ok kids

i think i’ve about settled on the 3 contenders

first up

up is the Flock model that hardly looks like itself anymore

i was having a hard time getting rid of the wiggle

in a 2 component form

without resorting to an exponential aerobic component ramp

that ramped up quicker than what the published VO2 kinetics

would suggest

so

i reached into the parts bin a pulled out the linear feedback mechanism

from the 3 parameter Critical Power model

turning the simple intuitive little equation we all loved

power(t) = w1/t*(1-exp(-t/tau1) + w2/t*(1-exp(-t/tau2))

in to this freakish thing:

power(t) = (pow2*tau2/x*(1-exp(-x/tau2))) + w1 * (1 / (x - w1/((pow2*tau2/x*(1-exp(-x/tau2))) - pow1)))

as ugly as it looks

it fits curves beautifully

at least on the 10 complete(ish) data sets above

(its the blue curve)

next up in red

is about as optimized the 2 Component Flock model gets

which turns out is

http://www.ncbi.nlm.nih.gov/pubmed/11944100

the same thing mathematically as this Alvarez model

i say mathematically

because the author’s take on it is that

power decreases

by the exponential function

tau/t*(1-exp(-t/tau))

which in my mind to an extent misses the main point of the the Flock model that

the fraction of W’ available increases

by the exponential function

(1-exp(-t/tau))

with the net effect being

the rate limited phase followed by the capacity phase

so that its not just

the old shool W’ that can be quantified as a capacity / time

but

the aerobic component does the same thing

we just typically about it more often during the rate limited phase only

either way

last up in green

is the Peronnet model which is the VO2 max model

that states that after 420 seconds

the fraction of VO2max that can be sustained dereases linearly with the LN of time

(it also uses the exponential ramp but optimizes with a tau that seems a bit more plausible)

in terms of lineage

Monod begot Lloyd begot Ward Smith begot Peronnet begot Alvarez

and

Monod begot Morton

and

i showed up way late to the party talking all kinds of crazy

and started kicking ass

which is basically my style

and

as it turns out

a little inbreading

finds the happy middle ground

see the close up above

…

the red curve is basically a bit too curvy

the green curve a bit too straight

the 3 parameter CP isn’t even on here cuz it would look like the weird kid flyin off into space

while the blue

(which incidentally can be aproximated very closesly for a long time by simply tilting CP with a linear factor like when if first busted out the crayons this summer)

hits that happy place by not overchasing too much

(yes the difference is that subtle)

which is why the images above the curve are the residuals

plotted with the why axis of only +/- 5 %

meaning

their all good

just

ones a touch better or so it seems

but if your goal is to fit the curve

then fit the curve

(right?)

interestingly with a tilted CP

it basically acts like two sequential CPs and then bends over to tag

Pmax

and could without much difficulty be taught to tag up again between 45 - 60 min simply through weighted fitting/fit point selection

…

given that 2 of these models

have been published and been around

and findable by even someone just getting into the game

it begs the question

WHY?

were these not compared to the WKO4 model during webinars ?

(i keep hearing Andy’s ho hum voice repeating : i tried them all )

hell even Grappe

http://www.fredericgrappe.com/?p=911http://www.fredericgrappe.com/?p=911

made a laughably simplified version of the Peronnett model

power = VO2max power * LN time

for durations greater than 5 minutes

funny enough though

it works just fine…

anyways

right then good chat

next if i feel like it we’ll get into some of the pros and cons

they all have their things