## A Problem with Spitfires

Posted in Cute Problems, History, The Universe and Stuff with tags , , , , , on July 25, 2017 by telescoper

This problem stems from an interesting exchange on Twitter last night, prompted by a tweet from the Reverend Richard Coles:

I think his clerical vocation may be responsible for the spelling mistake. The answer to his question doesn’t require any physics beyond GCSE but it does require data that I didn’t have access to last night.

Here’s a version for you to try at home with all the necessary numbers (though not necessarily in the right units):

A model of a Mark VI Spitfire showing its two 20mm cannons.

A Supermarine  Mark VI (Type 350) Spitfire fighter aircraft weighing 6740 lb is initially travelling at its top speed of 354 mph. The aircraft is armed with two Hispano-Suiza HS.404 20mm cannons, one on each wing, each of which is fed by a drum magazine containing 60 rounds. Each projectile  fired from  the cannon weighs 130 grams, the rate fire of each cannon is 700 rounds per minute and the muzzle velocity of each shell is 860 m/s.

(a) Calculate the reduction in the aircraft’s speed if the pilot fires both cannon simultaneously until the magazines are empty, if the pilot does nothing to compensate for the recoil. Express your answer in kilometres per hour.

(b) Calculate the average deceleration of the aircraft while the cannons are being fired, and express your result as a fraction of g, the acceleration due to gravity at the Earth’s surface which you can take to be 9.8 ms-2.

(c) A Mark 24 Spitfire – which is somewhat heavier than the Mark VI, at 9,900 lb (4,490 kg) – is armed with 4×20mm cannons, two on each wing. The inboard cannon on each wing has a magazine containing 175 rounds; the outboard one has 150 rounds to fire. Repeat the above  analysis for these new parameters and comment on your  answer.

## Battle of Britain Day

Posted in Film, History with tags , , , on September 15, 2015 by telescoper

Today is the 75th Anniversary of the day that historians regard as the climax of the Battle of Britain. To commemorate this, a huge flypast will take place across the South of England. Unfortunately, the weather isn’t too great today, and I don’t think it will be quite the spectacle that was intended, although Purple, Brown and Black sections are due to fly over Brighton from RAF Goodwood and perhaps the clouds will have broken up by the time they get here. Normally Battle of Britain Day is commemorated on a Sunday, as 15th September 1940 lay on a Sunday.

I had a friend – now long dead – who served as a fighter pilot in the RAF during the Battle of Britain and I once asked him about the tactics they used. He explained that they didn’t really have any tactics. When scrambled they were usually lucky if they managed to get to the right altitude before the enemy were on them. And if they did, they just flew head on at the incoming planes and tried to shoot them down. There was little point in attacking a big formation from behind with a handful of planes, which was the usual situation: you might pick off one or two but the bombers would carry on to their target. You had to attack from the front in order to scatter them. He added that on a good day, if you were feeling exceptionally brave, you might even keep your eyes open as you screamed straight into the enemy at getting on for 400 mph.

Another event of 15th September 1940 exemplifies the almost insane courage of the RAF pilots. A formation of Dornier bombers penetrated the British air defencesa as central London, where it was engaged by planes from a number of RAF squadrons, including the Hurricane of Flight Sergeant Ray Holmes. Holmes got into position to shoot down one Dornier, but when attempted to fire he discovered he had run out of ammunition. In an act of amazing bravery he decided to ram the Dornier. He succeeded ins slicing off the plane’s tail and it came down on Victoria Station. Somewhat improbably, Holmes managed to bale out and, though injured, survived to fight again. He died in 2005.

The other thing that this event reminded me of was the film Battle of Britain. The movie is a bit dated now, largely because some of the special effects don’t really stand up to modern comparisons: no cgi when it was made, for example. The best thing about it for me, though, is the wonderful music written for the film by William Walton, especially in the following sequence where the dogfights are shown with only the music as soundtrack. This turns the shots of terrifying close-range combat into a something a lot more than an action movie. It’s a work of art.

The context of this sequence is, as far as I know, historically accurate. Over the summer of 1940 the Luftwaffe had sent raid after raid over to attack Britain, these raids increasing in size as time went on. Hugh Dowding, Head of Fighter Command at that time, refused to let his planes be drawn into a huge battle against numerically superior forces and instead kept most of his planes in reserve, sending up only a squadron or half a squadron to meet the incoming planes. Thanks to the breaking of the German Air Force Enigma code, Dowding knew that the Luftwaffe pilots had been handing in grossly exaggerated reports of how many planes they had been shooting down. Convinced that the RAF was on the brink of collapse, the Germans launched an enormous air raid on September 15th 1940 intended to deliver the knockout blow and prepare the way for invasion.

