500m World Best Score?

[Nosmo]

The pm3 doesn't show the average watts while rowing, but shows it on the log card afterwards? Okay, thanks. There are probably a couple dozen features on the pm2 I like better, and two features on the pm3 that I like.

Actually the pm3 remembers the last (I think) 10 workouts without using the log card including splits. With the log card it remembers many more.

The mathematical calculation of pace from pm1 watts is precise. For a given wattage, the pace is exactly the same every time.

By this I assume you mean instentaneous power and pace. Correct? OR do you mean something else entirely?

The pace converted internally from the pm1 watts should be the same as the pace calculated mathematically from the watts. But it isn't.

What do you mean here? I think you must mean that the average power and average pace on the PM1 for a given interval are not related by the mathematical formula.
Correct?

When I did the same tests on the pm2 monitor, the mathematical calculation came out exactly to the same pace that was internally converted on the monitor.

What you mean here is that the average pace for a piece and the average watts on the pm2 are related by the mathematical formula.
Correct?


FInally did you understand my explaination of the "time average" in the previous post?

[johnlvs2run]

The mathematical calculation of pace from pm1 watts is precise. For a given wattage, the pace is exactly the same every time.

By this I assume you mean instentaneous power and pace. Correct? OR do you mean something else entirely?

I meant the mathematical formula calculates the final/current average time/pace from the watts.

Regarding the pm1 monitor, the (1) pm1 watts and (2) mathematical calculation from watts to current/final average pace/time, are always correct.

The instantaneous pace appears to be directly calculated from the instantaneous watts, and not affected by the internal rounding effect. Thus the instantaneous pace is always correct.

The internal conversion of watts to current and final average pace/time is subject to the variability and inaccuracy of the internal "rounding up" feature, and thus is not ever correct except by rare chance.

The pace converted internally from the pm1 watts should be the same as the pace calculated mathematically from the watts. But it isn't.

What do you mean here? I think you must mean that the average power and average reading on the PM1 for a given interval does not agree with the mathematical formula. Correct?

Right. They have never matched nor agreed on the pm1. They have always matched and agreed on the pm2+.

When I did the same tests on the pm2 monitor, the mathematical calculation came out exactly to the same pace that was internally converted on the monitor.

What you mean here is that the average pace for a piece and the average watts on the pm2 are related by the mathematical formula. Correct?

Yes, the relationship is exact. Every time I checked them on the pm2+ monitor the average watts came out exactly to the average/final pace/time. The mathematical calculation came out the same as the internal conversion.

FInally did you understand my explaination of the "time average" in the previous post?

Yes, thank you.

[rlholtz]

I made a boo-boo when comparing PM1 to PM2 by plugging in watts in the calculator. 1:45 on PM1 yielded a predicted 1:45.5+ when entering watts, not an equivalent time.

So... ~0.6 slower/500 on PM2.

Today I rowed two 2 K's on my B, first at 1:54.4 pace, second at 1:53.6. Interstingly, wattage predicts 0.9 and 0.6 seconds faster respectively on the PM2.

I am beginning to believe in the PM1's variability.

[Nosmo]

I made a boo-boo when comparing PM1 to PM2 by plugging in watts in the calculator. 1:45 on PM1 yielded a predicted 1:45.5+ when entering watts, not an equivalent time.

So... ~0.6 slower/500 on PM2.

Today I rowed two 2 K's on my B, first at 1:54.4 pace, second at 1:53.6. Interstingly, wattage predicts 0.9 and 0.6 seconds faster respectively on the PM2.

I am beginning to believe in the PM1's variability.

I am not questioning PM1's variability, I am questioning what it means. If the PM1 does a time averaged wattage, (or stroke average wattage) then there will not be a one-to-one correspondance between average speed and average power. They are merely measuring two different things. I always assumed the PM1 did a time average for wattage. There is nothing wrong with doing it that way, except perhaps it confuses people.

Would someone please do the experiment from Paul's example on a PM1. Row for 300W for a few minutes, then row at 100W for the same time. I'd be willing to bet that the average power reported is very close to 200W. Try to do this at a constant stroke rating--or at the very least keep the rating constant for a given power.

