Transition between elliptical and arch-shaped cross sections (space shuttle)

[Pipcard]

I've been trying to model the cancelled Japanese space shuttle "HOPE-X" based on this reference.

What I got was this. Ugly, isn't it?


This is what it's supposed to look like.


As you can see, the front is dome shaped. The top half of the dome gradually transitions to an arch shape, while the bottom half gradually transitions to a flat bottom.

Here's what I have so far,


but I'm not sure what to do next.