Dowding knew that they were coming, and put every available plane at the RAFs disposal into the air. The survival of this country was at stake during this battle. There were no reserves. When the Luftwaffe arrived over Britain their pilots were aghast to find the air filled with Spitfires and Hurricanes whose pilots, having been consistently outnumbered in the battles so far, relished the chance to fight for once with something close to numerical equality with the enemy. The RAF scored a decisive victory, convincing Hitler to abandon his plans for an invasion in 1940.

## Six Spitfires

Posted in History with tags , , , on August 18, 2015 by telescoper

I am indebted to James West for sharing this picture of no fewer than six Supermarine Spitfires seen earlier today over the Solent..

Six planes is half a Squadron. Seventy-five summers ago, during the Battle of Britain, such a tiny force would frequently have been scrambled to take on over 100 incoming enemy planes. And not only over the South of England. This day in 1940, August 18th, was a particularly tough one for the RAF and has come to be known as the Hardest Day, with heavy losses on both sides.

I can’t help reflecting upon the fact that the pilots involved in that momentous conflict were not only so few in number, but also so very young. Nineteen or twenty was typical, the same age as the undergraduate students I teach at work.

So few and so young, but without their courage and skill the world would have slipped into unimaginable darkness.

Lest we forget.

## The Day the War came to Tyneside

Posted in Biographical, History with tags , , , , , , , , on August 6, 2010 by telescoper

We’re now approaching the 70th anniversary of August 15th 1940, the day that most historians regard as the start of the Battle of Britain. There had been a great deal of aerial combat, especially over the English Channel, in the weeks following the fall of France and the evacuation from Dunkirk in 1940, but August 15th was the day when the German Luftwaffe initiated a series massive daytime raids aimed at knocking out Britain’s air defences. Over the following weeks they nearly succeeded. It was only an erroneous change of tactics by the Luftwaffe, away from targetting the airfields and towards the terror bombing of cities, that gave the Royal Air Force time to recover from the punishment it had been taking. Eventually, by late September 1940, the threat of invasion, which at one point appeared imminent, had finally subsided.

I’m sure there will be many commemorations of the Battle of Britain over the next week or so, in which tributes will be paid to the few of The Few that survive to this day and, of course, those that gave their lives in the momentous struggle which happened all those years ago. There will be much talk of famous places such as Kenley, Northolt and Biggin Hill,  key sector airfields for 11 Group, responsible for defending London and the South East, which were under massive attack on August 15th and over the following days and weeks.

But it wasn’t just the South-East that was attacked on August 15th 1940. An enormous incoming raid from the North of France was met by Spitfires and Hurricanes of 10 Group and a terrifying dogfight involving about 200 aircraft brewed up over Portland. Further North, 12 Group’s defences were probed by bombers flying from Denmark intent on destroying airfields in Yorkshire.

And then there was 13 Group, which was charged with the task of defending Scotland and the North-East of England. The map below (courtesy of the RAF website) shows the location of their principal airfields and radar installations in 1940. The Operations HQ for 13 Group, RAF Newcastle,  was in Kenton, not far from the location of what is now Newcastle Airport. In fact I cycled past the place countless times when I used to work at Cramlington without knowing what it was. Then it was opened to the public for a time and all the maps, charts and telephones were still there. I felt a distinct shudder when I saw it.

I’ve always been fascinated by history. I read a lot of books about it and in Britain you’re never very far from the site of some historical event, perhaps a castle or the site of a bloody battle. Whenever I travel I also try to visit places of historical interest. Reading is fine, but there’s no subsitute for being there and seeing it for yourself.

It’s quite a different matter when history comes after you rather than you going to find it. The idea that such a familiar place (to me) as Kenton could have been so central to the epic struggle that was the Battle of Britain brings it home that the things we take for granted haven’t always been so secure. When I was a kid growing up in Newcastle, Biggin Hill seemed to me as distant as Dunkirk or El Alamein, but the idea of German planes flying over such places as the Farne Islands and Tynemouth is something that still gives me the shivers. I’m sure the people of Iraq felt the same way about the American and British planes that bombed their country during the two Gulf Wars…

I’ve therefore decided to post the following short account of some of what happened on August 15th 1940 in my own neck of the woods, partly because of what I said in the previous paragraph and partly because the numerical facts are are pretty representative of the situation all around the country on that day seventy years ago. I got the details from a book called The Narrow Margin by Derek Wood and Derek Dempster, and you can find a more complete report here where there is a full account of every day’s action during the Battle of Britain.

