# Under-expanded nozzle at sea level - is it a problem?

I'm designing a solid rocket motor with a fixed pressure in the combustion chamber $$p_{cc} = 70~bar$$. When it comes to the choice of the right nozzle, I have to consider the proper expansion ratio, in order to maximize the average thrust coefficient $$C_f$$ over the burning time $$t_b$$: $$\bar{C_f} =\frac{1}{t_b} \int_{0}^{t_b}{C_f(t)dt}.$$ The design is based on isentropic relations and so, if the expansion ratio of the nozzle is too small - say 5 - it follows that the nozzle will be underexpanded already at sea level.

Are there any cons of designing a nozzle that will never be adapted? Why should the nozzle be adapted at a particular altitude if the ascension trajectory is exactly vertical?

• Using an under-expanded nozzle means a loss of efficiency, using an over-expanded nozzle means excessive additional weight of the nozzle. A compromise between weight and efficency valid for all ambient pressures should be found. – Uwe May 31 '19 at 10:57