coast downs I did a couple of days ago. 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 for this example let's simply assume wind was zero and everything was exactly as noted above.
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
Importantly, notice that the initial speeds are different for the two coast downs.
Here's the challenge: based on these data, estimate my CdA and Crr. Show your work, and state any additional assumptions you may need.
This was on my commuter bike with heavy duty tires and I was wearing street clothes so don't give me crap about my drag numbers.
Bonus question: it's easy to figure out the average slope over the test section. What was the maximum slope (nearest 0.1% is okay)?
Bonus question #2: why is it important to start the coast downs at different speeds?
There are several ways to do this but if you happen to have a way to record speed accurately and precisely then it's a bit less of a hassle than it used to be. And, many riders now have GPS units on their handlebars that can record speed. That's the point of this post: even if you don't have a power meter but have a way to record speed you can do this.
You'll still need a place to test that's protected from the wind and traffic. And, you'll get better results if you have one of those dedicated wheel sensors for speed rather than relying on the GPS signal -- that's especially true if your test venue relies on tall trees to help protect it from the wind. Don't use "smart" recording -- set your GPS to record second-by-second.
Here are speed data from two coast downs I did a couple of days ago. 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 for this example let's simply assume wind was zero and everything was exactly as noted above.
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
Importantly, notice that the initial speeds are different for the two coast downs.
Here's the challenge: based on these data, estimate my CdA and Crr. Show your work, and state any additional assumptions you may need.
This was on my commuter bike with heavy duty tires and I was wearing street clothes so don't give me crap about my drag numbers.
Bonus question: it's easy to figure out the average slope over the test section. What was the maximum slope (nearest 0.1% is okay)?
Bonus question #2: why is it important to start the coast downs at different speeds?
Last edited by RChung; 10-21-11 at 06:40 AM.
#2
fuggitivo solitario
nah, i'll just use aerolab
you don't expect your students not to cheat after you have given them an easy way out, do you?
you don't expect your students not to cheat after you have given them an easy way out, do you?
#3
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
So, what's your answer?
#4
fuggitivo solitario
That's an acceptable method. I don't expect them to do square roots or logarithms with paper and pencil, so using Aerolab is fine. The main point is that if you have a way to record speed you can do coastdowns, get the data into Aerolab, and fiddle with it. Plus, if you do a coastdown you don't have to worry about the accuracy of your power meter -- you know the power was zero.
So, what's your answer?
So, what's your answer?
i mean, energy cost on rider is what, Crr component (fixed, dependent only on mass), CdA component (speed dependent), and gravitational (doable if you know the grade of road). Cda being dependent on the medium through which you are moving, relative ground speed, and speed at which medium is moving. So assume zero wind, it's just ground speed and the density of air (which you provided).
The true answer is that i'm too lazy, so there
#5
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
Fair enough. I'm usually too lazy to do it that way, too: pure coastdowns are more hassle than being able to do (powered) loops.
However, if you did solve the challenge, one of the important lessons that applies even if you have a power meter is from bonus question #2: vary the speed of your loops.
One more tip if you don't have a power meter and want to do coastdowns: either make sure your legs are always in the same position for each coastdown or (better) "spin" your legs slowly but without putting any power into the pedals so that you'll get a truer reading of your aero drag when you're pedaling.
However, if you did solve the challenge, one of the important lessons that applies even if you have a power meter is from bonus question #2: vary the speed of your loops.
One more tip if you don't have a power meter and want to do coastdowns: either make sure your legs are always in the same position for each coastdown or (better) "spin" your legs slowly but without putting any power into the pedals so that you'll get a truer reading of your aero drag when you're pedaling.
#6
Wheelsuck
Join Date: Jun 2007
Posts: 6,158
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
OK, let me take a stab.
Assumptions: All inertia is linear.
convert speeds to m/s for convenience.
The runs are at 2 speeds are so you can separate rolling resistance from aero resistance.
The max slope is calculated by atan(max accel)*g, then convert to slope from angle
((kinetic + potential energy at the start) - (kinetic energy at the finish)) / Time = power @ average speed
Run2-Run1 = aero power
Aero drag = aero power / average run speed
Dynamic pressure ~= 1/2 *air density * average speed^2
Cd = aero drag / (surface area * dynamic pressure)
Rolling resistance force = run 1 power / average run speed
Crr = Rolling resistance force / (mass * g)
----------------------------------------------------------------
Am I on the right track?
Assumptions: All inertia is linear.
convert speeds to m/s for convenience.
The runs are at 2 speeds are so you can separate rolling resistance from aero resistance.
The max slope is calculated by atan(max accel)*g, then convert to slope from angle
((kinetic + potential energy at the start) - (kinetic energy at the finish)) / Time = power @ average speed
Run2-Run1 = aero power
Aero drag = aero power / average run speed
Dynamic pressure ~= 1/2 *air density * average speed^2
Cd = aero drag / (surface area * dynamic pressure)
Rolling resistance force = run 1 power / average run speed
Crr = Rolling resistance force / (mass * g)
----------------------------------------------------------------
Am I on the right track?
#7
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
Ah, you're definitely on the right track. Here's a hint: integrate the power equation over time to convert it into a work equation.
Exactly.
Not quite. That's close to true for the max change in slope but not the slope itself.
The runs are at 2 speeds are so you can separate rolling resistance from aero resistance.
The max slope is calculated by atan(max accel)*g, then convert to slope from angle
#9
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
Also, define the protocol for a "coast down".
#10
Resident Alien
Join Date: Jul 2007
Location: Location, location.
