London girl, 13, who helped win the Battle of Britain

The work was done by lamplight, over a small kitchen table in North London

Night after night throughout the early months of 1934, Captain Fred Hill and his 13-year-old daughter Hazel burned the midnight oil, plotting graphs and labouring over complex algorithms.

It was tiring, unrewarding work but they both sensed how vital it would prove to be. 

And their instincts would before long be ratified by history because their intricate calculations would go on to help the RAF secure victory in the Battle of Britain — a triumph that many historians now believe changed the course of World War II.

Firepower for freedom: Spitfires in formation. The image is from new book To Defeat The Few

Firepower for freedom: Spitfires in formation. The image is from new book To Defeat The Few

Firepower for freedom: Spitfires in formation. The image is from new book To Defeat The Few

Bent together over their graphs, father and daughter concluded that the new generation of aircraft being built by the Government to prepare for a future war should be armed not with four powerful machine guns but eight — an idea that was seen as deeply radical, even impossible, at the time.

Yet only then, the Hills had come to believe, would the new generation of Spitfires and Hurricanes have sufficient firepower to bring down enemy aircraft.

A scientific officer in the Air Ministry, Captain Hill managed to convince his superior officers of the importance of his and Hazel’s findings — and six years later, in 1940, their calculations were put to the test in the skies above Britain as the RAF fought Adolf Hitler’s much-feared Luftwaffe in a four-month battle that has been described as the most important military campaign ever fought.

Night after night throughout the early months of 1934, Captain Fred Hill and his 13-year-old daughter Hazel (above) burned the midnight oil, plotting graphs and labouring over complex algorithms

Night after night throughout the early months of 1934, Captain Fred Hill and his 13-year-old daughter Hazel (above) burned the midnight oil, plotting graphs and labouring over complex algorithms

Night after night throughout the early months of 1934, Captain Fred Hill and his 13-year-old daughter Hazel (above) burned the midnight oil, plotting graphs and labouring over complex algorithms

‘Without victory in the Battle of Britain, it’s almost certain we would have been invaded by Germany,’ says military historian Stephen Bungay, who adds that without the Hills’ persistence ‘it could have been a very different outcome’.

Yet until now the compelling story of the schoolgirl who helped to win a war has been sadly untold. Hazel’s only public recognition was in a memoir written by her father’s superior officer in the Air Ministry.

Now, 80 years after the Battle of Britain — and ten years since the mother of four sons passed away aged 90 — the RAF has publicly acknowledged Hazel’s heroic contribution for the first time, paying tribute in a fascinating BBC documentary in which the modest schoolgirl is described as an ‘inspiration’.

‘It’s just wonderful that Hazel’s story is reaching the light of day,’ says Group Captain James Beldon, the RAF’s director of defence studies.

‘What a great inspiration to young people today, and young girls in particular, who can look upon someone like Hazel in the 1930s making such an important contribution to our later success in the Battle of Britain, which was vital to this country’s survival.’

Few would disagree. In July 1940, the fate of the free world hung in the balance, as RAF pilots bravely fought off deadly attacks from the Nazi air force.

Outnumbered three to one, their victory was by no means certain and depended on their skill and bravery; many were barely out of their teens.

Those magnificent men did have one crucial advantage: their flying machines were the latest generation of fighters — Spitfires and Hurricanes.

That those aircraft carried eight guns was thanks to the persuasive efforts of Captain Hill. Four guns, the RAF had long believed, were the maximum possible — any more and the planes would be rendered too slow and too difficult to manoeuvre, becoming easy pickings for enemy fighters.

Cast-iron evidence was needed to back up the claims that eight guns would work — so Fred had turned for help to his 13-year-old daughter. An only child, Hazel was close to her father — and happened to be a talented mathematician.

‘My mother was partially dyslexic, and she had terrible trouble spelling,’ her eldest son Robin, 69, recalls now. 

