500m World Best Score?

[Nosmo]

John, are your measurements done with average watts?

Yes, for individual pieces. I didn't bother to do this for reps.

You both seem to agree that the watts were correct.

Yes we appear to agree on this.

The pm1 didn't have any firmware. Probably the only way the difference can be found is to calculate the watts mathematically, to compare each individual result with the internal conversion of each individual piece, and then to keep doing this a significant number of times. For there to be no difference, then the two results must be identical indefinitely. However I found them to not be the same even once.

The PM1 did have firmware, i.e. it was most likely burned in at the factory (i.e. write once memory or was put in ROM). It was not user upgradeable. So it is possible that the firmware did change, i.e. that C2 changed the program to correct some mistake.

Again, if you are using average watts, which I think you must be, then I would expect the total time for a given distance to change from piece to piece even if the average power is the same.
In math speak: speed is proportional to the cubed root of power. BUT... the average of the cube roots is not the cube root of the average.

[johnlvs2run]

I must have had the lastest version of the pm1, as mine was from right before the model C and the pm2 came out from concept2.

I believe the opposite of the cube root is the cube. In any case the mathematical calculation never came out right on with the pm1, not close, not even once, and it came out right on with the pm2+ every time.

[Nosmo]

I must have had the lastest version of the pm1, as mine was from right before the model C and the pm2 came out from concept2.

I believe the opposite of the cube root is the cube. In any case the mathematical calculation never came out right on with the pm1, not close, not even once, and it came out right on with the pm2+ every time.

Yes and the mean of cube is also not the cube of the mean.
Well perhaps the averages watts are calculated differently (time weighted vs distance weighted?--have to think about this).

I do believe both you and Paul, I'm just trying to come up with a plausable explaination of why your results are so different.
I'm going to see if I can find my an old training log and see what I come up with with the PM1.

[yehster]

Well perhaps the averages watts are calculated differently (time weighted vs distance weighted?--have to think about this).

I don't think it would make sense to calculate/use distance weighted power for a couple reasons. First fundamentally, since power is energy / unit time it's definitely easier to compute a time weighted average. Just measure total energy and divide by time.
Second, isn't "distance" on the erg a totally artificial number. I doubt that a reasonable engineer would use a computed value, that is in fact dependent on the value(instantaneous power) you are trying to average. Just seems like extra complexity that can be avoided and is likely to get you in trouble. Especially given that the PM1 has less computing power, it really seems unlikely that an engineer would do this.

Also, if you rowed for 5 minutes at 100 watts, then 5 minutes at 300 watts, and compared that to rowing 10 minutes at 200 watts, you get a much shorter distance the first way, than the second way, even though your total energy input to the erg and average powers are the same. I guess my statement here is really just a restatement of "the mean of the cube is not necessarily equal to the the cube of the mean".

[rlholtz]

Gentlemen:

After all this debate I did an experiment; couldn't help myself.

I set my PM 1 to record time elapsed to row 500 meters... Then I set out to row at an average pace of...1:45. The result, I figured, would tell me if I had wounds to lick, since I had thought a 7:02 2K on my machine was indeed a 7:02. I plugged in the total watts on the calculator found on the website Mr. Rupp graciously proffered and compared the split it revealed (1:45.17) to the split my PM1 spat out (1:44.95). Perhaps my wounds are meerly scratches.

Comments?

[Nosmo]

Gentlemen:

After all this debate I did an experiment; couldn't help myself.

I set my PM 1 to record time elapsed to row 500 meters... Then I set out to row at an average pace of...1:45. The result, I figured, would tell me if I had wounds to lick, since I had thought a 7:02 2K on my machine was indeed a 7:02. I plugged in the total watts on the calculator found on the website Mr. Rupp graciously proffered and compared the split it revealed (1:45.17) to the split my PM1 spat out (1:44.95). Perhaps my wounds are meerly scratches.

Comments?

No wonds at all. SOunds like rounding error.

[Nosmo]

Well perhaps the averages watts are calculated differently (time weighted vs distance weighted?--have to think about this).

I don't think it would make sense to calculate/use distance weighted power for a couple reasons. First fundamentally, since power is energy / unit time it's definitely easier to compute a time weighted average. Just measure total energy and divide by time.
Second, isn't "distance" on the erg a totally artificial number. I doubt that a reasonable engineer would use a computed value, that is in fact dependent on the value(instantaneous power) you are trying to average. Just seems like extra complexity that can be avoided and is likely to get you in trouble. Especially given that the PM1 has less computing power, it really seems unlikely that an engineer would do this.

