## cascading tau and cascading time ranges as an option to solve start parameters for Damien’s multi-tank Golden Cheetah model

in the previous posts i introduced the Wilkie correction as well as suggested the scalability.

this post just refines those thoughts a touch and suggests an approach for Damien to solve for the start parameters for the upcoming multi-tank Golden Cheetah model which can then be further optimized in his model.

y~pow1*tau1/x*(1-exp(-x/tau1)) + pow2*tau2/x*(1-exp(-x/tau2)) -pow2*tau1/x*(1-exp(-x/tau1))

where

pow1 = anaerobic

pow2 = aerobic

but can be further scaled as

y ~ pow0 * tau0/x * (1-exp(-x/tau0)) + pow1 * tau1/x * (1-exp(-x/tau1)) - pow1 * tau0/x * (1-exp(-x/tau0)) + pow2 * tau2/x * (1-exp(-x/tau2)) - pow2 * tau1/x * (1-exp(-x/tau1)) + pow3 * tau3/x * (1-exp(-x/tau3)) - pow3 * tau2/x * (1-exp(-x/tau2))

where:

pow0 = ATP/CP power

pow1 = Lactic power

pow 2 = Glycogen power

pow 3 = Fat power

and the tau for the Wilkie correction just cascades down from the system above it by the Ward-Smith simplification

and since

in this model

Power(max)(n) = W’(n) / tau(n)

so it is easy enough to go back and forth between rate and capacity.

to keep the model solvable

time ranges are selected where you pick the broadest range of time

where the model can be simplified down to 2 components (ie 4 parameters)

so that additional components can be solved for by cascading down the time ranges