University of Cantebury’s mathematical answer for producing NZ’s next cycling medals at the Olympics

A University of Canterbury mathematical model is helping high performance athletics race faster by showing them what impact their body gear and riding positions will have on their timing.

‘What if’ is an often-asked question, particularly around high performance cyclists seeking to win in world cycling circuits. How does a cyclist get maximum speed? What if he wears special sportswear? What if he changes the position of his handle? How does changing the ‘power’ applied to the cycling motion change the outcome of the race?

Answering these questions have been the preoccupation of some scientists, including the University of Canterbury’s Dr Lindsey Underwood (Mechanical Engineering Department) who has been using mathematics to predict how an individual racer can achieve maximum speed by making changes, to among others, position or equipment used.

Working with her supervisor professor Mark Underwood, Dr Lindsey’s model found that although body shape, sizes, shape and riding experience differed, all the athletes in the study showed a reduction in drag of over 1% by making changes to their equipment –  for example, wearing a shoe cover.

Handlebars, skinsuits and timing

Her model also found that by lowering the handlebars and their heads, cyclists could also reduce the drag effect on their race. Changing skinsuits, however, delivered the most significant reduction in drag. As it turns out, the choice of material and how the seams were placed have a significant impact on the drag effect.

By changing positions a few times, a cyclist could shave up to 8 seconds off a race while changing equipment could save up to 5 seconds in race time.

Dr Underwood, who came from the UK, to pursue her studies at the University of Canterbury, says although there have been models built along these lines, most of them were focused on road cyclists while hers was centred on track cyclists.

She says the model helps paint a picture – using data on frontal area, bike mass, rider weight among others – of how much time the athlete would save by just using a different bike. Similarly, the model would help provide a picture of what would happen to the timing if a cyclist increased his power at different segments of the track, whether on the straight or bent segments.

The mathematical model has since been used to analyse different pacing strategies to determine if the power output of the rider for the individual pursuit is actually the best strategy to use, she says.

In her research, a bike rig was designed and manufactured for being used with the open-circuit wind tunnel so that the aerodynamic drag of cyclists and bike equipment could be measured. The University of Canterbury’s Department of Engineering has two wind tunnel facilities - a closed circuit wind tunnel that can reach speeds up to 200 kilometres per hour and an open circuit wind tunnel that can produce speeds up to 45kph.

University of Canterbury's Dr Lindsey Underwood, left, with members of the New Zealand cycling team in San Diego.

The High Performance Team from Bike New Zealand had approached the university for some help in order to identify ways in which their track cyclists could go faster, predominantly through changes to the position of their cyclists, but also through modifications to the equipment.

“Track cyclists can win races by milliseconds, so any gains that can be made in terms of aerodynamics can be the difference between a medal or no medal at an Olympics or world championships,” she says.

Her model calculates the finishing time for a particular individual’s race. To build the predictive model as close to a real race, Dr Underwood had to include as many inputs as possible, especially the factors affecting a cyclist’s acceleration.

To validate the model, power data captured by training monitoring tool, SRM, was compared to the finishing time forecast in the calculations, to the actual finishing time for a particular race. According to her published research, the mathematical model was validated using SRM data for 11, elite track cyclists, and was found to be accurate to 0.31s (0.16%).

Challenges

Dr Underwood says what was also challenging, in building the model, was capturing accurate data from the SRM power meter (a little recording tool cyclists use to monitor their performance) and figuring ways to collect as much power data from the athletes without interfering with what they are doing.

She says because the load cell between the fixed and floating platforms of the  cycle rig (the device that supports a bike) measures voltage, a programme had to be created in LabView, to convert the drag into voltage, by one of the electrical technicians.

“I modified some of this programme so I could obtain some extra data, which was a challenge as I'd never used this programme before. A bigger challenge was working with the athletes to ensure they got something out of all the testing as well.

“It's hard work pedalling on the cycle platform with 45-50kph wind coming out of the wind tunnel, and to measure lots of different changes required the athlete to repeat this over a day or 2. The athletes and coaches have ideas about what positions and equipment they want to test, and so do we, so we need to ensure we work with the athletes and coaches to get the best gains we can.”

Dr Underwood's thesis on the Aerodynamics of Track Cycling