If the average power is 200W (rather then 182W) in the above experiment, then one cannot assume there is a problem with the PM1! This only means that the reported power changed from a time average power in the PM1 to a "speed equivelent average power" in the PM2/3/4. It does not mean that the PM1 and PM2/3/4 will report different times for the same effort!

[johnlvs2run]

I am not questioning PM1's variability, I am questioning what it means.

It means the pm1 internal conversion from watts to pace is not accurate.

I always assumed the PM1 did a time average for wattage. There is nothing wrong with doing it that way, except perhaps it confuses people.

I don't know how the internal workings of the pm1 were set up. I suppose it could be right and still not be accurate. However, I find that not being so useful, as compared to the pm2 where the internal conversion and a mathematical calculation are the same.

The pm2 unfortunately doesn't work on the model D, so I'm not using it any more. And I've not used the pm1 for several years.

All of the pieces that I tested were at a variable pace. Usually I start more slowly and pick up the pace to the finish. The results were the same as previously stated, the pm2 being accurate and the pm1 being inconsistent and not accurate.

[PaulS]

There has been a lot of words during this discussion, and many of them simple do not make any sense, or are convoluted enough that trying to decipher them would be a waste of time.

In my experiments, I ran a PM1 and PM2 simultaneously off sensors getting data from the same flywheel (on a model B it's very easy to install a second sensor). I did multiple 500m Pieces, at a wide range of paces, and recorded the total time for each PM. I rowed them at paces that could be done at relatively steady state, but of course there were minor variations throughout each, but the final times are the Avg Pace for the 500m. I don't recall there being a genuine "Avg Watts" on the PM1 that keeps getting discussed, perhaps I can dig out an old PM1 and see if there even is such a metric, though it makes no difference, as I was comparing times, which we all know are a derived figure based on a virtual boat speed converted directly from the Power figure.

After plotting the respective times, and knowing the conversion formula, I noticed that the differences where not linear. I.e. The PM1 times were slower for slow paces, and faster for Fast paces, the point at which they were virtually the same was at a 1:55.0 500m piece, not hard to replicate and I did so several times. I then looked for a formula that would modify the standard Watts to Pace calculation so that the observed paces would match what the calculation would yield.

The Table that was linked to earlier is generated by the use of the C2 standard formula and the standard formula with the variable offset factor that fit the observed times best.

The problem with the PM1 was that it gave different Pace values for a given Watt calculation.

384.x watts = 1:35.x (PM1) 1:37.x (PM2)
230.x watts = 1:55.x (PM1) 1:55.x (PM2)
188.x watts = 2:04.x (PM1) 2:03.x (PM2)

I put the "x" to signify that there are fractional differences, but quite small for the numbers that I chose.

Cheers.

[Nosmo]

I am not questioning PM1's variability, I am questioning what it means.

It means the pm1 internal conversion from watts to pace is not accurate.

I always assumed the PM1 did a time average for wattage. There is nothing wrong with doing it that way, except perhaps it confuses people.

I don't know how the internal workings of the pm1 were set up. I suppose it could be right and still not be accurate. However, I find that not being so useful, as compared to the pm2 where the internal conversion and a mathematical calculation are the same.

The pm2 unfortunately doesn't work on the model D, so I'm not using it any more. And I've not used the pm1 for several years.

All of the pieces that I tested were at a variable pace. Usually I start more slowly and pick up the pace to the finish. The results were the same as previously stated, the pm2 being accurate and the pm1 being inconsistent and not accurate.

John,
Sorry to be such a hard ass, but you still have provided no evidence that the PM1 does the calculation of pace with any thing but small rounding errors. What you have demonstrated is that that it does not do the same thing that the PM2 does, and that it does not do what you think it should.

