I'm not a power meter expert, as my subsequent questions will display. I'd love input from folks who understand the instrumentation and/or the engineering-human interplay better than I do. Bonus points for expressing confidence level of answers. I know many of you have amassed huge quantities of time thinking and writing on similar topics and I am grateful for your time if you choose to answer any or all of these.

(My assumption is that the answer may vary for many of these questions, depending on the make/model/type of power meter.)

1. My understanding is that power meters measure either torque (force about an axis) or uni-directional force (up and down by use of a strain gauge or piezo electric crystals etc), and they measure cadence. Then, the power meter calculates "power" my doing some quick multiplication and sending that calculated variable out for display on a head unit, right?
   
   
2. My understanding is that they calculate and report power every 1 second to the head unit. Is that correct?
   
   
3. When during the pedal stroke do they measure force or torque? Surely it's more often than every 1 second. What is a common sampling rate? 100Hz? 1000Hz?
   
   
4. Do they aggregate the force data by averaging it? Or do they use the peak force? Median? By what mathematical process does the power meter decide what force or torque number to use in the calculation to produce the number sent to the head unit as it's single "1Hz power measurement." (assuming I was correct in question number 2 above)
   
   
5. In the case of systems measuring just force and not angular force (torque), as I believe is the case for pedal power meters (using piezoelectric crystals?), do they use the same averaging or force data selection method as used in systems measuring angular force? Surely not. I hope not. I won't be surprised if the answer is yes, it's the same and we're all just accepting it.
   
   
6. When does a power meter measure cadence? High sampling rate aggregated in some way like force or torque is? Or just based on the cycle frequency of the force data? If the latter, the implication is that during system accelerations where cadence is increasing, power calculation will actually reflect cadence that is half a pedal stroke behind what it is if it were being sampled at something closer to continuously. (ie. 100Hz or 1000Hz). See implications and data below.
   
   
7. What effect does temperature have on force or torque measurements? Thinking about climbing Mt. Lemmon starting at 4pm, for example. Or in cases of overnight riding during summer in arid environments where temp swings can be 30+ degrees.
   
   
8. Safe to assume pedal-based power meters do not measure power added by pulling up on the pedals during a sprint?
   
   
9. I usually see discussion of power meter error expressed in terms of it's error in the 100-400W range (around most human's FTP values). Usually expressed as a percentage. Does that percentage grow as power increases? Does it grow systematically as power increases? Or does it grow idiosyncratically to the individual as they approach max 1-second power efforts? Both? By what magnitude? How do you know this?
   

Implications if force or torque cycle frequency-based cadence calculations are used by any given power meter, related to number 6 above:

This would result in power reporting that, as a percentage, is half the rate of change in cadence lower during an acceleration. Correct me if I'm wrong. Similarly, if sprinting uphill after a hard leadout but slowing because of high drag + high grade, power calculation would be erroneously high by half of the rate of change in cadence.

Here is some real-world data from two days ago on Zwift, if they're using a simple torque cycle frequency calculation, rather than a faster sampling rate for cadence calculations.

Fun fact re: Zwift: after this sprint, they continued to accelerate my character for 2 seconds after my power had dropped to 0, on flat ground. Fun times in data smoothing in software / UI land. :)

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Dr. Alex Harrison | Founder & CEO | Sport Physiology & Performance PhD
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1. It also depends on what ANT+ or bluetooth protocol is used. Some PM send processed "power" data, others send data closer to raw data.
2. It too depends on the ANT+ or bluetooth protocol. But indeed most PM on the market send messages with 1 Hz only. Some can send proprietary, mostly bluetooth, messages with higher sampling rates.
3. I think SRM in the older times had 200 Hz internal sampling, others I don't know.
4. I don't know, most PMs are black boxes.
5. I don't know, but pedal PMs have to measure the complete force vector
6. Some PMs use one or more reed switches to get the time for one revolution or a fraction of them. Some PMs use acceleration sensors.
7. Its very complicated, conventional strain gauges change electric resistance when strained. Temperature affects thermal expension of the substrate and the strain gauge as well the electronics. (I prefere a well desigened PM over one with electronic temperature compensation).
8. At least Assiomas and Wahoos do it. Assiomas and Wahoos do deal with power cranks.
9. I don't know what the PM sellers express with their error. For load zells the error is usually expressed as percentage of full-scale.
   

