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Estimating drag without a power meter

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Gandalf

Oct 24, 11 18:38

Post #26 of 49 (2052 views)
 Re: Estimating drag without a power meter [Ale Martinez] [In reply to] Quote | Reply
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:

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lanierb

Oct 24, 11 18:39

Post #27 of 49 (2050 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
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.
If you use the Garmin, be sure to turn "smart recording" (the default) off first. Also, note that the Garmin records data points once per second except that it records an extra data point every time you hit "lap", so the first and last intervals of a lap are actually shorter than one second and are of random length. If you assume that they are one second you will be making a small error in the delta calculations, and the error will be different for each run because of different speeds and because the first and last intervals are of random lengths (so one run they might be very short and another they might be nearly one second).

RChung

Oct 24, 11 20:18

Post #28 of 49 (2027 views)
 Re: Estimating drag without a power meter [lanierb] [In reply to] Quote | Reply
lanierb wrote:
RChung wrote:
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.

If you use the Garmin, be sure to turn "smart recording" (the default) off first. Also, note that the Garmin records data points once per second except that it records an extra data point every time you hit "lap", so the first and last intervals of a lap are actually shorter than one second and are of random length. If you assume that they are one second you will be making a small error in the delta calculations, and the error will be different for each run because of different speeds and because the first and last intervals are of random lengths (so one run they might be very short and another they might be nearly one second).

Right. In this example I did only two runs because I was simply trying to show that it could be done, and done with pretty minimal equipment. I'd do at least one more in a real attempt, then compare the runs against each other. 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.

I don't hit a lap button -- I like to get my position set and start to coast before I enter the test section so I don't have to move my hands or head or anything, even if only to hit a lap button. Instead, I transform speed into distance and from the speed and change in speed and mass I build up a preliminary elevation profile for the course. It's pretty clear where the slope begins, or where it transitions to the flat, and then steepens again; so once that's identified I can count in distance backward and forward to match the test sections. May sound hard but it's not, really, and it frees me up from remembering to mark the sections. Basically, I try to make the data collection as simple and brainless as possible even if it means I have to do an extra calculation when I get home. Many other protocols require that you hit a certain speed at a certain point or hold your speed or equalize mass or something else. I'm usually too stupid to remember all those things when I'm on the bike so it makes sense to account for it later.

I usually use a power meter so my legs are turning but if I were doing coast downs I'd either have to remember to hold my legs in exactly the same position each run or else I'd just soft pedal so I don't have to remember where to put my legs (see the caveat above). Then when you get home try to be better about weighing yourself and checking the air density than I am.

[Edit:] Just to clarify: I prefer to test with a power meter. It's simpler and faster, and because I can "widen" the speed range I can get similar or better precision with fewer runs. However, if I did not have a power meter and I wanted to estimate my drag, I'd do coast downs with speed recording. It's slower and more of a hassle but it will work.

(This post was edited by RChung on Oct 24, 11 20:38)

RChung

Oct 24, 11 20:21

Post #29 of 49 (2026 views)
 Re: Estimating drag without a power meter [Kevin in MD] [In reply to] Quote | Reply
Kevin in MD wrote:
This Month's "Sport Biomechanics" has a rundown of ways to estimate drag.

The coast down is in there as well as a couple I hadn't thought of.

One is to take a picture of the rider from the front and in the frame also have something that is a reference area, maybe a 0.5 meter by 0.5 meter square. Then cut out the reference area and the parts of the rider and then weigh them to compare. My analytical chemistry professor told me years ago this is how he did integration on chemical equipment years ago.

Of course we also have a a number of ways to do this electronically these days as well using gim p or photoshop or whatnot.
That just gives you frontal area, not Cd.

The Debraux et al. article in Sports Biomech. discusses coast downs but those coastdowns were on a level surface (in a hallway, I think) with three electric eye timers to determine initial speed and time to a particular distance. Recording speed at fixed intervals allows us to use non-level venues, if needed.

Jiowa

Oct 24, 11 20:34

Post #30 of 49 (2017 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
You'll still need a place to test that's protected from the wind.

I'm planning on trying this after a change a few things on my ride. But do you ever test, I'm sure you use a different method, drag on semi windy days to see what setup/position works best in a crosswind? Of course it won't yield true cda values but it's sometimes windy come race day.

I'm thinking I will test my stuff on several occasions to see what changes with wind.

