This concept of ergodicity requires that the data be stationary, specifically, that the data exhibit no time-dependence in any of the statistical moments. Figure 7 presents a plot that is representative of the RMS drag value (second statistical moment) versus time. For this particular run, 20 seconds of data were taken corresponding to approximately 10,000 data points. The result of this run is one "test point" - the average of all 10,000 data points for this run. The data exhibit a trend to converge to approximately 0.8 lb - the value is actually meaningless. The very fact that this plot shows ANY time dependence, as opposed to being a straight line, is VERY significant. This plot shows that the flowfield is NOT ergodic. Consequently, the entire data set is suspect from an accuracy standpoint. The concept of ergodicity requires, regardless of the particular ensemble (data set) analyzed, that there will be no time-dependence in the ensemble - that all test points will yield identical results. In order to achieve an accurate result, repeat runs would be necessary to achieve some type of ensemble average. This ensemble average would provide a more accurate estimation of the "true" drag level. How many repeat runs are necessary for this one test point? The only way to know for sure would be to make perhaps a dozen or more and plot the average value from those runs.
One can now understand the problem encountered. If our original test matrix involved several model configurations at several velocities, 100 test points could be involved - say five days of testing at $4000/day. Now, if we are required to repeat each test point 10-15 times to achieve our desired accuracy goals, we now need 50-75 days and $300,000.
The most significant trends apparent within the test data are the dynamic influence of wheel rotation and the rider pedaling. Additionally, the effect of subtle changes in body position during the run is significant. While the dynamic trends are of interest, the most useful information to the rider is some type of accurate, time-averaged drag value. Accurate time-averaging, however, does require the assumption of flowfield ergodicity. As the flowfield surrounding the cycle and rider within the wind tunnel is clearly NOT ergodic, "real" drag values are meaningless for short-duration testing. In order to achieve meaningful drag levels, the test plan must allow for sufficient repeat runs for each test point. What are the reasonable limits to data quality? For this test, the customer wished to know drag levels to 0.06 lb or approximately the predicted measurement uncertainty level. This was not possible after the fact, as the flowfield was clearly not ergodic and the test plan and funding did not allow for any additional testing. Some of the information obtained was useful. In particular, specific effects during a given run, such as the effect of head-up versus head-down, provided a repeatable increment from run to run. So, even though the absolute level of the drag was never determined, a highly accurate measurement could be made of the effect of handlebar droop, head-up versus head-down, and pedaling versus stationary. In addition, as the effect of pedaling was the primary reason the flowfield was not ergodic, all data taken while the rider was stationary data were valid.
For this particular technique, the sources for uncertainty are neither the instrumentation nor the data acquisition system. Rather, the close-coupled nature of the balance and test vehicle system creates a flowfield environment that is not ergodic. The presence of the rider and the dynamics due to the pedaling required to achieve proper flowfield simulation force the assumption of ergodicity to be invalid. This raises serious doubt about the certainty of the measured drag levels. Only through repetition of one particular test condition will sufficient data be available for an ensemble average. This will provide a more accurate estimation of the "true" drag level.