1. pretty close
2. They will calculate power more often than 1 second but according to the ANT+ protocol they report it at a regular interval, likely 1 second. I'm not familiar with the BT protocol.
3. They measure the full 360°. The sampling rate depends on the manufacturer and they rarely release that spec
4. I don't know, I would guess it's average force.
5. I don't know
6. This will depend on the manufacturer but I'm sure it's more than once per rev.
7. There are different forms of temperature compensation. Placing two rosettes in opposite directions is one way to cancel out measurement inaccuracies from expansion but the likely way they do it is to measure torque and record it's offset at different temperatures then build a table to read expansion values from. This is one form of characterization, it's likely they use this or something similar.
8. I would assume they do measure it
9. You don't know this, typically measurement uncertainty is expressed as a percent of full scale across the measurement range. The only way to know exactly is to have a calibration map done and a gauge R and R study. Manufacturers rarely release that info. Normally, you would expect the measurement to be within the stated accuracy more than 80% of the time or within about 1.6 standard deviations.

Zwift does some weird stuff after they receive the measurement data from the selected device.

So this all goes back to an interesting discussion that Dan and I have been having about the value of HR and RPE. Both very "old school."

To me, the "accuracy" - really *precision* - of powermeters is probably more of a bug than a feature. I.e., a PM that's accurate +/- 3% might actually be *better* than one that is 1%, and I think it's because it gives you more permission to take the number as a "suggestion" rather than as gospel.

Powermeters are invaluable for pacing in an Ironman. Ironman pace should feel quite easy for the first hour or so. Your PM can help keep you from digging a hole that's going to be hard to crawl out of at the end. It doesn't need much than about 5% accuracy to do that well. Even 10% is probably good enough, especially if you couple it with HR.

The other problem with power is that it is less transferrable than people think. There used to be "rules of thumb" for how much to drop your FTP in aerobars. That never made any sense to me. If your FTP in aerobars was lower than your FTP in your drops, you needed a bike fit. This is less true indoors - I find riding aerobars hard indoors to be quite a bit harder than outdoors, but I suspect this has more to do with the low-inertia environment on a trainer. But still, even indoors, FTP should be quite close.

BUT on a gravel bike? Or - as I'm finding more recently - on a MTB? It can vary a lot. And actually is highly dependent on both skill and terrain. Your FTP on very technical terrain will be lower than on non-technical terrain. And your FTP as you become more skilled will go up, irrespective of overall *fitness*, because the physical cost of bike handling will go down.

I was a die hard power meter rider when I was a pro. And I attribute a lot of my success to being an early adopter of training *by power.* But as I've gotten older, I've seen the wisdom of training more often *with power* rather than *by* it. And training more often *by* HR and - especially and most often - *by* RPE. I hope the distinction is clear, but the "by" to me is the guiding metric for your workout. It's what determines what you *should do* rather than reflecting what you are doing (or, post hoc, did; that's what I mean by "with").

Yes, for sure, some days PMs run "hot" - this is one of the biggest issues I have with the "analysis" that accompanies power meter files from races; it's disappointing to me that the numbers are treated as absolute, especially when they are so obviously flawed. And some days they run "cool." Take the hot days as truth if they make you happy. And shrug off the cool days. Use it as a tool, not as a master. Hopefully articles like Ray's and the ones that Dan and I have written will help people make better use of their PMs, and to view their flaws and inaccuracies as things not to rail against but rather to understand and to give you a bit of freedom.

