Recently, there has been much discussion on the Ciclosport HAC4's power measuring capability. The HAC4 does not use a power-measuring pickup as the SRM, Power Tap, or Polar power systems do; rather, it estimates wattage based on well-understood calculations involving a rider's weight, speed, and the altitude change. The HAC4's manual states:
"The displayed output measurements are made in consideration of average friction, good road conditions, and the set weight [of rider plus bike and equipment]. The output can be measured more accurately when ascending (accuracy + or - 20W, if the wind is strong then the measurements may vary more from the actual output). If the tour is flat, then the average output is displayed (accuracy + or - 40W). During descents power -> 0."
Despite this, the question persists: how does a device like the Ciclosport HAC4 compare for power accuracy with the other devices? Never having seen either a HAC4 or the data from one makes me eminently qualified to address this. As far as I know no one has yet (January 2003) published a direct comparison of a HAC4 with any of these power meters, in part because analyzing HAC4 data files is not trivial. Nonetheless, by knowing how the HAC4 calculates power it is possible to make guesses about its accuracy.
The Achilles' heel of speed-and-altimeter devices is that they do not measure either the rider's aerodynamic drag characteristics (CdA) or the windspeed. Therefore, one might expect them to do well for steep hillclimbs (since the speed is low and thus the aero drag component of power is also low), less well when the road is flat or rolling (where much of one's power is spent on overcoming aero drag and little on overcoming gravity), and poorly on flat roads when the wind is blowing and other conditions are variable. However, a Polar S710 happens to collect exactly the necessary speed and altitude data and, if it has the optional power module, wattage data against which to compare. If only we had a file somewhere with those data... hmmm. By golly, I believe several such files exist. In particular, the Rosetta Stone data were collected during the course of a rolling, 80km ride, and are discussed here. As it happens we know that the day on which this ride took place was not particularly windy. As such, this type of ride should be a not too-tough, not too-easy test for an indirect estimation device such as the HAC4.
The general approach will be to calculate the power that one could have seen based on the speed and altitude data collected by the S710 and treat it as if it came from a HAC4. Since the power equations are well-known, the biggest remaining problem is that we lack an estimate of the internal value for aerodynamic drag that the HAC4 actually uses. I therefore chose a value for aero drag that makes the calculated mean power equal to the actual mean recorded by the S710. This is a critical assumption and it means that we cannot compare the overall mean power but only the pattern of disparity between the observed and estimated values.
With that important caveat in mind, note also that the HAC4 records data at 20 second intervals, so I consolidated the data I had into 20-second chunks and based the calculations on that. Here is a graphical comparison of the first hour of the ride, with the observed power data from the Polar S710 in black (at 5-second intervals) and the estimated power based on speed and altitude data from the "pseudo-HAC4" in red (at 20-second intervals).
Keep in mind that the estimated wattages (in red) were constructed to have the same mean as the observed wattages (in black), so what's important is to compare their relative patterns, not their levels. In that sense, the estimates are constructed to produce a fairly favorable comparison and might be considered an "optimistic" bound on how well a speed-and-altimeter based device might perform.
Qualitatively, the estimates track the observed power moderately well in the sense that when observed power is high, the estimates are too, and when the observed power is variable then so, too, are the estimates. However, as one would expect when comparing a 20-second observation to a 5-second observation, the estimates can't capture all of the variability, with highs that are not so high and dips and swells that get averaged into smooth curves. The plot above can be compared to the plot shown for the Rosetta Stone ride, with the conclusion that for this particular ride, estimates based on speed and altitude change differ more from the other three power meters than the power meters differ from each other.