Posts: 13,089
Mentioned: 158 Post(s)
Tagged: 0 Thread(s)
Quoted: 349 Post(s)
Likes: 0
Liked 10 Times
in
6 Posts
That said we all know you're an engineer. Googling the "Girls of MIT' produced mostly financial resource applications and gender pay equality studies. For my local community college I had to agree that I was over 18 before I could even see the search results.
And I was serious about the protocol you were using because depending on the hill and run out, MV might not be affected by start speed.
Besides, the only guys you're going to get to play here have long attention spans.
#11
Senior Member
Join Date: Sep 2008
Posts: 598
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
I get Crr = 0.0064 and CdA = 0.378 m^2. Basically you do as above and write out the energy budget. It looks like
alpha * Crr + beta * CdA = gamma
where
alpha = -mg*integral(v)
beta = -0.5*rho*integral(v^3)
gamma = 0.5 m(vf^2-vi^2) - mgh
Doing this for each run you gives you a 2x2 set of linear equations that can be solved for CdA and Crr.
I'd say the two runs are needed to disentangle CdA, Crr, and the unknown elevation profile. If you could just ride your bike on flat ground, or use the altimeter data, then only one run is needed since you could do a nonlinear fit to the expected v(t).
In principle, now that you have CdA and Crr, you can calculate the force of gravity as the balance of all the other forces (aero, rolling, net). The peak would tell you when you hit max slope. But I don't think you have the time resolution to calculate dv/dt cleanly enough for that to work well. Then again I didn't try it.
Do I get a cookie?
alpha * Crr + beta * CdA = gamma
where
alpha = -mg*integral(v)
beta = -0.5*rho*integral(v^3)
gamma = 0.5 m(vf^2-vi^2) - mgh
Doing this for each run you gives you a 2x2 set of linear equations that can be solved for CdA and Crr.
I'd say the two runs are needed to disentangle CdA, Crr, and the unknown elevation profile. If you could just ride your bike on flat ground, or use the altimeter data, then only one run is needed since you could do a nonlinear fit to the expected v(t).
In principle, now that you have CdA and Crr, you can calculate the force of gravity as the balance of all the other forces (aero, rolling, net). The peak would tell you when you hit max slope. But I don't think you have the time resolution to calculate dv/dt cleanly enough for that to work well. Then again I didn't try it.
Do I get a cookie?
#13
Senior Member
Join Date: Sep 2008
Posts: 598
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
#14
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
How about a hot dog cuz, ladies and germs, we got a WEINER. You can get max slope by plugging the Crr and CdA back into the power equation and solving for the slope. Overall average slope is -1.8%, but the slope isn't constant. It maxes out about two-thirds of the way through the test section at -4.1%.
#16
Wheelsuck
Join Date: Jun 2007
Posts: 6,158
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
#17
Senior Member
Join Date: Sep 2008
Posts: 598
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
Like I said, you can do that calculation, but the output is going to be really noisy because of the dv/dt term. Probably at best you can say -4.1 +/- 1.
#18
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
So, here's the main point: if you have a way to record second-by-second speed (and more riders are buying devices that can do this every day) then you can do coastdowns that will let you estimate both CdA and Crr.
1. You must roll over the same section of road (at least) twice, at different speeds.
2. Do this on a calm day, in a place free of traffic.
3. Weigh your total all-inclusive weight.
4. Go to weatherunderground.com or some other weather site and figure out the air density.
5. Do your very best to find out the true elevation change between the start and end of your test section.
This is more hassle than using a power meter but it's not impossibly hard.
1. You must roll over the same section of road (at least) twice, at different speeds.
2. Do this on a calm day, in a place free of traffic.
3. Weigh your total all-inclusive weight.
4. Go to weatherunderground.com or some other weather site and figure out the air density.
5. Do your very best to find out the true elevation change between the start and end of your test section.
This is more hassle than using a power meter but it's not impossibly hard.
#20
Senior Member
Join Date: Sep 2008
Posts: 598
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
#22
fuggitivo solitario
i'm gonna throw this a bit OT
now that we got rchung on the board, i'd like to ask him how well the virtual elevation should fit the real elevation for the data to have meaning. Would something like the two examples above be usable or not?
Also, something about the way elevation is calculated. Assuming that temperature and pressure stays pretty constant, how trustworthy is it to use a computer that calculates altitude by using a barometer (e.g. Joule 2.0)?
now that we got rchung on the board, i'd like to ask him how well the virtual elevation should fit the real elevation for the data to have meaning. Would something like the two examples above be usable or not?
Also, something about the way elevation is calculated. Assuming that temperature and pressure stays pretty constant, how trustworthy is it to use a computer that calculates altitude by using a barometer (e.g. Joule 2.0)?
#23
Senior Member
Join Date: Sep 2008
Posts: 598
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times
in
0 Posts
#24
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
Yeah, maybe 0.1% is a tad optimistic -- but there's something wrong with your dv/dt. I'm guessing you were just using a simple difference? Real roads don't change slopes as drastically as you're estimating.
#25
Perceptual Dullard
Thread Starter
Join Date: Sep 2009
Posts: 2,413
Mentioned: 36 Post(s)
Tagged: 0 Thread(s)
Quoted: 915 Post(s)
Liked 1,132 Times
in
488 Posts
Also, something about the way elevation is calculated. Assuming that temperature and pressure stays pretty constant, how trustworthy is it to use a computer that calculates altitude by using a barometer (e.g. Joule 2.0)?
https://jasperga.blogspot.com/2009/11...s-no-joke.html