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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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On my phone right now, but mathematically fir an R square correlation where power is constant, HR and pulse power are the same thing. There was no need to do an extra step.

Address more of your questions after dinner and bedtime.

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:

From Frank Day

I am a little confused by your conclusions after your analysis. Pulse power is my method of evaluating efficiency at the output we are testing at, not normalizing power vs effort. Anyhow, you are finding a pretty good correlation between pulse power and pedal speed but not when looking at a specific crank length in a small time frame. Not sure what that means but the whole idea of this effort is that crank length doesn’t matter, only pedal speed does, at least when sitting upright. Your analysis would seem to support that idea and support the results of Martin. If that is the case then why are you then saying all this work means nothing and your guess is the improvement seen is due to fitness changes. One other thing that goes against your assessment is, I think, Dave trains differently than most. He seems to take zero time off, doing pretty much the same thing every day of the year. It would seem his fitness never changes significantly. Dave can comment on this better than I but that is my impression.

Frank Day

I think the point is that if you look at the results of the recent tests on 150mm cranks, there is virtually 0 correlation in the data. That means that despite the claims of 100% repeatable testing, the data that's coming out is all over the place. A set of equipment that allows you to repeat the same testing protocol doesn't guarantee you will get the same outcome every time. In this case, the test results are all too spread to draw any conclusion without significantly more data points.

Removing the Nov 10th test would make it a 0.9 correlation, so it certainly isn't the 1st test that is skewing things. Then you look at the adding the most recent 175mm test on 11/25 and that massively throws a wrench in the system. Same pulse power but at a much high pedal speed. ie...there isn't enough quality data to show any reasonable correlation, or there is no correlation to be found.

Do we get to pick which tests are outliers and which ones to include in the data? Probably not the best way to approach things...
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Re: My testing to try and find best crank length with my Velotron [Sean H] [ In reply to ]
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Sean H wrote:
I just wanted to thank you kind souls for keeping this thread going. It's a Festivus for the rest of us.

It's actually pretty fun if you ignore his posts and just read the responses.

The point is, ladies and gentleman, that speed, for lack of a better word, is good. Speed is right, Speed works. Speed clarifies, cuts through, and captures the essence of the evolutionary spirit.
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Re: My testing to try and find best crank length with my Velotron [iamuwere] [ In reply to ]
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iamuwere wrote:
h2ofun wrote:


I am using a 34/32 on the 18.6% grade. I do not think 45 is that bad since this grade is the exception, not the norm. What do you spin a 18.6% grade at?


around 75rpm or so- up to mid 80's

I guess you are a stud, and I am a wuss.

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Re: My testing to try and find best crank length with my Velotron [Toby] [ In reply to ]
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Toby wrote:
Sean H wrote:
I just wanted to thank you kind souls for keeping this thread going. It's a Festivus for the rest of us.


It's actually pretty fun if you ignore his posts and just read the responses.

Thanks, folks like you will have us break 10000 views shortly. Dan must be loving the clicks.

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:
JasoninHalifax wrote:
You may be onto something, but data is still limited.

The problem is that you only have one data point with 175mm cranks since you started, which means that you have to use old data, and you aren't in the same physical condition as you were a year ago. You may be better, may be worse, may be the same, but that still needs to be controlled for.

looking at R-squares going back to 2016- 0.5 correlation between average rpm (which is an actual rpm, not a guess) and "pulse power", which I'm assuming is your method of normalizing power vs effort? .5 correlation between crank length and pulse power, and .6 between pedal speed and pulse power.

However, if you isolate a specific crank length and similar timeframe (during which your fitness presumably didn't change much), then the correlation disappears. r square between pedal speed and only pulse power drops to 0.2 for 175mm cranks from Oct 30 2016 to Jan 22 2017. for 150's its only 0.02 - i.e. no correlation whatsoever....

My GUESS is that the improvements in power at a particular HR are due primarily to fitness, not crank length or pedal speed, but keep on keepin' on. You may have something, you may not...




h2ofun wrote:
Derekl wrote:
h2ofun wrote:
DBF wrote:
What improvements?
Obviously if you slow down your cadence your heart rate is going to be lower. That is not necessarily better.



