# How to select appropriate orbital rocket stage thrust?

I’ve been working on a preliminary design of a small-lift launch vehicle capable of sending a small satellite into LEO. Given the required $$\Delta v$$ (~9 km/s for LEO), the mass distribution, including the required propellant mass for each stage and the total, can be calculated by using the well-known optimal rocket staging method. However, the method does not tell the size of the engine of each stage, i.e. the thrust and the burn time. Many sources just assume some thrust-to weight ratio value that is greater than 1 to get the rocket out of gravity well.

My question therefore is: how do I select the appropriate required thrust for each stage of the launch vehicle?

What I think might lead to the solution involves trajectory design of the rocket. For instance, in a gravity turn trajectory, higher thrust leads to lower gravity loss but higher aerodynamic drag loss and the opposite applies for lower thrust. The optimal amount of thrust is therefore the point where the total loss is minimum. Furthermore, thrust is also limited by the maximum dynamic pressure the rocket can handle and the maximum acceleration the payload can withstand. I am not quite sure if determining optimal thrust through trajectory design is the right direction, and trajectory optimization is a large and complex subject by its own. Plus, $$\Delta v$$ loss might not be the only factor for thrust optimization.