Advice needed on a root vegtable system

[Harlequin]

I'm thinking about growing root vegies (carrots etc.) and I'm struggling a little with the mental shape of how the system would work. At the moment my experience is all with NFT systems growing leafy plants.

My understanding is I would need at least a 12" deep growing medium, probably a combination of Perlite and Vermiculite for carrots to grow well. What I am thinking is a 14" deep trough with a drain in the bottom, a mesh an inch or so above the bottom so there will be an open space at the bottom of the pot. Then to flood the system from the top and then allow the nutrient to drain out the bottom.

My thoughts / concerns are the timing for the flood drain cycle. Should I use sprayers or drips or try flooding the whole pot? I could always valve the drain so the pot will fill and hold the water for a time and then drain.

Or am I making this too complicated?

Doing some research this is what I am thinking of building...