Doesn’t anyone read my posts or all the testing we recently posted? Anyhow, it isn’t obvious reducing cadence reduces HR if at the same time one increases ones power. Dave has increased his power about 10% with this change with a slightly lower HR. Tell me you wouldn’t take that change!

Frank Day


"You" shouldn't be allowed to post, Frank.

And Dave didn't increase his power by 10% by changing cadence or crank length. The fact that you two believe that is why nobody is taking any of this seriously.



If you haven’t noticed I am not posting. Dave is simply reposting my thoughts to him (since the protocol is mine and I understand it better than anyone) and being honest in letting you all know those are my thoughts and not his.

That having been said I am curious as to how you would interpret the Martis data regarding whether there has been any real power change or not since starting this effort and if so how to explain it. How should that data be interpreted?

Frank Day


Yep, I train all year long. I try not to get out of shape all year long. I race pretty much all year long. The only thing I stop is swimming for 5 months, which shows in my slow swim times.

From Frank Day


I am a little confused by your conclusions after your analysis. Pulse power is my method of evaluating efficiency at the output we are testing at, not normalizing power vs effort. Anyhow, you are finding a pretty good correlation between pulse power and pedal speed but not when looking at a specific crank length in a small time frame. Not sure what that means but the whole idea of this effort is that crank length doesn’t matter, only pedal speed does, at least when sitting upright. Your analysis would seem to support that idea and support the results of Martin. If that is the case then why are you then saying all this work means nothing and your guess is the improvement seen is due to fitness changes. One other thing that goes against your assessment is, I think, Dave trains differently than most. He seems to take zero time off, doing pretty much the same thing every day of the year. It would seem his fitness never changes significantly. Dave can comment on this better than I but that is my impression.

Frank Day


Where on earth are you getting that I;m saying that all this work means nothing? It isn't well controlled, but aside from that, determining that certain factors are NOT important is as important as determining that other factors are important. Here's the thing, I don't particularly care what the finding is, but you appear to have a bias in wanting to show that your theory is correct. That's fine, it's human nature, but you really have to let go and figure out ways to prove that your theory is wrong. If you try various ways to disprove your own theory, and consistently it comes out that you are unable to do so, then the theory might have merit. But it really looks like you are trying to prove it right rather than try and find ways in which it is wrong.

You are making a very large assumption that Dave's fitness never changes significantly, but a) you are looking for small changes, not significant ones, so a small change in fitness can have a significant impact on that small effect, and b) if you don't actually run regular baseline tests to determine whether Dave's fitness has actually changed or not, that is just an assumption. I, on the other hand, am assuming no such thing. It's a more conservative approach that I'm taking.

(edited point (a) in the last paragraph for clarity)

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Last edited by: JasoninHalifax: Nov 29, 17 17:40
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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:
JasoninHalifax wrote:
Pulse power R squares of the Marti's rides from September '17 to Nov 29, 2017.



First, I want to thank you for doing this work, something I do not have the knowledge nor tools to do myself.

I am not sure what can be learned from this. 6 data points with a very tiny spread means the daily variation in performance will have a huge effect on results. Plus we know that power is an independent variable regarding measured efficiency so that first test, with the markedly lower power is skewing everything. Also, I think that first day is an outlier because, as I said earlier, I think he approached that ride differently than the others. I would like to see that day eliminated from your analysis as both the highest and lowest PP have essentially the same pedal speed. That first result is messing everything up. If you rerun the result I would expect a R^2 correlation to pedal speed to be 0.5 or so, not bad for 5 data points. More useful, I think would be to also include the data from last year so substantial differences in pulse power can be evaluated. Didn’t you already do that and see a much better correlation, like 0.6? But, even more useful, would be if you only included the older tests that were around 220 watts so the power variable was having a smaller influence on the results.

One thing your analysis does demonstrate is that power is another important metric in the efficiency equation. Makes my choosing to do my analysis at a set and constant power look smart me thinks.