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"Non est ad astra mollis e terris via." - Seneca | rappstar.com | FB - Rappstar Racing | IG - @jordanrapp

 

this is a very reasonable take, and i like the with/by description. too much training by power can cause burnout and morale issues, by causing one to take the imagined precision of the numbers too seriously.

but used to help triangulate with other data, its very valuable. i like to use private strava segments on climbs and loops for tests periodically, where i can then triangulate speed/RPE/HR/power and really get a good picture compared to other efforts.

i don't stress any more about the numbers i'm hitting in a given workout, and adjust and treat it holistically. even on test days, i know there's some imprecision unless im in a university lab.

High-precision low-accuracy data is the bane of the sport and fitness tech industry. It's also the number one marketing tool.

Much easier to provide high-precision numbers with moderate accuracy and validity than it is to provide moderate precision with high accuracy and validity.

Unfortunately when companies present high-precision low-accuracy data with a pretty graph and lots of conveyed confidence, even though the numbers aren't valid, accurate, decision-informing, or valuable, it makes people believe that the data are valuable and drives sales.

Hence, we'll continue to see high-precision, low-accuracy number-generating sensors proliferate until more companies take a stand against the wasteful genesis, storage, and analysis, of useless (or worse) data and start being value-driven and decision-informative before deciding to measure or calculate yet another "metric."

**steps off soapbox**

@Rappstar, I think we see perfectly eye to eye on everything you said. Well said. PM's are a useful tool. I get down in the weeds only to better analyze the data given the nuance in how it is actually collected, calculated and reported, rather than taking the outputs as sacrosanct. And I just like to know how to game my PM so I can maximize the inaccurate number if gives me. :)

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You got a lot of questions.

1. There are two ANT+ protocols: one sends power to the head unit, the other sends crank torque; in the latter case, the head unit has to combine crank torque with cadence to get power.
2. Depends on the protocol, but the ANT+ protocol is to send data at 4Hz. However, most head units discard 3 out of 4 of those packets and only record one of them. There are ANT+ devices that will capture at 4Hz, but only people who are obsessive (hi there) ever check these devices.
3. Depends on the device. SRMs used to say that they polled the torque at something like 200Hz, but others (like the Power Tap and the Quarq and Stages polled at closer to 64Hz). The old SRM used a reed switch to measure cadence so it would gather up torque samples in-between closings of the reed switch and then get average torque, and send that to the head unit. Others (like the Power Tap) reported at a fixed interval (i.e., it wasn't event-triggered). Reed switches are a reliable technology, but they can only tell where the crank is when it passes the switch; the advantage of accelerometer-based cadence sensors is that they sorta kinda know (with some noise) where the crank is in the middle of a pedal stroke. That said, most of the power meters (but not all) don't use the information about where the crank is while in the middle of the pedal stroke even though, in theory, they could.
4. Depends on the manufacturer. Each one does their own proprietary thing, including how they handle noise in their measurements. That's a black box.
5. Pedals needs to know where they are in the stroke cycle and their orientation, so they use accelerometers and piezoelectric sensors to know which direction is up, down, tangential, and radial. Then they have to sort through the data, handle noise, and eventually report back to the head unit.
6. As mentioned above, cadence measurement depends on whether the PM uses a reed switch or accelerometers. Exceptions included the Power Tap hub, and the old Polar S710 chain PM system. They didn't actually need cadence: the PT only needed the rotation speed of the rear hub, the Polar chain system used chain tension and chain speed sensors. That said, the PT did provide an estimate of cadence: if you looked at the raw (64Hz) data, you can see "pulses" in torque. There are typically two pulses per crank rotation, so you can look at the pulse frequency and estimate cadence. Note that the power doesn't depend on that estimated cadence: the Power Tap knew the hub rotation speed and the hub torque, so it was just calculating the estimated cadence as a convenience for the rider. I've examined the accuracy and precision of the Power Tap cadence estimates before -- in general, not bad.
7. So, temp changes used to be the bane of power meters because the strain gages had to be attached to a substrate that could be affected by temperature. Accordingly, most strain gages had to be mounted in a special configuration (a rosette) and then re-zeroed whenever there were large swings in temperature. All modern power meters now include electronic temperature compensation circuitry, but if the temp swings are large enough and sudden enough, they won't be sufficient to ensure high quality data. In those cases, you have to go back to manual zeroing.
8. I'm pretty sure they do.
9. So, the way that manufacturer's cite accuracy and error is typically over the range of power. That's not what most people think. It means if the PM is rated for 0-2000w, +/- 1% means +/- 20 watts. I never pay attention to what they're rated at. When I use power data, I need to check the accuracy.