For a start it appears that the Luftwaffe thought that most of Britain’s fighter defences were committed to the South. They were probably aware of the effectiveness of the long-range Radio Direction Finding (RDF, now known as radar) network known as Chain Home, but disregarded it because they thought there would not be many planes around to intercept them even if they were detected. The raid over Tyneside was despatched from Stavanger in Norway and flew in a roughly south-westerly direction across the North Sea.

At 12.08, RDF trackers began to plot the path of a formation of “twenty plus” incoming aircraft opposite the Firth of Forth at a range of over 90 miles. As the raid drew closer, the estimated number was revised up to thirty, in three sections, approaching from the North-East and heading SW towards Tynemouth.

The radar operators of 13 Group hadn’t had as much practice as their colleagues further south in 11 Group, which probably accounts for the difficulty they had in estimating the number of incoming planes. Nevertheless, with a full hour’s warning, the controller was able to put squadrons in excellent positions to attack, with 72 Squadron Spitfires in the path of the enemy off the Farne Islands and 605 Squadron over Tyneside. Nos 79 and 607 were also put up, but while the latter was in the path of the raid, No. 79 was initially too far north.

No. 72 Squadron from Acklington was the first to make contact, seaward of the Farne Islands. Closing rapidly with the incoming aircraft, it came as a distinct shock when the “thirty” materialised as sixty-five Heinkel 111s and thirty-four Messerschmidt-110s (or ME110s for short), i.e. almost a hundred aircraft. The RAF squadron facing them comprised a mere 11 Spitfires.

When I first read the numbers involved I could hardly believe them. Imagine being outnumbered almost ten to one, but knowing that you had no choice but to attack. Reading through the RAF daily reports makes it clear that these odds were by no means unusual. Time and time again during August 1940, a squadron or half a squadron would be scrambled to meet inbound formations of 100-plus aircraft. Although the RAF pilots were both brave and skillful, facing such an overwhelming weight of numbers against them it was inevitable that the attrition rate would be high. It was the steady loss of pilots, rather than planes shot down, that almost brought the RAF to its knees.

The only chance of an effective defence a small group of fighters could offer was to scatter the massed formation by attacking from the front, trying to disrupt them so much that they would not find their targets inland. That was the plan anyway; it didn’t always work. In the absence of a Squadron-Leader, 72 Squadron was led by Flight-Lieutenant Edward Graham, who, as it turned out that day, led one of the most spectacularly successful air combats of the War.

Thirty miles off the coast, the squadron sighted the enemy.  As the RDF stations had predicted, the Germans were flying in three formations – the bombers ahead and the fighters in two waves stepped up to the rear. Misled by the supplementary fuel tanks slung below their wings, which looked like bombs, Graham and his pilots took the closer wave for Junkers 88 bombers whereas they were in fact (twin-engined) ME110s of the fighter escort.

The incoming formation was so vast in comparison with Graham’s small force that he hesitated for a moment, uncertain at what point and from what direction to attack.  Apparently unable to bear the suspense, one of his pilots asked him whether he had seen the enemy aircraft. With a stutter which was habitual, but which deteriorated in times of stress, he replied

Of course I’ve seen the b-b-b-bastards, I’m trying to w-w-w-work out what to do.

The reply was to became famous throughout Fighter Command. I don’t blame him for stuttering. If it had been me I would have been filling my pants.

But he didn’t hesitate for long. The Spitfires had had plenty of time to gain height during their long flight from the coast, and were about three thousand feet above the enemy’s mean height.  Making the most of his advantage, he decided to lead the squadron in a deliberate frontal attack, diving out of the Sun to achieve maximum surprise. Each pilot was free to choose his own target.  Two-thirds attacked bombers or supposed bombers, the remaining third the second wave of fighters, correctly identified as ME110s.

The attack was startlingly effective and caused widespread panic among the German planes whose pilots had been told not to expect that much opposition.  Jettisoning their external tanks, some of the ME110s formed a defensive circle, while others dived almost to sea level and were last seen heading East.  The bombers, less an indeterminate number destroyed by Graham’s squadron, then split into two formations, each accompanied by some of the remaining fighters. One formation headed for Tyneside, apparently with the intention of bombing the sector station at Usworth; the rest turned South-East towards two aerodromes at Linton on Ouse and Dishforth which they had been ordered to attack. Some of them jettisoned their bombs and headed back to Norway, leaving several of their number in the sea.