German photo of Luftwaffe flying over the Channel. To Defeat The Few, by Paul Crickmore and Douglas Dildy, is published by Osprey and costs £30

German photo of Luftwaffe flying over the Channel. To Defeat The Few, by Paul Crickmore and Douglas Dildy, is published by Osprey and costs £30

German photo of Luftwaffe flying over the Channel. To Defeat The Few, by Paul Crickmore and Douglas Dildy, is published by Osprey and costs £30

‘This got her into trouble as she was obviously highly intelligent, so teachers thought she was naughty and lazy. I think when she did mathematics, she had none of these problems, which is why it appealed to her so much.’

Armed with the new ‘calculating machines’ of the time — to our eyes, very rudimentary computers — father and daughter worked long into the night analysing the data at their kitchen table. Their complicated calculations showed conclusively that each Spitfire needed to be capable of firing 1,000 rounds a minute — per gun.

They also calculated the exact distance the Spitfire — whose top speed was about 360mph — had to be from the enemy to hit them: just 755 ft. 

‘The biggest thing was the huge increase in speed of the new fighters, which was way beyond anything people had experienced before,’ says mathematician Niall MacKay.

‘What they had to do was take trials conducted at a much lower speed, then work out what would be necessary for a really high-speed fighter. That would have been particularly difficult.’ 

Not least for someone just into her teens. ‘You wouldn’t expect most 13-year-olds to be able to do that kind of maths so she must have been a remarkable mathematician,’ says Stephen Bungay.

Their conclusions — presented by Captain Hill in July 1934 — stunned officials. ‘They called it ‘staggering’,’ Hazel’s youngest son Ted says. ‘I think some higher echelons of the RAF said that it was going too far.

Most of them had grown up with World War I fighters that had one or two guns. The idea of four guns was radical, and eight was incredible.’

Nonetheless, the generals were persuaded, and as Britain headed inexorably towards war, the planes were put into production.

Finally, in July 1940, the Hills’ calculations were put to the test when Britain came under enemy bombardment in a campaign that led to more than 1,000 British planes being shot down. Germany’s Messerschmitts and other planes suffered nearly twice as many losses — but the margin of victory proved terrifyingly narrow.

‘There are stories of German bombers getting back to France with more than 200 bullet holes in them. The calibre of the bullets we were fitting was only just sufficient,’ says Group Captain Beldon. 

‘While many German bombers may have been damaged beyond repair, they were insufficiently damaged to shoot down.’

In other words, just a slight shift in calculations — and four fewer guns per plane — could have meant a very different result.

A German Messerschmitt after crashing in Kent in 1940. The image is from new book To Defeat The Few

A German Messerschmitt after crashing in Kent in 1940. The image is from new book To Defeat The Few

A German Messerschmitt after crashing in Kent in 1940. The image is from new book To Defeat The Few

‘It’s amazing how history can hang by a fine thread,’ says Ted. ‘If [Hazel] got the calculations wrong, if she hadn’t been asked to help, and the decision hadn’t been made to go for eight guns, who knows what could have happened?’

Hazel was, at least, briefly rewarded for her extraordinary efforts: after watching a Spitfire in action at the Hendon air show in 1936, she was given permission to sit briefly in the cockpit of the aircraft she had helped design.

After school, she studied medicine at university in London — graduating in 1943 and joining the Royal Army Medical Corps, where she treated injured soldiers who had returned from Dunkirk, civilians injured in the Blitz and returning prisoners of war.

At the end of the war Hazel became a female GP — very unusual at the time — and in 1948 married Chris Baker, one of the soldiers she had treated.

They moved to Wednesbury, Staffordshire, where Hazel took a groundbreaking position in the new National Health Service, setting up a child health clinic before training as a psychiatrist and publishing pioneering research into school phobia, anorexia and autism.

She did all this while raising her four sons Robin, Richard, 67, Frank, 66, and Ted, 64.

Yet while Hazel never tried to hide her contribution to her father’s work, she remained modest about it.

‘She told us she had helped her father with some important calculations but it was really only after she died in 2010 and we started to go through some of her paperwork that we realised the extent of her involvement,’ Robin says.

‘She was proud of it, but I don’t think it was where her heart lay. If she wanted to be remembered for anything, I think it would be for her medical work.’

Nonetheless, her sons are thrilled to see their mother’s contribution finally acknowledged. 