1. There are indeed 4 defined cycling power ANT+ protocols. Power Only, Wheel Torque, Crank Torque and Crank Torque Frequency. Most PMs send ANT+ messages with around 4 Hz, but again most update the message stream only with around 1 Hz. I don’t know how individual cycling computers handle the 4 Hz message stream. For example with a WASP ANT+ to WIFi bridge I can collect the raw and complete message stream. I have a special powertap version which indeed gave a true 4 Hz stream. SRMs up to PM7 also do higher than 1 Hz in ANT+.

Doing my best to answer these to the best of my engineering and cycling knowledge, but the inner workings of individual meters is not public knowledge, so deep things like sampling rate are largely unknown.

=======
(My assumption is that the answer may vary for many of these questions, depending on the make/model/type of power meter.)

1. My understanding is that power meters measure either torque (force about an axis) or uni-directional force (up and down by use of a strain gauge or piezo electric crystals etc), and they measure cadence. Then, the power meter calculates "power" my doing some quick multiplication and sending that calculated variable out for display on a head unit, right?
   
   Yes, the simplest way to do so is to measure only perpendicular to the direction of the crankset (tangential load) as that is the only vector capable of producing power into the wheel. Pedals and BB meters have some extra complications. A torque meter and a strain/force meter are functionally the same thing, it's just which object they are attached to. Most modern ones use strain gauges coupled with gravity-read cadence sensors. Force*distance/time=power.
   
   
   1. My understanding is that they calculate and report power every 1 second to the head unit. Is that correct?
      
      There's different reporting protocols for different PM's and head units. 1 second is common, SRM famously had a high sampling rate in their own head unit that made it popular wit track sprinters. Due to the cadence measurement shortcomings and the use case for 99% of PMs a sampling rate less greater than 1/sec is rarely used.
      
      
   2. When during the pedal stroke do they measure force or torque? Surely it's more often than every 1 second. What is a common sampling rate? 100Hz? 1000Hz?
      
      Again, different for different meters. You can buy off the shelf strain gauges with any number of sampling rates. I don't see much reason to sample above 100Hz. That would capture ~80 data points on every revolution. This is against a backdrop of constant (ish) cadence multiplier (over 1-2 previous revolutions). The tech simply isn't there yet (at the consumer level) to introduce instantaneous cadence to the equation.
      
      
   3. Do they aggregate the force data by averaging it? Or do they use the peak force? Median? By what mathematical process does the power meter decide what force or torque number to use in the calculation to produce the number sent to the head unit as it's single "1Hz power measurement." (assuming I was correct in question number 2 above)
      
      The force can be sampled at an independently high rate compared to cadence. I'm sure it integrates the force to find the 'area under the curve' of the data received. No verification, but that is the most obvious and simplest way to capture the most accurate data.
      
      
   4. In the case of systems measuring just force and not angular force (torque), as I believe is the case for pedal power meters (using piezoelectric crystals?), do they use the same averaging or force data selection method as used in systems measuring angular force? Surely not. I hope not. I won't be surprised if the answer is yes, it's the same and we're all just accepting it.
      
      I'm not sure I understand this. A properly calibrated meter should as a first pass data manipulation correct the measurements so only tangential force is used.
      
      
   5. When does a power meter measure cadence? High sampling rate aggregated in some way like force or torque is? Or just based on the cycle frequency of the force data? If the latter, the implication is that during system accelerations where cadence is increasing, power calculation will actually reflect cadence that is half a pedal stroke behind what it is if it were being sampled at something closer to continuously. (ie. 100Hz or 1000Hz). See implications and data below.
      
      Idk how various PM's measure data, but the underlying assumption is that cadence is steady throughout the stroke, which it is not. The simplest cadence sensor measures gravity but it takes half a rev or so to realize the assumed TDC is the true TDC, just because of the additional noise of the pedal stroke and road forces.
      
