The purpose of this model is to predict an swimmers’s pace and performance across a range of popular event distances, extending this into the triathlon context, based on 2 or 3 past performances
and using a choice of 3 theoretical bases.

### The Critical Swim Speed Model (Wakayoshi et al.)

Similar to the Critical Power Model, this model due to

Wakayoshi et al.
can be used to estimate a swimmers functional threshold pace or pace at some other duration. It has been subject to some criticism because the use of pace rather than power in such a model has
far less theoretical basis and accordingly it's utility as an estimator may at
times be limited.

### The Fatigue Curve (Riegel)

The Fatigue Curve Model of

Riegel
models the time dependency of an athlete’s fatigue or endurance, opposite sides of the same coin, expressing a simple “log-log”
regression relationship between pace and distance which has been shown to fit the decay in an athlete’s pace extraordinarily well.

### The Critical Power Curve (Monod)

The Monod Critical Power model has been mentioned elsewhere on this site as a popular tool to predict performance in terms of a (a cyclists) sustainable power output, using power field tests
as inputs. We see no reason why this model will not also work well in the context of swimming, where a swimmers pace is determined more by the relationship between power and
hydronamic drag than a simple fatigue model.

### A Model of Swimming Power

The model of swimming power which we incorporate is based on the work of

Toussaint but coincidentally
returns the same numbers as the swim power calculator included in the popular triathlon software "Race Day".

Briefly, a swimmers power output is comprised of 2 components:

- Pd. Power required to overcome drag (form a and skin friction drag)
- Pk. Power required to change the kinetic energy of water (a swimmer enters a relatively static body of water but leaves it with some fore-aft
motion as a side-effect of the propulsion effort).

Power invested in Pd is always useful in forward motion, whereas power invested in Pd is essentially wasted. The greater the ratio of a swimmers Pk
to Pd the more inefficient his stroke. In our swim power model we apply the mathematics of Toussaint where Pd is related to the swimmers body size, scales at the cube of swim velocity,
and assume that the ratio of Pd/Pk = 0.6 which is an average of values observed empirically and applies to highly trained swimmers.

### Sub-FTP Pacing in Multi-Sport

The nature of multi-sport events dictates that athletes invariably choose not to perform at their maximum pace as may be predicted by a model
which considers only the single disciplines in isolation, especially in the longer events. We are aware of some consensus that
triathletes, depending on ability and training status, tend to pace at “85-95% FTP in the HIM swim leg and “75-85%” FTP for the IM
swim leg. For this reason we also provide pace and time estimates for these events at these percentages of FTP, an estimate which you can elect to base on either the CSS, FC or CP model.

### Training Zones

A natural extension of all of the above is to quote the training zones implied by the FTP estimates either from one of the above models.
We calculate popular swim pace training zones suggested by Dr. Phil Skiba author of

**Scientific Training for Triathletes** and Bill Sweetenhamn author of

**Championship Swim Training**.

### Inputs – Physical Parameters

- Height (cm). Input rider height in cm. This value is used to estimate the swimmers body surface area (BSA) relevant to swim power calculation.
- Weight (kg). Input rider weight in kg. This value is used to estimate the swimmers body surface area (BSA) relevant to swim power calculation.

### Inputs – Test Performances

Input times for 2 or 3 recent performances at available distances.

### Outputs – Model Prediction

- CSS. Predicted pace or event time using the Critical Swim Speed Model.
- FC. Predicted pace or event time using the Fatigue Curve Model.
- CP. Predicted pace or event time using the Swim Power & Critical Power Model

### Outputs – @ % FT (1 hour pace) Using Model

Sub-FTP pace or event times for longer triathlon events. Specify the model you would prefer to use as the source of the FTP.