Mitchell’s elliptical wing was thin enough to be fast and stiff enough to carry an engine that doubled in power. In 1939 it flew behind 1,030 hp; by 1944 the same shape flew behind 2,000, and the Spitfire IX of 1942 outclimbed the Mk V it replaced and was roughly 110 km/h faster at 30,000 ft, most of that from the two-stage Merlin. Almost no other 1936 design survived the whole war in front-line service.

The first Spitfires carried eight rifle-calibre Brownings, four in each wing, firing about 1.7 kg of bullets a second for eighteen seconds. Against armoured bombers that was too little, and from 1941 two 20 mm Hispano cannon took the middle of the wing. The cannon’s heavier shell mattered more than its rate of fire: one hit did what a dozen bullets could not.

Chain Home radar saw the raids forming over France; the sector control rooms plotted them and sent squadrons up only when they were needed; 100-octane petrol, much of it shipped from the United States, let the Merlin run twelve pounds of boost for five minutes at a time. The Spitfire and Hurricane were the sharp end of a system, and it was the system that made the Luftwaffe’s losses unsustainable.

Wing guns do not fire straight ahead: they are angled inwards to meet at a chosen range, a setting squadrons argued over and that came down to about 230 metres during 1940, so the eight streams of bullets arrived together on one patch of enemy aircraft. Too far or too close and they arrived apart. With the Hispano of the Mk Vb, from 1941, the arithmetic changed: two cannon and four machine guns fired about 3.5 kg a second and a 20 mm shell exploded inside what it hit.

Power against altitude from the type of supercharger, weight of fire against the other nine, and Breguet range with the armour and drop-tank trades. Simplified models, each scaled to this aircraft’s published figures, so the shapes are honest and the third decimal is not.