I also tried with two performances, and it does not match with Peronnet and Thibaut formula.
You probably know that the Canadian physiologists Peronnet and Thibault have found (1,2,3) that for each runner a linear relation exists between the %vVO2Max and ln(t_lim/t_vVO2), with :
- t_lim the time that could be sustained by the runner at the velocity corresponding to %vVO2Max considered ;
- t_vVO2 : the time that could be sustained by the runner at vVO2Max
The slope of this linear relashionship is the "Aerobic Edurance Index" (AEI) of the runner, and indicates the decrease of speed as the duration of the event increases (from 5k, to 10k, to HM for instance). So, the less negative the slope is, the more the runner is able to maintain speed as the duration of the event increases, the best his aerobic endurance is.
Typically, a very good AEI is about ~ –4.5 to –5 (Paula RADCLIFFE is –4.7 for instance). (4) The level of the AEI has been found to be largely connected with the proportion of Slow-Twitch vs Fast-Twitch fibers (the more ST, the best the AEI is). Of course, provided the performances you use to compute the AEI of a specific runner have been optimized (same absolute level, and in both cases similar conditions, and optimal training for the distance).
Now, when you consider a runner with PBs of 13:11 at 5k and 27:23 at 10k, so with a very good AEI of –4.9, based on Peronnet's formula a HM time of 1h00'17 could be predicted for this runner, (4) that is already more realistic than the value provided by your algorithm...
But now, if another runner has the same PB in 10k of 27:23, but is faster at the 5k with a 13:05 PB, that means he looses more rapidly speed as the duration of the even increases than the first runner, and so his AEI is poorer (–5.75 exactly). Thus, his HM performance should be WORSE than the one of the first runner, and the second runner have a less good aerobic endurance, but with your algorithm we find THE OPPOSITE...
This is another point that is unrealistic with your modeling.
(1) Peronnet, F. & Thibault, G. (1987). Analyse physiologique de la performance en course à pied, révision du modèle hyperbolique. J Physiol. 82, 52-60
(2) Peronnet, F. & Thibault, G. (1989). Mathematical analysis of running performance and world running records. J Appl Physiol. 67, 453-465
(3) you may also see (sorry, it is in French) :
http://www.fredericgrappe.com/wp-content/uploads/2011/10/Indice%20d%20endurance%20et%20profil%20de%20performance%20en%20cyclisme%20%20etude%20preliminaire.pdf
(4) The AEI could be determined provided you have at least two optimized performances from this web site (also in French...) :
https://plans-entrainement.net/estimateur-de-performances-calculateur-dallures/