‘Society is made up of ordinary people making a difference — and she is one of those people,’ says Ted. ‘We are very proud of her.’

The Schoolgirl Who Helped To Win A War is on the BBC News channel at 1.30pm tomorrow, with repeats across the weekend.

The battle to beat the Few: Unseen photos show the Luftwaffe facing RAF firepower during bombing raids of England’s south coast… as Hitler hoped to strike a decisive blow and pave the way for invasion

  • Incredible previously-unknown images showed the battle of the skies between the German and British
  • Hitler had wanted to weaken Britain’s forces enough for the Nazis to invade and take over
  • But these pictures show his Operation Sealion failed thanks to the efforts of RAF heroes known as The Few
  • They successfully outwitted and out-fought the Luftwaffe to keep Britain safe and start turning tide of the war

A trove of unseen photos showing a different side to the Battle of Britain has been unearthed ahead of the famous conflict’s 80th anniversary.

The fascinating images, which feature dramatic scenes of bombing raids on the south coast, tell the story of the battle from the German perspective.

Many have been brought into the modern day thanks to a colourisation process that adds more layers of detail to the historic shots.

The Battle of Britain began on July 10, 1940, as Hitler sought a decisive blow paving the way for the invasion of Britain.

He declared that the aim of Operation Sealion was to ‘occupy it completely’, ordering the Luftwaffe to ‘overpower the English air force… in the shortest possible time’.

However, in the face of the brave resistance of ‘The Few’, Hitler called it off that October, with the Luftwaffe switching to bombing British cities.

All of the pictures are featured in new book To Defeat The Few, have been curated by British historian Paul Crickmore and US retired fighter pilot Colonel Douglas Dildy from the German archives.

He said: ‘It was completely vital that The Few rose to the occasion in the way they did.

‘You can’t overestimate the importance of the Battle of Britain in keeping us afloat in the war, so we could be the base from which to launch the invasion of France in 1944.’

Two sections from 65 Squadron, making up a flight of six aircraft, on a training flight as they prepared to take on the Luftwaffe. They were the line of defence against Hitler and the Nazis Operation Sealion, which aimed completely occupy Britain by overpowering the airforce and exhaust the spirit of the British people in the shortest possible time.

Two sections from 65 Squadron, making up a flight of six aircraft, on a training flight as they prepared to take on the Luftwaffe. They were the line of defence against Hitler and the Nazis Operation Sealion, which aimed completely occupy Britain by overpowering the airforce and exhaust the spirit of the British people in the shortest possible time.

Two sections from 65 Squadron, making up a flight of six aircraft, on a training flight as they prepared to take on the Luftwaffe. They were the line of defence against Hitler and the Nazis Operation Sealion, which aimed completely occupy Britain by overpowering the airforce and exhaust the spirit of the British people in the shortest possible time.

A German Messerschmitt ditched into a field near Eastbourne on September 30 after being shot down on a bombing run. The Luftwaffe was said to have the edge in the air and shot down three fighters for every two they lost. But British factories able to produce three times more replacements than Messerschmitts were made so the German aerial tactics were nullified

A German Messerschmitt ditched into a field near Eastbourne on September 30 after being shot down on a bombing run. The Luftwaffe was said to have the edge in the air and shot down three fighters for every two they lost. But British factories able to produce three times more replacements than Messerschmitts were made so the German aerial tactics were nullified

A German Messerschmitt ditched into a field near Eastbourne on September 30 after being shot down on a bombing run. The Luftwaffe was said to have the edge in the air and shot down three fighters for every two they lost. But British factories able to produce three times more replacements than Messerschmitts were made so the German aerial tactics were nullified

This aircraft, flown by Oblt Fronhoefer, crashed into the ground near Ulcombe, Kent, just after 6.45pm on August 15. It had been based in Calais, France, but was shot down by the brave British forces. Fighter Command headquarters used radar systems to help squadrons intercept approaching German aircraft, helping them to turn the tide against the Luftwaffe

