The work was done in the lamplight over a small kitchen table in North London.
In the early months of 1934, Captain Fred Hill and his 13-year-old daughter Hazel burned the midnight oil night after night, plotted diagrams, and worked on complex algorithms.
It was a tiring, rewarding job, but both sensed how important it would be.
And her instincts would soon be confirmed by history because her intricate calculations would help the RAF win the battle of Britain – a triumph that many historians today believe has changed the course of World War II.
Firepower for freedom: Spitfires in formation. The picture comes from the new book To Defeat The Few
The father and daughter concluded that the new generation of aircraft that the government was building to prepare for future war should not be armed with four powerful machine guns, but with eight – an idea that was considered to be profoundly radical and was even considered impossible at the time.
Only then, the Hills believed, would the new generation of spitfires and hurricanes have sufficient firepower to shoot down enemy planes.
As a scientific officer in the Aviation Ministry, Captain Hill managed to convince his superiors of the importance of his and Hazel's findings – and six years later, in 1940, their calculations in the sky over Britain were put to the test when the RAF battled Hitler's dreaded Air Force against Adolf in a four-month battle that has been called the most important military campaign ever.
In the first months of 1934, captain Fred Hill and his 13-year-old daughter Hazel (top) burned the midnight oil night after night, drew diagrams and worked on complex algorithms
"Without the victory in the air battle for Britain, Germany would almost certainly have entered Germany," says military historian Stephen Bungay, who could have achieved a completely different result without the "persistence" of the hills. "
So far, the captivating story of the schoolgirl who helped win a war has unfortunately not been told. Hazel's only public recognition came from a paper her father's manager wrote to the Department of Aviation.
Now, 80 years after the Battle of Britain – and ten years since the mother of four sons died at the age of 90 – the RAF has publicly recognized Hazel's heroic contribution for the first time and in a fascinating BBC documentary in which the humble schoolgirl plays, paid tribute as "inspiration".
"It's just wonderful that Hazel's story sees the light of day," said group captain James Beldon, director of defense studies at the RAF.
"What great inspiration for young people today, and especially for young girls who can see someone like Hazel in the 1930s, who makes such an important contribution to our later success in the Battle of Britain that is essential to the survival of this country was crucial. "
Few would disagree. In July 1940, the fate of the free world was at stake when RAF pilots bravely warded off deadly attacks by the National Socialist Air Force.
Her victory was by no means certain and depended on her skill and bravery. Many were hardly teenagers.
These great men had one decisive advantage: their flying machines were the latest generation of fighters – spitfires and hurricanes.
Captain Hill's convincing efforts made it possible for these aircraft to carry eight cannons. Four cannons, the RAF had long believed, were the maximum – more, and the planes would be too slow and too difficult to maneuver, which became an easy choice for enemy fighters.
Cast-iron evidence was required to support claims that eight weapons would work – so Fred had asked his 13-year-old daughter for help. As an only child, Hazel was close to her father – and happened to be a talented mathematician.
"My mother was partially dyslexic and had terrible spelling problems," recalls her oldest son Robin, 69, now.
German photo of the Luftwaffe flying over the canal. To Defeat The Few by Paul Crickmore and Douglas Dildy is published by Osprey and costs £ 30
"That got her in trouble because she was obviously highly intelligent, and the teachers thought she was naughty and lazy. I think when she did math she didn't have any of these problems, which is why it appealed to her. & # 39;
Armed with the new "calculators" of the time – computers that were very rudimentary for us – father and daughter worked late into the night and analyzed the data at their kitchen table. Their complicated calculations conclusively showed that every Spitfire had to be able to fire 1,000 rounds per minute – per weapon.
They also calculated the exact distance the Spitfire – the top speed of which was about 360 miles an hour – had to be from the enemy to hit them: only 755 feet.
"The greatest thing was the enormous speed increase of the new fighters, which went far beyond anything that people had experienced before," says the mathematician Niall MacKay.
“They had to run tests at a much slower speed and then figure out what it would take a really fast hunter to do. That would have been particularly difficult. & # 39;
Not least for someone who is just a teenager. "You wouldn't expect most 13-year-olds to master this kind of math, so she must have been a remarkable mathematician," said Stephen Bungay.
The officials were astonished at the conclusions Captain Hill presented in July 1934. "They called it" stunning, "says Hazel's youngest son, Ted. "I think some higher levels of the RAF have said that it is going too far.
Most of them had grown up with World War I fighters who had one or two cannons. The idea of four cannons was radical and eight were incredible. & # 39;
Nevertheless, the generals were convinced, and when Britain went to war unstoppably, the planes went into production.
Finally, the Hills calculations were put to the test in July 1940 when Britain came under enemy fire in a campaign that resulted in the shooting down of more than 1,000 British aircraft. Germany's Messerschmitts and other aircraft suffered almost twice as many losses – but the profit margin turned out to be terribly narrow.
