The

Monod (Critical) Power Model
is an excellent framework for modelling bike rider’s ability at durations up to about an hour. The model decomposes rider’s ability to deliver power into two components:

- Anaerobic Work Capacity (AWC). A fixed quantity of work capacity in joules which can be spent at a rate of the riders
choosing. For example – keeping in mind that a watt is “1 joule per second”- if AWC is 9,000 joules then the rider may
deliver power anaerobically at the rate 150 watts for a minute (9000 / 60 seconds), 75 watts for 2 minutes (9000 / 120),
7.5 watts for 20 minutes (9000 / 1200) or 2.5 watts for 1 hour (9000 / 60 x 60). Anaerobic power delivery is of course
added to power delivered aerobically and completely explains the shape of the critical power curve when graphed.
- The “Critical Power” component – a level of power output the rider may deliver aerobically and for a period of
time which is not theoretically limited in time.

In practise the Monod model works very well and frequently demonstrates a good fit to rider’s performances in events
lasting around or under an hour. Take for example some of the power outputs known to have been delivered by Bradley
Wiggins in recent years. The Monod model would interpret them as under and with a very good “fit”.

### Limitations of Monod Critical Power

At very short durations the model starts to fail. Why? Because a rider’s ability to spend Anaerobic Work Capacity
has a peak rate which is constrained by neuromuscular capacity. Yes a rider can opt to spend his AWC over a minute
or 30 seconds, but the sheer amount of power implied over say 15, 10 or 5 seconds may be unrealistic.

The bigger limitation of the model is in modelling performances of more than an hour, making it a poor choice for
predicting performance in cyclo sportives, and “long” triathlons such as half and full IronMan. The problem is that
according to the Monod model a rider with an AWC of 9,000 joules could add 2.5 watts to his Critical, aerobically
delivered, power over 60 minutes, 1.25 watts over 2 hours, and so on out to a full day of riding. Something is
clearly lacking when a model predicts that a rider’s average power output over 2, 4 or 6 hours will be within 1
watt of his output at 1 hour.

### Fatigue Curves

The limitation of the Monod model is that it takes no account of fatigue, the mysterious and complex phenomenon
which decays a rider’s aerobic power output by more and more as a ride becomes longer. Fatigue it ‘self is complex,
it can be attributed to physical factors acting either centrally or peripherally throughout the riders body, or it
can be attributed to psychological mechanisms which work to protect the body from excessive damage. Readers interested
in the complexities of fatigue may be interested in a review paper by

Knicker et.al..

The nice thing about modelling performance in terms of power is that we seldom need to consider the complexity of
what is going on inside a rider’s body, we don’t really care, because all we’re interested in, all that matters,
is how these complexities ultimately define that rider’s pattern of power delivery. The fatigue curve model of

Riegel
does exactly this and no more. It looks at rider’s average power across two or more test durations and then
fits a curve to those performances using log-log regression of power and time. The model’s subsequent predictions of
that rider’s ability, his fatigue curve, tend to define an excellent fit to reality as many sports scientists who observe
power data will confirm.

### Applications

Fatigue curves are the model of choice for predicting power output at durations in excess of 60 or 90 minutes. We
apply a fatigue curve to predict sustainable power output for event durations in much of our event modelling, including our

Popular Event Models.
Actually we have to “roll down” the fatigue curve, iteratively solving for the best
power output at which a rider could expect to complete an event of the relevant length. Why? Because the faster we
go the more quickly we complete an event, and the more quickly we complete it the higher power we can sustain, and
the higher power we can sustain the more quickly we complete the event…and so on until this sort of algorithm says stop…

### Inputs

- The only required inputs are field tested observations of sustainable power at 2 or 3 of the selectable durations. You can input values in the "Tested" column
only, or additionally input values in the "Scenario" column to study the effect of changes in tested power values.
- Rider weight in Kilos is required to also express Wattage outputs as wattages per kilo.
- Tested / Scenario. When applicable you can select between displaying numbers based on the "Tested" or "Scenario" power inputs.

### Outputs

- FF(T) / Fatigue Factor (Time) - The time period over which the riders sustainable power output is expected to halve.
- FF(P) / Fatigue Factor (Power) - The number of watts by which the riders sustainble power output is expected to fall when time duration doubles.
- R^2. "R Squared" measures the "goodness of fit" of the model. Think of this number as a percentage, where 1 = 100% and would indicate the model could perfectly account
for the riders sustainable power at any duration.
- Predicted Power for Duration. The riders Mean Maximal Power predictions
according to the Fatigue Curve model at a popular range of durations upto 60 minutes.
- The chart displays tested power values and the corresponding curve of predicted power. When applicable it also shows scenario values and the scenario power curve in a lighter colouring.
The Monod Power curve which would be suggested by the same inputs appears in a purple coloring for comparison.

### Power Training Zones

These outputs specify the bounds of popular "zones" of training intensity in watts. These values are based on the riders "Functional Threshold Power" which is the 60 minute
power prediction.