Boost Phase

Coast phase:

h = deltaV^2/2g

I would propose that the following are design parameters and should be left to the optimization of designer: drag, mass initial and final, and burn time tb. You'll note that Isp shows up in both terms of the boost equation with gravity as a constant. If we divide hb/Isp we get our figure of merit for model rocketry. In other words how much altitude can you generate for a given design. If you prefer Isp is directly proportional to cost so roughly speaking Altitude/$.

Taking this new figure of merit I compared the performance of the various high altitude record holders by impulse. The assumption being that these designs have all been fully optimized for mass, drag, and motor selection. I have grouped them by total impulse class as well as single vs staged design. I looked primarily at the lower impulse classes trying to avoid the complications of going super sonic. The first thing that jumps out is the altitude does not double with doubling impulse as the first order prediction from the rocket equation. For example doubling the impulse from F to G only results in 30% more altitude. Perhaps less surprising the two stages designs are slightly more efficient than the single stage designs. This is likely due to the increased burn time achieved by dividing the same total impulse into two ore more motors.

General trends when optimizing for altitude.

1) Smaller impulse rockets are more "efficient" than larger impulse rockets. ie Altitude/$

2) When selecting a motor you want as long a burn time as possible for a given impulse.

3) It is more efficient to divide the total impulse between multiple motors. ie 2-stages better than one.