      
   6. What effect does temperature have on force or torque measurements? Thinking about climbing Mt. Lemmon starting at 4pm, for example. Or in cases of overnight riding during summer in arid environments where temp swings can be 30+ degrees.
      
      Temperature compensation in force meters is well modeled, and shouldn't be a large source of error. Differential heating and cooling of the pedal/crankarm will likely be a bigger error, where the temp read and force meter are separated. Again, the further it gets from the calibration point the greater the potential for error.
      
      
   7. Safe to assume pedal-based power meters do not measure power added by pulling up on the pedals during a sprint?
      
      My guess is that pedal based meters calibrate by determining vertical via accelerometer and cranks TDC, then infer the direction they are facing from there. This requires an omnidirectional force sensor (or at least and up/down left/right). There's no reason to
      think this setup would be unable to measure a upward force in the same way it measures a downward force.
      
      
   8. I usually see discussion of power meter error expressed in terms of it's error in the 100-400W range (around most human's FTP values). Usually expressed as a percentage. Does that percentage grow as power increases? Does it grow systematically as power increases? Or does it grow idiosyncratically to the individual as they approach max 1-second power efforts? Both? By what magnitude? How do you know this?
      
      Yes, but for a few reasons. The force meters have a margin of error, the more they stretch away from the calibration state the greater the uncertainty. The cadence (when not a magnet) has a shorter frequency and the same amplitude of gravity to measure against, so while the signal amplitude has the same height and curvature (read: standard deviation) the distance between peaks decreases, so the relative accuracy goes down.
      
      
   Implications if force or torque cycle frequency-based cadence calculations are used by any given power meter, related to number 6 above:
   
   This would result in power reporting that, as a percentage, is half the rate of change in cadence lower during an acceleration. Correct me if I'm wrong. Similarly, if sprinting uphill after a hard leadout but slowing because of high drag + high grade, power calculation would be erroneously high by half of the rate of change in cadence.
   
   Here is some real-world data from two days ago on Zwift, if they're using a simple torque cycle frequency calculation, rather than a faster sampling rate for cadence calculations.
   
   Fun fact re: Zwift: after this sprint, they continued to accelerate my character for 2 seconds after my power had dropped to 0, on flat ground. Fun times in data smoothing in software / UI land. :)
   
   Yes, a noted shortcoming of PMs is responding to quick gear changes, where the force change is picked up prior to the cadence change. I'm no too concerned tho. Was this Zwift example from a crank/pedal based PM? You wouldn't expect this from a trainer power meter. And tbf most Zwift issues are from their own software, not so much PMs.
   
   Hope that's helpful, and I'm sure there some things that are outdated or superceded.
   

First, bows, down, humbly not worthy to question you my lord, etc etc.

But....

Here I think you are conflating accuracy of powermeters with the use of the FTP formula to convert the measurements into FTP. And note that powermeters are tested for accuracy against actual scientific known values. FTP is an abstract measure that has been shown to be helpful, but there's no actual reference that can be compared to as to what FTP actually truly is.

I appreciate there is a reality check that of course people need something useable in real time to inform effort, and at the moment then average power and FTP are the two choices we have.

Apologies if I am getting this wrong, but what I read in your post is that as there is a questionable real world specificity in how to react to an FTP that is potentially greater than the stated accuracies of the powermeters. However, where I think the flaw is in this is that the way FTP is calculated is on the measured data including the error, and so there is a chance that the FTP formula 'damps' this error. Or it could magnify it.

Many many moons ago my thesis looked at this in a quite different field. By this I mean how uncertainty (unknown accuracy) of inputs into a complex calculation system produced variables in the output. Some got magnified, some got damped.

Where I do agree with Jordan and others is that there is a point where the data is good enough. And regardless if there is some uncertainty, issues with precision or accuracy, then the real question is does it effect our ability to make a sound choice in response. Remember, the entire point of having a power meter is to get better value from training, and to be able to adjust race efforts to optimise performance. And the most imprecise bit of that system is the control that we have between brains and legs when at close to race efforts to judge an energy output of say 265W vs 270W.