Frank Day

Eliminating the first day bumps the r square for pedal speed vs pulse power up from 0.021 to 0.029. i.e. still essentially zero. But I don't like excluding data points without a good reason. The fact that the first series was nearly a year ago is a pretty good reason.

What this particular finding shows is that within a small window of cadence and pedal speeds, that the effect is tiny. and that actual research is frickin hard. But you can use this finding to guide future tests.

BTW, I'm doing this with MS Excel. If you are conducting this experiment, then you really DO need to know how to analyse the data. Otherwise you are going waste a lot of time and effort to collect a lot of data that leads nowhere. What I've done is 1st year university level stats, which I learned back in 1988, I was probably drunk or half asleep from morning practice at the time. It isn't hard....

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:
The effort on the Nov 9th was when I had no idea what was going to happen with Martis since I expected just the same bad numbers. I did not push things since I was learning how to handle the testing course with a different bike setup. Since then, I have done a much job attacking the hills, both, up and down.
I have no idea how realistic the Velotron virtual course software is but it sounds like you're now attributing improvements to your power profile over the course. Since you've stated on numerous occasions your tests are 100% repeatable are you using the same power profile every time you ride? It doesn't sound like it if you're putting out more effort attacking the hills. That is of course the correct way to ride a real course but with a virtual course who knows.

In any case, it sounds like just another uncontrolled variable that will confound any conclusion you might have.

Good luck.
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Re: My testing to try and find best crank length with my Velotron [gregf83] [ In reply to ]
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Of course, it doesn't really matter since the data shows virtually the same correlations with or without that Nov 9th result.


gregf83 wrote:
h2ofun wrote:
The effort on the Nov 9th was when I had no idea what was going to happen with Martis since I expected just the same bad numbers. I did not push things since I was learning how to handle the testing course with a different bike setup. Since then, I have done a much job attacking the hills, both, up and down.
I have no idea how realistic the Velotron virtual course software is but it sounds like you're now attributing improvements to your power profile over the course. Since you've stated on numerous occasions your tests are 100% repeatable are you using the same power profile every time you ride? It doesn't sound like it if you're putting out more effort attacking the hills. That is of course the correct way to ride a real course but with a virtual course who knows.

In any case, it sounds like just another uncontrolled variable that will confound any conclusion you might have.

Good luck.

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Re: My testing to try and find best crank length with my Velotron [Sean H] [ In reply to ]
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Sean H wrote:
I just wanted to thank you kind souls for keeping this thread going. It's a Festivus for the rest of us.

I like playing with numbers....

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:
I guess you could attribute his 10% power improvement from last year to this to a better fit but this just doesn’t wash with me. I would be surprised if anyone has ever demonstrated (in a study) power changes as much as 1% from a better fit. Yet, you want to attribute a 10% improvement to this change? Can you point us to any work in this area demonstrating this is reliably possible?

I've seen this several times, primarily with people who previously had really poor positions, or had been riding significantly longer cranks. However, the improvements are not really gains, the changes in position are preventing losses. If I were to throw the 175mm cranks that came stock on my old tri bike back on, I'd see a significant drop in power, because I wouldn't be able to get over the top of the pedal stroke...

"I'm thinking of a number between 1 and 10, and I don't know why!"
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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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JasoninHalifax wrote:
On my phone right now, but mathematically fir an R square correlation where power is constant, HR and pulse power are the same thing. There was no need to do an extra step.

Address more of your questions after dinner and bedtime.


Yes, I know that but I felt the extra step was necessary to help people understand that HR is a measure of efficiency. Pulse power I think helps make that clearer. Most people I would think would understand that more power per heart beat is a good thing although you wouldn’t guess that from some of the responses to this thread.

Frank Day

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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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JasoninHalifax wrote:
Sean H wrote:
I just wanted to thank you kind souls for keeping this thread going. It's a Festivus for the rest of us.


I like playing with numbers....

Tell jason I asked that because when I imported his excel spreadsheet into Numbers I was told it couldn’t import all the formulas so only imported values. However, because of his answer I think I have figured it out. As with many things looks simple once one knows how.