“There are stories of German bombers returning to France with more than 200 bullet holes. The caliber of the bullets that we assembled was just enough, ”says Group Captain Beldon.
"While many German bombers were damaged beyond repair, they weren't damaged enough to fire."
In other words, just a slight shift in the calculations – and four fewer cannons per plane – could have resulted in a completely different result.
A German Messerschmitt after a crash in Kent in 1940. The picture comes from the new book To Defeat The Few
"It's amazing how history can hang together," says Ted. "If (Hazel) had misunderstood the calculations, if she hadn't been asked for help and the decision had not been made for eight weapons, who knows what could have happened?"
Hazel was rewarded, at least briefly, for her extraordinary efforts: after seeing 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 to design.
After school she studied medicine at the University of London – she graduated in 1943 and joined the Royal Army Medical Corps, where she treated injured soldiers who had returned from Dunkirk, lightning-wounded civilians and returning prisoners of war.
At the end of the war, Hazel became a general practitioner – very unusual at the time – and married Chris Baker, one of the soldiers she had treated, in 1948.
They moved to Wednesbury, Staffordshire, where Hazel held a groundbreaking position in the new National Health Service, set up a children's health clinic before completing psychiatrist training and publishing groundbreaking research on school phobia, anorexia, and autism.
She did all of this while raising her four sons, Robin, Richard (67), Frank (66) and Ted (64).
Although Hazel never tried to hide her contribution to her father's work, she remained humble.
"She told us that she had helped her father with some important calculations, but it wasn't until she died in 2010 and we started going through some of her paperwork that we realized the extent of her involvement," says Robin.
"She was proud of it, but I don't think her heart was there. If she wanted to be remembered for anything, I think it would be for her medical work. & # 39;
Nevertheless, her sons are excited that her mother's contribution is finally recognized.
"Society is made up of ordinary people who make a difference – and they're one of those people," says Ted. "We are very proud of them."
The schoolgirl who helped win a war is on the BBC news channel tomorrow at 1:30 p.m. and repeats itself over the weekend.
The Fight Against the Few: Invisible photos show how the Air Force was exposed to RAF firepower in bombing raids on the English south coast … when Hitler hoped to strike a decisive blow and pave the way for an invasion
- Incredible previously unknown pictures showed the battle of the sky between Germany and Great Britain
- Hitler had wanted to weaken the British armed forces to such an extent that the Nazis could invade and take power
- But these images show that his Operation Sealion has failed thanks to the efforts of RAF heroes known as The Few
- They have successfully outsmarted and fought the Air Force to protect Britain and turn the war
Before the 80th anniversary of the famous conflict, a lot of invisible photos were discovered that show another side of the Battle of Britain.
The fascinating images, which show dramatic scenes of bombing raids on the south coast, tell the story of the battle from a German perspective.
Many have been brought into the modern age thanks to a coloring process that gives the historical photographs more levels of detail.
The battle for Britain began on July 10, 1940 when Hitler was looking for a decisive blow that paved the way for the invasion of Britain.
He stated that Operation Sealion's goal was to "fully occupy" and ordered the Air Force to "overpower the English Air Force … in the shortest possible time."
Given the brave opposition from "The Few", Hitler canceled this in October, when the Air Force switched to bombing British cities.
All images are included in the new book To Defeat The Few, curated by the British historian Paul Crickmore and the US fighter pilot Colonel Douglas Dildy from the German archive.
He said: “It was absolutely important that the few came to the occasion as they did.
"You can't overestimate the importance of the Battle of Britain to keep us afloat in the war. So we could be the base from which to launch the invasion of France in 1944."
Two 65th Squadron sections, which formed a flight of six planes, were on a training flight as they prepared for the Air Force. They were the line of defense against Hitler and the Nazi Operation Sealion, which aimed to fully occupy Britain by overpowering the Air Force and exhausting the spirit of the British people in no time.