FWIW I always struggled to get value from HRM data on the bike, running was more useful for me (pre GPS), but by same score I now use pace over HRM to judge efforts in real time, but do use HR in post analysis for running.

I'm glad your handle is "mathematics" and not "engineering." :)

mathematics wrote:

A torque meter and a strain/force meter are functionally the same thing

Er, I'd be careful there. Maybe at a simplistic level. But to get from strain to force can be more complicated than a simple correlation. The effects of force on a piece of metal can be nonlinear (*cough*Shimano*cough*). There's a lot to account for. Reality astounds theory, to paraphrase the Car Talk guys.



Strain gages don't have sampling rates. They are analog devices that produce varying electrical resistance as the gage deforms. Sampling rates come into play when you couple them with an A2D. Every modern A2D I've worked to hook up to a strain gage samples at thousands of Hz. Per Harry Nyquist, the ideal would be to sample the strain gage at double its bandwidth. Otherwise you're effectively throwing away data. And I don't know why you'd do that. There's negligible energy or part cost sampling well above 1 kHz. The bandwidth will be published by the strain gage manufacturer, and part of the downselect process in selecting a gage appropriate for the task. You want to run your processing as much as possible at the clock rate of your uC and downsample at the last possible moment, like just before sending over Bluetooth.




To be more specific, a common way of "aggregating" force data would be to use a digital process estimator that incorporates a model of the process being estimated (power from force and cadence) along with error models for each sensor used as an input. My first reach into the toolbox would be to try a Kalman Filter (which astound me to this day in practice in their simple genius and great utility - they are everywhere). If the Kalman Filter or one of its derivatives isn't used in the vast bulk of PMs I'd be very surprised.



An assumption of constant cadence per stroke would very much surprise me. You'd be sampling accelerometers and gyros thousands of times (or more) per pedal stroke and would be able to update an instantaneous estimate of cadence and absolute crank position at that same rate...again at the uC clock rate. Yes, all sorts of noise in accels and gyros, accelerations exceeding 9.8m/s^2, etc. But digital filters are good at that stuff. Part of the genius of the Kalman filter class of estimators is they excel at accounting for measurement noise and estimating accurate process noise - to delve into controls-speak.

This is brilliant and this thread is turning into another great off season deep dive into sport adjacent things that align with people's expertise. Truly awesome stuff.

(Tbf, about mathematics, my schooling was chemical engineering so not a ton of electronic or programming involved).

For the sampling rate, I totally get what you're saying about the infinite analog rate, I never realized the digital sampling rate from there could be arbitrarily high with such little penalty. That's wild.


The only spot where I'll question is the cadence. I'm not sure if you could fundamentally separate the signal from the noise enough (especially on a bumpy road) to determine cadence by anything other than gravity. This assumption is somewhat born out (at least for Stages PMs for me) by the common sight of the power output lagging when shifting quickly. Shift two gears easier, keep pushing the power, and you get a spike for a second or two. Reverse for shifting harder.

I guess the question in getting at is: over the span of 1 revolution, is there an actual difference between an assumption of constant cadence and an integration of instantaneous cadence and instantaneous power? The power equation is just force x distance / time. If the cadence is 60rpm but fluctuates instantaneously during the stroke, the distance is fixed and the time is fixed so the only thing left is the total force. Maybe it's just a possible vs. practical thing.

