String/fret/bridge/nut geometry question

First - a disclaimer. I have lots of woodworking experience, but am new to all things ukulele. I have scratch built a couple of kits for friends and am now building another, learning from issues that came up with the first two.

As I prepare to make the saddle, bridge, and nut, I plan to aim for 2.5mm string height above the twelfth fret and a string length of 345mm

At first glance, it seems to me it would make sense to design the nut and the bridge and saddle so the strings will be exactly parallel to the tops of the frets. Would there be any benefit to dropping the nut by .5mm (or 1mm) and raising the bridge by a corresponding amount to maintain 2.5mm over the twelfth fret while slightly changing the geometry of the strings in relation to the plane of the frets?

It's generally considered best to have the top of the bridge level with the plane of the frets, i.e. place a straight edge along the frets and it should just fall in line with or sit on the top of the bridge. You are then in the right ballpark to adjust the saddle and nut. 2.5mm maybe a good starting point for the height at the 12th fret, but to give you an idea about nut height(depth of slot), place a capo on the first fret and check the height at the 2nd fret and that will give an indication of how low the string can be over the first when not capoed( if that makes sense). If the saddle is made so that the height at the 12th fret is approx 2.5mm when the capo is on the first fret, then you can see that the strings are far from parrallel to the frets. Hope this helps.

Thanks, Mikey. I have just realized I have been mixing up which piece is the saddle and which is the bridge. LOL - I did say I was new to all things ukulele!

I understand what you're saying now, and will take that back to my CAD programme to refine my thoughts.

Just to make sure there’s no confusion, understand that any instrument that has the strings parallel to the fretboard would be unplayable. You need to understand how a string vibrates. When you pluck an open string the area of maximum displacement is the center of the string (12th fret). The area under the 1st fret moves very little. Some numbers to keep in mind,
Bridge/saddle height above the top 3/8”, +/- 1/16”
Saddle height above bridge 1/8”, +/- 1/16”
Action height at 12th fret .080 to .120”
Fretboard thickness.120 to.160”.

And the key to all of these working is the neck angle.