This aircraft, flown by Oblt Fronhoefer, crashed into the ground near Ulcombe, Kent, just after 6.45pm on August 15. It had been based in Calais, France, but was shot down by the brave British forces. Fighter Command headquarters used radar systems to help squadrons intercept approaching German aircraft, helping them to turn the tide against the Luftwaffe

This aircraft, flown by Oblt Fronhoefer, crashed into the ground near Ulcombe, Kent, just after 6.45pm on August 15. It had been based in Calais, France, but was shot down by the brave British forces. Fighter Command headquarters used radar systems to help squadrons intercept approaching German aircraft, helping them to turn the tide against the Luftwaffe

A German crew servicing their bomber, part of the KGr 100 specialist pathfinder unit which was based at Brest in France. By now the Nazis had invaded France and taken their grip on the country to focus on other targets, including Britain. The brave actions of The Few meant they were never able to go any further after fights for supremacy in the area were won by the RAF

A German crew servicing their bomber, part of the KGr 100 specialist pathfinder unit which was based at Brest in France. By now the Nazis had invaded France and taken their grip on the country to focus on other targets, including Britain. The brave actions of The Few meant they were never able to go any further after fights for supremacy in the area were won by the RAF

A German crew servicing their bomber, part of the KGr 100 specialist pathfinder unit which was based at Brest in France. By now the Nazis had invaded France and taken their grip on the country to focus on other targets, including Britain. The brave actions of The Few meant they were never able to go any further after fights for supremacy in the area were won by the RAF

German Dornier bombers passing over the Netherlands in May 1940 on a bombing run as the Luftwaffe began their campaign of the skies. At the time they were the largest and most formidable air force in Europe. The way the fleet of aircraft was designed was as close-support weapon who were supposed to move in tandem with troops fighting on the ground

German Dornier bombers passing over the Netherlands in May 1940 on a bombing run as the Luftwaffe began their campaign of the skies. At the time they were the largest and most formidable air force in Europe. The way the fleet of aircraft was designed was as close-support weapon who were supposed to move in tandem with troops fighting on the ground

German Dornier bombers passing over the Netherlands in May 1940 on a bombing run as the Luftwaffe began their campaign of the skies. At the time they were the largest and most formidable air force in Europe. The way the fleet of aircraft was designed was as close-support weapon who were supposed to move in tandem with troops fighting on the ground

Portsmouth in the grip of a bombing raid during WWII

Portsmouth in the grip of a bombing raid during WWII

A prisoner of war index card for German Airforce crew member Walter Scherer

A prisoner of war index card for German Airforce crew member Walter Scherer

Pictures of Portsmouth during a bombing raid during World War II in July 1940. Families were warned of the attack by air raid sirens and took shelter as the Lutwaffe’s Messerschmitts filled the air (left). German pilot Walter Scherer was taken as a prisoner of war in a document (right) that listed his characteristics as well as his profile and front view portrait

German bombers leading a formation with the aircraft in the background known to be was lost in the sea off Portland, Dorset on 12 August 1940. The Luftwaffe suffered so many casualties that Adolf Hitler soon turned his attention to night-time Blitz campaigns of cities like London, Coventry and Liverpool in an effort to try and overcome the brave efforts of the RAF

German bombers leading a formation with the aircraft in the background known to be was lost in the sea off Portland, Dorset on 12 August 1940. The Luftwaffe suffered so many casualties that Adolf Hitler soon turned his attention to night-time Blitz campaigns of cities like London, Coventry and Liverpool in an effort to try and overcome the brave efforts of the RAF

German bombers leading a formation with the aircraft in the background known to be was lost in the sea off Portland, Dorset on 12 August 1940. The Luftwaffe suffered so many casualties that Adolf Hitler soon turned his attention to night-time Blitz campaigns of cities like London, Coventry and Liverpool in an effort to try and overcome the brave efforts of the RAF

This aircraft, a Spitfire X4111, lying damaged on the ground after being completely written off in a dog fight in August 1940. It had only been delivered to 602 Squadron at RAF Westhampnett, West Sussex, earlier in the day but was soon prepped to fly when it was hit by the Luftwaffe. From August 12 through to September 15, the Germans shot down more planes than the RAF

