Mathematics in War: Attack of Port Stanley Airfield

Mathematics in War: Attack of Port Stanley Airfield

Written on the 35th anniversary of the Falklands war, in commemoration of all those who gave their lives. I have delayed writing this until all relevant papers and files have been released into the public domain. Some of my recollections are now rather vague, but the story is true. Now read on.

In 1982, I was working as part of a small policy analysis team, providing reports and advice to the management board of the Royal Air Force. The team were located on the first floor of the main headquarters building of the Ministry of Defence, in Whitehall, London, just opposite number 10 Downing Street. My responsibilities covered all existing and planned air-to-ground weapons. At the request of the air staff, I had completed a review of the stockpile of such weapons using linear programming to help decide the best mix. This had indicated the need to increase significantly the number of general purpose guided weapons to complement more specialist weapons. I had through this work established good links with the senior military officers in the building.

The chief of the air staff was asked by the secretary of state for defence to establish a way of attacking Port Stanley airfield using one or more Vulcan aircraft. This airfield was the one useful concrete runway on the Falkland Islands, and was being used by the Argentinian forces as one of their main links back to the mainland.

The analysis had to be done in a few days as input to a high-level briefing by the chief of the air staff, I was told. An RAF air commodore was immediately nominated as my point of contact with the chief of the air staff. An operations cell to manage the initial response to the Argentinian invasion had been set up in the building, and I was given direct access through two steel barred doors to the RAF group captain (an ex-Vulcan pilot) who was in control of this. His desk sat at the rear of a long, low room festooned with cables, TV monitors, and the desks of very busy people.

In discussion with him, I established some of the parameters of the operation such as the height of the aircraft over the target. I then retrieved a large-scale map of Port Stanley airfield from the map store in the basement of the building, several floors underground.
With some help, I rapidly established the name of the UK construction firm that had constructed the airfield in the first place and phoned them up. They gave me the precise composition of the runway surface (such as the thickness of the concrete and what was underneath it). Colleagues at the Royal Aircraft Establishment (as it then was) could then calculate for me the size of a crater made by a 1,000lb bomb dropped from a Vulcan. All of this was achieved in a day.

The key to success was calculating the optimal bomb load. Too many would increase the lift requirement on the airframe unnecessarily leading to higher than required fuel usage and too many air-to-air refuellings or even to possible ditching of the aircraft in the South Atlantic. Too few would jeopardise the ultimate aim of the mission; to strike the runway and deny its use. The bomb bay of the Vulcan allowed three packages of 1000lb bombs to be carried in total. Each of these packages consisted of two slung rows. The first row contained four bombs with the second row of three bombs fitting snugly into the gaps between those in the first row. These mechanical constraints reduced the problem to carrying 7, 14 or 21 bombs.

I calculated the throw of the bombs and their scatter along the mean track of the aircraft, assuming the statistical error contributions were normally distributed and independent. This included Blackett’s factor of two on the variance, to take account of real war conditions, derived from analysis during World War II. I was also asked to calculate the likelihood of the Vulcan dropping its payload on the nearby town of Port Stanley. I did this by adding to the random statistical errors a set of systematic errors due to, for example, not realising which end of the runway was which.

This analysis confirmed that all 21 would be required to have a reasonable chance of striking the runway, but the chance of hitting the town was low. This immense payload (9.5 metric tonnes) had to be hauled across several thousand miles of ocean.  It meant refuelling aircraft refuelling other refuellers to get them into the right position to refuel the Vulcan. The plan involved ferrying all of the aircraft to Ascension Island and then flying on from there to strike the target.

The group captain worked out the intervalometer settings on the aircraft that would need to be used to set the timing between bomb releases (this was not trivial because the Vulcan was designed to deliver nuclear weapons). This gave, with the actual speed of the aircraft, the spacing between the craters on the ground.  We iterated this a few times to make sure it would work. I also calculated, if all else failed, an offset relative to a known feature visible to the pilot, from which the bomb delivery should begin. All of this took about another day.

Finally, I thought about how to present my working in a way easily grasped by busy people. In 1982 there were no PCs and no MS OfficeTM; or the equivalent. It took several weeks to have viewgraphs professionally drawn up, so I simply hand-drew the bomb craters on three strips of plastic (seven on each strip) to the correct scale of the large map of the airfield, and wrote out my analysis of the chance of getting a bomb on the runway in terms of the number of bombs, the height of the aircraft and the angle of the aircraft track relative to the runway (all of which were important in deciding the final aircraft flight path). This I had typed by the local typing pool on the second floor, under an urgent ticket, and quickly peer-reviewed by a colleague.

Heading towards the end of day three, I then briefed the RAF air commodore. He let me know, in case I needed to supply more backup material, that this information was first briefed to the secretary of state the same day, and then briefed by the chief of the air staff to the War Cabinet, chaired by Mrs Thatcher, the then Prime Minister. Mrs Thatcher herself played around with the strips of plastic and the map before declaring that 21 bombs would have to be used, and so it was decided. I had worked flat out for several long days. As I left the building that evening, feeling the cold London air on my face, I paused on Westminster Bridge, worried that it would all go wrong. Fortunately, when the attack went ahead, one bomb struck the runway, as reported across the world’s press and media.

From the official RAF history of the operation, named Black Buck [1], we have the following:

Of the 21 bombs, one hit the runway at its mid-point cratering the concrete, the rest fell to one side and caused serious damage to airfield installations, aircraft and stores. After the attack, the plan called for the Vulcan to return to 300ft to avoid the defences. Since no reaction was detected from the Argentine defences, [the pilot] Withers immediately climbed to an economic cruising level to save fuel. The return trip went exactly as planned, the rendezvous with the Nimrod and the additional tanker support were straightforward after the events of the long night. XM607 touched down at Ascension at the end of an astonishing 15 hours and 50 minutes in the air, which included 18 air-to-air refuellings. For this extraordinary, record-breaking mission and their superb airmanship throughout, Flt Lt Withers and Sqn Ldr Tuxford were awarded the Distinguished Flying Cross and the Air Force Cross respectively.

The cascade of effects

The immediate (military) effect was disruption of take-offs from Port Stanley airfield. However, Operation Black Buck not only reached and bombed the target but, in doing so, showed the Argentinians that the RAF had the potential to hit targets in Argentina [2]. This resulted in a number of air defence squadrons being redeployed to the north of the country, effectively denying their use for the rest of the conflict. At the political level, the consequent success of the task force (due to the brave men and women on board, many of whom gave their lives during that action) bolstered the Prime Minister’s position in helping to confront the Soviet Union during the
Cold War period.

James Moffat CMath FIMA


  1. Black Buck, (accessed January 2017).
  2. British Air and Space Power Doctrine AP 3000 (4th edition) Air Staff, Ministry of Defence, (accessed February 2017).

Reproduced from Mathematics Today, April 2017

Download the article, Mathematics in War:  Attack of Port Stanley Airfield (pdf)

Image credit: WESTON SUPER MARE, UK – JUNE 21: Avro Vulcan Bomber aircraft XH5 by © Cpphotoimages /

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