Frank Day

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Re: My testing to try and find best crank length with my Velotron [Warbird] [ In reply to ]
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Warbird wrote:
h2ofun wrote:
I guess you could attribute his 10% power improvement from last year to this to a better fit but this just doesn’t wash with me. I would be surprised if anyone has ever demonstrated (in a study) power changes as much as 1% from a better fit. Yet, you want to attribute a 10% improvement to this change? Can you point us to any work in this area demonstrating this is reliably possible?


I've seen this several times, primarily with people who previously had really poor positions, or had been riding significantly longer cranks. However, the improvements are not really gains, the changes in position are preventing losses. If I were to throw the 175mm cranks that came stock on my old tri bike back on, I'd see a significant drop in power, because I wouldn't be able to get over the top of the pedal stroke...


So, in your view, my attempting to eliminate losses in Dave, apparently with some success, should not be seen as gains?

Frank Day (

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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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Jason wrote "I think the point is that if you look at the results of the recent tests on 150mm cranks, there is virtually 0 correlation in the data. That means that despite the claims of 100% repeatable testing, the data that's coming out is all over the place. A set of equipment that allows you to repeat the same testing protocol doesn't guarantee you will get the same outcome every time. In this case, the test results are all too spread to draw any conclusion without significantly more data points.

Removing the Nov 10th test would make it a 0.9 correlation, so it certainly isn't the 1st test that is skewing things. Then you look at the adding the most recent 175mm test on 11/25 and that massively throws a wrench in the system. Same pulse power but at a much high pedal speed. ie...there isn't enough quality data to show any reasonable correlation, or there is no correlation to be found.

Do we get to pick which tests are outliers and which ones to include in the data? Probably not the best way to approach things…”

I never claimed that the results were 100% repeatable. There will always be noise in the data. if there were not there would be no need for statistics. What Dave meant by that was these tests were being done in controlled conditions on a research quality ergometer and frame capable of adjusting to keep fit the same (although he reached those limits). Such conditions should minimize the noise resulting in more reliable results.

While more data is always preferable the results are pretty good with r^2 coefficients about 0.7. That is better than most of the stuff posted here (or anywhere else) IMHO. Further, it is not unusual for researchers to throw out outliers when analyzing data. It all comes down to making the best sense of what you have.

Frank Day (

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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h2ofun wrote:
Warbird wrote:
h2ofun wrote:
I guess you could attribute his 10% power improvement from last year to this to a better fit but this just doesn’t wash with me. I would be surprised if anyone has ever demonstrated (in a study) power changes as much as 1% from a better fit. Yet, you want to attribute a 10% improvement to this change? Can you point us to any work in this area demonstrating this is reliably possible?


I've seen this several times, primarily with people who previously had really poor positions, or had been riding significantly longer cranks. However, the improvements are not really gains, the changes in position are preventing losses. If I were to throw the 175mm cranks that came stock on my old tri bike back on, I'd see a significant drop in power, because I wouldn't be able to get over the top of the pedal stroke...



So, in your view, my attempting to eliminate losses in Dave, apparently with some success, should not be seen as gains?

Frank Day (

It is a gain in terms of how much power was being applied as compared to before. But not a gain in terms of "he got stronger", rather he isn't shooting himself in the foot anymore...

"I'm thinking of a number between 1 and 10, and I don't know why!"
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Re: My testing to try and find best crank length with my Velotron [Warbird] [ In reply to ]
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Warbird wrote:
h2ofun wrote:
Warbird wrote:
h2ofun wrote:
I guess you could attribute his 10% power improvement from last year to this to a better fit but this just doesn’t wash with me. I would be surprised if anyone has ever demonstrated (in a study) power changes as much as 1% from a better fit. Yet, you want to attribute a 10% improvement to this change? Can you point us to any work in this area demonstrating this is reliably possible?


I've seen this several times, primarily with people who previously had really poor positions, or had been riding significantly longer cranks. However, the improvements are not really gains, the changes in position are preventing losses. If I were to throw the 175mm cranks that came stock on my old tri bike back on, I'd see a significant drop in power, because I wouldn't be able to get over the top of the pedal stroke...