Thanks for the feedback and input, this stuff is so interesting

Thank you (and all others) very much for taking the time. Very informative.
This seems to be a common refrain. Frustrating on its face but understandable. These are consumer products after all, not lab instruments.
I recall reading this back in my start in the sport and I now fully appreciate why they might desire that. "I want to capture all my watts and half a second is an eternity to delay!
I have a better handle on this now. I confused the situation by assuming (simplemindedly) that maybe power pedals were measuring force purely in the direction tangential to the surface of the pedal. Glad to hear this is not the case. I recall using tools in the biomechanics lab circa 2008-2010 that were very rudimentary and uniplanar, so I thought that maybe consumer tech was still so simple. Glad to hear they're able to measure and calculate true tangential forces. :)

This is concurred by others here, so thank you for lending more confidence here. Had no idea they were using omnidirectional force sensing, but that makes sense and glad that that exists and that it's being used.
Had no idea, but yes that makes sense.
It was purely assumed by me, given that Zwift, and all power meters seem to lag more in cadence than in force measurement, by way of sampling frequency. The numbers I calculated are just calculated based on the assumption that the cadence was half a revolution behind. I have no hard (measured) evidence that that is true, but all that has been said in response to my questions about cadence measurement here lead me to believe that my assumption is right. Open to other interpretations.

Thanks again.

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Thank you for entertaining them. I learned a great deal from your response.

When I see RChung, mathematics, dcrainmaker, trail, BergHugi, pk, etc etc etc in a thread... I can't not ask some burning questions.

One follow-up question if I may:

Are you saying that if a PM is designed to measure power values of between 0 and 2000 watts, and they report a ±1% accuracy, that at ANY power along the continuum of all measurable power values for that power meter, it might be ± 20W?? As in, I'm riding along at 90 W but it might actually be 70 W or 110 W.

If that's right, what I'd really love to have reported is something akin to "volatility" of the ±X% accuracy value. Intuitively, it seems like the volatility of the error is relatively low, because if I ride steady state at what feels like 200W, I often have no greater variance in instantaneous power than 195-205W for stretches of >30 seconds. Which means that at the very least, it's not ±1% every second, but maybe rather more like ±1% every hour? day? week?

I'm not asking this question well, but perhaps you understand what I'm trying to get at. Or maybe I'm misunderstanding what you meant by "if the PM is rated for 0-2000w, +/- 1% means +/- 20 watts" entirely...

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Dr. Alex Harrison | Founder & CEO | Sport Physiology & Performance PhD
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Yes, Duncan. You are absolutely correct. It's the imprecision of FTP - and not the powermeter - that really is the bug. But I suppose it's the two are so intrinsically linked in most people's minds. I think it really became clearest to me when "my FTP" dropped by about 10% when I started mountain biking. And that, really, my FTP on my mountain bike varies a ton... depending on how technical the trails are. Like, yes, my FTP on my road bike also varies. But it swings much less, because on the MTB it is affected by what *else* I need to put my energy into in terms of how technical the trail is.

I guess I'd lean on the powermeters just because they at least state a +/-% accuracy. People talk about FTP or HR threshold without any sense of "fuzziness."

So yes, I was conflating the two. But intentionally so.

I guess maybe the only spot where I'd quibble a *bit* is this:


this is, essentially, the Norwegian method. The Norwegian method, fundamentally, argues that *everything* is really a derivative of lactate. HR, power, ... everything. Lactate is what actually matters. It is the "actual" reference as to what FTP is in true practical (measurable in real time) terms.


control systems engineer?

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"Non est ad astra mollis e terris via." - Seneca | rappstar.com | FB - Rappstar Racing | IG - @jordanrapp

Just an observation, some PM are slower than others to determine power. For example my Rotor 2InPower from around 2016 takes about 2 seconds to update the data stream. On a track it can cause problems when there is such a time shift between speed and power (speed sensors with reed switches are generally fast and give 4 Hz sampling). I have the impression, that often PM using accelerometers are slow, maybe the Karman filtering is not implemented efficiently.

Not trying to step on RChung's toes because he is the absolute master of the field.

There seems to be some common sources of error on strain gauges, a few of which apply to power meters.

Measurement object-does it move predictably under force? For a crankset I believe the answer is yes.

Alignment of installation, the construction of the strain gauge, an accuracy but not precision issue. Reading 10% low consistently is still valuable, if it's consistent.

Measurement frequency-probably a non issue with such a relatively slow moving input

Now the interesting ones:
Radius for measurement objects subject to bending loads -i don't know if this is negligible for cranksets, especially with the various manufacturers

Strain gauge creep due to adhesive - does the glue have a subtle viscosity that delays and/or blunts the instantaneous strain?

