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How thick is the Vulcan's wing root?
Short answer
About 2.13 m (7 ft). The Vulcan's delta wing was so thick at the root that it housed the engines, air intakes, fuel and the weapons bay; that thickness was precisely one of the advantages sought with the delta planform: great structural strength and plenty of internal volume.

A wing that doubled as a fuselage
The Avro Vulcan was designed almost as a flying wing. The delta planform allowed for a very robust structure and, above all, a thick profile near the fuselage. According to the aircraft's technical description, the wing root section was about 2.13 m (7 ft) thick, enough space to house weapons and fuel and to integrate the engines, which were arranged in pairs on each side of the bay, with large air intakes opening right at the leading edge of the root.
Thin airfoils for a thick wing
The fact that the root was thick in absolute terms doesn't mean the wing was thick in proportion. The airfoil used was a modified NACA 0010 at the root and a modified NACA 0008 at the tip, that is, symmetrical airfoils of moderate relative thickness. The delta's huge chord meant that percentage translated into considerable height where the wing joined the central fuselage.
What changed in the design
Avro's initial project was even more radical: a flying wing with the engines stacked within the wing and two separate bomb bays, located outside the engines. During development the wing thickness was reduced, and that reduction made it impossible to keep the bays divided and the engines stacked. The solution was to place the four jets side by side, in pairs, on either side of a single central bay, with a somewhat larger fuselage.
The result was a bomber with very clean lines, in which almost everything bulky was buried within the wing. That same thick root is what, seen from the front, gives the Vulcan its unmistakable silhouette of a triangle with two large mouths on either side of the cockpit.
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