A cyclist expends power to overcome a number of forces including gravity, air resistance or aerodynamic drag, acceleration, rolling resistance, wheel bearing and drivetrain friction.
Fortunately it has long been possible to reflect all of these forces in a mathematical model of cycling power such that we can understand with high precision the power a rider would
need to produce to achieve a certain speed or event time or conversely the speed or time that could be expected for a given power output. We incorporate such a model into the following calculators
which can be applied to practical analysis of racing.

Use this model to calculate the power output required to achieve a certain time on a simple one-sector course or to understand how required power output is spent in terms of
components required to overcome the different forces of resistance.

Use this model to study the impact of several variables on required power, given a certain speed, or on speed given a certain power output. The kinds of variables you can study
include weight, road gradient and aerodynamic drag.

This is a 10 sector course model that can be used to model power, speed or time applicable to events such as time trials and cyclo sportives. As an extension you can easily
study the impact of air pressure on time trial performances.

Use this model to experiment with variable power pacing strategies while checking that your pacing plan remains within the limits of the rider critical power curve.

VAM or "Velocity Ascended, Metres Per Hour" is a metric of climbing ability developed by Doctor Michele Ferrari.

Both a physiology and a power & speed model. Use it to evaluate the tradeoff between reduced power due to oxygen sparsity and aerodynamic benefit of thin air in terms of the combined effect
on a riders speed at altitude.

You know your power, weight and the gradients of the climbs you will be riding in a target event. But what gearing do you need? This calculator combines a "speed given power" and a "cadence
given gearing" calculator so that that you can accurately determine a comfortable minimum gear.

Rolling resistance is the second most important use of a rider's power after aerodynamic drag. But which tyres choices can help you reduce it, and what are the differences between
clinchers and tubulars, butyl and latex inner tubes? This calculator can tell you.

Acceleration is an important part of bunch or criterium racing and sprinting. This model allows you to study the power cost of rider and bike weight in this so-called "non steady state"
cycling as well as the importance of wheel weight and inertia, a key consideration when shopping for wheels.

How far can a cyclist go in an hour? It's a beautifully simple challenge with a beautifully simple answer - but it depends! Use this compact utility to model or estimate an hour record
performance on any of the velodromes used historically or planned for future record attempts.

The vast majority of the performance differentials between cyclists of all levels are due to differences in sustainable power output, weight or aerodynamic drag. It follows that riders wanting to
improve have just 3 major options: increase sustainable power, reduce weight, or reduce their aerodynamic drag known as CdA. Since it is now routinely possible to meter a riders power output and trivial
to measure rider or component weight most riders and coaches have a firm grasp of the disciplines required to improve both. Conversely aerodynamic drag minimisation, in spite of being hugely
important to cycling speed, has often been neglected due to the difficulties or costs involved in measuring it.

Fortunately riders equipped with a power meter can now benefit from modern ride modelling techniques to discover, tweak and optimise their aerodynamic drag profiles with a good level of accuracy.
Moreover we subscribe to a school of thought that aerodynamic drag can be more realistically measured on the road, throughout a realistic ride duration, than momentarily in a wind tunnel.

We currently recommend 3 methods of aerodynamic drag estimation depending on circumstances:

With this method the rider completes a circuit containing some significant elevation change. We then use power and speed data to model virtual elevation, matching this to the circuit elevation such
that we solve for CdA.

This is a method suited to flat road or velodrome environments in which the rider completes a number of test runs at a range of speeds. We then use corresponding power and speed data to find a
relationship between the two which is explained by a certain CdA.

## The Holistic Method

This is a method made possible by GPS elevation profiles or altimetry and applies high resolution modelling of a test circuit. Simply put, if we know the profile of a circuit, we know an
applicable wind vector and we know the riders power output through all segments of that circuit then there is only one CdA which explains his lap time.

A futher method of aerodynamic drag estimation demonstrates how aerodynamic drag and rolling resistance can be estimated in a special zero-power case by a rider without a power meter.

