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The header tank is bulged out at the top and the bottom.What may be the reason for this?Can't simple cylinder tanks be used instead?enter image description here

Elon Musk also posted the image of Starship fuel header tank.

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    $\begingroup$ What in this image is a "header tank"? Most stages don't have them. $\endgroup$ Apr 7 '20 at 9:56
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A simple cylinder with flat circular sheets at both ends is less stable and would be heavier than a cylinder with hemispherical or elliptical ends.

A sphere has the best ratio of volume to surface and also of mass to volume. Material stress caused by internal pressure is homogenusly distributed over the surface.

If a sphere's diameter is too big for the rocket, a (short) cylinder with hemispheres at both ends is the second best optimal form. But for the cylindrical part stress in axial direction is only half of that in tangential (circumference) direction.

See Wikipedia and the Kesselformel, only the german version has the essential formulas for axial and tangential tension.

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    $\begingroup$ @Auberron To put it more simply-- a sphere is the most resistant to pressure of any shape. See, for example, the info at engineering.stackexchange.com/questions/2419/… $\endgroup$ Apr 7 '20 at 12:31
  • $\begingroup$ There is an english version of the page, it is linked in wikipedias sidebar: en.wikipedia.org/wiki/Barlow%27s_formula $\endgroup$
    – Polygnome
    Apr 7 '20 at 21:10
  • $\begingroup$ @Polygnome I know there is an english version too but the essential formulas for axial and tangential tension are missing. $\endgroup$
    – Uwe
    Apr 7 '20 at 21:31
  • $\begingroup$ @Polygnome If you hit the "Translate this page" (at least in Chrome) is the output useable? $\endgroup$ Apr 8 '20 at 13:10

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