If the PM1 displays a stroke averaged or time averaged power then there is no problem having average watts and average pace disagree. It is expected. It is theoretically impossiple to use a mathematical formula to convert from average power to average pace. There simply is not enough information. Simply put the cube of the means is not the mean of the cubes.
Just to be redundent: Time average watts and average pace are two different quantities and one cannot convert from one to the other by a mathematical formula.
Paul did the test of the PM1 and PM2 and found small differences between the two. You are claiming big differences, which is easily explained as a time average of watts.

You don't find the display of average watts useful on the PM1. Fine, but that does not mean it is wrong or not accurate. OR even that it is not useful for others.
I'm done arguing this point. Until some tests the PM1 to show that it does not do time or stroke averaged watts I have nothing more to say.

[PaulS]

Just to confirm the above:
5 minutes @ 100watts = 988m
5 minutes @ 300watts = 1425m
Total 2413m in 10 minutes = 181.7 watts Avg

10 minutes @ 200watts = 2490m

Paul, Any idea what the the PM1 would produce in these situations?
My quess is that that the PM1 would say either 200W for both cases, or in the first case would read something based on the number of strokes in each segment.

No, the PM1 has such an undetailed recall capability that I have no idea what the "Watts" that comes up when changing units after a piece has been completed is truly representing. The idea that it could be a weighted in some manner is interesting, or it could be that it simply represents the last stroke pulled, which could cause very large variations if it were assumed to be an average of any sort.

That I pursued the experiment I did, had to do with discussions with c2jonw where I confirmed that the way in which watts was being calculated was the same code as being used in the later PM's. The defects in pace conversion had to do with using a look-up table rather than a live calculation from the raw watt number. There is also the potential for some DF calculations to throw things off a little because it also was updated every 17 strokes instead of each individual stroke.

Once the DF has been determined, the PM may as well be an analog speedometer that gives a certain distance credit per flywheel revolution. The genius of the electronic PM's was that as DF changed due to environmental variables, the power input requirements for a give pace would remain the same by accounting for those variables with the DF.

Nosmo, Just to be clear, I found a variable difference between the PM1 and PM2, they reached parity at a 1:55 pace, but the further from that pace the larger the discrepancy. Basically the "2.8" exponent in the conversion formula changes by the sum of a constant for each second in pace. I have no idea how that particular error was introduced into the system, but it was far to consistent to simply be a rounding error, IMO. Could have been something specific to the microprocessor that was in use in the PM1, but that's just a guess.

[Nosmo]

John,
First of all let me apologize for being rather cranky in my response yesterday. I was cranky about something else that had nothing to do with the forum. I hope you at least understand my point even if you disagree with it. If not I will be willing to explain it hopefully more clearly.

Paul,
One could set the display to watts on the PM1. The main reading would be instantaneous watts for each stroke. Below that, there was a smaller watt reading that varied slowly. The smaller number is what I think of as average watts. I have always assumed it was a simple time average.
Edit: What I mean my time average, is the most straight forward definition of average. The PM2/3/4 actually do a "weighed" average--if they didn't, one could not convert between watts and average pace.

Years ago when there was only a model A, I recall reading in something from Concept II that the power was proportional to the speed raised to the 2.75. They claimed this was a empirical fit of measured data. (There is some chance I am wrong about this since it is from memory, but I am fairly certain it is true)
If I understand what you say, your measurements show the PM1 uses the speed raised to the 2.8, and as we know the PM2/3/4 uses speed cubed.
The engineering books will say for a given geometry, that the wind resistance (for turbulent flow) varies with the velocity cubed, but they also will have a coefficient of drag in the equation which has a slow variation with speed (or more precisely Reynolds number which is a non-dimensional quantity proportional to speed, some reference length related to the geometry of the system, and inversely proportional to the viscosity of air). Since the coefficient of drag varies with speed, one could rewrite the equation with a constant coefficient of drag and a variable exponent, which would be less then 3.
For example if one takes two cylinders, and spins the inner one, while keeping the outer stationary, at low speeds the power required will be proportional to velocity. Then there will be several transitions to various fluid states and the power required will suddenly jump. As one increases the speed, the flow becomes chaotic then turbulent. Once it becomes turbulent the power required to spin the inner cylinder will vary as speed raised to about 2.5, as the speed increases the exponent will slowly increase and asymtopically approach 3. (At Reynolds numbers of about one million, the exponent will be about 2.92. I actually spent a couple of years of my life measuring this.)