The separate parts of the remaining formation finally reached the coast, one near Acklington and the other south of Sunderland. The first formation, engaged successively by the remaining (No. 79) squadron from Acklington, the triple-A batteries defending the Tyne area, and some Hurricanes of 605 Squadron which had come south from Scotland, dropped most of their bombs in the sea. The second, engaged by a squadron of Spitfires from Catterick, a Hurricane squadron from Usworth and the anti-aircraft artillery from the Tees batteries, dropped theirs almost as ineffectively near Sunderland and Seaham Harbour.

Overall, backed by the guns of the 7th Anti-Aircraft Division under Major-General R.B. Pargiter, 13 Group’s aircraft destroyed at least eight Heinkels and seven 110s without suffering a single casualty themselves, although several civilians were killed by bombs and there was considerable damage on the ground, including a few airfields. It is known that, in addition to the enemy losses reported during this period, many German aircraft struggled back to their bases with battle damage and some were written off after crash-landings.

This was one of the most successful actions fought during the entire Battle of Britain and its effect was that that 13 Group met no further daylight raids for the duration. However, it was just one episode in a struggle that became increasingly desperate as the summer of 1940 dragged on. As I said at the start, the defences of 11 Group came particularly close to breaking point, but eventually recovered and the expected invasion never materialised.

The rest, as they say, is history…

## Spitfire!

Posted in Bute Park with tags , , , on June 27, 2009 by telescoper

Well, that’s something you don’t see every day!

I was sitting in the garden just now, doing the crossword, when I heard the unmistakeable sound of a World War II fighter aircraft flying overhead. I looked up and there it was, right over my house. A Spitfire no less. The outline was instantly recognisable, especially because it was flying so low, on account of its curious elliptical wing shape. It was also low enough for the extraordinary roar of the Rolls Royce engine powering this exceptional aircraft to shake the windows in my house!

I once had the chance to sit in the cockpit of a Spitfire, in an aircraft museum, not one that was flying! The thing that struck me most was how very small and cramped it was, and I’m not particularly tall (although I’m a bit wider than I used to be).

It turns out that the appearance of this aircraft in the skies over Cardiff was related to an event called Armed Forces Day which is happening in Bute Park, just a matter of yards from my house.

Seeing the plane reminded me of the 60th anniversary commemoration of the Battle of Britain in 2000 during which the newspapers reprinted contemporary accounts of the summer of 1940 during which Britain stood alone, and on the brink of the abyss. The thing that struck me most about the heroic pilots who saved this country from invasion was that they were all so young. The same age, in fact, as the students I teach. I wonder how many of todays 18-20s really understand the scale of the sacrifices made by the corresponding generation of 1940?

I had a friend – now long dead – who served in the RAF during the Battle of Britain and I once asked him about the tactics they used. He explained that they didn’t really have any tactics. When scrambled they were usually lucky if they managed to get to the right altitude before the enemy were on them. And if they did they just flew straight at them and tried to shoot them down. There was little point in attacking a big formation from behind with a handful of planes, which was the usual situation. You might pick off one or two but the bombers would carry on to their target. You had to attack from the front in order to scatter them. He added that on a good day, if you were feeling exceptionally brave, you might even keep your eyes open as you screamed into them at getting on for 400 mph.

The other thing that this event reminded me of was the film Battle of Britain. The movie is a bit dated now, largely because some of the special effects don’t really stand up to modern comparisons: no cgi when it was made, for example. The best thing about it for me, though, is the wonderful music written for the film by William Walton, especially in the following sequence where the dogfights are shown with only the music as soundtrack. This turns the shots of terrifying close-range combat into a something a lot more than an action movie. In fact, this is a real piece of art.

The context of this sequence is, as far as I know, historically accurate. Over the summer of 1940 the Luftwaffe had sent raid after raid over to attack Britain, these raids increasing in size as time went on. Hugh Dowding, Head of Fighter Command at that time, refused to let his planes be drawn into a huge battle against numerically superior forces and instead kept most of his planes in reserve, sending up only a squadron or half a squadron to meet the incoming planes. Thanks to the breaking of the German Air Force Enigma code, Dowding knew that the Luftwaffe pilots had been handing in grossly exaggerated reports of how many planes they had been shooting down. Convinced that the RAF was on the brink of collapse, the Germans launched an enormous air raid on September 15th 1940 intended to deliver the knockout blow and prepare the way for invasion.

Dowding knew that they were coming, and put every available plane at the RAFs disposal into the air. He staked everything on this battle. There were no reserves. When the Luftwaffe arrived over Britain they found the air filled with Spitfires and Hurricanes whose pilots, having been consistently outnumbered in the battles so far, relished the chance to fight for once with something close to numerical equality with the enemy. The RAF scored a decisive victory, convincing Hitler to abandon his plans for an invasion in 1940.