Hysteresis of the gauge system - does the gauge system return to calibration position with no loss of power? Surely a small amount of loss is incurred with wires sliding against backing and backing sliding against adhesive.

A power meter that fluctuates by 1% at any power output is incredibly useful. A power meter that focuses by 20w at any output is useless. By my reading of the strain gauge limitations it seems that strain gauge accuracy is mostly linear, and over timeframes long enough for cadence to even out them PM accuracy should be linear as well.

[kind of hoping to be proven wrong, this thread is overflowing with knowledge. Waiting actually to get back in my lane of practicality]

Shamelessly cribbed from https://www.hbkworld.com/...ntal-stress-analysis

You're right to question. If someone can state the specific engineering definition of "error" used in PM marketing, I'd sure like to know what it is. Power2Max uses the term "precision" in their +/- 1%. Others use "accuracy." Similar type instruments in my field - defense applications - would have a table of different numbers, each with specific definitions indicating bias, maximum instantaneous error, noise, sensitivity (what's the smallest possible force or power differential that can be detected), types of bias and their likelihood, temperature sensitivity. I

From what I've seen in DCR's excellent characterization work one suspiciously non-specific number is simply not enough. Different types of error happen in different situations. Some exhibit bias at parts of the power range, e.g. some more error soft-pedalling. More seem to differ from each other during sprints or sudden attacks. Some being a bit slow to respond, others reporting different power than the other PMs used to compare it with. One number doesn't work for this. That DCR uses around a dozen graphs to characterize PM "accuracy" during an in-depth review is good evidence of this.

Interesting, good point about the additional energy needs for balance/steering/'suspension' when MTBing. I'd always just put it down to the much wider fluctuations in power meaning the NP formula, and by extension our interpretation of out FTP(MTB) ends up being lower. Also the reduced efficicency from outputting that power at suboptimal cadence compared to when on road or TT where you can select you cadence to within 5rpm.

Not systems engineer, second degree was in transport with a specialism in traffic modelling. So I was looking at how the daily fluctuations in traffic flows / turn counts along with errors in the way drivers (and vehicles) are modelled to accelerate/decelerate and a whole load of other bits of data propogate through microsimulation (individual driver/vehicle/second by second level detail) city wide models. Was rather lucky I'd already met my wife at that point, as I didn't get many repeat dinner invites.....

Sliding back into this thread...

I feel like Jordan's quote above is probably the best way of saying what I was attempting to say at the very begining.

Having tested so many of these units, and seen so many wonky power moments - from every company, for every reason under the sun, I've come to realize that obsessing about 1-5w high or low on a given ride (or heck, half the time 8-10w) simply isn't real-world. Every single power meter brand I've tested, from dual-sided and not, has had unexplainable weirdness at some point over the years.

Instead, I focus my testing on the data I have at the time, trying to ferret out whether those weirdness things happen on the regular, or, so unproduceably rarely that it doesn't impact most usage (or, my testing). And then, to try and define if those weirdness things are reproduceable. And lastly, to try and determine whether or not those weirdnesses actually rise enough to impact the goal of the power recording/analysis/etc.

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My tiny little slice of the internets: dcrainmaker.com

I feel your pain.

There are so many ways for a power meter to be off. What I look for is whether I can use it for aero testing because that's a much more demanding use for power data. As I've said, I originally came up with VE as a way not to assess aero drag but as a way to check the accuracy of power (and speed) data. Training FTP turns out to be one of the least demanding things you can do with power data -- but by far the most common. Most riders don't use their PMs for aero or Crr testing so they don't actually need very much accuracy (trueness) *or* precision. I think you once told me that everything's a use case. My use case is demanding so I've been forced to learn a lot about how PMs fail. A side effect that I don't see much in the discussion of aero testing is that I've had to come up with a way to assess the accuracy and precision of drag parameters and to figure out whether errors are a result of poor experimental technique, poor experimental control, or poor performing power and speed data.