A German Messerschmitt crashed into a field near Eastbourne on September 30 after being shot down in a bombing raid. The Air Force is said to have the advantage in the air and shoot three fighters for every two lost. But British factories that could produce three times more replacements than Messerschmitt's were built, so the German air tactic was abolished
This aircraft, which was flown by Oblt Fronhoefer, crashed into the ground near Ulcombe, Kent, shortly after 6.45 p.m. on August 15. It was based in Calais, France, but was shot down by the brave British forces. The headquarters of the Jagdkommando used radar systems to help squadrons intercept approaching German aircraft and turn the tide against the Air Force
A German crew waiting for their bomber and part of the KGr 100 Special Pathfinder unit based in Brest, France. Meanwhile, the Nazis had invaded France and got a grip on the country to focus on other destinations, including Britain. The Few's bold actions meant they could never go further after the RAF won battles for supremacy in the region
German Dornier bombers who drove over the Netherlands in a bombing raid in May 1940 when the Luftwaffe started their campaign. At that time, they were the largest and most impressive air force in Europe. The way the aircraft fleet was designed was a weapon with close support that was supposed to move with troops fighting on the ground
Pictures of Portsmouth during a bombing raid in World War II in July 1940. Families were warned of the attack by air raid sirens and sought protection when the Lutwaffe's knife smiths filled the air (left). The German pilot Walter Scherer was recorded in a document (right) as a prisoner of war, in which his characteristics, his profile and his portrait were listed from the front
German bombers leading an aircraft formation in the background were lost in the sea off Portland, Dorset on August 12, 1940. The Air Force suffered so many casualties that Adolf Hitler soon turned his attention to night flash campaigns from cities like London, Coventry and Liverpool to overcome the RAF's courageous efforts
This aircraft, a Spitfire X4111, was damaged on the ground after being completely written off in a dog fight in August 1940. It had only been delivered to the 602 Squadron of the RAF Westhampnett in West Sussex earlier in the day, but was soon prepared to fly when it was hit by the Air Force. From August 12 to September 15, the Germans shot down more planes than the RAF
The menacing sight of German aircraft patrolling the canal just before the series of attacks known as the Battle of Britain. The Air Force actually held the edge over the Allies in dogfights and shot them down at a ratio of 1.77 to 1. It prompted the Allies to change their approach and keep their planes on the ground as possible so as not to become an Air Force lure
A German Messerschmitt fighter in the air battle for England who is gliding into the sky and ready to strike against the British armed forces. September 15 was the day on which the RAF – known as The Few – began to win the air combat battle on that day. This was a remarkable victory for the defenders who inflicted heavy losses on the German fleet
Spitfire fighters from the 225 Squadron fly over the English countryside and fly in formation over the green fields below. The brave resistance of the few angered Hitler, who had to change tactics by October and order the Air Force to bomb British cities. The factories had increased aircraft production so much that they built far more aircraft than the Germans
German BF 109 fighters fly in formation as they continue their deadly mission above the clouds towards the British coast. They were said to have been superior in air-to-air combat, but their numbers were insufficient to overcome the UK manufacturing advantage, which meant that their mission to destroy Flight Command could never be achieved
This fascinating black and white image is a high-resolution reconnaissance image of Dover, which was taken by the German Air Force. The spy shot was captured to find out where anti-aircraft guns can be hidden before attacking after they launched a day-to-day attack from France on September 15, 1940, the day of the Battle of Britain
British anti-aircraft fire tears the tail and wings of enemy aircraft as they zoom through the air, trying to engage with the RAF heroes who have overproduced and considered their tactics. This image shows an area between Bristol and Cardiff and marks a success for the British armed forces after German spy planes failed to discover the powerful weapons
The Reichsmarschall Hermann Göring, the commander in chief of the Luftwaffe, can be seen in a color image on the left. He remained in control of the fleet until the last days of the war, but lost publicity when the Allies were able to bomb German cities. Air Chief Marschall Hugh Dowding, richtig gesehen, entwickelte Taktiken, die der RAF halfen, die Luftwaffe abzuwehren und die Luftschlacht um England zu gewinnen
Ein deutsches Aufklärungsfoto, das die Swingate-Sendestation in der Nähe von Dover mit ihrem Sperrballonschirm zeigt. Die Nazis schickten eine Reihe von Spionageflugzeugen nach Großbritannien, um herauszufinden, auf welche Gebiete sie zielen sollten und an welchen Stellen sie vermeiden sollten, am Flugabwehrfeuer vorbeizukommen. Sie wurden auch oft eingesetzt, um Bodentruppen zu helfen, wohin sie gehen sollten.
KÄMPFER AM HIMMEL: SPITFIRE GEGEN MESSERSCHMITT
Hersteller: Vickers-Armstrong Ltd.
Art: Britischer einsitziger Kämpfer
Motor: Rolls Royce Merlin
Geschwindigkeit: 387 mph
Angebot: N / A
Decke: 36.000 Fuß
Steiggeschwindigkeit: 2300 Fuß pro Minute
Armament: Modell Mk 1A – 8 Browning .303 Maschinengewehre (4 in jedem Flügel).
Dimensions: Länge: 28 Fuß 11 Zoll, Höhe: 11 Fuß 5 Zoll, Flügelspannweite: 26 Fuß 10 Zoll, Flügelfläche: 242 Quadratfuß
Hersteller: Messerschmitt AG
Art: Deutscher einsitziger Kämpfer
Motor: Daimler-Benz DB 600
Geschwindigkeit: 354 mph
Angebot: 460 Meilen
Decke: 36.900 Fuß
R.aß vom Aufstieg: 3.345 Fuß pro Minute
Armament: 3 x 20 mm MG FF Kanone und 2 x 7,92 mm MG17 Maschinengewehre.
Dimensions: Länge: 29 Fuß 7 Zoll, Höhe: 8 Fuß 2 Zoll, Flügelspannweite: 32 Fuß 6 Zoll, Flügelfläche: 173,3 Quadratfuß
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