If you are a teacher then please also visit my new site: intermathematics.com for over 2000+ pdf pages of resources for teaching IB maths!

Modelling a Nuclear War

With the current saber rattling from Donald Trump in the Korean peninsula and the instability of North Korea under Kim Jong Un (incidentally a former IB student!) the threat of nuclear war is once again in the headlines.  Post Cold War we’ve got somewhat used to the peace afforded by the idea of mutually assured destruction – but this peace only holds with rational actors in charge of pushing the buttons.  The closest we have got to a nuclear war between 2 nuclear powers was in the 1962 Cuban missile crisis – and given the enormous nuclear arsenals of the US and the then USSR this could have pretty much ended civilization as we know it.  In that period, modelling of the effects of nuclear war was a real priority.  So let’s have a look at some current modelling  predictions for the effects of a nuclear war.  Those of a nervous disposition may wish to look away!

The picture at the top of the post is the nuclear blast radius calculated from this site.  It shows the effects of a 100 megaton airburst (equivalent to 100 million tonnes of TNT explosive).  This is the biggest nuclear bomb that the USSR ever tested.  If dropped on London it would have a fireball radius of 6km, an air blast radius of 33 km (destroying most buildings) and a thermal radiation radius of 74km.  The site estimates that this single bomb would cause 6 million deaths and another 6 million injuries.  And remember this is a single bomb – there are collectively around 15,000 nuclear weapons in the world (the majority shared between the US and Russia).

Nuclear Winter

Whilst the effects of a single bomb would be absolutely catastrophic for both a country and also for the global economy, it would not be an extinction event for humanity – however scientists have modelled the consequences of a nuclear war which would effect the climate to such an extent that it could lead to global mass extinctions.

Let’s have a look at one of those papers – the pessimistically titled:

Nuclear winter revisited with a modern climate model and current nuclear arsenals: Still catastrophic consequences.

In this paper the authors look at 2 scenarios – the long term climate effect of (a) the detonation of 1/3 of the world’s arsenal of nuclear weapons and (b) the detonation of the full arsenal of the world’s nuclear weapons.  Let’s leave to the side that this would almost certainly end civilisation as we know it – but what would be in store for those lucky (?) enough to survive such an event?

Changes to global temperature and rainfall

This above graphic is a double line graph – with the red lines relating to changes in temperature and the black line corresponding to the changes in precipitation.  The middle 2 lines relate to case (a) and the bottom 2 lines  relate to case (b).  The y axis relates to years.  You can see from this graph that a large nuclear war where 1/3 of the nuclear arsenal was released would have a significant effect on both global temperatures and rainfall.  5 years after the detonations you would have a global temperature 3-4 degrees lower than normal, and even a decade later it would still be a degree lower than normal.  For the full nuclear arsenal case the effects would be catastrophic – a average global drop in temperature of close to 9 degrees 2-3 years after the event.  To put this in context – the last ice age had global temperatures around 5 degrees lower than present.   Meanwhile the average rainfall would drop by around 1.6mm/day equivalent to a 45% global drop in rainfall.

Localised effects of changes in precipitation

This above graphic shows the distribution of the effects of precipitation following the detonation of the full nuclear arsenal one year on.  You can see that not all parts of the globe are equally effected. The countries near the equator see a massive drop in rainfall (more than 3.5mm/day) along with large parts of North America and Western Europe

Localised effects in the change in temperatures:

This above graphic shows the distribution of the effects of temperature following the detonation of the full nuclear arsenal one year on.  As with the rainfall, you can see startling changes – parts of North America would be 20-30 degrees colder than average, parts of Russia 30-35 degrees colder.  You can see the misleading nature of global temperature averages here.  The global average temperature drop after 1 year was “only” 5 degree – but the parts where the majority of people live see temperature drops many times this.  The global average is brought up by the relatively small change in global ocean temperatures.

Results of a nuclear winter

These changes to the climate alone would be sufficient to destroy agricultural production for the global food chain for a number of years.  One gloomy assessment in 1986 referenced in the paper is that the majority of people who had somehow survived the nuclear bombs and radiation would in any case die in the following years of starvation as crops failed across the globe.  So in short given have the ability to cause our own extinction event, let’s hope those with their fingers on the nuclear buttons are rational enough never to press them.

Essential Resources for IB Teachers

If you are a teacher then please also visit my new site.  This has been designed specifically for teachers of mathematics at international schools.  The content now includes over 2000 pages of pdf content for the entire SL and HL Analysis syllabus and also the SL Applications syllabus.  Some of the content includes:

1. Original pdf worksheets (with full worked solutions) designed to cover all the syllabus topics.  These make great homework sheets or in class worksheets – and are each designed to last between 40 minutes and 1 hour.
2. Original Paper 3 investigations (with full worked solutions) to develop investigative techniques and support both the exploration and the Paper 3 examination.
3. Over 150 pages of Coursework Guides to introduce students to the essentials behind getting an excellent mark on their exploration coursework.
4. A large number of enrichment activities such as treasure hunts, quizzes, investigations, Desmos explorations, Python coding and more – to engage IB learners in the course.

There is also a lot more.  I think this could save teachers 200+ hours of preparation time in delivering an IB maths course – so it should be well worth exploring!

Essential Resources for both IB teachers and IB students

I’ve put together a 168 page Super Exploration Guide to talk students and teachers through all aspects of producing an excellent coursework submission.  Students always make the same mistakes when doing their coursework – get the inside track from an IB moderator!  I have also made Paper 3 packs for HL Analysis and also Applications students to help prepare for their Paper 3 exams.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.