The grid fins on Starship are serrated, why? Does it help in transonic maneuvers?
Source: Starbase Factory Tour with Elon Musk [Part 1], YouTube, at 30:28
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Such design, with hyperbolic leading edges, has been invented by MBDA (Airbus branch for missile systems) represented by BAE Systems (defense contractor), and is described in the European patent 3 599 442 A1 filed on July 2018:
The curve helps reducing drag, especially at supersonic velocities, an important factor for missiles and rockets, for which fuel is very limited.
Having a hyperbolic curve for the leading edge planform shape provides for a lower drag, in particular a lower wave drag. This means that the grid fins could be used as efficient lift and control devices/surfaces for supersonic flight vehicles.
Fins in place at the top of a 70 m-tall Super Heavy Booster 4:
The booster is used for the SpaceX Starship program. Curved leading edges are pointing at the ground, in the position required for booster return to its launchpad (video of the return trip). Fins are indeed used for the atmospheric flight. In space attitude is controlled using thrusters or reaction wheels.