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I was reading about wave drag and Concorde recently and found some contradictory information relating to drag. For example Wikipedia says:

Afterburner was added to Concorde for take-off to cope with weight increases that came after the initial design, and was used to push through the transonic drag barrier.

And they add the following image (it's sad that they don't mention what kind of aircraft it relates to):

enter image description here

But this image (from this article) suggest that aircraft with swept wings don't experience this sudden drag at transonic speeds, only later. Concorde has swept wings so it should experience max drag coefficient near mach 2 but it didn't have to use afterburners at this speed. How can it be? Were afterburners in Concorde necessary to break sound barrier, or only used for climbing?

enter image description here

Maybe someone knows some specific drag parameters at different speeds and would care to share, as I could't find anything specific...

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Concorde afterburners were reducing overall fuel consumption.

To understand why there is a special drag penalty around Mach 1, please read this answer.

Now to your graphs in the question body. The first one with the steep drag peak at Mach 1 is for a straight wing which never was designed to fly trans- or supersonically. You do get such results, but only if you use the wrong design for the task.

The next graph shows how the drag peak is shifted to higher Mach numbers with sweep. This is true for the wing alone. This graph is most likely valid for a sheared wing: A straight, high-aspect ratio wing which is rotated around its vertical axis in the windtunnel. But an airplane is more than just the mid-span wing. Swept wings need a center section which adds drag which does not shift with sweep angle; see below for test results (source: Hoerner's Fluid Dynamic Drag, section XV).

Minimum drag coefficient over Mach for wings with aspect ratio 4 and different sweep angles

Minimum drag coefficient over Mach for wings with aspect ratio 4 and different sweep angles

The last plot shows generic full airplane data, so it doesn't apply to a specific design but shows how things typically look like. Individual designs might still look quite different; for the F-16, for example, the drag coefficient triples between sub- and supersonic speed and stays roughly constant between Mach 1.3 and Mach 2.0 due to careful shaping which avoids the transsonic Mach peak almost completely.

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