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Here is a photo of SpaceShip 2's exhaust shortly after ignition during the test flight in January

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Why do they have that segmented structure, and how does it affect thrust?

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Those are Mach diamonds. They form due to the interaction of the exhaust flow with its own supersonic shockwaves. All rockets and some jet engines produce them; their visibility varies with the propellant combination, mixture ratio and environmental conditions.

The flow pattern doesn't appreciably affect thrust since it takes place after the exhaust has left the nozzle (where thrust is produced).

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