That's a very difficult question to answer. There is no secret formula in bow making with wood.
For a FG bow, you make it a specified thickness, shape, and width, and you get a predictable result. Not so with wooden bows. Depends on the wood, depends on the design, depends on what you want as a final result. I can't offer you a secret formula, or a specific thickness... they don't exist.
I think if I had three different bows, all with similar designs, and perhaps even with the same wood (or wood combinations), that they would all end up with different thickness dimensions. Wood is a natural material, and even wood of the same species will have variable densities. For me, that's part of the joy... not knowing... not being able to predict the final outcome with exact certainty.
You could probably end up close to 50# using hickory backed ipe and making it a pyramid bow with wide flat limbs, but it would be a gamble at 3/8" total thickness. I would definitely start thicker and tiller to desired effect.