Waterworth optimization of integral algorithm Skiba recommends using a static value for DCP (citation needed). DCP can be calculated dynamically (the average until time t) or calculated once for the entire workout and used as a static value.
DCP is the difference between CP and the average power of the intervals in which the power was below CP. The numbers 546, -0.01 and 316 are determined in Skiba’s original article and do not change between persons. Where W′ bal( t) is equal to W′ bal at time t, W’ is the amount of available energy above CP, t the time for which W′ bal is calculated, u the iterator of the summation, W′ exp( t) amount of energy above CP that is used at time u ( expended), e the Euler number and τW′ a time constant that describes the recovery speed. The integral algorithm is the best known algorithm to calculate W’balance and has been scientifically validated⁵. All the algorithms are implemented in the Python library athletic_pandas. The algorithms that are discussed are the original (integral) Skiba² algorithm, an optimization (approximation) of the Skiba (integral) algorithm by Dave Waterworth³ and the Froncioni/Skiba/Clarke (differential) algorithm⁴. If that article is too complicated then this article will probably be too complicated as well, sorry about that… The article is probably not complete and also not intended to judge or validate any of the algorithms. If you are not familiar with these, Jones et al. It is assumed that the reader is familiar with power duration models, the 2-parameter critical power model and the W’balance concept. In this article a comparison is made of the different W’balance algorithms that are circulating.
Goldencheetah intervals window update#
Update 8 March 2018: It was brought to my attention that I made a mistake in the formula of the differential algorithm: the denominator in the fraction should be W’, not W’bal(t-1). Update 7 March 2018: After feedback from Philip Skiba and Andy Froncioni I updated the text about the origin of the differential algorithm.
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