Saving the world one equation at a time

How can you ensure the safe operation of nuclear reactors when it is too dangerous to physically check their cores? Nick Warren, Head of Statistical Modelling at the Health and Safety Laboratory, explains how his team have developed the only truly independent and impartial model for estimating the viable life expectancy of the UK’s nuclear reactors.

The Science Directorate uses mathematical models to anticipate and prevent hazards
The Mathematical Sciences team uses applied mathematics, physics and software to simulate real-world conditions to anticipate and prevent hazards.

According to the average Hollywood blockbuster, you’re only really qualified to avert global disaster if you have superpowers. But even then, it’s an expensive business.

For example, it’s been estimated that, in real life, the climactic battle at the end of the most recent Superman film would have cost the taxpayers of Metropolis around $750 billion worth of physical damage and $2 trillion in economic impact, with hundreds of thousands of people missing, injured or killed.

As the work of the Health and Safety Executive’s (HSE) Science Directorate shows, however, you don’t need x-ray vision or superhuman strength to save lives or the world – just the right expertise, experience and mathematical skill to make a difference.

The Health and Safety Laboratory

The Science Directorate is largely based at the Health and Safety Laboratory (HSL) in Buxton, Derbyshire. Originally established in 1911 as an experimental station to investigate explosions and hazards in coalmines, the Laboratory’s remit has since grown to investigate, research and reduce health and safety risks right across every sector of industry.

Down the years, the Science Directorate’s specialists have worked on many high-profile incidents and cases. These include the 1987 Kings Cross fire, believed to have been started by a discarded match on a wooden escalator; the Potter’s Bar rail crash, attributed to a faulty set of points on the Norfolk-London line in 2002; and, more recently, the collision between two carriages –one empty, one containing 16 people - on the ‘Smiler’ rollercoaster at Alton Towers.

As one of the world’s leading providers of health and safety solutions, HSE’s Science Directorate now employs more than 400 scientific, technical and medical experts, specialising in disciplines as diverse as ergonomics, falls prevention, fire explosion safety, nanotechnology, microbiology and behaviour change.

At their purpose-built laboratory and large-scale experimental facility, the efforts of these experts are helping to make our work environment and everyday lives safer across the UK and the world.

For example, HSL’s Falls Prevention team ensured that the floor of Heathrow Airport’s Terminal 5 is not only hardwearing, but also has slip-resistant qualities to protect the 31 million passengers who walk upon it each year.

While HSL’s ergonomists help major manufacturers such as Toyota and Honda to optimise the interactions between employees and their workplace to minimise the risk of workplace ill-health and accidents.

Securing Britain’s safety and energy supplies

As a result, there’s no such thing as a typical day or job in the Science Directorate. Take the work of its Mathematical Sciences Team.

Mathematical modelling helps us reach those parts, where it’s just too expensive, impractical or dangerous for conventional research or experiments to go.

For instance, using applied mathematics, physics and specially designed software, the Mathematical Sciences Team can simulate real-world conditions to predict the possible transmission of infectious diseases, anticipate the hazards posed by flammable gas clouds and better understand the spread and effects of toxic substances when they enter the human body.

One of the team’s most complex challenges is to estimate with confidence the viable life expectancy of the nuclear reactors that generate over a fifth of the electricity consumed in the UK.

Unlike others around the world, Britain’s Advanced Gas-cooled Reactors use a core made of graphite bricks to keep the nuclear reaction needed to generate electricity under control. Fuelled by uranium, this nuclear chain reaction generates heat that converts water to superheated steam. At pressure, this steam drives a series of turbines to produce electricity.

The interlocking tubular graphite bricks that make up the reactor’s core play a crucial safety role. They both moderate and sustain the chain reaction and, with operating temperatures reaching more than 500oC, are cooled by pressurised carbon dioxide gas. Over time, these graphite cores – which cannot be renewed or replaced – are subject to the ageing effects of radiation and regulators need to assess just how many years these bricks and, ultimately, the reactor can operate safely.

It is too expensive and potentially dangerous for anyone to check the condition of each and every one of these graphite bricks. That’s where the Mathematical Sciences Team steps in. Working with the School of Metallurgy and Materials at the University of Birmingham and the Nuclear Graphite Research Group at the University of Manchester, the team have developed the only truly independent and impartial model to predict the behaviour of the graphite core in these situations.

