Motor thrust / isp improvement at high altitude?

I'm trying to figure out the performance improvement at higher altitudes for some higher power motors (K's and L's). To really get accurate, I'd need to know things like nozzle geometry, chamber pressure, chamber temperature, specific heat ratio, molecular weight of the exhaust, etc. I could approximate it as the nozzle exit area x (14.7psi - ambient pressure), but I don't have the nozzle.

1. Is there an easy way to estimate performance improvement at a lower ambient pressure?
2. If not, does anyone have some detailed data for any K or L range motors?

Thanks in advance!
Dave

To be honest, the improvement is extremely minimal, much less than the normal motor to motor variation. Almost every motor in high power rocketry is underexpanded, and your approximation of nozzle exit area multiplied by pressure difference is probably the way to go.

As for all the other stuff you mentioned, I'm pretty sure it's unnecessary if you have the knowledge that the exhaust flow is underexpanded. You should be able to get a fairly accurate estimate just with the ambient pressure and nozzle area, unless I've forgotten something.

As for how large the nozzle area is? I'm not positive about that. Jeroen Louwers posts here sometimes, and I'm sure he can give you detailed info about CTI motors. I'm not sure about AT though.