The coastdown method of CdA & Crr estimation is a special case of the Virtual Elevation (Chung) Method in which the rider simply "coasts down" a small hill with zero power, 2 or more times.
Similar mathematics to the Virtual Elevation and Regression methods are then used to compute CdA & Crr given a known loss of height. This method can be tricky to execute well but one obvious
appeal is that it is open to riders who do not have a power meter.

Modelling of aerodynamic drag also has great applications in the evaluation of aerodynamic components.

Use this tool to evaluate a database of "aero" components (wheels and frames) in terms of their benefits under conditions and on courses YOU define. This
model offers an interesting alternative view of
the achievable "time savings" and "power savings" increasingly quoted by the
component manufacturers.

Aerodynamics in cycling is all about the effort required to move a rider through the air but what when that air is moving? Wind strength and direction is hugely important to the cyclist
and features in pacing and equipment choice where yaw angles are a key consideration. But what if wind strength and direction cannot be forecast with certainty? Historical patterns of
local winds can be used to infer the probability distribution of race winds and best visualised as a "Wind Rose". Use this utility to build a wind rose for your location of interest.

Power meters are helping coaches and cyclists to understand rider physiology in ways that were not previously possible
or at least difficult without access to a sports science laboratory. This understanding and the value derived from
riding with a power meter can be greatly enhanced with some simple models of key physiological variables.

At a fundamental level riders and coaches now think about ability in terms of a critical or mean maximal power curve which
describes how sustainable cycling power decays with increasing time, largely due to size and distribution of anaerobic work
capacity. These curves are frequently used to analyse changes in a riders fitness or as a comparison between riders but they
can also be used to estimate functional threshold power (60 minute critical power) from shorter tests or to set apropriate
power levels for interval training. The critical power curve is formalised in the Monod Critical Power model.

## Fatigue Curves - Riegel's Model

Monod Critical Power is an excellent tool for modelling cycling performances upto around an hour however the power outputs it predicts take no account of fatigue.
Since fatigue becomes a more significant factor in longer rides we recommend the Fatigue Curve concept of Riegel when modelling and predicting power
in longer events. The Fatigue Curve model has much the same applications as the Monod model and we use it by default when suggesting the sustainable power output
that should serve as an input in our endurance Event Models.

Modern training for cycling emphasises physiological terms such as VO2max, anaerobic threshold and efficiency but these have
often lacked a sense of meaning outside of the sports science laboratory. This is a shame because together they can precisely define
a riders sustainable power output, alternatively power output can be used to estimate VO2max, the gold standard of potential in aerobic sports.
We demonstrate the relationships with a simple model that emphasises the reason we do so-called VO2max and threshold intervals.

## Anaerobic Work Capacity & Maximum Accumulated Oxygen Defecit

How do you think about anaerobic capacity? The chances are you see it as an ability to accumulate an oxygen debt at key points in a race
which must be repaid, sooner or later. It is no coincidence that the gold standard measure of anaerobic capacity is known as Maximum
Accumulated Oxygen Defecit (MAOD) - although you may not have heard of it because it has historically been measured only in a laboratory.
Now, with just a power meter and a heart rate monitor, you can achieve a good estimate of rider MAOD and use this as an objective way to
track the effectiveness of anaerobic capacity training.

Both a physiology and a power & speed model. Use it to evaluate the tradeoff between reduced power due to oxygen sparsity and aerodynamic benefit of thin air in terms of the combined effect
on a riders speed at altitude.

Maximising watts per kilo is a common goal among cyclists. But what component of a rider's current weight is comprised of fat and how much of a wattage per kilo uplift could he or she
expect given body fat reduction to a safe minimum level? This calculator combines body fat estimators based on skinfolds analysis or Body Mass Index (BMI) and provides some useful
additional calculations for cyclists. You can further use this calculator to estimate pro riders body fat percentages using data in the CPL rider database.

The Monod Critical Power model is very good at identifying a riders Critical Power (CP) and Anaerobic Work Capacity (AWC) from "best effort" power data relating to 2 or more
short fitness tests and lets us understand very clearly how a rider might spend their AWC. But it says nothing about how that AWC may be reconstituted during "recovery" or
when a rider is delivering a power output below CP. This utility implements a model developed by Skiba et al. to demonstrate how a riders rates of AWC reconstitution can be
established using power data and how this information can be used to model "AWC Balance" relating to a specific ride. Forward looking modelling of AWC Balance can be applied
to develop better interval training sessions or optimal pacing strategies while retrospective analysis of AWC Balance offers a powerful tool in "post-mortem" analysis of racing failures.