Do you have any advice or thoughts regarding this?

RChung

Oct 24, 11 20:47

Post #31 of 49 (2013 views)
 Re: Estimating drag without a power meter [Jiowa] [In reply to] Quote | Reply
Jiowa wrote:
I'm planning on trying this after a change a few things on my ride. But do you ever test, I'm sure you use a different method, drag on semi windy days to see what setup/position works best in a crosswind? Of course it won't yield true cda values but it's sometimes windy come race day.

If you don't have a way to measure wind speed and direction on the bike it will be hard to figure out the effects. Having said that, in one of my early attempts I used a triangular "loop" course, and I'd done enough tests on nearly calm days that I figured I could do "virtual wind" rather than "virtual elevation" estimates on non-calm days as long as the wind was constant in speed and direction. It turns out that even small swirls and gusts make the analysis hard enough to be kind of discouraging. Maybe I could do it on a slightly windy day if I used a big open flat parking lot without a lot of wind-intervening obstacles -- but I decided to wait until I can measure wind speed and direction. So now I try to test only on calm or nearly calm days.

[Edit:] Let me clarify: when I first started doing field testing, my position was so horrendous that there was lots of room for improvement and I could get by with pretty lousy technique and not entirely calm days because the changes I was making were pretty big. After the low hanging fruit got picked I needed to be more careful about all the things that can add noise to the drag estimates. Basically, the smaller the change you're looking at, the more careful you have to be about testing. So, if you're just starting out, yeah, you might be able to learn something from testing on not-completely-calm days. However, after a while you're going to have to be more careful.

(This post was edited by RChung on Oct 24, 11 21:38)

Ale Martinez

Oct 25, 11 5:32

Post #32 of 49 (1963 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:
CptanPanic wrote:
Can you post a spreadsheet that calculates this?

I 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.

Robert, the model I used for regresion is based on end-to-end conservation of energy (deltaPE+deltaKE = workAeroDrag + workRRdrag), so:

[M*g*h + 1/2*M*(Vi^2-Vf^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr

where Vi=initial velocity, Vf=final velocitiy, Vi=velocity at i second from start, h=descent from start to finish.

In the spreadsheet al terms are divided by [M*g*sum(Vi)] to use standard linear regresion formulas in excel.

Ale Martinez
www.amtriathlon.com

(This post was edited by Ale Martinez on Oct 25, 11 5:40)

Ale Martinez

Oct 25, 11 5:42

Post #33 of 49 (1956 views)
 Re: Estimating drag without a power meter [Gandalf] [In reply to] Quote | Reply
Gandalf wrote:
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:

Ale Martinez
www.amtriathlon.com

RChung

Oct 25, 11 7:14

Post #34 of 49 (1920 views)
 Re: Estimating drag without a power meter [Ale Martinez] [In reply to] Quote | Reply
Ale Martinez wrote:
Robert, the model I used for regresion is based on end-to-end conservation of energy (deltaPE+deltaKE = workAeroDrag + workRRdrag), so:

[M*g*h + 1/2*M*(Vi^2-Vf^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr

where Vi=initial velocity, Vf=final velocitiy, Vi=velocity at i second from start, h=descent from start to finish.

In the spreadsheet al terms are divided by [M*g*sum(Vi)] to use standard linear regresion formulas in excel.
Ah, got it. This is why I should leave all the spreadsheet calculations to others -- I think I knew that there was a regression formula somewhere in Excel but I'd forgotten it. Can you not do zero intercepts in Excel's regression?

You formula works for dt = 1 second (and all other measures in metric and speed in m/s).

And, that reminds me: if you're going to do something like this coast down technique, it might be handy to have the test section entry and exit points be on relatively flat spots, i.e., don't try to make the end points be on the downhill slope itself. The reason is that since you're only getting 1 second resolution on the speed (and therefore, distance) it'll be harder to exactly match the h between the two runs if the start and end are on a hill.

Ale Martinez

Oct 25, 11 8:40

Post #35 of 49 (1890 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:

Robert, the model I used for regresion is based on end-to-end conservation of energy (deltaPE+deltaKE = workAeroDrag + workRRdrag), so:

[M*g*h + 1/2*M*(Vi^2-Vf^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr

where Vi=initial velocity, Vf=final velocitiy, Vi=velocity at i second from start, h=descent from start to finish.

