Coandă Rocket Nozzle

I had previously proposed to utilize the ambient air to contribute to the thrust of a rocket like in turbofan engines. This would only work for the first stage of a rocket. My recent idea is a more realistic solution, to use Coandă effect.

The idea is to divert the air flowing around the rocket shell towards the nozzle. This would work for single nozzle rockets. For multiple nozzles the design would be more complicated and the effect would be less. The Coandă effect is the tendency of a fluid jet to stay attached to a surface of any form. Specially designed stepped layers would keep the air attached until the end of the nozzle. The diverted air would be heated with the exhaust gases and contribute to the thrust like in high bypass turbofan engines. The stepped layers can mostly be made of composite light materials. Only sections close to the nozzle need to withstand high temperatures.