So, in your view, my attempting to eliminate losses in Dave, apparently with some success, should not be seen as gains?

Frank Day (

It is a gain in terms of how much power was being applied as compared to before. But not a gain in terms of "he got stronger", rather he isn't shooting himself in the foot anymore...

This,

Find a reasonable fit, whether through a professional fit or your own trial and error. Ie the best fit for you.

Then drop your seat 2 inches and see what happens when you do an FTP test.

What we are seeing here is a change from really bad, to (hopefully) getting better....

Maurice
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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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Jason Wrote: "Eliminating the first day bumps the r square for pedal speed vs pulse power up from 0.021 to 0.029. i.e. still essentially zero. But I don't like excluding data points without a good reason. The fact that the first series was nearly a year ago is a pretty good reason.

What this particular finding shows is that within a small window of cadence and pedal speeds, that the effect is tiny. and that actual research is frickin hard. But you can use this finding to guide future tests.

BTW, I'm doing this with MS Excel. If you are conducting this experiment, then you really DO need to know how to analyse the data. Otherwise you are going waste a lot of time and effort to collect a lot of data that leads nowhere. What I've done is 1st year university level stats, which I learned back in 1988, I was probably drunk or half asleep from morning practice at the time. It isn't hard….”

One doesn’t need to know how to calculate R^2 or anything else to do this work. This is not a research project but an attempt to minimize efficiency losses in Dave from a poor pedal speed. That can be done with enough test data and the eyeball test. I have 85 data points in the hoods with a R^2 of 0.7 but I still have to look at the curve and estimate the peak and even if done mathematically it would not be perfect because the data isn’t perfect. That having been said, I had a good idea of where his peak was within a week but I just pushed the data numbers to confirm my initial thought.

So, it took 85 data points to get that kind of correlation. It seems unreasonable to criticize the Martis analysis when there are less than 10 data points plus the data is even more unreliable because power isn’t controlled. Martis is not part of the testing protocol but has been useful to convince Dave that the changes we are making will truly benefit him. He knows how he rides that course, what he used to do and what he does now. He is impressed. He is the only one that really counts in my opinion. He posts here to get contrarian views and he gets plenty of them but I’ll bet money not one of them has convinced him those increases are not real.

Frank Day

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Re: My testing to try and find best crank length with my Velotron [gregf83] [ In reply to ]
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gregf83 wrote:
h2ofun wrote:
The effort on the Nov 9th was when I had no idea what was going to happen with Martis since I expected just the same bad numbers. I did not push things since I was learning how to handle the testing course with a different bike setup. Since then, I have done a much job attacking the hills, both, up and down.
I have no idea how realistic the Velotron virtual course software is but it sounds like you're now attributing improvements to your power profile over the course. Since you've stated on numerous occasions your tests are 100% repeatable are you using the same power profile every time you ride? It doesn't sound like it if you're putting out more effort attacking the hills. That is of course the correct way to ride a real course but with a virtual course who knows.

In any case, it sounds like just another uncontrolled variable that will confound any conclusion you might have.

Good luck.

I did not say I had the same power for all tests. For the HR test, it is an erg file.

But then trying to test against a real life bike effort, I use martis to left me know how it may really change in the real world, without having to find a road section that is tough and safe. My comment about martis is why I would say 100% the same, is because I can ride it at any time and alway have the same parameters that I want, meaning, basically same house temp, not cars, animals, etc to deal with. No weather. Etc. The closest I can get to a real world test that can be repeated.

So, just do not understand why some try to say something that basically has not been said, but I get some just want to attack anything we write, rather than looking at the big picture and saying, maybe he might find something different I could think about. But Nah. Not even Dan is interested. Just too many who are set in their ways. Oh well.

Dave Campbell | Facebook | @DaveECampbell | h2ofun@h2ofun.net

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Lions don't lose sleep worrying about the sheep
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Re: My testing to try and find best crank length with my Velotron [elf6c] [ In reply to ]
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elf6c wrote:
lol, Apex Trainwreck has been achieved.

I just watched the movie Split, which has the main character jump between a bunch of split personalities. Seeing posts from Dave and Frank Day follow up in quick tempo and sometimes being mixed is basically just as weird as in the movie.