This aircraft, a Spitfire X4111, lying damaged on the ground after being completely written off in a dog fight in August 1940. It had only been delivered to 602 Squadron at RAF Westhampnett, West Sussex, earlier in the day but was soon prepped to fly when it was hit by the Luftwaffe. From August 12 through to September 15, the Germans shot down more planes than the RAF

This aircraft, a Spitfire X4111, lying damaged on the ground after being completely written off in a dog fight in August 1940. It had only been delivered to 602 Squadron at RAF Westhampnett, West Sussex, earlier in the day but was soon prepped to fly when it was hit by the Luftwaffe. From August 12 through to September 15, the Germans shot down more planes than the RAF

The menacing sight of German aircraft patroling the Channel shortly before the series of attacks known as the Battle of Britain. The Luftwaffe actually held the edge over the Allies in dogfights, shooting them down at a ratio of 1.77 to 1 lost. It prompted the Allies to change approach and keep their planes on the ground when possible to not rise to the Luftwaffe bait

The menacing sight of German aircraft patroling the Channel shortly before the series of attacks known as the Battle of Britain. The Luftwaffe actually held the edge over the Allies in dogfights, shooting them down at a ratio of 1.77 to 1 lost. It prompted the Allies to change approach and keep their planes on the ground when possible to not rise to the Luftwaffe bait

The menacing sight of German aircraft patroling the Channel shortly before the series of attacks known as the Battle of Britain. The Luftwaffe actually held the edge over the Allies in dogfights, shooting them down at a ratio of 1.77 to 1 lost. It prompted the Allies to change approach and keep their planes on the ground when possible to not rise to the Luftwaffe bait

A German Messerschmitt fighter in the Battle of Britain gliding in the skies ready to strike against the British forces. September 15 was the day when  the RAF - known as The Few - started winning the battle with aerial combat that day marked a notable victory for the defenders who inflicted heavy losses on the German fleet

A German Messerschmitt fighter in the Battle of Britain gliding in the skies ready to strike against the British forces. September 15 was the day when  the RAF - known as The Few - started winning the battle with aerial combat that day marked a notable victory for the defenders who inflicted heavy losses on the German fleet

A German Messerschmitt fighter in the Battle of Britain gliding in the skies ready to strike against the British forces. September 15 was the day when  the RAF – known as The Few – started winning the battle with aerial combat that day marked a notable victory for the defenders who inflicted heavy losses on the German fleet

Defiant fighters from 255 Squadron over the English countryside, flying in formation over the green fields below. The brave resistance of The Few infuriated Hitler, who had to switch tactics by October and order the Luftwaffe to bomb British cities. Factories had ramped up aircraft production to the point where they were building far more planes than the Germans

Defiant fighters from 255 Squadron over the English countryside, flying in formation over the green fields below. The brave resistance of The Few infuriated Hitler, who had to switch tactics by October and order the Luftwaffe to bomb British cities. Factories had ramped up aircraft production to the point where they were building far more planes than the Germans

Defiant fighters from 255 Squadron over the English countryside, flying in formation over the green fields below. The brave resistance of The Few infuriated Hitler, who had to switch tactics by October and order the Luftwaffe to bomb British cities. Factories had ramped up aircraft production to the point where they were building far more planes than the Germans

German BF 109 fighter aircrafts fly in formation as they continue their deadly mission above the clouds towards the shores of Britain. They were said to have had superiority in air-to-air combat, but their numbers were insufficient to overcome the British production advantage, meaning their mission to try and destroy Flight Command could never be achieved

German BF 109 fighter aircrafts fly in formation as they continue their deadly mission above the clouds towards the shores of Britain. They were said to have had superiority in air-to-air combat, but their numbers were insufficient to overcome the British production advantage, meaning their mission to try and destroy Flight Command could never be achieved

German BF 109 fighter aircrafts fly in formation as they continue their deadly mission above the clouds towards the shores of Britain. They were said to have had superiority in air-to-air combat, but their numbers were insufficient to overcome the British production advantage, meaning their mission to try and destroy Flight Command could never be achieved