In the spreadsheet al terms are divided by [M*g*sum(Vi)] to use standard linear regresion formulas in excel.

Ah, got it. This is why I should leave all the spreadsheet calculations to others -- I think I knew that there was a regression formula somewhere in Excel but I'd forgotten it. Can you not do zero intercepts in Excel's regression?

You formula works for dt = 1 second (and all other measures in metric and speed in m/s).

And, that reminds me: if you're going to do something like this coast down technique, it might be handy to have the test section entry and exit points be on relatively flat spots, i.e., don't try to make the end points be on the downhill slope itself. The reason is that since you're only getting 1 second resolution on the speed (and therefore, distance) it'll be harder to exactly match the h between the two runs if the start and end are on a hill.

In Excel SLOPE function I've used does not allow to force intercept to zero but, the more general LINEST, yes.

Yes, I used SI and assumed dt=1, it would'nt be difficult to avoid the last restriction but formulas are simpler/cleaner that way.

The only significant slopes around here are bridges so I would start/finish in flat spots. BTW, assuming same configuration/position and no wind, which would be a good number of runs to do with this method to have good estimates of CdA and Crr ?

Ale Martinez
www.amtriathlon.com

RChung

Oct 25, 11 9:00

Post #36 of 49 (1878 views)
 Re: Estimating drag without a power meter [Ale Martinez] [In reply to] Quote | Reply
Ale Martinez wrote:
BTW, assuming same configuration/position and no wind, which would be a good number of runs to do with this method to have good estimates of CdA and Crr ?
I don't really know -- I almost always do the "powered" version, which is faster and less hassle. I brought this up only for those who don't have power meters. I would think slightly longer rather than shorter runs would help, and slightly wider rather than narrower differences in the "entry" speed would help. In this particular approach, doing replicates starting at the same initial speed doesn't do very much to improve the parameter estimates.

However, that's also why I always recommend calculating and plotting the VE profile, whether you're doing coast downs or powered tests. They're a pretty good diagnostic of overall fit, so if one run looks really different than the others you know that something was wrong somewhere, and if all of the profiles are "noisy" then you know that the overall fit isn't good. There are statistical ways to determine formal measurements of goodness of fit and error but unless you're trying to publish a paper or satisfy anal retentive critics it's hardly worth it.

lanierb

Oct 25, 11 9:23

Post #37 of 49 (1857 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
Just following up on Robert's post. I did a coast down test like this one last week just out of curiousity (I usually use powered tests) and I did 3 slow runs and 3 fast runs and it worked very well. To help obtain accurate estimates you want as much variation in entry speed as possible. I.e., you want some really slow runs and some really fast ones. The more extreme you can get this the better it will be. This will let you separate Crr and CdA. Even if you already know your Crr it will help identify CdA precisely. Also, I would suggest not using too steep of a hill because on a steeper gradient the initial speed will cease to matter pretty quickly. A very gentle hill is best, or at least a hill that starts off gently so that the initial speed difference persists for a long while.

Some other things Robert alluded to but didn't spell out: ideally you want (a) zero wind, (b) zero cars in either direction, (c) zero bikes anywhere near you, and (d) follow the same exact line on the pavement as closely as possible each run so that distance and rolling resistance are the same each time. If a car passes you during a run, definitely scrap that run.

karlaj

Oct 25, 11 9:47

Post #38 of 49 (1840 views)
 Re: Estimating drag without a power meter [lanierb] [In reply to] Quote | Reply
Guys, thanks for posting this.
lanierb, Good to know about gentle hills -- at first figured big steep hills would have been better, but you're right that to get an accurate value for CdA and Crr, you want those "x" values to be far apart. So practically, you want starts from a near standstill on one run, moderate start on the next, and a flying start near terminal velocity on the last. Wash, rinse, repeat to gather more data.
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osugasman

Oct 25, 11 10:04

Post #39 of 49 (1832 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
Thanks!!!

"A useless man is a waste, two is a law firm, and three or more is a Congress." -John Adams

Tom A.

Oct 25, 11 11:10

Post #40 of 49 (1806 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:
BTW, assuming same configuration/position and no wind, which would be a good number of runs to do with this method to have good estimates of CdA and Crr ?

