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Since Starship has to feed its engines in two kind of situations :

-during ascent, acceleration is colinear to Starship's longitudinal axis.

-at the end of the belly dive, acceleration is normal to Starship's longitudinal axis.

Why is the bottom of both LOX and LCH4 tanks curved the way they are? At first glance it looks like having a central piping/engine feeding, is the most efficient and safest solution to feed engines during ascent, yet it requires using header tanks to restart after belly dive.

Wouldn't a reversed curvature combined with radial feeding allow the engines to work in both configurations, without needing header tanks? (radial feeding located at belly side)

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The header tanks are needed to control slosh during landing and to store landing propellant during orbital operations and in transit on interplanetary missions.

Without header tanks, the propellants would absorb far more heat in space, and with reversed curvature they would accumulate in shallow rings around the periphery of the lower domes during landing. This is about the worst case possible as far as slosh is concerned, and would make it very difficult to ensure the engines are supplied with liquid propellants without any gas during the landing burn.

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    $\begingroup$ Couldn't anti sloshing baffles and using advantage of "atmospheric ullage" solve the first issue? (I agree with second issue regarding the far better volume/surface ratio of spherical header tanks) $\endgroup$
    – qq jkztd
    Mar 3, 2021 at 18:05
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    $\begingroup$ Baffles damp the sloshing, they don't eliminate it, and the same damping action would also slow the return to level following a disturbance. It would be very difficult to get the last dregs of propellant out of such a tank while the vehicle's maneuvering around and trying to land. $\endgroup$
    – Christopher James Huff
    Mar 3, 2021 at 18:46

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