Caution: math zone ahead
During 2001-2002 I wrote a report describing a comprehensive approach for modeling the water-rocket thrust phase. The 311KB pdf document contains 26 pages of math and descriptions which allow one to predict the velocity of a rocket after it has expended all the energy contained in the pressurized gas.
I subsequently implemented these thrust and flight equations into
Sim Water Rocket,
an applet that lets you predict water-rocket performance without getting a headache.
Sustainer rockets
In 2003 I wrote a short mathematical analysis explaining why a sustainer rocket, the topmost stage of a two-stage rocket, ought to be designed for a particular velocity in order to maximize apogee height.
The analysis applies to conventional model rockets as well as water rockets.