The model runs simulations, using data gained from regular inspections of reactors, core graphite samples and other sources, which enable regulators to evaluate operators’ safety plans, increase their understanding of graphite’s properties and inform regulation.

No mathematical model can be 100% accurate, but in assessing their predictions the team at HSL compensate for any uncertainties in order to advise regulators appropriately. But mathematical modelling is just one of the clever ways in which experts in HSE’s Science Directorate are protecting Britain’s safety.

Preparing for the worst

Accidents will always happen, whether as a result of natural causes such as floods or landslides or man-made hazards like chemical explosions or major fires. And every one of us faces a degree of risk in our daily lives. But some sections of the population are at greater risk than others, i.e. because of their age, occupation or location.

Trying to estimate how many and which people could be impacted when the unexpected or unknown happens, particularly in areas that are hard to evacuate, is a seemingly impossible task. But it is crucial to ensuring effective planning and response by the Government and our emergency services.

HSL’s expert Data Analysts created the National Population Database (NPD) to help solve that challenge. This incredibly useful tool, which combines geographical data from sources such as the Ordnance Survey with current population statistics, enables operators to estimate the likely population of any particular area at a particular time.

Government can use this data to quantify the number and specific types of people such as children, the elderly or hospital patients at risk in the event of a major incident and plan appropriately to help those affected as quickly and effectively as possible.

That’s not all. This database can also tell you about different kinds of buildings and how many of them are at risk from a hazard; identify those workplaces that have the greatest need for risk management; and even estimate the likely costs arising from a major disaster, taking into account factors such as loss of activity and cleaning up afterwards.

It’s an invaluable resource and the Department for Environment, Food and Rural Affairs (DEFRA), local authorities and other organisations are now using the database to help them with contingency planning.

So the next time, you’re sat in the cinema or at home watching some Hollywood hero save the day, spare a thought for the experts of HSE’s Science Directorate working quietly behind the scenes at HSL to ensure the health and safety of people across Britain and the world.


  1. Clare

    Really enjoyed this blog- reminded me of some of the parts of my Physics degree I particularly enjoyed before deciding to go into HR. I did a module on nuclear reactors and while our material didn't go beyond the structure and theory, getting an insight into their workings was really interesting. Good to see there's a mathematical model to see how reactor moderators weather over time!

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  2. Anna

    Fascinating, if I had my time again I would have loved to have started my career in this line of work, oh if only I had been slightly good at maths & physics!!

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  3. Hazel Mackintosh

    Sending to my son who has just started maths, physics, chemistry and economics A levels, hoping it will inspire him...

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  4. Chris

    Fantastic blog - really interesting stuff!

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  5. MATT

    I love maths - sign me please!

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  6. Anne Keen

    Hmmm. Do the math. I rather think that in the UK we do the maths.

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  7. Chris Donohue

    I was really annoyed by the link to this piece- Do the Math. We have enough Americanisms turning up in our day to day work. Maths not Math!!

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  8. James

    @Chris Donohue You are quite correct that it is maths and not math but the link writer is just quoting a well-known American phrase so it would be wrong to amend it to the UK English.

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  9. James Logan

    Many Americanisms in speech, Math v Maths, I understand, but the dreadful use of UK English I cannot. Mixing tenses, past and present, looks, and sounds appalling. "the next time you're sat in the cinema, or at home...". Sat is past tense, i.e. that is something that has already happened, not something that will, or may, happen. Correct useage should have been "the next time you're sitting in the cinema, or at home...". Where does it stop? I'll went to the shops tomorrow to bought some things I really needed. See what I mean?, a nonesense. Otherwise not a bad article.

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    • Tony

      Actually "you're sat" is a sort of future perfect, a more colloquial, possibly less prestigious, more northern variant of "you are seated". Unlike some languages, English does not require the use of the future tense with "will" or "shall", or even the present continuous (verb to be + "-ing") to indicate futurity. The adverbial phrase "Next time" fulfils that function by itself. Grammar begins as a description of acceptable usage, rather than a rule book of what people can and cannot say. In any analysis it is wise to put value judgments aside.

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