The relationship between power output for a given effort is given by
Where e is the relitive exertion effort relitive to max heart rate,
and P_{VO_2} is the VO_2 \max power:
where c_{O_2} is the effective calorific content for oxegen, about 20 kJ/l for burning mostely carbohydrate. \eta is the muscle efficiency, about 20 % and m is the body mass.
If i have a {VO_2}_\max of 75~ml/kg/min and a body mass of 74 kg my P_{VO_2} works out to be
\frac{75*20}{60}*0.2*74 = 370 W
If my max HR is 180 bbm, resting HR is 47 bbm and threshold HR is 160 then e works out to be
\frac{160-47}{180-47} = 0.85
so my threshold power would work out as
P_\text{thr} = 370*0.85 = 314.5 W
which is pretty much bang on 95% of my max 20 min power:
P_\text{thr} = 0.95 P_{\max 20 min} = 0.95 * 332 = 315.4
If i do a 20 min const power effort and my avg HR is 143 max HR is 154 and i average 300W, can i calculate a {VO_2}_\max.
As befor my max HR is 180 bbm and resting HR is 47 bbm, then:
working backwards
We can see that going off avg HR for the effort we are coming up a bit high, whereas the max HR for the effort is pretty much bang on P_{VO_2 \max} again.
Going further
V_{O_2 \max} = \frac{P_{VO_2 \max} 60}{ c_{O_2}~\eta~m } = \frac{375 * 50}{20 * 0.2 * 74} = 76~ml/min/kg
20*70/60*74*0.2*0.9
306.36
20*75/60*74*0.2
370.0
(154-47.)/(180-47)
0.8045112781954887
370*0.75
314.5
0.95* 332
315.4
300/0.80
375.0
375*60/(20 * 0.2 * 74)
76.01351351351352