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Why does the Vulcan's wing have a curved leading edge?
Short answer
Because of a flight problem: the pure delta of the first Vulcans suffered buffeting as it approached its Mach limit. The "phase 2" wing reduced the sweep from the root to mid-span, so the leading edge traces a kinked arc, and with it that buffeting disappeared.

The flaw of the pure delta
The prototypes and the first production Vulcan B.1s flew with a delta wing with straight leading edges. While exploring, with the second prototype, VX777, the high, fast part of the flight envelope at the Boscombe Down test centre, a mild buffet and other undesirable characteristics appeared when approaching the Mach limit, including an alarming tendency to enter an uncontrollable dive. For a bomber with no defensive armament, that was considered unacceptable.
The solution: the phase 2 wing
The answer was the wing known as "phase 2". The sweep angle was reduced from the root to roughly mid-span, so that the leading edge stopped being a straight line and instead traced an arc with a characteristic kink. Spanish-language sources also link the buffet to fatigue cracking of the wing, another reason to change it before the aircraft entered service. The phase 2 wing eliminated the shaking, and an automatic Mach trimmer took care of countering the tendency to dive by applying elevator as speed increased.
From the B.1 to the B.2
The first B.1s with straight leading edges were later modified with the kinked-edge wing. The B.1 XA889, already fitted with the phase 2 wing, was delivered in March 1956 for the trials for the type's first certificate of airworthiness. Later came the larger, thinner phase 2C wing, which VX777 debuted in 1957 and which became the wing of the Vulcan B.2. That curved leading edge is today one of the features that set the Vulcan apart from other deltas of its era.
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