This fascinating black and white picture is an high-altitude reconnaissance image of Dover taken by the German air force. The spy shot was captured in an effort to try and work out where anti-aircraft guns could be hidden before they went on the attack after taking off from France for the daytime raid on September 15, 1940 - Battle of Britain Day

This fascinating black and white picture is an high-altitude reconnaissance image of Dover taken by the German air force. The spy shot was captured in an effort to try and work out where anti-aircraft guns could be hidden before they went on the attack after taking off from France for the daytime raid on September 15, 1940 - Battle of Britain Day

This fascinating black and white picture is an high-altitude reconnaissance image of Dover taken by the German air force. The spy shot was captured in an effort to try and work out where anti-aircraft guns could be hidden before they went on the attack after taking off from France for the daytime raid on September 15, 1940 – Battle of Britain Day

British anti aircraft fire rips through the tail and wings of enemy planes as they zoom through the air trying to engage with the RAF heroes who had out-produced and out-thought their tactics. This image is of an area between Bristol and Cardiff and marks a success of the British forces after German spy planes had failed to detect the powerful weapons

British anti aircraft fire rips through the tail and wings of enemy planes as they zoom through the air trying to engage with the RAF heroes who had out-produced and out-thought their tactics. This image is of an area between Bristol and Cardiff and marks a success of the British forces after German spy planes had failed to detect the powerful weapons

British anti aircraft fire rips through the tail and wings of enemy planes as they zoom through the air trying to engage with the RAF heroes who had out-produced and out-thought their tactics. This image is of an area between Bristol and Cardiff and marks a success of the British forces after German spy planes had failed to detect the powerful weapons

Reichsmarschall Hermann Goring

Reichsmarschall Hermann Goring

Air Chief Marshal Hugh Dowding

Air Chief Marshal Hugh Dowding

Reichsmarschall Hermann Göring, the commander-in-chief of the Luftwaffe, is seen left in a colourised picture. He kept control of the fleet until the last days of the war but lost the public when the Allies were able to bomb German cities. Air Chief Marshal Hugh Dowding, seen right, developed tactics that helped the RAF stave off the Luftwaffe and win the Battle of Britain

A German reconnaissance photograph showing the Swingate transmitting station near Dover with its barrage balloon screen. The Nazis sent a number of spy planes to the UK to try and work out what areas they should target as well as spots to avoid to try and slip past anti-aircraft fire. They were also often deployed to try and help ground forces in where they should go.

A German reconnaissance photograph showing the Swingate transmitting station near Dover with its barrage balloon screen. The Nazis sent a number of spy planes to the UK to try and work out what areas they should target as well as spots to avoid to try and slip past anti-aircraft fire. They were also often deployed to try and help ground forces in where they should go.

A German reconnaissance photograph showing the Swingate transmitting station near Dover with its barrage balloon screen. The Nazis sent a number of spy planes to the UK to try and work out what areas they should target as well as spots to avoid to try and slip past anti-aircraft fire. They were also often deployed to try and help ground forces in where they should go.

FIGHTERS IN THE SKY: SPITFIRE VS MESSERSCHMITT

Manufacturers: Vickers-Armstrong Ltd

Type: British single-seat fighter

Engine: Rolls Royce Merlin

Speed: 387 mph

Range: N/A

Ceiling: 36,000ft

Rate of climb: 2,300 ft per minute

Armament: Mk 1A model – 8 Browning .303 machine guns (4 in each wing).

Dimensions: Length: 28ft 11in, height: 11ft 5in, wingspan: 26ft 10in, wing area: 242 sq ft

 Source: RAF 

Manufacturers: Messerschmitt AG

Type: German single-seat fighter 

Engine: Daimler-Benz DB 600 

Speed: 354 mph

Range: 460 miles

Ceiling: 36,900 feet

Rate of climb: 3,345 ft per minute

Armament: 3 x 20 mm MG FF Cannon and 2 x 7.92mm MG17 machine guns.

Dimensions:  Length: 29ft 7in, height: 8ft 2in, wingspan: 32ft 6in, wing area: 173.3 sq ft

 

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