Tom Anhalt said:
Could you define "a slope not significantly different from unity" a little better?
Ask, and ye shall receive...
Here are the raw data from the first Velodyne vs. SRM comparison I did back in 1997 (which Bruce Sargeant posted on the web back in 1998):
Velodyne power (W) SRM power (W)
50 54
100 107
150 159
200 207
250 257
300 305
350 355
slope = 0.9979 (95% CL = 0.9798, 1.0158)
intercept = 6.7 (95% CL = 2.7, 10.7)
R^2 = 0.9998
So, as you might expect, power measured at the crank by the SRM was higher than power measured (set) at the rear wheel by the Velodyne, with the difference being reflected by a higher intercept, with a slope not different from unity.
Here are the raw data from the first Velodyne vs. PowerTap comparison that I did (which I posted to the web back in 1999):
Velodyne (W) PowerTap (W)
50 51
100 101
150 150
200 197
250 245
300 292
350 344
400 396
slope = 0.9771 (95% CL = 0.9617, 0.9926)
intercept = 2.1 (95% CL = -1.8, 6.0)
R^2 = 0.9998
This time, with power measured at the rear wheel using the PowerTap, the intercept barely achieved significance (P=0.03), with the difference in the slope presumably being due to the "true" difference between the devices.
Skipping over the numerous other
formal cross-comparisons that I've done, here are the data from the most recent head-to-head comparison that I've done between the PowerTap and SRM (last spring):
PowerTap (W) SRM (W)
54 58
110 114
157 163
211 214
257 265
308 315
Slope = 1.0133 (95% CL = 0.9910, 1.0356)
Intercept = 2.9 (95% CL = -1.6, 7.4)
R^2 = 0.9998
This time, neither the slope nor the intercept were significantly different from one and zero, respectively, but obviously the difference is primarily reflected in the intercept, not the slope.
Unfortunately, I can't tell you the exact state of the chain for any of the above, although I can say that 1) I replace my chains yearly or when wear reaches 0.5%, whichever comes first, and 2) all data were collected w/o shifting gears (and thus are not confounded by chainline issues...including the fact that the sensitivity of the PowerTap and SRM vary with chainline).
The only data set that I do have with a chain that I know was quite new (<100 mi use) come from my track crankset (average of three trials on different days during the summer of '04):
Velodyne power (W) SRM power (W)
50 58
100 109
150 158
200 206
250 259
300 311
350 360
Slope = 1.0078 (95% CL = 0.9934, 1.0223)
Intercept = 7.1 (95% CL = 3.9, 10.1)
R^2 = 0.9998
Obviously, it would be better to compare the SRM against the PowerTap, but the latter won't fit a track frame, so the Velodyne is the only option. In any case, these data are
very similar to what I got back in 1997 (using a different SRM and a different Velodyne).
The bottom-line conclusion sthat I draw from these data are:
1) all three devices are extremely linear;
2) taking into consideration power loss in the drivetrain, all three are quite accurate; and
3) when data are collected in this manner are subjected to linear regression analysis, power losses in the drivetrain are primarily reflected in a different intercept, and not a different slope.
Now let's turn to the data from the Ergomo Pro that I tested:
10/14/2005
SRM power (W) Ergomo power (W)
61 84
111 132
160 170
210 218
258 262
306 298
10/15/2005
SRM power (W) Ergomo power (W)
61 95
111 143
161 191
210 212
259 257
309 312
258 260
208 229
158 164
109 128
59 89
Clearly, the response of the Ergomo is non-linear (as reported by Peter Wright), with the Ergomo greatly overestimating power at lower power outputs, but underestimating power at higher power outputs (also as reported by Peter). Having observed this, I decided to test whether it was due to an imbalance in terms of how I apply power, and did several tests using only my left leg - representative data are shown below:
SRM power (W) 0.5 x Ergomo power (W)
69 81
108 122
150 166
If you plot these data along with the other numbers above, you'll find that they are quite consistent, i.e., the non-linearity of the Ergomo was apparent regardless of whether I pedaled with one leg or two, thus ruling out a R/L imbalance as the primary cause.
One final comment: as you might guess from the date, all of the Ergomo data above were collected before they modified their installation instructions (in fact, data such as those above are likely what led to their modification). Specifically, while the b.b. was oriented such that the internal circuit board was close to vertical and everything was tightened to specifications, I did not face the b.b. shell or chase the threads. Now that this is a stated requirement, I've been tempted to do some more experiments, but have given away the Ergomo, and don't have the heart to ask for it back (nor do I really have the time these days for such things, as there are bigger fish to fry, so to speak). Moreover, the fact that Peter has obtained similar results
despite (presumably) strictly adhering to the new installation instructions leads me to believe that it probably wouldn't make a difference.
Bottom line: I don't think discrepancies between an Ergomo and a PowerTap can be blamed on drivetrain friction (esp. since similar discrepancies have been observed in comparison to an SRM).