Hey Bob, hope you are doing well. My understanding is that Coggan analyzed blood lactate response to power above first lactate threshold (the aerobic one, LT1):
and determined the following:
Perhaps not surprisingly, an exponential function provided the best fit, but a power function of the following form proved to be nearly as good:
blood lactate (% of lactate at LT) = power (% of power at LT)^3.90; R2=0.806, n=76
Based on these data, a 4th-order function was used in the algorithm for determining the IF (the exponent was rounded from 3.90 to 4.00 for simplicity’s sake).
So instead of using an exponential function to relate power and blood lactate, Coggan approximated using a 4th order function.
Then the 30-second average part:
the important facts are 1) the half-lives (50% response time) of many physiological responses are directly or indirectly related to metabolic events in exercising muscle, and 2) such half-lives are typically on the order of 30s. Thus, to account for this fact the power data were smoothed using a 30 second (~1 half-life) rolling average before applying the 4th order weighting as described above.
That is all straight from Coggan’s paper Training and racing using a power meter: an introduction and I have the 25 March 2003 revision which can be found on the Internet.
@cwiggum so to answer your question, the formulas are based on an estimate of how your muscles respond (as measured by blood lactate) to increasing power levels.