What is the science behind Performance Modelling applied to on-the-bike Power and Pace simulation, and can I trust it? These are important questions.
Power & Speed
The relationship between power and speed is the foundation of Performance Modelling and we model it using long established certainties of physics, specifically Newton’s Second law relating to
conservation of energy. When a 70 kilo rider on a 7 kilo bike climbs a 5 per cent grade at a certain speed we know exactly what power he needs to overcome earth’s gravitational pull. Similar
principles apply to the calculation of power required to overcome aerodynamic drag, rolling resistance, and to accelerate. These principles have long been applied to cycling and with good
Martin et al
showed how a mathematical model of road cycling power predicted required power to within 2% of power outputs recorded using SRM’s. Now consider that a well calibrated SRM claims accuracy of +/-2% and we’re
Assuming Newton’s physics are sound then the important factor in performance modelling becomes quantification of model parameters.
The simplest way to use a power-speed model is to assume a very simple course of a certain distance with a certain average gradient between start and finish. Unfortunately this simple usage – still
adopted by many in ascent analysis – leads to accurate estimates of power or pace only in rare circumstances. Let us imagine an extreme example of why this doesn’t work – a rider climbing and descending
a hill. Applying the model simply the average gradient of this rider’s course is zero – pan flat – while this clearly isn’t so. Better results require a much more detailed representation of course profile.
We use GPS coordinates with corresponding geological survey elevation data to create a high resolution representation of the terrain making up a particular course. Typically this means a course is
decomposed into hundreds of sectors and we compute the power speed relationship for each one. A rider’s entry speed in sector S is the speed he exits sector S-1. Courses with significant changes
in altitude also require adjustments to air pressure which typically falls by 1mb every 10 metres of elevation gain.
Example high resolution bike course profiles for the IronMan & 70.3 Worlds in Kona & Henderson...
Rider & Bike Weights
These are easy to measure using modern digital scales. The least error prone method to weigh a bike is to subtract the weight of a rider holding his bike from his weight alone.
Aerodynamic Drag (CdA or “Drag Area”)
This is an important input.
- It can be estimated using anthropometric (body size) estimators established in scientific research.
Bassett el al.
determined a relationship between height, weight and frontal area (the A part of CdA) while
determined a relationship to drag coefficient (the Cd part of CdA).
- It can be estimated using aerodynamic field test protocols. We discuss and provide models to assist with the calculations in the main protocols - see
- It can be measured precisely, consistent with the same physical principles underlying a cyclists power-speed relationship, in a wind tunnel.
- Component specific drag numbers are now widely available in the public domain - subject to some unknowns and a level of trust - from leading aerodynamic wheel and frame manufacturers.
- Drag interactions between rider, bike and wheel systems rely on common observations concluded from practical wind tunnel analysis.
Air density is an important input in power-speed modelling as it influences the power a rider requires to overcome aerodynamic drag. Air pressure, temperature and humidity together define
density. These variables can all be sourced from simple weather reports. In the case of predictive event modelling we use a weather service to determine the most probable weather scenarios
at a particular location on a particular date.
Wind Speed & Direction
Wind effects are the trickiest model inputs to get right. As with atmospheric variables we can rely on a weather service to envisage probable scenarios in the case of predictive event
modelling. In historic event analyses (see our
Pro Race Analysis
) we apply what we call “Continuous Weather”.
This means we update wind variables in model calculations with the same resolution as historical time-of-day weather recordings and apply the appropriate winds to riders as they progress
through course sections using their event start time for synchronisation.
A meteorologist's view of Race Day at Kona, 2012...
Coefficient of Rolling Resistance
There is now lots of data in the public domain relating to the Crr of specific tyre choices and how these scale from roller tests, through different inflation pressures, and onto an asphalt
road. We rely on this data to conduct power-speed modelling with good estimates of rolling resistance power demands.
These conclude the main considerations that promote accuracy in event modelling.
When we extend Performance Modelling to account for energy expenditure, energy budgeting – effectively a carbohydrate and fat fuel demand analysis – and to develop variable power and
optimal pacing strategies consistent with physiological limitations we rely on models of physiology.
Gas analysis used to determine an athlete’s fuel utilisation at varying work intensities is one of the most common and well understood disciplines in sport and exercise science.
Physiological limitations relating to pacing rely on the Critical Power concept of Monod & Scherrer, the Fatigue Curve concept of Riegel, and other emerging models relating to anaerobic work
capacity recharge rates.