Indirect VO2 max testing

I suspect it's because T represents time to exhaustion and implies expending a certain weight scaled energy in joules per kg for the time or IOW sustaining a certain watts/kg work rate till exhaustion. That brings weight scaling into the equation which seems to make sense for a treadmill test of a weight bearing activity like running.

There are similar formulas based on P_VO2 Max for cyclists and I suspect the formula you listed suffers from the same problems, trying to estimate the anaerobic or AWC contribution which varies between athletes and skews the results. The problem is that power generated completely aerobically at VO2 Max or P_VO2 Max should not reflect any anaerobic contributions but we can't just turn off our bodies reliance on anaerobic processes. The best we can typically do is to pre-exhaust the majority of the anaerobic component through ramped tests or through methods like Andy's approach of taking the final minutes of a 'well paced' 3km or 4km pursuit as an estimate of P_VO2 Max under the assumption that the standing start and first minute or so uses up most of a rider's AWC and reduces the contribution from anaerobic sources in the latter portions of the pursuit.

Bottom line, there are a number of formulas that attempt to estimate VO2 Max gas exchange rates based on power output or time to exhaustion at a particular workload but they're all estimates with varying degrees of accuracy when applied across a range of athletes so take the results with a grain of salt.

-Dave