Earlier quoted context omitted.
I saw a paper that examined pressure fed, turbo pumps, and electric. Electric beats both pressure fed and turbo pumps at the size Rocket Lab is targeting. At large sizes turbines beat electric but the plumbing is much more complex and technically challenging. I'm suspicious that electrics are viable for first stages where performance advantage is less important. For first stages the cost is linear with ISP. Where it'…
I would love to read that paper if you can find it! Does metal 3D printing mitigate any of these challenges? Or is the problem a packaging problem where there is a minimum size required for the mechanical parts?
https://www.aacademica.org/hernan.emilio.tacca/9.pdf
I did some more looking, the linked study says that turbopumps scale better then electric as the burn time increases. Because burning fuel and oxidizer is more weight efficient than batteries. At short burn times that's offset by the increased weight of the turbopump.
Along with my earlier comment, the Proton first stage only burns for 130 seconds. Which puts first stages in the short burn category where eletrics do well. *but never as good as turbo pumps. Which supports the idea that electric systems can compete for large first stages by being simple, cheap, and reliable.
More whack is relanding first stage electric fed rockets. Ala SpaceX.