What this means is that the exponent is not constant. I would expect the range of speeds seen on the concept II ergometer is small enough to be considered constant, but I would be very surprised if it was exactly three.

What is sounds like to me is that Concept II changed their formula between the PM1 and PM2. Quite possibly the exponent on the model B is different from Models C and D. (Does the Model B and C use different flywheels? The B and D are certainly different).
Concept II appears to me to really know what they are doing. They probably decided to change things between the PM1 and PM2 and that the differences were small enough not to matter. IF the flywheels changed then things may have been more consitant by changing the formula (the look up table is just a precalculated formula). They probably decided to use the exponent of 3 (since they are doing calculations rather then a lookup, it may be much simplier).
What is important is that all the machines are consistent and repeatable. The are some necessary errors in the erg when measuring power (for example the force of the shock cord), so consistency between runs and between machines is much more important absolute accuracy.
All of this is a long way of saying, the difference between the monitors you report may have been intentional and not a mistake.

[PaulS]

Nosmo,

Mod B, C, D, E flywheels all have the same Moment of Inertia, the magentics on the B and C were the same (3 pulses per rev) but the D and E use something a bit different for the power generation and have 6 pulses/rev.

The PM1 "error" could well have been an "on purpose", but it was not relayed that way to me when it was discussed. In fact, the reason I waas left to come up with a way to calculate the differences was that no actual formula seemed to exist. Though we did have a formula for avg watts for the Model A, that coincided quite well with todays formula that converts pace to watts or vice versa. It just turned out that Pace was Time/Mile (on the Analog Speedometer/ODO). For all the fuss and 25 years later it was nice to see that they did a rather bang on job of what they started out to do. Though the Mod A mile turned out to be just slightly harder than the PM2 (and later) 500m. IOW, the physics managed to hold up to several decimal places. One issue is that the Mod A flywheel has a DF in the 2,000 range, and all PM's other than ones set up specifically to allow for that hit an error condition and display paces for watts that are fraction of what is really being input.

[johnlvs2run]

Hi Nosmo,

I guess the pm1 rounding errors could be considered small but I didn't like them at all. For example when the mathematical calculation of pace from watts would give me a time of 19:55 for the 5k and the internal (actual) conversion gave me a time of 20:23, then that is quite significant as far as I am concerned.

I finally clicked a 19:57.4 with the pm1 then 5 days later 39:55.4 with the pm2 - calculation from watts matching exactly - then my first 5k with the pm2+ 7 days after that in 19:35.1 - again with the calculation from watts matched up exactly with the time from the internal conversion.

My splits for any of these 5k's or other single events were not exactly even all the way. I'm hardly even bothered to look them up but on the 10k the 1/2's were 20:07.0 and 19:48.5. On the last 5k the 2k splits were 7:54.4, 7:50.0 and the last 1k in 3:50.7, not exactly even pace but yet the mathematical calculation matched exactly with the internal conversion to the final time and the pace.

Those never matched even once wiith the pm1. Basically I agree with you and think you are right on when you said the difference appears to be the pm1 rounding effect by which the internal conversion was adjusted. I can buy that if the internal conversion was ever accurate in the first place. Perhaps it was, as the instantaneous display always looked exactly correct. The average pace never did.

It is theoretically impossiple to use a mathematical formula to convert from average power to average pace.

That may or may not be true. If I look at my calculator 100 times and I can see that it's black, but someone writes a long explanation of plugging sensors on the calculator to show that it's white, but still every time I observe the calculator it is black, then I have to still conclude that based on my numerous observations of the calculator, it is black.

In fact I am looking at the calculator right now and it's black. In fact I still have the pm1 monitor, and it's black. So if someone says that well before 12:00 it's black but after 12:00 it's white, but I have looked at my calculator many times before and after 12:00 and I still see it is still black regardless of what time it is, then I have to still conclude that it's black. Perhaps there was some kind of a reflection in the information that came from that sensor that gave someone else some kind of different results with MY calculator. I don't know. But still, every time that I look at my calculator, and it is MY calculator after all, it is black.

