Shipbucket

if I look at the distribution of weight (at least in height direction)
you have an similarly sized gun, lower in the ship
you have somewhat heavier radars, but about the same in CoG height
you have an VLS battery on the same position as the Mk 13
you have 2 helicopters as well on the main deck
you have an heavier powerplant
you have an heavier sonar

so all in all, it seems like your CoG will be lower, not higher.

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If I increase the height of the forecastle and the superstructure, would that solve the cog dilemma?

enlarging/heightening the superstructure would help, or lowering the relative large beam (by increasing length and/or draft) or enlarging the radar suite.
without full calculations I cannot really say how it would end up, but just keep in mind the center of gravity should be higher then on the perry, and the higher you add weight, the better it is. you have to reason a bit, if you enlarge the beam you enlarge the displacement and with that the total weight of the ship, and that should go somewhere

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Drawings are credited with J.Scholtens
I ask of you to prove me wrong. Not say I am wrong, but prove it, because then I will have learned something new.
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So I have increased the draft with 4 pixels, made the hangar 4 pixels taller, increased the height of the forward part (foc'sle) with 6 pixels, made the bridge 10 pixels taller and increased the length by 22 pixels. I hope that helps.

I'd note that FFG-7 had an aluminium superstructure. Aluminium is still used on warships but only for non-structural elements such as funnels and masts. This change alone would raise the VCG a bit.

RP1

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along with the steel superstructure RP1 mentions, that should do the trick quite nicely, I think. it is looking about right now, I think.

on a sidenote, great to see you contributing a lot more, RP1!

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Drawings are credited with J.Scholtens
I ask of you to prove me wrong. Not say I am wrong, but prove it, because then I will have learned something new.
Shipbucket Wiki admin

I don`t suppose I should redesign the bridge to look better?

A further round of idea's

Forget the Perry FFG size/requirement (early 1970's era !)
Think late 2010's/late 2050's era !!!!!!!!!!!!!!!

US ship-designer "Gibbs and Cox" International Frigate - late 1990's/early 2000's design (a mini Burke)
With 1 x 5" gun, 1 x CIWS RAM, 8 SSM, 32 VLS, hangar for helico, AEGIS, 2 directors & so

(lovely to see a much more updated/recent version with a 57 or 76mm gun, a CIWS (laser or RAM), 32 VLS forward, maybe 8 or 16 VLS amidships ? & a full integrated mast (without SPG-62 director's).
Heuhen,

Karle,

Again the hate on cannister launchers. Why?

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Source Materiel is always welcome.

It's an irrational hate. He doesn't need an explanation. I mean, he wants to use VLS Harpoon in a future warship, when the USN is already firing LRASM (Long Range Anti-Ship Missile) test shots...

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Would you please not eat my gun...