I was trying to do some piston shape research and came up with a question. I am by no way at all learned in engine things, but rather just trying to understand things better. I was looking at flat tops, high domes, and pop ups. For sake of arguement, I am sticking with a flathead (more simple). My question is potentially a dumb one, but I was curious as to why there is no such thing as a concave piston head (convex cylinder head). Machining wise, the head would suck, due to the fact that the convex shape protrudes from the flat plane. On the contrary though, the main reason I ask is because it seems more durable. The load due to the combustion would force directly on the middle of the piston head, instead of beig pushed right into the rings. Also, the design would force the air to the perimeter, which I would think would be good for a flathead? Please see the quick and dirty diagram below for a better representation. Again, it might seem dumb, but whenever it comes time for me to understand why, I usually come up with ideas of why not.
There are Heron head designs, which have the combustion chamber in the piston. I've forgotten which motorcycle manufacturers used them... Moto Guzzi and Moto Morini maybe? The head for a Heron combustion chamber is even flatter than a "flathead", it does not protrude into the combustion chamber. Here's a picture of a Moto Guzzi head for example: The force due to combustion isn't going to be moved anywhere though. Pressure will act normal to the surface no matter if the dome is concave or convex, it doesn't slide down the surface to the side or center.
Google "Heron head" and read the Wikipedia article. The ones I've seen are the old 430 Lincolns, but I think the 409 was close to that. Breathing is the problem as the valves tend to be vertical and the port makes a bigger bend (i.e. the valve isn't angled towards it). Just the opposite of a hemi. Many smog motors used dished pistons to lower the compression with no other changes, and we remember how well they ran.
OK you're talking flathead so valve size is not an issue as it would be with OHV. The other problem would be flow from the valves to the cylinder. You can 'relieve' the side of the cylinder down towards the top ring to improve flow but you really need space in the head. And even if you managed that, combustion would and flow would be worse than it already is with part of it trapped on the opposite side of the head. Good to think out side the box, er cylinder though, never know what ideas it may lead to.