Hazel was already a talented mathematician at age 13 and she did the calculations, on their kitchen table and at offices after workers had gone home, for her father that promoted the idea that the coming Hurricane and Spitfire fighter aircraft should have 8 rather than 4 or 6 Browning 303 machine guns with scientific evidence.
It was estimated that pilots would only have about 2 seconds on target at a close range during which to fire and they had to produce enough weight of fire in that time to destroy an enemy aircraft. The calculations proposed that destruction of the enemy aircraft would only be possible with 8 machine guns, an idea that was quite revolutionary at the time.
There were counter arguments at the time, that the weight of 8 machine guns would rob the fighters of their speed and agility, and initial designs had only 4 machine guns in total which Hazel and her father argued with evidence would not have been enough to work as a proper fighter aircraft.
The point was made that air superiority was often made on slim advantages and that hurricanes and spitfires having 8 machine guns gave them an advantage in air to air combat and significantly helped them win the battle of Britain.