Also, if you rowed for 5 minutes at 100 watts, then 5 minutes at 300 watts, and compared that to rowing 10 minutes at 200 watts, you get a much shorter distance the first way, than the second way, even though your total energy input to the erg and average powers are the same. I guess my statement here is really just a restatement of "the mean of the cube is not necessarily equal to the the cube of the mean".

OK, but Looking through my log books I came accross a 70' work out wiht highly variable splits (between 2:39 and 201) on my model D. Average power 160W calculated average pace 209.9. PM3 says averave time in 209.9. So average power should produce the average pace with such variable splits. However it does, just like john reports.

EDIT: I meant: So average power should NOT produce the average pace with such variable splits IF THE POWER WAS TIME AVERAGED. end edit

ON a model B, I find 2 warm ups at 2500m. 10:18.6 at 195.5W, and 10:10.8 at 203.1W. Using the formula for Wattage these times come out to 10:07.1, and 9:59.5.

Tentitive conculsion (need to varify with more data): The times will be very similar between PM1 and the PM3, as will the instentaneous power however the reported average power will be different between them.

The model B average power is a time averaged and cannot be used to find averaged pace unless the piece is run steadily. The model D is a weighted average and the average power will calculate the average pace. This is exactly what John says he observed.
Since Paul actually did a direct comparison between the PM1 and PM3 (or was it PM2?), then I do believe him that there is a small difference in speed between the two.

Again I need to check more data. I think this makes sense, even if it is counter intuitive as Yehster explains above. Even though distance is an artifical number on the erg, this it is what Concept II and every one who races cares about!

[PaulS]

Well perhaps the averages watts are calculated differently (time weighted vs distance weighted?--have to think about this).

I don't think it would make sense to calculate/use distance weighted power for a couple reasons. First fundamentally, since power is energy / unit time it's definitely easier to compute a time weighted average. Just measure total energy and divide by time.
Second, isn't "distance" on the erg a totally artificial number. I doubt that a reasonable engineer would use a computed value, that is in fact dependent on the value(instantaneous power) you are trying to average. Just seems like extra complexity that can be avoided and is likely to get you in trouble. Especially given that the PM1 has less computing power, it really seems unlikely that an engineer would do this.

Also, if you rowed for 5 minutes at 100 watts, then 5 minutes at 300 watts, and compared that to rowing 10 minutes at 200 watts, you get a much shorter distance the first way, than the second way, even though your total energy input to the erg and average powers are the same. I guess my statement here is really just a restatement of "the mean of the cube is not necessarily equal to the the cube of the mean".

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

Another way to look at it:
1000m @ 100watts = 5:03.6
1000m @ 300watts = 3:30.5
Total Time = 8:34.1 for 2k = 164.9 watts Avg

2000m @ 200watts = 8:02.0

[johnlvs2run]

Tentitive conculsion (need to varify with more data): The times will be very similar between PM1 and the PM3, as will the instentaneous power however the reported average power will be different between them.

The (1) average watts and (2) instantaneous display on the pm1 appear to be accurate, consistent, and comparable with the pm2 monitors. The pm2's are by far the most accurate of the monitors.

Interestingly, it looks like the pm3/4's don't have average watts.

The internal conversion from watts to (3) times and average pace on the pm1 is where the inaccuracy and inconsistency occurs. As the issue is the pm1 internal conversion from watts to pace/time, the times and average pace on the pm1 are not accurate nor consistent, and are not comparable to the pm2/4.

[yehster]

If one did a 100Wx5 min/300Wx5 min piece as I proposed, what does the PM report as the average wattage? I'm guessing that it'll report the 181.7 which Paul computed, and not the 200 Watts which is the time averaged power.

Again I need to check more data. I think this makes sense, even if it is counter intuitive as Yehster explains above. Even though distance is an artifical number on the erg, this it is what Concept II and every one who races cares about!

I guess it's not completely counterintuitive. You are correct that distance and time are what we care about, and so the monitor must keep track of that over the duration of the entire erg piece. It only needs the power/energy input on a per stroke basis. So in the interest of simplifying the system it reports the average power based on distance/time rather than "integrating" power dt.

Although this also makes me wonder about the calories burned number (which is inaccurate anyway but the calories burned "ticks" up as your piece progresses. Does the erg add up the energy it computes each stroke? Or is it doing a computation based on distance/time?

[Nosmo]

....
Although this also makes me wonder about the calories burned number (which is inaccurate anyway but the calories burned "ticks" up as your piece progresses. Does the erg add up the energy it computes each stroke? Or is it doing a computation based on distance/time?

