How maths plus eating while running equals your best marathon

How maths plus eating while running equals your best marathon
Runners take on the Two Oceans Marathon in Cape Town on 20 April 2019. (Photo: EPA-EFE / Nic Bothma)

Runners tackling this weekend's Two Oceans Marathon could find an unlikely source of help in future.

Whether standing at the starting line for a high school cross-country competition or, years later, at the cold, rainy 2018 Boston Marathon, I have always been nervous before races.

In November 2021, I was again at the starting line, this time at the Monumental Marathon in Indianapolis. And while I’ve always prepared for a race, this time I did it differently.

I’d spent the previous three years doing scientific research as part of my doctoral programme at the University of Tennessee, Knoxville, showing, mathematically, how to use nutrition and training to run an optimal race.

While there is significant research on pacing, training and eating, there has been little done at the intersection of maths and running. The research that has been done focuses mainly on shorter races, such as the 800m, instead of longer distances, and none of it focuses on the practice of eating while running. I wanted to find out how a marathon runner could maximise energy output to run the fastest possible race.

Kenyan Eliud Kipchoge wins the Tokyo Marathon 2021 on 6 March 2022. (Photo: Kim Kyung-Hoon / Pool / AFP)

My colleagues Suzanne Lenhart, Guoxun Chen and William Hager and I combined mathematics with research from the worlds of nutrition and sports science to identify how a runner’s speed should change throughout a race – and how much and when to eat during the run.

Marathon performance

The marathon emerged from an ancient Greek legend of Pheidippides, a messenger who ran 40km from Marathon to Athens in 490 BC to bring news about a Persian invasion – or possibly, to announce the Athenians’ victory.

More than 2,000 years later, in 1896, the first modern Olympics included a marathon. The next year, the first Boston Marathon was held. The race, probably the most famous of more than 1,100 marathons organised in the US each year, will mark its 126th anniversary on 18 April.

Completing a 26.2-mile (42.2km) marathon requires both training and strategy. Pacing is key: A runner who takes off at a sprint can’t expect to maintain that speed. In the 1920s, runners first realised the need to stoke energy during long-distance runs and began sucking on hard candies during races. Today, a lucrative industry sells energy gels, gummies, sports drinks and other in-race nutritional products.

That’s because running is an energy game, fuelled by stored fat and glycogen. During high exertion, the body burns mainly glycogen, a complex carbohydrate structure used to store energy in the muscles and liver.

That’s where nutrition planning comes in. The body has plenty of stored fat, but a limited supply of glycogen, enough to run maybe 24.1km. Eating carbohydrate-loaded meals leading up to a race builds glycogen stores.

Eliud Kipchoge celebrates after winning the INEOS 1:59 Challenge in Vienna, Austria on 12 October 2019, becoming the first person to run a marathon in under two hours. (Photo: EPA-EFE / Christian Bruna)

But high-speed or long-distance running can exhaust available glycogen, triggering a miserable and well-known experience known as “bonking” or “hitting the wall”. When the body runs out of sugar to burn, muscles cramp up and, in extreme cases, a runner may experience dizziness or confusion, or even collapse. The antidote: consuming simple sugar during a race.

Modelling racing biology

To show scientifically how to run the fastest possible race, my colleagues and I built a computer model. It relies on various personal parameters such as a runner’s weight and ability to absorb oxygen, which is calculated by most sports watches.

Other factors include the rate at which a runner burns calories and how quickly the body clears lactate, a compound that makes the muscles feel heavy when it accumulates. We incorporated equations for speed; changes in available energy from fat and glycogen; and the energy boost from food consumed during the race.

Then we programmed in our goal: Determining how a simulated marathoner can run the most efficient 42.2km race.

We evaluated various combinations of speed and available energy alongside fuel intake, ranging from 100 to 1,100 calories. Overall, our model shows that maintaining a fairly constant speed from start to finish helps a runner achieve top performance.

Runners head to the finish line of the 123th Boston Marathon on 15 April 2019. (Photo: EPA-EFE / Herb Swanson)

The results differ significantly from person to person. The model reveals an individual’s best speed and calculates the number of calories they should take in, based on personal needs, and when to consume them. The model also generates graphs to visually depict results. All can be improved with dedicated training, making a runner more energy efficient.

Optimising performance

Since this model is based on biological phenomena, not data, we needed to validate the approach. So we compared a simulation of Eliud Kipchoge’s 2019 world record-breaking marathon against his actual performance. Kipchoge, the first to complete a marathon in under two hours (1:59:40), gave an amazing physical performance that was optimised by a team of experts.

To compare our simulation with his actual race, we put in his personal parameters alongside the 800 calories he consumed. Our model proved extremely accurate: The simulation differed from Kipchoge’s performance by just one second per mile.

I then used myself to test our model on a runner with a different skill level. I stood on the starting line of the Indianapolis Marathon, prepared to use the model’s pacing strategy and in-race nutrition plan to consume five 100-calorie gels. I finished in 2:37:14, a major personal best for me, more than 15 minutes faster than I’d run to date. The simulation again proved strong: It differed from my true race time by less than 1%.

The ultimate goal of this work is to create a user-friendly application that allows runners to plan in-race nutrition and calculate their best speed, both of which are crucial to running the optimal marathon. DM/Reuters

First published by The Conversation via Reuters Connect.

Cameron Cook is a PhD graduate and researcher at the University of Tennessee.


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Comments - Please in order to comment.

  • Kanu Sukha says:

    “Results differ significantly person to person” is the most significant observation the author makes ! Most ‘average’ runners make the mistake of thinking what works for one, will work for another … looking for a magic ‘formula’ that works, instead of measuring and understanding their own bio-mechanics and nutritional requirements. It take s special kind of individual to be perceptive of those requirements, without the ‘scientific’ approach and ‘backup’ the author had access to. Starting at the ripe old age of 45 to the running scene, over the 27 or so years I discovered (sometimes gratuitously or fortunately) many of the ‘secrets’ the author refers to. My biggest revelation was the discovery that I could not maintain the same intensity of exertion the longer the distance … and for optimum results had to adjust the intensity. Having gone up to a 100 miles … these days the 5k park run seems my limit ! And I enjoy every minute to be able to finish just that. Wishing all out Oceans participants this year the very best.

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