From your reaction on this has only gotten worse. Makes you wonder if there's some kind of record for missing the point. I'm not so sure which of the 2 is winning ...
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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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Now that I know how to do R^2 analysis in numbers I did some quick looking

Linear coefficient could never be 1 even with perfect data because the line should not be linear since the cost of pedaling a bicycle varies with the square of the cadence. I compared the R^2 of a linear trend line to a polynomial. Polynomial won, but not by much, 0.7 to 0.69









Frank Day

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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So does that give you high confidence in a peak to this particular relationship? It doesn't with me...your polynomial equation plots out as a pretty close to straight line.

the reason that you do the math is because eyeballs lie, eyeballs are are drawn to outliers like the one dandelion that pops up its stem after you finish mowing the lawn.


h2ofun wrote:
Now that I know how to do R^2 analysis in numbers I did some quick looking

Linear coefficient could never be 1 even with perfect data because the line should not be linear since the cost of pedaling a bicycle varies with the square of the cadence. I compared the R^2 of a linear trend line to a polynomial. Polynomial won, but not by much, 0.7 to 0.69









Frank Day

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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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JasoninHalifax wrote:
So does that give you high confidence in a peak to this particular relationship? It doesn't with me...your polynomial equation plots out as a pretty close to straight line.

the reason that you do the math is because eyeballs lie, eyeballs are are drawn to outliers like the one dandelion that pops up its stem after you finish mowing the lawn.


h2ofun wrote:
Now that I know how to do R^2 analysis in numbers I did some quick looking

Linear coefficient could never be 1 even with perfect data because the line should not be linear since the cost of pedaling a bicycle varies with the square of the cadence. I compared the R^2 of a linear trend line to a polynomial. Polynomial won, but not by much, 0.7 to 0.69









Frank Day


No, I don’t believe that data is showing me the peak. All it is saying to me is that there is indeed a relationship. The reason is I wasn’t gathering data to show this mathematically as a research project. If I were I would need to have the distribution of data points equal across the pedal speed distribution. I did not do this so there are fewer at the very high and very low end of the spectrum so these are having a smaller impact on the curve. Both lines are continuing to increase even at a pedal speed of 65 cm/sec, equivalent to 150 mm cranks at a cadence of about 40. That doesn’t pass the smell test. At least the polynomial is curving down suggesting efficiency doesn’t continue to increase all the way down to a cadence of zero.

So, once I felt I had demonstrated to myself that I had passed the peak I focused most of the testing around that pedal speed. If I were an academic researcher I would still be doing 200 mm cranks at a cadence of 100 and 150 mm cranks at a cadence of 30. I am not.

So, if the protocol is bad sometimes the math lies and the eyeball test wins. Dave’s peak efficiency is not at a pedal speed of 60 cm/sec or slower which is what the math is saying. In this case, I think it is clear to the average eyeball the peak lies between 100 and 120 cm/sec.

Frank Day

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Re: My testing to try and find best crank length with my Velotron [JasoninHalifax] [ In reply to ]
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Jason writes: "So does that give you high confidence in a peak to this particular relationship? It doesn't with me...your polynomial equation plots out as a pretty close to straight line.

the reason that you do the math is because eyeballs lie, eyeballs are are drawn to outliers like the one dandelion that pops up its stem after you finish mowing the lawn. “

We know from others work that efficiency changes with cadence (pedal speed) as an inverted U. Therefore we know (or should suspect) that Dave’s curve should conform to that pattern if we had enough data. I have taken what data we have and drawn what my eyeball says the curve should look like on his best days. I would look forward to hearing what you think his actual curve looks like and why?




Frank Day

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Re: My testing to try and find best crank length with my Velotron [h2ofun] [ In reply to ]
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So you're cherry picking data in order to conform to the result you want? OK...

Why not use his worst days? then the line is a straight one. Why not just use the peak value as optimum?

Your "eyeball" line doesn't take into account the day to day biological variation.

I don't really know or care what the curve looks like. Just following the data, and the data says noise.

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