The model based approach to performance prediction which has become popular in the sport of cycling, moreso since the windspread adoption of power meters, has much to offer the duathlete or
triathlete as well.

Among cyclists the

Monod (Critical) Power Model
is a popular tool to estimate a cyclist’s Functional (~Lactate) Threshold Power and the power output he ought to be able to maintain across a range of durations based
on data from two or more short field tests. In fact, by plugging the appropriate power number into a

Speed Given Power Model
we can also estimate the kind of pace the cyclist could be expected to maintain in a range of events.

We have spent some considerable time researching models through which similar concepts can be applied to the three disciplines of triathlon, primarily in the interests
of

**event time or pace prediction applied to standard distance triathlon events**, and present the following pace calculators. In each case you can choose from multiple underlying
models to access a range of pace predictions consistent with the type of assumptions you feel most comfortable with.

Use this model to predict swim pace and swim leg event times using a choice of 3 methodologies.

- The Critical Swim Speed (CSS) model of Wakayoshi et al.
- The Fatigue Curve model of Riegel.
- The Monod Critical Power model applied to swimming, where we incorporate
**a mathematical model of a swimmers power output** similar to that used in the popular triathlon software
“RaceDay”.

Use this model to predict bike speed and bike leg event times using a choice of 2 methodologies.

- Monod Critical Power. In this implementation you may specify field test data that does not include power (time and distance) and we will estimate power output as a key input to the model.
- The Fatigue Curve Model of Riegel which may be more suitable in performance prediction applied to longer events such as half and full IronMan.

Use this model to predict run pace and run leg event times using a choice of 3 methodologies.

- The VDOT model of Dr. Jack Daniels featured in “The Daniels Running Formula”.
- The Fatigue Curve model of Riegel.
- The Monod Critical Power model applied to running. We incorporate
**a mathematical model of runners power output** that we have developed consistent with published scientific research
into the energy cost and efficiency of running which reflects the impact of road gradient, wind and runner aerodynamic drag on the relationship between run pace and required power. In other applications
we believe this offers a significantly more accurate way to model the performance demands of running on varying run courses such as may be encountered in triathlon events.

Two key questions in the application of any model to the analysis of cycling must be "is it accurate?" and "what are the assumptions?"

Models of the relationship between cycling power and speed have been around for a long time and rely on the physical principles in

Newtons Laws of Motion as

applied to cycling.
The principal model of cycling power and speed used throughout this site is an implementation of that proposed in

Validation of a Mathematical Model for Road Cycling Power
which appeared in the Journal of Applied Biomechanics in 1998. This publication demonstrated the completeness and validity of the model
by comparison of model predicted and observed power values. The model calculates the power a cyclist would have to produce in order to achieve a certain speed on a certain course,
taking account of key physical and environmental parameters. In places this model is used to compute speed, time or the value of another parameter given a specified power.

The performance of any model is only as good as the accuracy of it's inputs which is why we often go into great detail measuring or estimating major variables such as air density, wind and
aerodynamic drag. Any assumptions or modelling approaches will generally be outlined. To some extent the use of consistent power models in the field derivation of aerodynamic drag measurements (i.e.
field testing of CdA) can improve the reliability of the models when used with that input.

In practise we have found theoretical values of a cyclists ride time, given a specified power and good parameters inputs, to fall consistently within +/-5% of actual ride time and frequently within +/-2%.
In the context of the stated accuracy of most cycling power meters at +/-2% we have great belief in the application of physical models to the analysis of cycling events and, more importantly, the analytical
power provded to the rider or coach. The more we use these models the more confidence we have in them - if you have used them feel free to let us know your findings.

### What Others Say

From casual observers to PhD qualified sports scientists we have seen an increasing use of models to predict cycling performance on the road. The following resources are worth a read.