The

**Monod Critical Power** model has consistently proven one of the most popular destinations on our site,
a great testament to the utility and importance of the underlying idea. Perhaps the pull of this model is its simplicity
- give it just 2 or 3 “all out” power numbers at 2 or 3 durations and you have a paradigm which not only indicates
a riders expected best power outputs at a range of durations, up to and including the 60 minute “FTP” duration,
but which also teases apart ability into “Critical Power”(CP) – a sustainable power output delivered by the aerobic
energy system - and “Anaerobic Work Capacity” (AWC) – a sort of finite energy “reserve” which can be added to
aerobic power output as and when required and at the rate required.

The more we’ve worked with the CP model the more it’s limitations have become apparent. The first issue one
tends to notice is that, in the absence of significant AWC or at ride durations beyond about an hour where a
constantly delivered AWC would make it very thinly spread, the prediction for a riders power output is essentially
a flat line equal to Critical Power. Something is wrong when a model predicts the same performance at 2, 3, or 4
hours as at 1 hour and we’d suggest that the issue is the total lack of any accounting for fatigue. It’s not
ideal to be gauging effort in longer events based on “X% of FTP” (rules of thumb) and so we’ve long reverted
to the “Fatigue Curve” (log-log) model of Riegel to model performance in multi-hour events such as Grand fondos
and long–course triathlon. Fatigue is multi-faceted and so a purely statistical model such as this does a
good job of capturing it all. Problem avoided.

The other big issue with the model, in terms of how widely it can be applied, is the way it treats AWC as a
once-only, finite amount of energy. Think about that for a minute – we’re saying that the energy available
to a rider over and above CP is a once-only amount which is available at the beginning of a ride but which,
once spent, never regenerates. This may be a fair assumption for a time trial where power output is sustained
at or above CP – and the CP model excels in evaluating this sort of thing - but what about when a rider dips
below CP? Surely the resultant “recovery” allows AWC to recharge somewhat? This limits the application of the
CP model when it comes to predicting or modelling performance or pacing in events which involve sub-CP recovery periods.

With this last limitation in mind one starts to think about the rate at which AWC might recharge. If a rider can
spend all of his AWC on a hill, how much of that AWC might be available on a subsequent hill if, somewhere in
between, the rider was able to get some sub-CP recovery time? How much of total AWC is recharged after 2 minutes, 5 minutes,
or 10 minutes? How does the power output during “recovery” and relative to the level of CP affect any rate of
recharge? Does the rate of recovery depend on the physiology of the specific rider we are evaluating and, if so,
how do we measure these things?

At CPL we’re certainly experimented with field testing of riders recovery rates based on running interval protocols
to exhaustion. But not so long ago

**Dr Phil Skiba and colleagues** published

this paper
which sets out a really appealing framework for not only determining the range of rates at which a rider might be
able to recharge AWC but also for extrapolating that knowledge into the modelling of “AWC balance” (the paper calls it W’ balance)
in subsequent training or race efforts. Now it’s just a hunch but

**this model (or some evolution thereof) may prove one of the most important,
most useful models in modern cycling** and so without further ado we present the resource on this page to demonstrate
how it works.

### Establishing CP & AWC

It is both logical and fundamental that 1) in order to model AWC balance a riders AWC must be established to act
as the starting balance and 2) in order to model recharge at below-CP cycling intensities then CP must be established.
The basic form of the Monod CP model is perfectly suited to establish these two numbers and we include in this
resource a simplified form (compared to our full model

here
) which serves for this purpose. By special request
we are also illustrating the impact on CP and AWC of changes in the input power numbers –

**this is really useful
information for coaches working to change the shape of a rider’s CP curve via training designed to improve power
at specific durations.**
Now with numbers for CP and AWC in hand one can proceed to evaluate recharge rates…

### Establishing AWC Recharge Rates - The Time Constant "Tau"

For various reasons related to Oxygen delivery dynamics and further physiological factors Dr Skiba’s framework models reconstitution
of AWC as an exponential function. Most people are familiar with the idea of exponentials – rates of change which start
out relatively slowly and then speed up or start out relatively quickly and then slow down – either as time goes by
or as some other relevant variable (in place of time) changes. Example – the wind gradient model we discussed

here
says that wind speed slows as above-ground height of a pocket of air falls, but this slowing gets exponentially more
pronounced as we get nearer to the ground and the air experiences ever more surface friction. (Pilots know this phenomenon as wind-shear).

In so far as this model is concerned all you need to know about exponentials is:

- AWC in below-critical power cycling is around 39% recovered after 1 Time Constant. eg 300 seconds
- AWC in below-critical power cycling is around 63% recovered after 2 Time Constants. eg 600 seconds
- AWC in below-critical power cycling is around 95% recovered after 3 Time Constants. eg 900 seconds
- Due to the gradual "convergence to asymptote" of an exponential functon, full recovery will in theory take a lot longer.
- The Time Constant is itself modelled as a curve and is lowest (fastest) when recovery power is a long way below critical power
and highest (slowest) when recovery power is very near to critical power.

**When we refer to the "Tau Curve" we mean the relationship between the Time Constant "Tau" and the difference between Recovery Power and Critical Power termed "DCP"
which defines how quickly an athlete will recover AWC relative to the number of watts at which they are recovering below Critical Power.** Whilst it may be a reasonable
aproximation to model every rider with the curve estabished in Skiba's study individual riders may be interested in more accurate, personalised modelling.

Establishing or "Calibrating" the Tau Curve for an individual rider requires completing a number of interval workouts to exhaustion and then back-calculating or
solving for the value of Tau based on this time to exhaustion. We feel that 3 tests may offer enough data to calibrate a reasonable "personal" curve without becoming too
onerous and in this utility you can upload a "csv" file with data from 3 tests which will then be used to define a Tau Curve.

**One possible protocol for these 3 tests which is implemented in the example file (the download is customised to the Critical Power & "CP4" established in the Monod
Calculator above) is:**
- In all cases - Intervals of 60 seconds with 30 second recovery, ridden to exhaustion.
- In all cases - Interval power of CP4 (the 4 minute sustainable power predicted by the rider's Monod CP Curve).
- Recovery power of: Test 1) 80% CP. Test 2) 50% CP. Test 3) 20% CP.
- Recovery power should be held as constant as possible. Remember we are essentially building a curve of the relationship between recovery rate and recovery power
so varying recovery power too much within an individual test is not going to lead to good results.
- Tests 1, 2 and 3 should take place on different days.

Naturally, in the CPL way, all you need do is create a file, hit "Solve Tau Function" and let is do the Math! The summary statistics and charts should be self explanatory.

### Modelling In-Ride AWC Balance

Understanding the dynamic process and rate by which a rider recharges or reconstitutes AWC is all very well but - given the pain involved in building the Tau Curve -
the application needs to be compelling. And of course it is. We see four applications:

- Real time modelling of AWC Balance on a next-generation bike computer (such as the SRM Powercontrol X or Garmin 5XX!)
- A better model for event pacing which can be optimised before the event. (By the time you read this such intelligence is probably already in our
Event Models.)
- Retrospective "post mortem" of "racing failures" i.e. better explanations of why a rider blew up or felt limited at some point in a race.
- A more intelligent way to develop interval workouts that predicts how to achieve or avoid exhaustion or extremely low AWC balances. (And by extension
athletes may one day have nowhere to hide as their coaches will know if a session was abandonded due to hitting a sound physiological limit
or simply lack of motivation...)

To demonstrate the power and application of this model we present an "Interval Session Builder" which simulates the last idea.