If someone else finds something else then honestly that is fine with me. I don't care. Anyone else is welcome to come up with any kind of explanation and try to prove it as they wish. But even so, it doesn't matter what they do, or say, my calculator is still black. Will it be white some day? Not likely. I could paint it white and then it would be white, but I'm not going to do that. I'm not trying to be facetious or anything, but just to address the issues at hand, the questions you have asked and some of the suggested illusions posed by others. I hope this helps and I do appreciate your interest in the accuracy of the pm1 and pm2 monitors.

Cheers and all the best with your rowing.

[PaulS]

The Abyss appears deep,
And black.

[Nosmo]

Paul,
Yes I understand that the moments of inertia are the same. My point being that if the geometry of the fly wheel changes (i.e the "fins" used to create drag) then the exponent in the watts calculation may well change. This is a fluid dynamics problem which are very complicated. While the "error" may not have been on purpose it may have been forced upon them by the change in design. Just a thought.

[Nosmo]

Hi Nosmo,

I guess the pm1 rounding errors could be considered small but I didn't like them at all. For example when the mathematical calculation of pace from watts would give me a time of 19:55 for the 5k and the internal (actual) conversion gave me a time of 20:23, then that is quite significant as far as I am concerned.

You seem to have misunderstood me. I have never claimed that this discrepancy is due to rounding errors. See below.

Those never matched even once wiith the pm1. Perhaps it was, as the instantaneous display always looked exactly correct. The average pace never did.

I understood that the first time you said so. In fact I've observed the same thing, I just never expected them to agree. No surprise here. They should not match unless you rowed each piece with exactly even splits. And yes the instantaneous display should always look exactly correct.
I am not disputing your observations of the behavior of the PM1 at all. In fact I never did. See below.

It is theoretically impossible to use a mathematical formula to convert from average power to average pace.

That may or may not be true. ....

So, one last time (didn't I say that before?):

I you understand the following, you will see that it is true.

If I rowed 5 minutes at 300W and 5 minutes at 100W, then my what is my average power. Hint: 200W

If I rowed 10 minutes at 200W then my what is my average power. Hint: 200W

If I rowed 5 minutes at 400W and stopped for 6 minutes then my what is my average power over the ten minutes. Hint: 200W

If I rowed 5 minutes at 150W and 5 minutes at 250W, then my what is my average power. Hint: 200W

In every case the average power is 200W, but the distance traveled will be different. If I told you only that I averaged power is 200W could you in tell me how far I rowed? Hint: no. You could not distinguish between the above examples. It is impossible in theory to do so. The PM1 is telling you that the average power is 200W.

The PM2 is not telling you your average power, its telling you the cube of the average of the cube root or your power. Hence you can convert from power to average pace on the PM2 but not on the PM1.

If the mathematical calculation of pace from watts gives you a time of 19:55 for the 5k, but the monitor reads 20:23 for the piece, that is an indication of how steadily you rowed the 5K. Not that the PM1 was wrong.

The difference here is the major reason that rowing at very close to a constant pace is the best strategy for breaking records.

Hopefully the calculator, uhmm..., I mean Abyss is a little less black.

[johnlvs2run]

Nosmo,

It sounds like you and Paul are saying is that the pm1 is method is correct, or better than the pm2 method.

That is fine I suppose.

I much prefer the pm2 to the pm1 or any of the other monitors.

Regarding the pm1 rounding - via this discussion with you and Paul, I am getting that the internal conversion of the pm1 is supposed to be accurate. I think Paul said he got from C2 that the internal formula is the same in all of the monitors.

However, from that they rounded up the result (they called it truncating). That rounding is apparently what threws the wrench in the works and made the pm1 time/pace so strange as regards the average watts, inconsistent and variable - but not so strange if you feel that is the way to do things of course. I guess you didn't say this but I am.