I don't really know -- I almost always do the "powered" version, which is faster and less hassle. I brought this up only for those who don't have power meters. I would think slightly longer rather than shorter runs would help, and slightly wider rather than narrower differences in the "entry" speed would help. In this particular approach, doing replicates starting at the same initial speed doesn't do very much to improve the parameter estimates.

However, that's also why I always recommend calculating and plotting the VE profile, whether you're doing coast downs or powered tests. They're a pretty good diagnostic of overall fit, so if one run looks really different than the others you know that something was wrong somewhere, and if all of the profiles are "noisy" then you know that the overall fit isn't good. There are statistical ways to determine formal measurements of goodness of fit and error but unless you're trying to publish a paper or satisfy anal retentive critics it's hardly worth it.

It's funny...the one thing I like about this approach is that the power values are VERY accurate ;-)

http://bikeblather.blogspot.com/

RChung

Oct 25, 11 11:33

Post #41 of 49 (1797 views)
 Re: Estimating drag without a power meter [lanierb] [In reply to] Quote | Reply
lanierb wrote:
Just following up on Robert's post. I did a coast down test like this one last week just out of curiousity (I usually use powered tests) and I did 3 slow runs and 3 fast runs and it worked very well.
Cool, ain't it? Though doing six coast downs just to prove a point requires more attention span than I usually have. I prefer doing powered tests.
Quote:
To help obtain accurate estimates you want as much variation in entry speed as possible. I.e., you want some really slow runs and some really fast ones. The more extreme you can get this the better it will be. This will let you separate Crr and CdA. Even if you already know your Crr it will help identify CdA precisely. Also, I would suggest not using too steep of a hill because on a steeper gradient the initial speed will cease to matter pretty quickly. A very gentle hill is best, or at least a hill that starts off gently so that the initial speed difference persists for a long while.

Some other things Robert alluded to but didn't spell out: ideally you want (a) zero wind, (b) zero cars in either direction, (c) zero bikes anywhere near you, and (d) follow the same exact line on the pavement as closely as possible each run so that distance and rolling resistance are the same each time. If a car passes you during a run, definitely scrap that run.
Good suggestions. Getting big differences in speed works for powered runs, too, if you want to get separate estimates of CdA and Crr. That's why I try to do some laps at low speed and power and others at high speed and power. Or, considering my power, not-quite-as-low speed and power. Replicates at the same speed (and power) are kinda wasted effort from a parameter estimation point of view.

You can really see the effect of a passing car on the VE profile. It's not subtle and it roils the air for a surprisingly long time.

RChung

Oct 25, 11 11:38

Post #42 of 49 (1793 views)
 Re: Estimating drag without a power meter [Tom A.] [In reply to] Quote | Reply
Tom A. wrote:
It's funny...the one thing I like about this approach is that the power values are VERY accurate ;-)
Yeah, that's the one and only thing. On another forum FDay thinks it's another nail in the coffin for power meters.

RChung

Oct 26, 11 5:46

Post #43 of 49 (1700 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:

Robert, the model I used for regresion is based on end-to-end conservation of energy (deltaPE+deltaKE = workAeroDrag + workRRdrag), so:

[M*g*h + 1/2*M*(Vi^2-Vf^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr

where Vi=initial velocity, Vf=final velocitiy, Vi=velocity at i second from start, h=descent from start to finish.

BTW, Ale, the first Vi is different from the second Vi?

That is, if you count the velocities as V0, V1, V2, ..., Vfinal then the model to estimate is
[M*g*h + 1/2*M*(V0^2-Vfinal^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr
where i = 1, 2, 3, ..., final

Gandalf

Oct 26, 11 7:10

Post #44 of 49 (1681 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
What did you use to record the speed. I have a garmin 310 and I don't think that will have the pinpoint accuracy nor frequency of data recording for this kind of excercise.
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Ale Martinez

Oct 26, 11 7:33

Post #45 of 49 (1674 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:

Robert, the model I used for regresion is based on end-to-end conservation of energy (deltaPE+deltaKE = workAeroDrag + workRRdrag), so:

[M*g*h + 1/2*M*(Vi^2-Vf^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr

where Vi=initial velocity, Vf=final velocitiy, Vi=velocity at i second from start, h=descent from start to finish.

BTW, Ale, the first Vi is different from the second Vi?

Sorry for the confussion, Vi stands for Vinitial in the left side of the equation but for V at i second from start inside the sums...

