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.
Edges like these reduce drag. They originated on Falcon9, where they fold away on ascent and fold out on return.
BUT, on Starship they don't fold away, saving the mass of the folding mechanism AND incurring the drag of flat edges on the way up.
@ElonMusk. Rotating the pointy edges to face upwards during launch will likely save drag on the way up too. Then rotate them down at the azimuth for return. Alternatively, sharpen the top edges the same, to cut both ways and maybe even save more mass? Then if the drag on the way up is reduced, might that imply a reduction in the mass of the mount-points as well?
Afterthought. Boosters will be reused a lot (maybe 100 x). (Mass and drag) saved by booster optimization will yield mass-to-orbit scaling of the product: (#launches x #boosters). Seems worth it.