An idea for a no-pump low-tech hydroponics setup. Two parallel V shaped wooden trays as you have designed say 4-8 ft. long structurally connected at each end. Separated about the width of approximately 1-2 trays. Provide a pivot point at each end centered between the trays. End view would look something like this:
Where "A" is the pivot point and "V" are the trays. Bottom ends of each tray connect with a pipe running to the bottom of the adjacent tray, so nutrients can flow easily from one tray to the other. From time to time walk up and push down (stand on it) the tray that is up in the air until the liquid runs into that tray and holds it down. The amount of up and down motion should be no more than to just drain the tray that is up. Each tray should be mounted such that its top is level when it is down and full of liquid.
My comments on the idea: This set up would only work if the plants liked to be wet then dry half the time. The unit can not be made too big so as to be too heavy to push down. The connecting tubes need to be big enough so as to not wait too long for the water to run from one tray to the other. Wouldn't use this with climbing vines or tall plants. This type of setup trades more sturdy structure or building materials for an electric pump. If electricity is available it's probably better to use a electric pump type setup as previously described. This is just an idea that someone may develop on to work out the rest of the bugs and possibly find an appropriate use.
Offered by Mike.