The calculation for calories burned is so ridiculous that I wouldn't even bother thinking about it.

[Nosmo]

The (1) average watts and (2) instantaneous display on the pm1 appear to be accurate, consistent, and comparable with the pm2 and pm3/4 monitors. The pm2 is by far the most accurate of the monitors.

Interestingly, it looks like the pm3/4's don't have average watts.

First you say average watts are the same with pm1 and the others, then you say the pm3/4 does not have average watts. So I'm confused by what you mean. Since the pm3 does give a wattagefor every split and every piece (stored in memory), I've always assumed that was average wattage for the piece.

Why do you say the pm2 is by far the most accurate of the monitors? Just curious

The internal conversion from watts to (3) times and average pace on the pm1 is where the inaccuracy and inconsistency occurs. As the issue is the pm1 internal conversion from watts to pace/time, the times and average pace on the pm1 are not accurate nor consistent, and are not comparable to the pm2/4.

Well I believe there are inaccuracies in the PM1. However I don't see how it can be inconsistant aside from some rounding errors.
Your reasoning and evidence so far suggests that there is merely a difference in how the monitors calculate average power. You may be right but it does not seem to be the most likely explaination.

With the PM1, I would like to see multiple rows of say 500m at as constant a power as possible and see what the times are. Then row the same multiple times at a variable pace but trying to get the same average power (or alternatively same final time). My guess would be that there would be little variation in time for the first case, but much larger variations in time (or alternatively power) for the second.
This is what one would expect if the PM1 used a time average (or stoke average--another possibility which would have been simple to program on the primitive chip in the PM1).

On the PM3 it seams that there is a one to one correspondence between pace and power regardless of how the piece is rowed. This means that on the PM3, the average power is not a time average.

Neither method is "incorect". They are just different and there are arguments for both methods.

[johnlvs2run]

you say average watts are the same with pm1 and the others, then you say the pm3/4 does not have average watts.

My only comparisons have been with the pm1 and pm2+. I haven't done any comparisons with the pm1 to the pm3 or 4 and will amend that part of my previous message for clarity. I have the pm3 now. I am selling my model B that has a pm2+.

the pm3 does give a wattage for every split and every piece (stored in memory), I've always assumed that was average wattage for the piece.

Oh I see. 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.

Why do you say the pm2 is by far the most accurate of the monitors?

The pm3/4's appear to round all the times in some fashion, and also there is some delay with the monitor getting started. During reps the monitor consistently "loses" 1 to 2 seconds per rep. I never had any problem with the pm2+ but the pm3 is quite funky.

Your reasoning and evidence so far suggests that there is merely a difference in how the monitors calculate average power.

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

The pace converted internally from the pm1 watts should be the same as the pace calculated mathematically from the watts. But it isn't. I compared these quite a few times and they didn't match even once. Because the mathematical calculation is accurate 100 percent of the time, this means that the pm1 internal conversion is not accurate. I found that the pm1 internal conversion did not match the mathematical calculation even once.

Also, the difference was not consistent. There is a variation in the difference. As example, one time the conversion might be close, another off by 1s per 500m, another time off by 2 to 3s per 500m and so on. I agree with you that the pm1 internal conversion is likely off due to the "rounding up" feature of the monitor, which is why the difference in accuracy with the pm1 internal conversation of watts to pace is inconsistent and variable. This is also why the instantaneous display on the pm1 is accurate, as it is not subject to the rounding.

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.

Thus the pm2 is accurate. The pm1 is not accurate and is not even consistently inaccurate to the same proportion every time, i.e. it has an inconsistent variability. The pm3/4 are not as accurate as the pm2 but are more accurate than the pm1.

This means that on the PM3, the average power is not a time average.

I'm not sure what this means. Please elaborate.

[Nosmo]

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.

[Nosmo]

This means that on the PM3, the average power is not a time average.

I'm not sure what this means. Please elaborate.

Look at Paul's first example above:

5 minutes @ 100watts = 988m
5 minutes @ 300watts = 1425m
Total 2413m in 10 minutes = 181.7 watts Avg

If one doess 5 minutes at 100 watts and 5 minutes at 300 watts then the time average power is 200 watts by definition.

However the PM 3 reads 181.7 Watts. Which is:
((100^(1/3) + 300^(1/3)) / 2) ^ 3
i.e. the cube of the average of the cube roots of power. Or one could say the "power based on the average speed." or more accurately the power one would have produced if one rowed at a constant speed.

I'll respond to your other comments later. Probably tomorrow.