RChung wrote:
That is, if you count the velocities as V0, V1, V2, ..., Vfinal then the model to estimate is
[M*g*h + 1/2*M*(V0^2-Vfinal^2)] = [1/2*rho*sum(Vi^3)] * CdA + [M*g*sum(Vi)] * Crr
where i = 1, 2, 3, ..., final

Exactly, that was the idea, then I divide all terms by [M*g*sum(Vi)] to use linear regresion with slope CdA and intercept Crr in the spreadsheet:

{ [1/2*rho*sum(Vi^3)] / [M*g*sum(Vi)] } * CdA + Crr = [M*g*h + 1/2*M*(V0^2-Vfinal^2)] / [M*g*sum(Vi)]
where i = 1, 2, 3, ..., final

Ale Martinez
www.amtriathlon.com

(This post was edited by Ale Martinez on Oct 26, 11 7:37)

Ale Martinez

Oct 26, 11 10:52

Post #46 of 49 (1632 views)
 Re: Estimating drag without a power meter [Gandalf] [In reply to] Quote | Reply
Gandalf wrote:
I have a garmin 310 and I don't think that will have the pinpoint accuracy nor frequency of data recording for this kind of excercise.

Hi Neil, It seems frecuency of data recording can be set to every second with 3.7 firmware:

Quote:

310XT ver 3.7 update includes:
...
- Added an every second recording option. The user no longer has to be paired with a power meter in order to get once per second recording. Go to Settings>System>Data Recording to enable.

http://forum.slowtwitch.com/gforum.cgi?post=3381646

WRT accuracy, it may be improved using a speed sensor (like the GSC-10) with proper calibration.

Ale Martinez
www.amtriathlon.com

(This post was edited by Ale Martinez on Oct 26, 11 13:13)

elpete

Nov 3, 11 6:36

Post #47 of 49 (1550 views)
 Re: Estimating drag without a power meter [Ale Martinez] [In reply to] Quote | Reply
Hey thanks for posting this up. Any tips on when to start/stop recording? Does it really matter as long as it's at the same points?

Nicko

Nov 3, 11 14:15

Post #48 of 49 (1517 views)
 Re: Estimating drag without a power meter [RChung] [In reply to] Quote | Reply
RChung wrote:
Ale Martinez wrote:
BTW, assuming same configuration/position and no wind, which would be a good number of runs to do with this method to have good estimates of CdA and Crr ?
I don't really know -- I almost always do the "powered" version, which is faster and less hassle. I brought this up only for those who don't have power meters. I would think slightly longer rather than shorter runs would help, and slightly wider rather than narrower differences in the "entry" speed would help. In this particular approach, doing replicates starting at the same initial speed doesn't do very much to improve the parameter estimates.

However, that's also why I always recommend calculating and plotting the VE profile, whether you're doing coast downs or powered tests. They're a pretty good diagnostic of overall fit, so if one run looks really different than the others you know that something was wrong somewhere, and if all of the profiles are "noisy" then you know that the overall fit isn't good. There are statistical ways to determine formal measurements of goodness of fit and error but unless you're trying to publish a paper or satisfy anal retentive critics it's hardly worth it.
Robert, what are your thoughts regarding the need for accurate hill height data vs the (very) fast speed dropoff on a "flat" venue? I.e. You get few data points at high aero drag but "the hill" doesn't have to be accurately measured since it can be travelled both ways (and ~cancel low wind). What trumps?

RChung

Nov 23, 11 9:35

Post #49 of 49 (1352 views)
 Re: Estimating drag without a power meter [Nicko] [In reply to] Quote | Reply
Nicko wrote:
Robert, what are your thoughts regarding the need for accurate hill height data vs the (very) fast speed dropoff on a "flat" venue? I.e. You get few data points at high aero drag but "the hill" doesn't have to be accurately measured since it can be travelled both ways (and ~cancel low wind). What trumps?
Sorry not to have answered earlier -- I didn't see your post until just now.

I think it's useful to have at least a little elevation profile "feature" that you can use to anchor the location on each run. On the one hand, a flat venue lets you approximately cancel the wind (as you pointed out) by doing runs in both directions but, on the other, if you want to estimate both CdA and Crr you need a fair amount of separation in the speed tracks. Hmmm. Well, since Crr scales like slope, I would guess that if your tires are low Crr you can use flatter venues, which would allow you to do two-way runs.

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